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[[Image:Splash-prop.jpg|right|720px]]<strong><font color="#4e1985" size="4">True 3D, Coherent, Polarimetric Ray Tracer That Simulates Very Large Urban Scenes In Just Few Minutes!</font></strong><table><tr><td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad- Taking out this picture for now for consistencyico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[Fileimage:urbanfdtd-ico.png| link=EM.Tempo]][[image:static-ico.png | link=EM.Ferma]] [[image:planar->ico.png | link=EM.Terrano is a physicsPicasso]] [[image:metal-based, siteico.png | link=EM.Libera]] [[image:po-specific, wave propagation modeling tool that enables engineers to quickly determine how radio waves propagate in urban, natural or mixed environmentsico. The rapid growth of wireless communications along with the high costs associated with the design and deployment of effective wireless infrastructures underline a persistent need for computer aided communication network planning toolspng | link=EM. Wireless engineers have long used simplistic statistical prediction models based on measurements that often exhibit considerable errors especially in areas having mixed building sizesIllumina]]</td><tr></table>[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Terrano_Documentation | EM.Terrano Tutorial Gateway]]'''

Since its introduction in 2002, EM.Terrano has helped wireless engineers around the globe model the physical channel and the mechanisms by which radio signals propagate from transmitters to receivers[[Image:Back_icon. png|30px]] '''[[EM.Terrano’s advanced ray tracing simulator finds the dominant propagation paths specific Cube | Back to the site in question. It calculates the true signal characteristics at the actual locations using physical databases of the buildings and terrain at a given site, not those of a statistically average or representative environment. EM.Terrano’s ray tracer is based on the shoot-and-bounce-rays (SBR) method, which utilizes geometrical optics (GO) in combination with uniform theory of diffraction (UTD) models of building edges.Cube Main Page]]'''==Product Overview==

The new ===EM.Terrano 2013 has been totally reconstructed based on our integrated [[EM.Cube]] software foundation. This integration has created the opportunity to inject a host of new powerful features such as a highly customizable terrain generator, DEM terrain import, complex building constructions, and versatile interior wall arrangements for indoor propagation modeling. As a result of this seamless interface with [[EM.Cube]]'s other modules, you can now model complex antenna systems in [[EM.Picasso]], [[EM.Tempo]] or [[EM.Libera]], and generate antenna radiation patterns than can be used to model directional transmitters and receivers at the two ends of your propagation channel. Conversely, you can analyze a propagation scene in EM.Terrano and import the rays received at a certain receiver location as coherent plane wave sources to [[EM.Picasso]], [[EM.Tempo]] or [[EM.Libera]]. You can also model periodic wall or ground structures using the periodic simulation capability of [[EM.Picasso]] or [[EM.Tempo]] and generate macromodels for their reflection and transmission coefficients as functions of the ray incidence angles. You can then define buildings or terrains in your propagation scene that are governed by such macromodels.Nutshell ===

== An EM.Terrano Primer ==is a physics-based, site-specific, wave propagation modeling tool that enables engineers to quickly determine how radio waves propagate in urban, natural or mixed environments. EM.Terrano's simulation engine is equipped with a fully polarimetric, coherent 3D ray tracing solver based on the Shooting-and-Bouncing-Rays (SBR) method, which utilizes geometrical optics (GO) in combination with uniform theory of diffraction (UTD) models of building edges. EM.Terrano lets you analyze and resolve all the rays transmitted from one ore more signal sources, which propagate in a real physical channel made up of buildings, terrain and other obstructing structures. EM.Terrano finds all the rays received by a receiver at a particular location in the physical site and computes their vectorial field and power levels, time delays, angles of arrival and departure, etc. Using EM.Terrano you can examine the connectivity of a communication link between any two points in a real specific propagation site.

=== Modeling Since its introduction in 2002, EM.Terrano has helped wireless engineers around the Wireless Propagation Channel===globe model the physical channel and the mechanisms by which radio signals propagate in various environments. EM.Terrano’s advanced ray tracing simulator finds the dominant propagation paths at each specific physical site. It calculates the true signal characteristics at the actual locations using physical databases of the buildings and terrain at a given site, not those of a statistically average or representative environment. The earlier versions of EM.Terrano's SBR solver relied on certain assumptions and approximations such as the vertical plane launch (VPL) method or 2.5D analysis of urban canyons with prismatic buildings using two separate vertical and horizontal polarizations. In 2014, we introduced a new fully 3D polarimetric SBR solver that accurately traces all the three X, Y and Z components of the electric fields (both amplitude and phase) at every point inside the computational domain. Using a 3D CAD modeler, you can now set up any number of buildings with arbitrary geometries, no longer limited to vertical prismatic shapes. Versatile interior wall arrangements allow indoor propagation modeling inside complex building configurations. The most significant recent development is a multicore parallelized SBR simulation engine that takes advantage of ultrafast k-d tree algorithms borrowed from the field of computer graphics and video gaming to achieve the ultimate speed and efficiency in geometrical optics ray tracing.

Every wireless communication system involves a transmitter that transmits some sort of signal (voice, video, data, etc[[Image:Info_icon.), a receiver that receives and detects the transmitted signal, and a channel in which the signal is transmitted into the air and travels from the location of the transmitter png|30px]] Click here to learn more about the location '''[[Basic Principles of the receiver. The channel is the physical medium in which the electromagnetic waves propagate. The successful design of a communication system depends on an accurate link budget analysis that determines whether the receiver receives adequate signal power to detect it against the background noise. The simplest channel is the free space. Real communication channels, however, are more complicated and involve a large number of wave scatterers. For example, in an urban environment, the obstructing buildings, vehicles and vegetation reflect, diffract or attenuate the propagating radio waves. As a result, the receiver receives a distorted signal that contains several components with different power levels and different time delays arriving from different anglesSBR Ray Tracing | Basic SBR Theory]]'''.

The different rays arriving at a receiver location create constructive and destructive interference patterns. This is known as the multipath effect. This together with the shadowing effects caused by building obstructions lead to channel fading. In many wireless applications, the total received power by the receiver is all that matters. In some others, the angle of arrival of the rays as well as their polarization are of immense interest. A fully polarimetric, coherent ray tracer like <table><tr><td> [[EMImage:Manhattan1.png|thumb|left|420px|A large urban propagation scene featuring lower Manhattan.Cube]]'s Shooting-and-Bouncing-Rays (SBR) solver lets you compute and resolve all the rays received by a receiver including their power levels, time delays and angles of arrival.</td></tr></table>

=== Line-of-Sight vsEM. Multipath Terrano as the Propagation Channel Module of EM.Cube ===

In a free-space line-EM.Terrano is the ray tracing '''Propagation Module''' of-sight (LOS) communication system'''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. EM.Terrano shares the signal propagates directly from the transmitter to the receiver without encountering any obstacles (scatterers)visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.

Click here With the seamless integration of EM.Terrano with [[EM.Cube]]'s other modules, you can now model complex antenna systems in [[EM.Tempo]], [[EM.Libera]], [[EM.Picasso]] or [[EM.Illumina]], and generate antenna radiation patterns that can be used to learn more about model directional transmitters and receivers at the theory two ends of your propagation channel. Conversely, you can analyze a propagation scene in EM.Terrano, collect all the rays received at a certain receiver location and import them as coherent plane wave sources to [[EM.Tempo]], [[EM.Libera]], [[EM.Picasso]] or [[Free-Space Propagation ChannelEM.Illumina]].

Electromagnetic waves propagate in the form of spherical waves with a functional dependence of e^j(&omega;^t-k₀R)/R, where R is the distance between the transmitter and receiver, <math>\omega = 2\pi f</math>, f is the signal frequency, <math>k_0 = \frac{\omega}{c} = \frac{2\pi}{\lambda}</math>, c is the speed of light, and &lambda;₀ is the free-space wavelength at the operational frequency[[Image:Info_icon. By the time the signal arrives at the location of the receiver, it undergoes two changes. It is attenuated and its power drops by a factor of 1/R², and additionally, it experiences a phase shift of <math>\frac{2\pi R}{\lambda_0}</math>, which is equivalent png|30px]] Click here to a time delay of R/c. The signal attenuation from the transmitter to the receiver is usually quantified by learn more about '''Path Loss[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]''' defined as the ratio of the received signal power (P_R) to the transmitted signal power (P_T). Assuming isotropic transmitting and receiving radiators (i.e. radiating uniformly in all directions), the Path Loss in a free-space line-of-sight communication system is given by Friis’ formula:

:<math> \frac{P_R}{P_T} = \left( \frac{\lambda_0}{4\pi R} \right)^2 </math><!--[[File:friis1== Advantages & Limitations of EM.png]]-->Terrano's SBR Solver ===

The above formula assumes EM.Terrano's SBR simulation engine utilizes an intelligent ray tracing algorithm that is based on the receiving antenna concept of k-dimensional trees. A k-d tree is polarizationa space-matchedpartitioning data structure for organizing points in a k-dimensional space. Normallyk-d trees are particularly useful for searches that involve multidimensional search keys such as range searches and nearest neighbor searches. In a typical large radio propagation scene, there is might be a polarization mismatch between large number of rays emanating from the transmitting and receiving antennastransmitter that may never hit any obstacles. In For example, upward-looking rays in an urban propagation scene quickly exit the case of directional transmitting and receiving antennascomputational domain. Rays that hit obstacles on their path, Friis’ formula takes on the following form:other hand, generate new reflected and transmitted rays. The k-d tree algorithm traces all these rays systematically in a very fast and efficient manner. Another major advantage of k-d trees is the fast processing of multi-transmitters scenes.

:EM.Terrano performs fully polarimetric and coherent SBR simulations with arbitrary transmitter antenna patterns. Its SBR simulation engine is a true asymptotic &quot;field&quot; solver. The amplitudes and phases of all the three vectorial field components are computed, analyzed and preserved throughout the entire ray tracing process from the source location to the field observation points. You can visualize the magnitude and phase of all six electric and magnetic field components at any point in the computational domain. In most scenes, the buildings and the ground or terrain can be assumed to be made of homogeneous materials. These are represented by their electrical properties such as permittivity &epsilon;<mathsub> \frac{P_R}{P_T} = G_T G_R \left( \frac{\lambda_0}{4\pi R} \right)^2 ( \mathbf{ \hat{u}_T \cdot \hat{u}_R } )r</mathsub><!--[[File:friis2and electric conductivity &sigma;.png]]-->More complex scenes may involve a multilayer ground or multilayer building walls. In such cases, one can no longer use the simple reflection or transmission coefficient formulas for homogeneous medium interfaces. EM.Terrano calculates the reflection and transmission coefficients of multilayer structures as functions of incident angle, frequency and polarization and uses them at the respective specular points.

where '''u_T''' It is very important to keep in mind that SBR is an asymptotic electromagnetic analysis technique that is based on Geometrical Optics (GO) and '''u_R''' are the unit polarization vectors Uniform Theory of the transmitting and receiving antennasDiffraction (UTD). It is not a &quot;full-wave&quot; technique, and G_T and G_R it does not provide a direct numerical solution of Maxwell's equations. SBR makes a number of assumptions, chief among them, a very high operational frequency such that the length scales involved are their gainsmuch larger than the operating wavelength. Under this assumed regime, respectivelyelectromagnetic waves start to behave like optical rays. Virtually all the calculations in SBR are based on far field approximations. In order to maintain a high computational speed for urban propagation problems, EM.Terrano ignores double diffractions. Diffractions from edges give rise to a large number of new secondary rays. The power of diffracted rays drops much faster than reflected rays. In other words, an edge-diffracted ray does not diffract again from another edge in EM.Terrano. However, reflected and penetrated rays do get diffracted from edges just as rays emanated directly from the sources do.

<table><tr><td> [[FileImage:losMultipath_Rays.png|thumb|left|500px|A multipath urban propagation scene showing all the rays collected by a receiver.]]</td></tr></table>

Figure: A Line-of-Sight (LOS) Propagation Scenario== EM.Terrano Features at a Glance ==

=== Multipath Propagation Channel Scene Definition / Construction ===

Free-space line-of-sight communications is an ideal scenario that is typically used to model aerial <ul> <li> Buildings/blocks with arbitrary geometries and material properties</li> <li> Buildings/blocks with impenetrable surfaces or space applications. In ground-based systems, the presence penetrable surfaces using thin wall approximation</li> <li> Multilayer walls for indoor propagation scenes</li> <li> Penetrable volume blocks with arbitrary geometries and material properties</li> <li> Import of the ground as a very large reflecting surface affects the signal propagation to a large extent. Along the path from a transmitter to a receivershapefiles and STEP, the signal may also encounter many obstacles IGES and scatterers such as buildings, vegetation, etc. In an urban canyon environment STL CAD model files for scene construction</li> <li> Terrain surfaces with many buildings arbitrary geometries and material properties and random rough surface profiles</li> <li> Import of different heights digital elevation map (DEM) terrain models</li> <li> Python-based random city wizard with randomized building locations, extents and other scatterers, a line orientations</li> <li> Python-based wizards for generation of sight between the transmitter parameterized multi-story office buildings and receiver can hardly be established. In such cases, the propagating signals bounce back several terrain scene types</li> <li> Standard half-wave dipole transmitters and forth among receivers oriented along the building surfaces. It is these reflected principal axes</li> <li> Short Hertzian dipole sources with arbitrary orientation</li> <li> Isotropic receivers or diffracted signals that are often received and detected by the receiver. Such environments are referred to as “multipath”. The group grids for wireless coverage modeling</li> <li> Radiator sets with 3D directional antenna patterns (imported from other modules or external files)</li> <li> Full three-axis rotation of rays arriving at a specific receiver location experience different attenuations imported antenna patterns</li> <li> Interchangeable radiator-based definition of transmitters and different time delays. This gives rise to constructive and destructive interference patterns that cause fast fading. As a receiver moves locally, the receiver power level fluctuates sizably due to these fading effects.receivers (networks of transceivers)</li></ul>

Link budget <ul> <li> Fully 3D polarimetric and coherent Shoot-and-Bounce-Rays (SBR) simulation engine</li> <li> GTD/UTD diffraction models for diffraction from building edges and terrain</li> <li> Triangular surface mesh generator for discretization of arbitrary block geometries</li> <li> Super-fast geometrical/optical ray tracing using advanced k-d tree algorithms</li> <li> Intelligent ray tracing with user defined angular extents and resolution</li> <li> Ray reflection, edge diffraction and ray transmission through multilayer walls and material volumes</li> <li> Communication link analysis for a multipath channel is a challenging task due to superheterodyne transmitters and receivers</li> <li> 17 digital modulation waveforms for the large size calculation of E_b/N₀ and Bit error rate (BER)</li> <li> Incredibly fast frequency sweeps of the computational domains involved. Typical entire propagation scenes usually involve length scales on the order scene in a single SBR simulation run</li> <li> Parametric sweeps of thousands scene elements like building properties, or radiator heights and rotation angles</li> <li> Statistical analysis of wavelengths. To calculate the path loss between the transmitter and receiver, one must solve Maxwell's equations in propagation scene</li> <li> Polarimetric channel characterization for MIMO analysis</li> <li> "Almost real-time" Polarimatrix solver using an extremely large space. Fullexisting ray database</li> <li> "Almost real-wave numerical techniques like time" transmitter sweep using the Finite Difference Time Domain (FDTD) method, which require a fine discretization of Polarimatrix solver</li> <li> "Almost real-time" rotational sweep for modeling beam steering using the computational domain, are therefore impractical Polarimatrix solver</li> <li> "Almost real-time" mobile sweep for solving largemodeling mobile communications between Tx-scale propagation problems. The practical solution is to use asymptotic techniques such as SBR, which utilize analytical techniques over large distances rather than Rx pairs along a brute force discretization of mobile path using the entire computational domain. Such asymptotic techniques, of course, have to compromise modeling accuracy for practical computation feasibility.Polarimatrix solver</li></ul>

Figure 1: A multipath propagation scene showing all the <ul> <li> Standard output parameters for received power, path loss, SNR, E_b/N₀ and BER at each individual receiver</li> <li> Graphical visualization of propagating rays arriving in the scene</li> <li> Received power coverage maps</li> <li> Link connectivity maps (based on minimum required SNR and BER)</li> <li> Color-coded intensity plots of polarimetric electric field distributions</li> <li> Incoming ray data analysis at a particular each receiver including delay, angles of arrival and departure</li> <li> Cartesian plots of path loss along defined paths</li> <li> Power delay profile of the selected receiver</li> <li> Polar stem charts of angles of arrival and departure of the selected receiver.</li></ul>

=== The SBR Method =Building a Propagation Scene in EM.Terrano ==

[[EM.Cube]]'s [[Propagation Module]] provides an asymptotic ray tracing simulation engine that is based on a technique known as Shooting-and-Bouncing-Rays (SBR). In this technique, propagating spherical waves are modeled as ray tubes or beams that emanate from a source, travel in space, bounce from obstacles and are collected by the receiver. As rays propagate away from their source (transmitter), they begin to spread (or diverge) over distance. In other words, the cross section or footprint === The Various Elements of a ray tube expands as a function of the distance from the source. [[EM.Cube]] uses an accurate equi-angular ray generation scheme to that produces almost identical ray tubes in all directions to satisfy energy and power conservation requirements.Propagation Scene ===

When A typical propagation scene in EM.Terrano consists of several elements. At a ray hits an obstructing surfaceminimum, you need a transmitter (Tx) at some location to launch rays into the scene and a receiver (Rx) at another location to receive and collect the incoming rays. A transmitter and a receiver together make the simplest propagation scene, representing a free-space line-of-sight (LOS) channel. In EM.Terrano, a transmitter represents a point source, while a receiver represents a point observable. Both a transmitter and a receiver are associated with point objects, which are one or more of the following phenomena may happen:many types of geometric objects you can draw in the project workspace. Your scene might involve more than one transmitter and possibly a large grid of receivers.

# Reflection from A more complicated propagation scene usually contains several buildings, walls, or other kinds of scatterers and wave obstructing objects. You model all of these elements by drawing geometric objects in the locally flat surface# Transmission through project workspace or by importing external CAD models. EM.Terrano does not organize the locally flat surface# Diffraction from an edge between two conjoined locally flat surfacesgeometric objects of your project workspace by their material composition. Rather, it groups the geometric objects into blocks based on a common type of interaction with incident rays. EM.Terrano offer the following types of object blocks:

{| class="wikitable"|-! scope="col"| Icon! scope="col"| Block/Group Type ! scope="col"| Ray Interaction Type! scope="col"| Object Types Allowed! scope="col"| Notes|-| style="width:30px;" | [[File:impenet_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Impenetrable Surface | Impenetrable Surface]] discretizes all the | style="width:200px;" | Ray reflection, ray diffraction| style="width:250px;" | All solid & surface geometric objects of the scene into flat triangular facets. Obviously, rectangular and cubic no curve objects preserve their geometric shapes through this discretization| style="width:300px;" | Basic building group for outdoor scenes|-| style="width:30px;" | [[File:penet_surf_group_icon. Objects with curved surfaces such as cylinderspng]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, cones or spheresSources, are approximated by Devices &quotOther Physical Object Types#Penetrable Surface | Penetrable Surface]]| style="width:200px;polymesh" | Ray reflection, ray diffraction, ray transmission in free space| style="width:250px;" | All solid &quotsurface geometric objects, no curve objects| style="width:300px; representations" | Behaves similar to impenetrable surface and uses thin wall approximation for generating transmitted rays, used to model hollow buildings with ray penetration, entry and exit |-| style="width:30px;" | [[File:terrain_group_icon. The geometric fidelity png]]| style="width:150px;" | [[Glossary of the resulting mesh depends on the specified mesh edge lengthEM. When a Cube's Materials, Sources, Devices & Other Physical Object Types#Terrain Surface | Terrain Surface]]| style="width:200px;" | Ray reflection, ray hits a triangular facetdiffraction| style="width:250px;" | All surface geometric objects, no solid or curve objects | style="width:300px;" | Behaves exactly like impenetrable surface but can change the propagating spherical wave is approximated as a plane wave at elevation of all the specular pointbuildings and transmitters and receivers located above it|-| style="width:30px;" | [[File:penet_vol_group_icon. The png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Penetrable Volume | Penetrable Volume]]| style="width:200px;" | Ray reflection and , ray diffraction, ray transmission coefficients of the and ray attenuation inside homogeneous material media| style="width:250px;" | All solid geometric objects, no surface are calculated at the operational frequency or curve objects| style="width:300px;" | Used to model wave propagation inside a volumetric material block, also used for creating individual solid walls and at interior building partitions and panels in indoor scenes|-| style="width:30px;" | [[File:base_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Base Location Set | Base Location Set]]| style="width:200px;" | Either ray generation or ray reception| style="width:250px;" | Only point objects| style="width:300px;" | Required for the particular definition of transmitters and receivers|-| style="width:30px;" | [[File:scatterer_group_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Point Scatterer Set | Point Scatterer Set]]| style="width:200px;" | Ray reception and ray incident anglescattering| style="width:250px;" | Only point, box and sphere objects| style="width:300px;" | Required for the definition of point scatterers as targets in a radar simulation |-| style="width:30px;" | [[File:Virt_group_icon. png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]| style="width:200px;" | No ray interaction| style="width:250px;" | All types of objects| style="width:300px;" | Used for representing non-physical items |}

A new reflected ray is generated at the specular point, which starts traveling and bouncing around in the scene. If the obstructing surface is penetrable, a second transmitted ray is generated and added Click on each type to the scene. If the ray hits the edge of an obstacle, learn more about it is diffracted from that edge. This leads to in the creation [[Glossary of a cone of new rays, which greatly complicate the computational problemEM. The Uniform Theory of Diffraction (UTD) is used to calculate the wedge diffraction coefficients at the edges of scattering blocks. Note that reflectionCube's Materials, transmission and diffraction coefficients are all dependent on the polarization of the incident plane waveSources, Devices & Other Physical Object Types]].

A receiver may receive a large number Impenetrable surfaces, penetrable surfaces, terrain surfaces and penetrable volumes represent all the objects that obstruct the propagation of electromagnetic waves (rays: direct line-) in the free space. What differentiates them is the types of-sight rays from physical phenomena that are used to model their interaction with the transmitter, impinging rays reflected or diffracted off the ground or terrain, rays reflected or diffracted from buildings or rays transmitted through buildings. Each received ray is characterized by its powerEM.Terrano discretizes geometric objects into a number of flat facets. The field intensity, delay phase and angles power of arrival, which are the spherical coordinate angles &theta; reflected and &phi; transmitted rays depend on the material properties of the incoming rayobstructing facet. The actual signal received and detected by the receiver is the superposition specular surface of a facet can be modeled locally as a simple homogeneous dielectric half-space or as a multilayer medium. In that respect, all these rays with different power levels and different time delays. Most of the timeobstructing objects such as buildings, you will be interested walls, terrain, etc. behave in the coverage map of an area, which shows how much power is received by a grid of receivers spread over the area from a given fixed transmitter.similar way:

Click here to learn * They terminate an impinging ray and replace it with one or more about the theory new rays.* They represent a specular interface between two media of [[SBR Method]]different material compositions for calculating the reflection, transmission or diffraction coefficients.

=== Using SBR An outdoor propagation scene typically involves several buildings modeled by impenetrable surfaces. Rays hit the facets of impenetrable buildings and bounce back, but they do not penetrate the object. It is assumed that the interior of such buildings are highly dissipative due to wave absorption or diffusion. An indoor propagation scene typically involves several walls, a ceiling and a floor arranged according to a certain building layout. Penetrable surfaces are used to model the exterior and interior walls of buildings. Rays reflect off these surfaces and diffract off their edges. They also penetrate the thin surface and continue their path in the free space on the other side of the wall. Terrain surfaces with irregular shapes or possibly random rough surfaces are used as an Asymptotic EM Solver ===alternative to the flat global ground. You can also build mixed scenes involving both impenetrable and penetrable blocks or irregular terrain. In the context of a propagation scene, penetrable volumes are often used to model block of rain, fog or vegetation. Base location sets are used to geometrically represent point transmitters and point receivers in the project workspace.

[[EM.Cube]]'s SBR simulation engine can be used Sometimes it is helpful to draw graphical objects as a versatile and powerful asymptotic electromagnetic (EM) solver. If you compare [[EM.Cube]]'s [[Propagation Module]] with its other computational modules, you will notice a lot of similarities. While other modules group objects primarily by their material properties, [[Propagation Module]] categorizes visual clues in the types of obstructing surfacesproject workspace. Besides sharing the same rayThese non-surface interaction mechanisms, all the physical objects belonging must belong to a surface virtual object group also share the same material properties. [[Propagation Module]] offers similar source types and similar observable types as the other computational modules. For instance, the Hertzian dipole sources used in a SBR simulation Virtual objects are identical to those offered in PO, MoM3D and Planar modules. The plane wave sources are identical across all computational modulesnot discretized by EM. [[Propagation Module]]Terrano's sensor field planesmesh generator, far field observables (either radiation patterns or RCS) and Huygens surfaces they are all fully compatible with [[EM.Cube]]'s other computational modulesnot passed onto the input data files of the SBR simulation engine.

As an asymptotic <table><tr><td> [[Image:PROP MAN2.png|thumb|left|720px|An urban propagation scene generated by EM solver, the SBR engine can be used to model large-scale electromagnetic radiation .Terrano's "Random City" and scattering problems"Basic Link" wizards. An example of this kind is radiation of simple or complex antennas in the presence It consists of 25 cubic brick buildings, one transmitter and a large scattering platforms. You have to keep in mind that by using an asymptotic technique in place two-dimensional array of a full-wave method, you trade computational speed and lower memory requirements for modeling accuracyreceivers. In particular, the [[SBR Method|SBR method]] cannot take into account the electromagnetic coupling effects among nearby radiators or scatterers. However, when your scene spans thousands of wavelengths, an SBR simulation might often prove to be your sole practical solution. </td></tr></table>

=== Pros and Cons of EM.Terrano's SBR Solver Organizing the Propagation Scene by Block Groups ===

[[In EM.Cube]]'s new SBR simulation engine utilizes an intelligent ray tracing algorithm Terrano, all the geometric objects associated with the various scene elements like buildings, terrain surfaces and base location points are grouped together as blocks based on their common type. All the concept of k-dimensional trees. A k-d tree is objects listed under a space-partitioning data structure for organizing points particular group in a k-dimensional space. k-d trees are particularly useful for searches that involve multidimensional search keys such as range searches the navigation tree share the same color, texture and nearest neighbor searchesmaterial properties. In Once a typical large radio propagation scenenew block group has been created in the navigation tree, there might be a large number it becomes the "Active" group of rays emanating from the transmitter that may never hit any obstacles. For exampleproject workspace, upward-looking rays which is always displayed in an urban propagation scene quickly exit the computational domainbold letters. Rays that hit obstacles on their path, on You can draw new objects under the other hand, generate new reflected and transmitted raysactive node. The kAny block group can be made active by right-d tree algorithm traces all these rays systematically clicking on its name in a very fast and efficient manner. Another major advantage of k-d trees is the fast processing of multi-transmitters scenes. Unlike the previous versions of the SBR solver which could handle one transmitter at a time navigation tree and would superpose all selecting the resulting rays at the end '''Activate''' item of the simulation, the new SBR shoots rays from all the transmitters at the same timecontextual menu.

<table><tr><td> [[Image:PROP MAN1.png|thumb|left|480px|EM.Cube]]Terrano's new SBR simulation engine performs fully polarimetric and coherent SBR simulations with arbitrary transmitter antenna patternsnavigation tree. The new engine solves directly for the vectorial field components at the receiver locations or field observation points. This is far more rigorous than the previous versions of the SBR solver which primarily utilized ray power calculations based on the two vertical and horizontal polarizations. In other words, [[EM.Cube]]'s new SBR engine is a truly asymptotic &quot;field&quot; solver. As a result, you can visualize the magnitude and phase of all six electric and magnetic field components at any point in the computational domain. For power calculations at the receiver location, an isotropic, polarization-matched, receiving antenna is assumed. </td></tr></table>

In most scenesIt is recommended that you first create block groups, the buildings and then draw new objects under the ground or terrain can be assumed to be made of homogeneous materialsactive block group. These are represented by their electrical properties such as permittivity e and electric conductivity s. More complex scenes may involve However, if you start a multilayer ground or multilayer building wallsnew EM. In such casesTerrano project from scratch, one can no longer use and start drawing a new object without having previously defined any block groups, a new default impenetrable surface group is created and added to the simple reflection or transmission coefficient formulas for homogeneous medium interfacesnavigation tree to hold your new CAD object. [[EM.Cube]] calculates You can always change the reflection and transmission coefficients properties of multilayer structures as functions a block group later by accessing its property dialog from the contextual menu. You can also delete a block group with all of incident angle, frequency and polarization and uses them its objects at the respective specular pointsany time.

It is very important to keep in mind that SBR is an asymptotic electromagnetic analysis technique that is based on Geometrical Optics {{Note|You can only import external CAD models (GO) and the Uniform Theory of Diffraction (UTD). It is not a &quot;full-wave&quot; techniqueSTEP, and it does not solve Maxwell's equations directly or numerically. SBR makes a number of assumptionsIGES, chief among themSTL, a very high operational frequency such that DEM, etc.) only to the length scales involved are much larger than CubeCAD module. You can then transfer the operating wavelength. Under this assumed regime, electromagnetic waves start imported objects from CubeCAD to behave like optical raysEM. Virtually all the calculations in SBR are based on far field approximationsTerrano. }}

An <table><tr><td> [[EMImage:PROP MAN3.Cube]] propagation scene typically consists png|thumb|left|720px|Moving the terrain model of several elements. At a minimum, you need a transmitter Mount Whitney originally imported from an external digital elevation map (TxDEM) at some location file to launch rays into the scene and a receiver (Rx) at another location to receive and collect the incoming raysEM. A transmitter and a receiver together make the simplest propagation scene, representing a free-space line-of-sight (LOS) channelTerrano. A transmitter is one of ]]</td></tr><tr><td>[[Image:PROP MAN4.png|thumb|left|720px|The imported terrain model of Mount Whitney shown in EM.Cube]]Terrano's several source types, while project workspace under a receiver is one of [[EMterrain group called "Terrain_1".Cube]]'s several observable types. A simpler source type is a Hertzian dipole. A simpler observable is a field sensor that is used to compute the electric and magnetic fields on a specified plane.</td></tr></table>

An outdoor propagation scene may involve several buildings (modeled as impenetrable surfaces) and an underlying flat ground or irregular terrain surface. An indoor propagation scene may involve several walls (modeled as thin penetrable surfaces), a ceiling and a floor arranged according to a certain floor plan. You can also build mixed scenes involving both impenetrable and penetrable blocks, possibly along with irregular terrain surfaces. Your sources and observables can be placed anywhere in the scene. Your transmitters and receivers can be placed outdoors or indoors. A complete list === Adjustment of the various elements of a propagation scene is given in the '''Physical Structure''' section of [[Propagation Module]]'s Navigation Tree as follows:Block Elevation on Underlying Terrain Surfaces ===

* Impenetrable Surfaces* Penetrable Surfaces* In EM.Terrano, buildings and all other geometric objects are initially drawn on the XY plane. In other words, the Z-coordinates of the local coordinate system (LCS) of all blocks are set to zero until you change them. Since the global ground is located a z = 0, your buildings are seated on the ground. When your propagation scene has an irregular terrain, you would want to place your buildings on the surface of the terrain and not buried under it. This can be done automatically as part of the definition of the block group. Open the property dialog of a block group and check the box labeled '''Adjust Block to Terrain Surfaces* Base PointsElevation'''. All the objects belonging to that block are automatically elevated in the Z direction such that their bases sit on the surface of their underlying terrain. In effect, the LCS of each of these individual objects is translated along the global Z-axis by the amount of the Z-elevation of the terrain object at the location of the LCS.

Impenetrable{{Note| You have to make sure that the resolution of your terrain, penetrable its variation scale and terrain surfaces building dimensions are all obstruct the propagation of electromagnetic waves (rays) in the free spacecomparable. What differentiates them is Otherwise, on a rapidly varying high-resolution terrain, you will have buildings whose bottoms touch the types of physical phenomena that are used to model their interaction with the impinging rays. Base terrain only at a few points are simply used to define transmitter and receiver locations parts of them hang in the scene. The following sections of this manual will describe each of these elements in detailair.}}

<table><tr><td> [[FileImage:PROP14(1)PROP MAN5.png|thumb|left|480px|The property dialog of impenetrable surface showing the terrain elevation adjustment box checked.]]</td></tr></table>

Figure 1: The Navigation Tree of <table><tr><td> [[EMImage:PROP MAN6.png|thumb|left|360px|A set of buildings on an undulating terrain without elevation adjustment.Cube]]'s </td><td>[[Propagation ModuleImage:PROP MAN7.png|thumb|left|360px|The set of buildings on the undulating terrain after elevation adjustment.]].</td></tr></table>

=== The Various Types Of Surfaces EM.Terrano's Ray Domain &amp; Blocks =Global Environment ==

In === Why Do You Need a SBR simulation, the propagating rays hit the surface of building structures, walls, terrain (or global ground) and bounce back into the scene (reflection). Some rays penetrate thin walls or other penetrable surfaces and continue their path on the other side of the surface (transmission). The field intensity, phase and power of the reflected and transmitted rays depend on the material properties of the obstructing surface. The specular surface can be modeled as a simple homogeneous dielectric half-space or as a multilayer structure. In that respect, the buildings, walls, terrain or even the global ground all behave in a similar way:Finite Computational Domain? ===

* They terminate an impinging The SBR simulation engine requires a finite computational domain for ray termination. All the stray rays that emanate from a source inside this finite domain and replace it with one or more new hit its boundaries are terminated during the simulation process. Such raysexit the computational domain and travel to the infinity, with no chance of ever reaching any receiver in the scene.* They represent When you define a specular interface between two media of different material compositions for calculating propagation scene with various elements like buildings, walls, terrain, etc., a dynamic domain is automatically established and displayed as a green wireframe box that surrounds the reflectionentire scene. Every time you create a new object, transmission the domain box is automatically adjusted and possibly diffraction coefficientsextended to enclose all the objects in the scene.

[[EM.Cube]] has generalized To change the concept of '''Block''' as any object that obstructs and affects radio wave propagation. Rays hit the facets of a block and bounce off the surface of those facets or penetrate them and continue their propagation. Rays also get diffracted off the edges of these blocks. In [[EM.Cube]]'s [[Propagation Module]]ray domain settings, blocks are grouped together by follow the type of their interaction with rays. [[EM.Cube]] currently offers three types of blocks for use in a propagation sceneprocedure below:

# * Open the Ray Domain Settings Dialog by clicking the '''Impenetrable Surfaces:Domain''' Rays hit the facets of this type of blocks and bounce back, but they do not penetrate the object[[File:image025. It is assumed that the interior jpg]] button of such blocks the '''Simulate Toolbar''', or buildings are highly absorptive.# by selecting '''Penetrable Surfaces:Menu > Simulate > Computational Domain > Settings...''' These blocks represent thin surfaces that are used to model the exterior and interior walls of buildings based , or by right-clicking on the &quot;Thin Wall Approximation&quot;. Rays reflect off the surface '''Ray Domain''' item of penetrable surfaces the navigation tree and diffract off their edgesselecting '''Domain Settings. They also penetrate such thin surfaces and continue their paths on ..''' from the other side of contextual menu, or simply using the wallkeyboard shortcut {{key|Ctrl+A}}.# * The size of the Ray domain is specified in terms of six '''Terrain Surfaces:Offset''' These blocks are used to provide one or more impenetrableparameters along the ±X, ground surfaces for the propagation scene. Rays simply bounce off terrain objects±Y and ±Z directions. The global ground acts default value of all these six offset parameters is 10 project units. Change these values as a flat super-terrain that covers you like.* You can also change the bottom color of the entire computational domainbox using the {{key|Color}} button.* After changing the settings, use the {{key|Apply}} button to make the changes effective while the dialog is still open.

<table><tr><td> [[Image:PROP15.png|thumb|left|480px|EM.Cube]]Terrano's [[Propagation Moduledomain settings dialog.]] allows you to define block groups of each of the above three types. Each block group has the same color or texture and its members share the same material properties: permittivity &epsilon;<sub/td>r</subtr> and conductivity &sigma;. Also, all the penetrable surfaces belonging to the same block group have the same wall thickness. You can define many different block groups with certain properties and underneath each introduce many member objects with different geometrical shapes and dimensions. The </table below summarizes the characteristics of each block type:>

{| class="wikitable"|-! scope="col"| Block Type! scope="col"|Physical Effects! scopeUnderstanding the Global Ground ==="col"|Admissible Object Types|-| Impenetrable Surface| Reflection, Diffraction| All Solid &amp; Surface CAD Objects|-| Penetrable Surface| Reflection, Diffraction, Transmission| All Solid &amp; Surface CAD Objects|-| Terrain Surface| Reflection| Tessellated Objects Only|}

Most outdoor and indoor propagation scenes include a flat ground at their bottom, which bounces incident rays back into the scene. EM.Terrano provides a global flat ground at z =0. The global ground indeed acts as an impenetrable surface that blocks the entire computational domain from the z =0 plane downward. It is displayed as a translucent green plane at z = Impenetrable Surfaces For Outdoor Scenes =0 extending downward. The color of the ground plane is always the same as the color of the ray domain. The global ground is assumed to be made of a homogeneous dielectric material with a specified permittivity &epsilon;_r and electric conductivity &sigma;. By default, a rocky ground is assumed with &epsilon;_r =5 and &sigma; =0.005 S/m. You can remove the global ground, in which case, you will have a free space scene. To disable the global ground, open up the "Global Ground Settings" dialog, which can be accessed by right clicking on the '''Global Ground''' item in the Navigation Tree and selecting '''Global Ground Settings... '''Remove the check mark from the box labeled '''&quot;Include Half-Space Ground (z&lt;0)&quot;''' to disable the global ground. This will also remove the green translucent plane from the bottom of your scene. You can also change the material properties of the global ground and set new values for the permittivity and electric conductivity of the impenetrable, half-space, dielectric medium.

[[File:PROP14(2)Alternatively, you can use EM.png|thumb|200px|[[Propagation Module]]Terrano's Impenetrable Surface dialog]] '''Empirical Soil Model''' to define the material properties of the global ground. This model requires a number of parameters: Temperature in &deg;C, and Volumetric Water Content, Sand Content and Clay Content all as percentage.

In outdoor {{Note|To model a free-space propagation scenes such as &quot;Urban Canyons&quot;scene, you are primarily interested in the wireless coverage in the areas among buildings. You can assume that rays bounce off the exterior walls of these buildings but do not penetrate them. In other words, you ignore the transmitted rays and assume that they are either absorbed or diffused inside the buildings. This is not an unrealistic assumption. [[have to disable EM.Cube]] offers &quot;Impenetrable Blocks&quot; to model buildings in outdoor propagation scenes. A penetrable block has a color or texture property as well as material properties: permittivity (e_r) and conductivity (Terrano's). By default, a brick building is assumed with &epsilon;_r = 4.4 and &sigma; = 0.001 S/m. Impinging rays are reflected from the facets of impenetrable buildings or diffracted from their edgesglobal ground.}}

To define a new impenetrable block group, follow these steps<table><tr><td> [[Image:Global environ.png|thumb|left|720px|EM.Terrano's Global Environment Settings dialog.]]</td></tr></table>

# Right click on either the '''Impenetrable Surfaces''' item of the Navigation Tree and select '''Insert New Block...''' A dialog for setting up the block properties opens up offering a preloaded material type (Brick) with predefined color and texture.# Specify a name for the block group and select a color or texture.# The electromagnetic model that determines ray-block interaction is selected under '''Specular Interface Type'''. Two options are available: '''Standard Material''' or '''User Defined Model'''. The former is the default choice and requires material properties, '''Permittivity''' (&epsilon;_r) and '''Electric Conductivity''' (&sigma;), which are set to &quot;Brick== Defining Point Transmitters &quotamp; by default. No magnetic properties are allowed Point Receivers for blocks.# Click the '''OK''' button of the dialog to accept the changes and close it.Your Propagation Scene ==

Under an impenetrable block group, you can draw any === The Nature of [[EM.Cube]]'s native solid or [[Surface Objects|surface objects]] or you can import external model files like STEP, IGES or STL. You can change the properties of an impenetrable surface. In the property dialog of the surface group, click on the table that list the properties to select and highlight a row. Then, click the '''Add/Edit''' button to open up the Transmitters &quot;Edit Layer&quot; dialog. In this dialog, you can change the name of the material and its permittivity and electric conductivity. The box labeled &quot;Specify Loss Tangent&quot; is unchecked by default. If you check it, you can specify the '''Loss Tangent''' of the material, which, in turn, updates the value of electric conductivity at the center frequency of the project. You can also use [[EM.Cube]]'s Material List, which will be explained later. Receivers ===

In EM.Terrano, transmitters and receivers are indeed point radiators used for transmitting and receiving signals at different locations of the propagation scene. From a geometric point of view, both transmitters and receivers are represented by point objects or point arrays. These are grouped as base locations in the "Physical Structure" section of the navigation tree. As radiators, transmitters and receivers are defined by a radiator type with a certain far-field radiation pattern. Consistent with [[File:PROP23EM.pngCube]]'s other computational modules, transmitters are categorizes as an excitation source, while receivers are categorized as a project observable. In other words, a transmitter is used to generate electromagnetic waves that propagate in the physical scene. A receiver, on the other hand, is used to compute the received fields and received signal power or signal-to-noise ratio (SNR). For this reason, transmitters are defined and listed under the "Sources" sections of the navigation tree, while receivers are defined and listed under the "Observables" section.

Figure: [[Propagation Module]]'s &quot;Edit Layer&quot; dialog corresponding to impenetrable surfacesEM.Terrano provides three radiator types for point transmitter sets:

[[File:PROP15(1)EM.png|thumb|200px|[[Propagation Module]]'s Penetrable Surface dialog]]Terrano also provides three radiator types for point receiver sets:

A typical indoor propagation scene usually involves an arrangement #Half-wave dipole oriented along one of walls that represent the interior of a building. The transmitters and receivers are then placed in the spaces among such walls. From the point of view of [[EM.Cube]]'s SBR simulator, walls act like thin penetrable surfaces. [[EM.Cube]] uses the &quot;Thin Wall Approximation&quot; to model penetrable surfaces. It assumes that rays simply penetrate a wall and exit at the same specular point on the opposite side of the wall. In other words, rays are not displaced by the walls, nor do they get trapped inside the walls three principal axes#Polarization-matched isotropic radiator#User defined (no internal reflectionarbitrary). This is equivalent to assuming a zero thickness for penetrable surfaces for the purpose of geometrical ray tracing, while the finite thickness of the &quot;thin&quot; surface is used for electromagnetic calculation of transmission coefficient. [[EM.Cube]] offers &quot;Penetrable Surface Blocks&quot; for the construction of rooms in indoor propagation scenes as well as modeling of hollow buildings and other structures. You can define many penetrable surface groups antenna with arbitrary thicknesses and material properties (color, texture, permittivity and electric conductivity).imported far-field radiation pattern

# Right click on one of the '''Penetrable Surfaces''' item in the Navigation Tree and select '''Insert New Block...''' A dialog for setting up the wall properties opens up offering a preloaded material type (Brick) with predefined color and texture.# Specify a name for the surface group and select a color or texture.# The properties of a penetrable surface There are identical three different ways to those of an impenetrable surface, plus an additional thickness property.# By default, define a brick wall with transmitter set or a thickness of 0.5 units is assumed. You can change the '''Thickness''' of the penetrable surface as well as its '''Permittivity''' &epsilon;_r and '''Electric Conductivity''' &sigma;.# Click the '''OK''' button of the dialog to accept the changes and close it.receiver set:

Under a penetrable surface group, you can draw any of [[EM.Cube]]'s native solid or [[Surface Objects|surface *By defining point objects]] or you can import external model files like STEP, IGES or STL. You can change point arrays under physical base location sets in the properties of a penetrable surface group including its default thickness. In the property dialog of the surface group, click on the table that list the properties to select navigation tree and highlight then associating them with a row. Thentransmitter or receiver set*Using Python commands emag_tx, click the '''Add/Edit''' button to open up the &quot;Edit Layer&quot; dialog. Similar to the case of impenetrable surfacesemag_rx, from this dialogemag_tx_array, you can change the material properties (permittivity emag_rx_array, emag_tx_line and electric conductivity) as well as '''Thickness''', which is expressed in emag_rx_line*Using the project units. You can also use [[EM.Cube]]'s Material List, which will be explained later."Basic Link" wizard

Figure 2: [[Propagation Module]]'s &quot;Edit Layer&quot; dialog corresponding to penetrable surfacesTransmitters act as sources in a propagation scene.A transmitter is a point radiator with a fully polarimetric radiation pattern defined over the entire 3D space in the standard spherical coordinate system. EM.Terrano gives you three options for the radiator associated with a point transmitter:

You can construct several thin walls and arrange them as rooms. A regular room can be built by placing four vertical wall objects together with an optional horizontal wall at the top for the ceiling. Alternatively, you may use [[EM.Cube]]'s hollow box objects or boxes with one or two capped end(s). '''Keep in mind that all the penetrable surfaces belonging to a group have the same wall thickness, which is initially set to 0.5 project units by default. Also, note that solid CAD objects belonging to a penetrable surface group are treated as air* Half-filled hollow structures.''' The thickness of penetrable surfaces is implied and not visualized when displaying objects in the project workspace.wave dipole* Orthogonally polarized isotropic radiators* User defined antenna pattern

The SBR simulation engine requires You can override the default radiator option and select any other kind of antenna with a finite computational domainmore complicated radiation pattern. All the stray rays that hit the boundaries of For this finite domain are terminated during the simulation processpurpose, you have to import a radiation pattern data file to EM. Such rays exit the Terrano. You can model any radiating structure using [[EM.Cube]]'s other computational domain and travel to the infinitymodules, with no chance of ever reaching any receiver in the scene[[EM. When you define a propagation scene with various elements like buildingsTempo]], walls[[EM.Picasso]], terrain, etc[[EM.Libera]] or [[EM.Illumina]], a dynamic domain is automatically established and displayed as generate a 3D radiation pattern data file for it. The far-field radiation patter data are stored in a wireframe box specially formatted file with green lines that surrounds the entire scenea &quot;'''. Every time you create a new object, RAD'''&quot; file extension. This file contains columns of spherical &phi; and &theta; angles as well as the domain is automatically adjusted real and extended to enclose all imaginary parts of the objects in the scenecomplex-valued far-zone electric field components '''E_&theta;''' and '''E_&phi;'''. You can change the size The &theta;- and color &phi;-components of the domain box through far-zone electric field determine the Ray Domain Settings Dialog, which can be accessed in one polarization of the following three ways:transmitting radiator.

# Click the '''Domain''' [[File:image025{{Note|By default, EM.jpg]] button of the Simulation Toolbar.# Select the '''Simulate''' &gt; '''Computational Domain''' &gt; '''Settings...''' item of the Simulate Menu.# Right click on the '''Ray Domain''' item of the Navigation Tree and select '''Domain Settings...'''# Use the keyboard shortcut '''Ctrl + A'''Terrano assumes a vertical half-wave dipole radiator for your point transmitter set.}}

The size of the Ray domain is specified A transmitter set always needs to be associated with an existing base location set with one or more point objects in terms of six '''Offset''' [[parameters]] along the ±X, ±Y and ±Z directions. The default value of all these six offset [[parameters]] is 10 project unitsworkspace. You can change them arbitrarily. After changing these valuesTherefore, use the '''Apply''' button to make the changes effective while the dialog is still openyou cannot define a transmitter for your scene before drawing a point object under a base location set.

[[FileImage:PROP15Info_icon.png|40px]]Click here to learn how to define a '''[[Glossary_of_EM.Cube%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Point_Transmitter_Set | Point Transmitter Set]]'''.

Figure 1: <table><tr><td> [[Propagation Module]]'s Domain Settings Image:Terrano L1 Fig11.png|thumb|left|480px|The point transmitter set definition dialog.]] </td></tr></table>

Most outdoor and indoor propagation scenes include Once you define a flat ground at their bottomnew transmitter set, which bounces incident rays back into its name is added in the scene. [[EM.Cube]]'s [[Propagation Module]] provides a global flat ground at z = 0. The global ground indeed acts as an impenetrable surface that blocks ''Transmitters''' section of the entire computational domain from the z = 0 plane downward. It is displayed as a translucent green plane at z = 0 extending downwardnavigation tree. The color of all the ground plane is always base points associated with the same as newly defined transmitter set changes, and an additional little ball with the transmitter color of (red by default) appears at the ray domain. The global ground is assumed to be made location of a homogeneous dielectric material with a specified permittivity &epsilon;_r and electric conductivity &sigma;. By default, a rocky ground is assumed with &epsilon;_r = 5 and &sigma; = 0.005 S/meach associated base point. You can remove open the global ground, in which case, you will have property dialog of the transmitter set and modify a free space scene. To disable the global ground, open up the Global Ground Settings Dialog, which can be accessed by right clicking on number of parameters including the '''Global GroundSource Power''' item in the Navigation Tree Watts and selecting the broadcast signal '''Global Ground Settings... Phase'''Remove the in degrees. The default transmitter power level is 1W or 30dBm. There is also a check mark from the box labeled '''Use Custom Input Power''', which is checked by default. In that case, the power and phase boxes are enabled and you can change the default 1W power and 0&quotdeg;Include Half-Space Ground (zphase values as you wish. [[EM.Cube]]'s ".RAD" radiation pattern files usually contain the value of &ltquot;0)Total Radiated Power&quot;''' to disable the global groundin their file header. This will also remove quantity is calculated based on the green translucent plane from particular excitation mechanism that was used to generate the bottom of your scenepattern file in the original [[EM. You can also change Cube]] module. When the material properties "Use Custom Input Power" check box is unchecked, EM.Terrano will use the total radiated power value of the global ground and set new values radiation file for the permittivity and electric conductivity of the impenetrable, half-space, dielectric mediumSBR simulation. '''Do not forget to disable the global ground if you want to model a free space propagation scene.'''

[[File:PROP4{{Note|In order to modify any of the transmitter set's parameters, first you need to select the "User Defined Antenna" option, even if you want to keep the vertical half-wave dipole as your radiator.png]]}}

Figure 2: <table><tr><td> [[Propagation Module]]'s Global Ground Settings File:NewTxProp.png|thumb|left|720px|The property dialogof a point transmitter set.]]</td></tr></table>

=== Terrain Surfaces vsYour transmitter in EM.Teranno is indeed more sophisticated than a simple radiator. It consists of a basic "Transmitter Chain" that contains a voltage source with a series source resistance, and connected via a segment of transmission line to a transmit antenna, which is used to launch the broadcast signal into the free space. The transmitter's property dialog allows you to define the basic transmitter chain. Click the {{key|Transmitter Chain}} button of the Transmitter Set dialog to open the transmitter chain dialog. As shown in the figure below, you can specify the characteristics of the baseband/IF amplifier, mixer and power amplifier (PA) including stage gains and impedance mismatch factors (IMF) as well as the characteristics of the transmission line segment that connects the PA to the antenna. Note that the transmit antenna characteristics are automatically filled using the contents of the imported radiation pattern data file. The transmitter Chain dialog also calculates and reports the "Total Transmitter Chain Gain" based on your input. When you close this dialog and return to the Transmitter Set dialog, you will see the calculated value of the Effective Isotropic Radiated Power (EIRP) of your transmitter in dBm. Global Ground ===

{{Note| If you do not modify the default parameters of the transmitter chain, a 50-&Omega; conjugate match condition is assumed and the power delivered to the antenna will be -3dB lower than your specified baseband power.}} <table><tr><td> [[File:PROP16NewTxChain.png|thumb|200pxleft|[[Propagation Module]]720px|EM.Terrano's Terrain point transmitter chain dialog.]]</td></tr></table>

A terrain surface acts as === Defining a custom, unlevel or irregular ground for your propagation scene. [[EM.Cube]]'s default global ground blocks the z &lt; 0 half-space everywhere Point Receiver Set in the computational domain. You can simply turn off the global ground and create one or more terrain objects and place them arbitrarily in the scene. You can also import an external terrain model or file. A terrain represents an impenetrable surface with a more complex surface profile. You can have one or more terrain objects of finite extents and place them on or above the global ground.Formal Way ===

Terrain objects have some important differences with objects Receivers act as observables in a propagation scene. The objective of a SBR simulation is to calculate the &quot;Impenetrable Surface&quot; typefar-zone electric fields and the total received power at the location of a receiver. You need to define at least one receiver in the scene before you can run a SBR simulation. Similar to a transmitter, a receiver is a point radiator, too. EM.Terrano gives you three options for the radiator associated with a point receiver set:

Just as other blocks are grouped by their colorBy default, texture and material composition, terrain objects are also grouped in EM.Terrano assumes that your receiver is a similar fashionvertically polarized (Z-directed) resonant half-wave dipole antenna. Before you You can generate change the direction of the dipole and orient it along the X or import Y axes using the provided drop-down list. An isotropic radiator has a new terrain object, first you have to define a terrain group perfect omni-directional radiation pattern in all azimuth and specify its color/texture and material propertieselevation directions. To define a new terrain groupAn isotropic radiator doesn't exist physically in the real world, follow these steps:but it can be used simply as a point in space to compute the electric field.

* Right click on the '''Terrain''' item in the Navigation Tree and select '''Insert New Terrain...''' A dialog for setting up the terrain properties opens up offering a of preloaded material type (Rock) with predefined green color and no texture.* Specify You may also define a name complicated radiation pattern for the terrain group and select a color or textureyour receiver set.* Similar to other blocksIn that case, you have need to specify the material properties, Permittivity (&epsilon;_r) and Electric Conductivity (&sigma;), of the terrain group. Rock with &epsilon;_r = 5 and &sigma; = 0.005 S/m is the default material choice for import a new terrainradiation pattern data file to EM.* Click Terrano similar to the '''OK''' button case of the dialog to accept the changes and close ita transmitter set.

You can change the properties of a terrain surface group from its property dialog. Click on the table that list the properties to select and highlight a row. Then{{Note|By default, click the '''Add/Edit''' button to open up the &quot;Edit Layer&quot; dialog, which is identical to the case of impenetrable surfaces. You can also use [[EM.Cube]]'s Material List, which will be explained later. When Terrano assumes a new terrain type is created, its node on the Navigation Tree becomes active. Under this node you can create and add new terrain objects. When a terrain node is active vertical half-wave dipole radiator for drawing, all CAD object creation tools are disabledyour point receiver set. You have three options for creating a new terrain object, which will be described in detail in the next sections of this manual:}}

# Use [[EMSimilar to transmitter sets, you define a receiver set by associating it with an existing base location set with one or more point objects in the project workspace.Cube]]'s '''Terrain Generator'''All the receivers belonging to the same receiver set have the same radiator type.# Import an external terrain file A typical propagation scene contains one or few transmitters but usually a large number of &quot;'''receivers.TRN'''&quot; type.# Import To generate a wireless coverage map, you need to define an external terrain file array of &quot;'''.DEM'''&quot; typepoints as your base location set.

<table><tr><td> [[FileImage:PROP18Terrano L1 Fig12.png|thumb|250pxleft|[[Propagation Module]]'s Terrain Generator 480px|The point receiver set definition dialog.]]</td></tr></table>

[[EM.Cube]] provides Once you define a convenient and powerful Terrain Generator for creating a variety of terrain [[Surface Objects|surface objects]]. [[EM.Cube]]'s Terrain Generator looks very similar new receiver set, its name is added to [[CubeCAD]]'s Surface Generator. However, whereas the Surface Generator creates a generic or polymesh surface object, Terrain Generator always creates another special type of object known as a '''Tessellated ObjectReceivers'''section of the navigation tree. A terrain object is much simpler than [[EM.Cube]]'s polymesh objects The color of all the base points associated with the newly defined receiver set changes, and is usually made up an additional little ball with the receiver color (yellow by default) appears at the location of triangular or quadrilateral facetseach associated base point. As such, terrain objects have limited editing capabilities. For example, you You can cut, copy, paste, translate or rotate terrain objects. But operations like scaling, mirroring, grouping (composite), arraying, exploding, linking or Boolean operations do not work on terrain objectsopen the property dialog of the receiver set and modify a number of parameters.

To create a new terrain object using Terrain Generator, first you need to define a terrain group in the Navigation Tree<table><tr><td> [[File:NewRxProp. Right click on the name png|thumb|left|720px|The property dialog of the terrain node and select '''Terrain Generator...''' from the contextual menu. This opens up the Terrain Generator Dialog. Using Terrain Generator, you can build a single terrain surface or an array of surfaces patched togetherpoint receiver set. Some of the available terrain models include:]]</td></tr></table>

# Flat Plane# Hill (Elliptic Quadratic)# Mountain (Elliptic Cone)# 1In the Receiver Set dialog, there is a drop-D down list labeled '''Selected Element''', which contains a list of all the individual receivers belonging to the receiver set. At the end of an SBR simulation, the button labeled {{key|Show Ray Data}} becomes enabled. Clicking this button opens the Ray Data dialog, where you can see a list of all the received rays at the selected receiver and 2-D Cliff# Gaussian Hump# Undulated Sinusoid# Undulated Sinc# Super-quadratic Plateau# Custom Function# XY Grid Datatheir computed characteristics.

In all of If you choose the above models"user defined antenna" option for your receiver set, you can it indeed consists of a basic "Receiver Chain" that contains a receive antenna connected via a segment of transmission line to the low-noise amplifier (LNA) that is terminated in a matched load. The receiver set 's property dialog allows you to define the height basic receiver chain. Click the {{key|Receiver Chain}} button of the surface object Receiver Set dialog to an any desired valueopen the receiver chain dialog. You set As shown in the lateral extents figure below, you can specify the characteristics of the surface and LNA such as its resolution along the X gain and Y directions noise figure in dB as well as the boxes labeled characteristics of the transmission line segment that connects the antenna to the LNA. Note that the receiving antenna characteristics are automatically filled from using contents of the radiation file. You have to enter values for antenna's ''Range Start''', '''Range StopBrightness Temperature''' as well as the temperature of the transmission line and the receiver's ambient temperature. The effective ''Range Step'Receiver Bandwidth''' is assumed to be 100MHz, which you can change for the purpose of noise calculations. The step values along Receive Chain dialog calculates and reports the X "Noise Power" and Y directions are a measure "Total Receiver Chain Gain" based on your input. At the end of surface smoothness: an SBR simulation, the smaller receiver power and signal-noise ratio (SNR) of the step valuesselected receiver are calculated and they are reported in the receiver set dialog in dBm and dB, respectively. You can examine the higher properties of all the resolution individual receivers and all the smoother individual rays received by each receiver in your receiver set using the resulting terrain object"Selected Element" drop-down list.

Some surface types have an additional shape factor called '''Alpha''' that is identical to the alpha parameter in the surface generator. For example, a Gaussian Hump is defined as exp(-r<suptable>2</suptr>/(2a<suptd>2</sup>)), where r is the polar radius[[File:NewRxChain. For a Super-quadratic Hump, the input parameter a defines the degree of the super-quadratic surfacepng|thumb|left|720px|EM. a = 2 corresponds to an ellipsoidTerrano's point receiver chain dialog. Larger values of a get close to a rectangular base with rounded corners. An undulated sinusoidal surface is defined by cos(pax/D<sub>x]] </subtd>)*cos(pay/D<sub>y</subtr>), and an undulated sinc is defined by D<sub>x</subtable>*D_y*sin(pax/D_x)*sin(pay/D_x)/(2pxy), where D_x and D_y are the X and Y dimensions, respectively. Terrain Generator creates a unit cell based on the specified surface type. From the same dialog, you can also produce an array arrangement of such unit cells. Simply enter any number of elements along the X and Y directions in the boxes labeled '''Array'''.

Figure: A 4 × 4 array of hill terrain objectsEM.Terrano allows you to define a digital modulation scheme for your communication link. There are currently 17 waveforms to choose from in the receiver set property dialog:

You can define any arbitrary surface by entering an equation of the two [[variables]] x and y as z = f(x,y). In this case, you have to select the '''Custom Function''' option in the dropdown list labeled '''Model'''. You should enter your equation as any mathematical expression in the box labeled '''Function f(x,y)'''. You can use any of EM.Cube's mathematical functions listed in the '''Function Dialog''' or combine several of them. Note that after selecting the custom function option, the height of the surface is determined by your equation, and the '''Height''' box is disabled. You can also introduce random noise and create a rough terrain. You can do this by setting a nonzero value for '''Noise''', which represent the RMS peak*OOK*M-toary ASK*Coherent BFSK*Coherent QFSK*Coherent M-valley amplitude of the surface roughness. The figures below show two custom terrain surfaces modeled by the equation z ary FSK*Non-Coherent BFSK*Non-Coherent QFSK*Non-Coherent M-ary FSK*BPSK*QPSK*Offset QPSK*M-ary PSK*DBPSK*pi/4 Gray-Coded DQPSK*M-ary QAM*MSK*GMSK (BT = (x0.y3)/20 defined over the range [0, 10] in both X and Y directions. Random noise has been added to both surfaces, with the noise amplitude being 0.2 and 0.5 for the left and right figures, respectively.

[[File:PROP21In the above list, you need to specify the '''No.png|400px]] [[File:PROP20Levels (M)''' for the Mary modulation schemes, from which the '''No. Bits per Symbol''' is determined. You can also define a bandwidth for the signal, which has a default value of 100MHz. Once the SNR of the signal is found, given the specified modulation scheme, the E_b/N₀ parameter is determined, from which the bit error rate (BER) is calculated.png|400px]]

FigureThe Shannon – Hartley Equation estimates the channel capacity: Two noisy custom terrain surfaces both defined as z = (x.y)/20: (Left) RMS noise amplitude = 0.2, (right) RMS noise amplitude = 0.5.

<math> C === Generating Grid-Based Terrain ===B \log_2 \left( 1 + \frac{S}{N} \right) </math>

Every time you create a new terrain object using Terrain Generatorwhere B in the bandwidth in Hz, an ASCII data file named &quot;GeneratedTerrain&quot; with a &quot;'''.TRN'''&quot; file extension is created and placed in your project folder. This C is [[EM.Cube]]'s simple native terrain file format that basically lists all the channel capacity (x, y, zmaximum data rate) coordinates of the generated surface points on a horizontal, rectangular XY grid. Terrain Generator simply takes your custom function definition or one of the selected catalog surface types and generates the digital elevation data on the specified gridexpressed in bits/s.

Another type The spectral efficiency of terrain model that the terrain generator provides channel is '''XY Grid Data'''. In this case, you define a rectangular XY grid with a uniform grid cell size along the X and Y directions and manually define the Z-elevation for each grid point. This is similar to the surface generator's &quot;2D Uniform Grid&quot; model type in [[CubeCAD]]. Based on your input to '''Range Start''', '''Range Stop''' and '''Range Step''' along X and Y, a 2D grid is set up and displayed in a table at the bottom of the terrain generator dialog. By default, all the Z-elevations are set to zero initially. You can click on each table cell and overwrite it with a new value. At the end, click the '''Create''' button of the dialog to add the new grid-based terrain object to the Navigation Tree.defined as

A grid-based terrain objectThe quantity E_b/N₀ is the ratio of energy per bit to noise power spectral density.It is a measure of SNR per bit and is calculated from the following equation:

<math> \frac{E_b}{N_0} === Importing &amp; Exporting Terrain Models ===\frac{ 2^\eta - 1}{\eta} </math>

You can import two types of terrain in [[EM.Cube]]'s [[Propagation Module]]. The first type is where &quoteta;'''.TRN&quot;''' terrain file, which is [[EM.Cube]]'s native terrain format. It is a basic digital elevation map with a very simple ASCII data file format. The resolution of the terrain map in the X and Y directions is specified in meters as STEPS. The (x, y, z) coordinates of the terrain points are then listed one point per line. The other type of terrain format supported by [[EM.Cube]] is the standard '''7.5min DEM''' file format with a '''.DEM''' file extensionspectral efficiency.

To import an external terrain model, first you have to create a terrain group node in The relationship between the Navigation Tree. Right click bit error rate and E_b/N₀ depends on the name of the terrain group in the Navigation Tree modulation scheme and select either '''Import Terrain...''' or '''Import DEM File...''' A standard [[Windows]] '''Open Dialog''' opens up, with the file detection type set to (coherent vs.TRN or non-coherent).DEM extensionsFor example, respectively. You for coherent QPSK modulation, one can browse your folders and find the right terrain model file to import.write:

You can also export all the terrain objects in the project workspace as a terrain file with a '''<math> P_b = 0.TRN''' file extension. You can even import a DEM terrain model from an external file and then save and export it as a native terrain 5 \; \text{erfc} \left(.TRN\sqrt{ \frac{E_b}{N_0} } \right) file. To export </math> where P_b is the terrain, select '''File''' &gt; '''Export...''' from [[Propagation Module]]'s '''File Menu'''. The standard [[Windows]] Save Dialog opens up with the default file type set to '''.TRN'''. Type in a name for your new terrain file bit error rate and click erfc(x) is the '''Save''' button to export the terrain data.complementary error function:

[[File:prop_manual<math> \text{erfc}(x) = 1-12_tn.png|800px]]\text{erf}(x) = \frac{2}{\sqrt{\pi}} \int_{x}^{\infty} e^{-t^2} dt </math>

Figur: An imported external terrain modelThe '''Minimum Required SNR''' parameter is used to determine link connectivity between each transmitter and receiver pair. If you check the box labeled '''Generate Connectivity Map''' in the receiver set property dialog, a binary map of the propagation scene is generated by EM.Terrano, in which one color represents a closed link and another represent no connection depending on the selected color map type of the graph. EM.Terrano also calculates the '''Max Permissible BER''' corresponding to the specified minimum required SNR and displays it in the receiver set property dialog.

=== Multilayer Surface Models A Note on EM.Terrano's Native Dipole Radiators ===

[[File:PROP26When you define a new transmitter set or a new receiver set, EM.png|thumb|200px|Propagation Module's Penetrable Surface Dialog showing Terrano assigns a threevertically polarized half-layer wall composition]]wave dipole radiator to the set by default. The radiation pattern of this native dipole radiators is calculated using well-know expressions that are derived based on certain assumptions and approximations. For example, the far-zone electric field of a vertically-polarized dipole antenna can be expressed as:

Most of the time<math> E_\theta(\theta, your outdoor propagation scene consists of simple buildings made of single\phi) \approx j\eta_0 I_0 \frac{e^{-layer walls with standard material properties jk_0 r}}{2\pi r} \left[ \frac{\text{cos} \left(&epsilon;_r and &sigma;\frac{k_0 L}{2} \text{cos} \theta \right). In the case of a single-layer impenetrable surface, the specular interface is an infinite dielectric half-space, which reflects the impinging rays. Single-layer penetrable surfaces, on the other hand, involve finite-thickness dielectric walls, which both reflect and transmit the incident rays. Similarly, most of your indoor propagation scenes involve simple single-layer penetrable walls with the specified material properties &epsilon;<sub>r\text{cos} \left( \frac{k_0 L}{2} \right) }{\text{sin}\theta} \right] </submath> and &sigma;. A thin wall acts like a finite-thickness dielectric slab that both reflects and transmits incident rays. In the case of the global ground or terrain objects, only ray reflection off the ground surface is considered.

In [[EM.Cube]]'s [[Propagation Module]], you can define multilayer surfaces with both reflection and transmission properties. You can define multilayer impenetrable buildings, multilayer penetrable walls, and multilayer terrain, with an arbitrary number of layers having different material compositions. You define a multilayer surface in the property dialog of a block, whether impenetrable, penetrable or terrain. In the section entitled '''Surface Type''', two options are available: '''Standard Material''' or '''User Defined Model'''. For simple multilayer walls, select the '''Standard Material''' option. You can add new layers with arbitrary thickness and material [[parameters]] to the existing layers. To insert a new layer, deselect any items in the layer list, and click the '''Add/Edit''' button to open the &quot;Add Layer&quot; Dialog. Here you can enter a name for the new layer and values for its '''Thickness''', &epsilon;<submath>rE_\phi(\theta,\phi) \approx 0 </submath> and &sigma;. You may also delete any layer by selecting and highlighting it and clicking the '''Delete''' button. You can move layers up or down using the '''Move Up''' and '''Move Down''' buttons and change the layer hierarchy.

You can also search [[EM.Cube]]'s material database by clicking the '''Material''' button of where k₀ = 2&quotpi;Add Layer/&quotlambda; or ₀ is the free-space wavenumber, &quotlambda;Edit Layer&quot; dialogs. This opens the '''Materials''' Dialog. Inside the material list select and highlight any row and click the '''OK''' button. The selected material will fill out all the fields in ₀ is the free-space wavelength, &quoteta;Add Layer₀ = 120&quotpi; or &quotOmega;Edit Layer&quot; dialogs. Inside is the Materials Dialogfree-space intrinsic impedance, you can type I₀ is the few first letters of any materialcurrent on the dipole, and it will take you to L is the corresponding row length of the listdipole.

[[FileThe directivity of the dipole antenna is given be the expression:PROP24.png]]

Figure: <math> D_0 \approx \frac{2}{F_1(k_0L) + F_2(k_0L) + F_3(k_0L)} \left[[EM.Cube]\frac{\text{cos} \left( \frac{k_0 L}{2} \text{cos} \theta \right) - \text{cos} \left( \frac{k_0 L}{2} \right) }{\text{sin}\theta} \right]'s material list.^2 </math>

When you start a new project in [[EM.Cube]]'s [[Propagation Module]] and draw a solid object like a box in the project workspace without having defined any surface groups, it is assumed to be of the impenetrable surface type. A default impenetrable surface group called Block_1 is automatically added to the Navigation Tree, which holds your newly drawn object. The default group has the material properties of &quot;Brick&quot; (&epsilon;<submath>rF_1(x) = \gamma + \text{ln}(x) - C_i(x) </submath> = 4.4 and &sigma; = 0.001 S/m.) with a dark brown color. You can continue drawing new objects in the project workspace and adding them under this block node. Or you can define a new surface type with different properties. By default, the last surface group that was defined is '''Active'''. The current active surface group is always listed in bold letters in the Navigation Tree. When you draw a new object, it is always inserted under the current active surface group. Any surface group can be activated by right clicking its name in the Navigation Tree and selecting the '''Activate''' item of the contextual menu.

You can move any object from its current surface group into any other available surface group. First select the object, then right click on its surface and select '''MoveTo &gt; Propagation &gt;'''. A submenu appears which lists all the available surface groups where you can transfer the selected object. You can also move objects among surface groups by selecting their names in the Navigation Tree and using the contextual menu. In a similar way, you can transfer objects from <math> F_2(x) = \frac{1}{2} \text{sin}(x) \left[[Propagation Module]] to [[EM.Cube]]'s other modules or vice versa. '''Keep in mind that all the external model files such as STEP, IGES, STL, etc. are first imported to [[EM.Cube]]'s [[CubeCAD]], from which you can transfer them to other modules.''' First select the object, then S_i(2x) - 2S_i(x) \right click and select '''MoveTo &gt;'''. In the submenu you will see a list of all the [[EM.Cube]] modules that have at least one available group where you can transfer your selected object. You can select multiple objects for transfer. When using the keyboard's '''Shift Key''' or '''Ctrl Key''' for multiple selection, make sure that those keys are held down, when you right click to access the contextual menu. </math>

<math> F_3(x) == Defining Sources &amp; Observables ==\frac{1}{2} \text{cos}(x) \left[ \gamma + \text{ln}(x/2) + C_i(2x) - 2C_i(x) \right] </math>

The simplest SBR simulation can be performed using a short dipole source with a specified field sensor plane. In this way, [[EM.Cube]] computes the electric and magnetic fields radiated by your dipole source in the presence of your multipath propagation environment. A &quot;classic&quot; urban propagation scene can be set up using a &quot;Transmitter&quot; source and an array of &quot;Receiver&quot; observables. A transmitter is a point radiator with a user defined radiation pattern. A receiver is a polarization-matched isotropic point radiator that collects the received rays at its aperture. Using receivers, you can calculate the received power coverage map of your propagation scene. You can also calculate your channel's path loss between the transmitter and all the receivers. <br /math> S_i(x) = \int_{0}^{x} \frac{ \text{sin} \tau}{\tau} d\tau </math>

[[File:PROP18(1).png|thumb|[[Propagation Module]]'s Transmitter dialog with In the case of a short half-wave dipole radiator selected]]Earlier versions of [[EM, L = &lambda;₀/2, and D₀ = 1.Cube]]'s [[Propagation Module]] used to offer an isotropic radiator with vertical or horizontal polarization as 643. Moreover, the simplest transmitter type. This release input impedance of [[EMthe dipole antenna is Z_A = 73 + j42.Cube]] has abandoned isotropic radiator transmitters because they do not exist physically in 5 &Omega;. These dipole radiators are connected via 50&Omega; transmission lines to a real world50&Omega; source or load. InsteadTherefore, the default transmitter radiator type there is now always a Hertzian dipole. Note certain level of impedance mismatch that before defining a transmitter, first you have to define a base set to establish violates the location of the transmitter. Most simulation scenes involve only a single transmitter. Your base set can be made up of a single point conjugate match condition for this purposemaximum power.

To define a new Transmitter Set, go to the '''Sources''' section of the Navigation Tree, right click on the '''Transmitters''' item and select '''Insert Transmitter.<table><tr><td> [[File:Dipole radiators.png|thumb|720px|EM.Terrano''' A dialog opens up that contains a default name for the new Transmitter Set as well as a dropdown list labeled '''Select Base Set'''. In this list you will see all the available base sets already defined in the project workspace. Select the desired base set to associate with the s native half-wave dipole transmitter set. Note that if the base set contains more than one point, then more than one transmitter will be created and contained in your transmitter set. After defining a transmitter set, the base points change their color to the transmitter color, which is red by defaultreceiver.]] </td></tr></table>

In On the &quot;Radiator&quot; section of other hand, we you specify a user-defined antenna pattern for the dialogtransmitter or receiver sets, you have two options to choose from: import a 3D radiation pattern file that contains all the values of E_{&quottheta;Short Dipole} and E_{&quotphi; and} for all the combinations of (&quottheta;User Defined, &quotphi;) angles. The default option is short Besides the three native dipole. A short dipole radiator has a '''Length'''''dl'' expressed in project unitsradiators, a current '''Amplitude''' in Amperes and a current '''Phase''' in degrees[[EM. The '''Direction''' of the dipole is determined by its unit vector that has Cube]] also provides 3D radiation pattern files for three X-, Y - and Z components-polarized half-wave resonant dipole antennas. By default, These pattern data were generated using a Zfull-directed short dipole radiator is assumed. You can change all wave solver like [[parametersEM.Libera]] 's wire MOM solver. The names of the dipole as you wish. Keep in mind that all the transmitters belonging to the same set have parallel radiators with identical properties.radiation pattern files are:

[[File:PROP1.png|thumb|[[Propagation Module]]'s Base Set dialog]]In order to tie up transmitters and receivers with CAD objects they are located in the project workspace, [[EMfolder "\Documents\EMAG\Models" on your computer.Cube]] uses point objects to define transmitters Note that these are full-wave simulation data and receiversdo not involve any approximate assumptions. These point objects represent To use these files as an alternative to the base of native dipole radiators, you need to select the location of transmitters and receivers in the computational domain. Hence, they are grouped together '''User Defined Antenna Pattern''' radio button as &quot;Base Sets&quot;. You can easily interchange the role of transmitters and receivers the radiator type in a scene by switching their associated bases. The usefulness of concept of base sets will become apparent later when you place transmitters the transmitter or receivers on an irregular terrain and adjust their elevationreceiver set property dialog.

To create a new base set, right click === A Note on the '''Base Sets''' item Rotation of Navigation Tree and select '''Insert Base Set...''' A dialog for setting up the Base Set properties opens up.Antenna Radiation Patterns ===

# Enter a name for the base set EM.Terrano's Transmitter Set dialog and change the default blue color if Receiver Set dialog both allow you wishto rotate an imported radiation pattern. It is useful In that case, you need to differentiate the base sets associated with transmitters and receivers by their color.# Click specify the '''OKRotation''' button angles in degrees about the X-, Y- and Z-axes. It is important to close note that these rotations are performed sequentially and in the Base Set Dialogfollowing order: first a rotation about the X-axis, then a rotation about the Y-axis, and finally a rotation about the Z-axis. In addition, all the rotations are performed with respect to the "rotated" local coordinate systems (LCS). In other words, the first rotation with respect to the local X-axis transforms the XYZ LCS to a new primed X^&prime;Y^&prime;Z^&prime; LCS. The second rotation is performed with respect to the new Y^&prime;-axis and transforms the X^&prime;Y^&prime;Z^&prime; LCS to a new double-primed X^{&prime;&prime;}Y^{&prime;&prime;}Z^{&prime;&prime;} LCS. The third rotation is finally performed with respect to the new Z^{&prime;&prime;}-axis. The figures below shows single and double rotations.

Once <table><tr><td> [[File:PROP22B.png|thumb|300px|The local coordinate system of a base set node has been added to the Navigation Tree, it becomes the active node for new object drawing. Under base sets, you can only draw point objectslinear dipole antenna. All other object creation tools are disabled]] </td><td> [[File:PROP22C. A point is initially drawn on png|thumb|600px|Rotating the XY plane. Make sure to change dipole antenna by +90&deg; about the Zlocal Y-coordinate of your radiator, otherwise, it will fall on the global ground at z = 0axis. You can also create arrays of base points under the same base set]] </td></tr></table><table><tr><td> [[File:PROP22D. This is particularly useful for setting up receiver grids to compute coverage maps. Simply select a point object and click the '''Array Tool''' of '''Tools Toolbar''' or use png|thumb|720px|Rotating the keyboard shortcut dipole antenna by +90&quotdeg;Aabout the local X-axis and then by -45&quotdeg;. Enter values for by the X, local Y or Z spacing as well as the number of elements along these three directions in the Array Dialog. In most propagation scenes you are interested in 2D horizontal arrays along a fixed Z coordinate (parallel to the XY plane)-axis.]] </td></tr></table>

=== Defining Transmitter Sets Adjustment of Tx/Rx Elevation above a Terrain Surface ===

A short dipole is When your transmitters or receivers are located above a flat terrain like the closest thing to an omniglobal ground, their Z-directional radiator. The direction or orientation of coordinates are equal to their height above the short dipole determines its polarizationground, as the terrain elevation is fixed and equal to zero everywhere. In many applicationspropagation modeling problems, your transmitters and receivers may be located above an irregular terrain with varying elevation across the scene. In that case, you may rather want to use a directional antenna for place your transmittertransmitters or receivers at a certain height above the underlying ground. You can model The Z-coordinate of a radiating structure using [[transmitter or receiver is now the sum of the terrain elevation at the base point and the specified height. EM.Cube]]'s FDTD, Planar, MoM3D or PO modules Terrano gives you the option to adjust the transmitter and generate a 3D radiation pattern data file receiver sets to the terrain elevation. This is done for itindividual transmitter sets and individual receiver sets. These data are stored in a specially formatted file with At the top of the Transmitter Dialog there is a check box labeled &quot;'''.RADAdjust Tx Sets to Terrain Elevation'''&quot; extension. Similarly, which contains columns of spherical &phi; and &theta; angles as well as at the real and imaginary parts top of the complex-valued far field components '''E_{Receiver Dialog there is a check box labeled &thetaquot;}''' and Adjust Rx Sets to Terrain Elevation'''E_&phiquot;'''. The &theta;- These boxes are unchecked by default. As a result, your transmitter sets or receiver sets coincide with their associated base points in the project workspace. If you check these boxes and &phi;-components of place a transmitter set or a receiver set above an irregular terrain, the far-zone electric field determine transmitters or receivers are elevated from the polarization location of their associated base points by the amount of terrain elevation as can be seen in the transmitting radiatorfigure below.

To define a directional transmitter radiator, you need to select the &quot;User Defined&quot; option better understand why there are two separate sets of points in the &quot;Radiator&quot; section of the Transmitter Dialog. You can do this either at the time of creating scene, note that a transmitter set, or afterwards by opening the property dialog of the transmitter set. In the &quot;Custom Pattern [[Parameters]]&quot;, click the '''Import Pattern''' button point array (CAD object) is used to create a uniformly spaced base set the path for the radiation data file. This opens up the standard [[Windows]] Open dialog, with the default file type or extension set to &quot;.RAD&quot;. Browse your folders to find the right data file. A radiation pattern file usually contains the value of &quot;Total Radiated Power&quot; in The array object always preserves its file header. This is used by default for power calculations in grid topology as you move it around the SBR simulationscene. However, you can check the box labeled &quot;'''Custom Power'''&quot; transmitters or receivers associated with this point array object are elevated above the irregular terrain and enter no longer follow a value for the transmitter power in Wattsstrictly uniform grid. [[EM.Cube]] can also rotate If you move the imported radiation pattern arbitrarily. In this casebase set from its original position to a new location, you need to specify the base points'''Rotation''' angles in degrees about the X-topology will stay intact, Y- and Z-axes. Note that these rotations are performed sequentially and in order: first a rotation about while the X-axis, then a rotation about the Y-axis, and finally a rotation about associated transmitters or receivers will be redistributed above the Z-axisterrain based on their new elevations.

<table><tr><td> [[FileImage:PROP19PROP MAN8.png|thumb|left|640px|A transmitter (1red)and a grid of receivers (yellow) adjusted above a plateau terrain surface.png]] [[File:PROP20The underlying base point sets (1blue and orange dots)associated with the adjusted transmitters and receivers on the terrain are also visible in the figure.png]]</td></tr></table>

Figure 1: [[== Discretizing the Propagation Module]]'s Transmitter dialog with a user defined radiator selectedScene in EM.Terrano ==

=== Multiple Transmitters vs. Antenna Arrays Why Do You Need to Discretize the Scene? ===

[[EM.Cube]]Terrano's SBR simulations are fully coherent and 3D-polarimetric. This means that solver uses a method known as Geometrical Optics (GO) in conjunction with the phase and polarization Uniform Theory of all Diffraction (UTD) to trace the rays are maintained and processed during from their bounces in originating point at the source to the sceneindividual receiver locations. Your propagation scene can have more than one transmitterRays may hit obstructing objects on their way and get reflected, diffracted or transmitted. During an EM.Terrano's SBR simulation, all the rays emanating solver can only handle diffraction off linear edges and reflection from all the transmitters are traced in the propagation scene. All the received rays at a given receiver location are summed coherently and vectoriallytransmission through planar interfaces. This is based on When an incident ray hits the principle surface of linear superposition. All the transmitters belonging to the same transmitter set have the same radiation properties. They are either parallel short dipole radiators with the same current amplitudes and phasesobstructing object, or parallel user defined radiators with identical radiation patterns. As these transmitters are placed a local planar surface assumption is made at different spatial locations, they effectively form an antenna array with identical elementsthe specular point. The array factor is simply determined by assumptions of linear edges and planar facets obviously work in the coordinates case of the base points. If you want to have different amplitude or phases, then you need to define different transmitter setsa scene with cubic buildings and a flat global ground.

If that radiators are indeed In many practical scenarios, however, your buildings may have curved surfaces, or the elements terrain may be irregular. EM.Terrano allows you to draw any type of an actual antenna array with a half wavelength spacing surface or sosolid geometric objects such as cylinders, we recommend that you import the radiation pattern cones, etc. under impenetrable and penetrable surface groups or penetrable volumes. EM.Terrano's mesh generator creates a triangular surface mesh of all the array structure instead and replace the whole multi-radiator system with a single point transmitting radiator objects in your propagation scene. This case is usually encountered in MIMO systems, and using an equivalent point transmitter which is an acceptable approximation because the total size of the array aperture is usually much smaller than the dimensions of your propagation scene and its representative length scalescalled a facet mesh. In that case, you need to position Even the equivalent point radiator at the radiation center walls of the antenna arraycubic buildings are meshed using triangular cells. This depends on the physical structure enables EM.Terrano to properly discretize composite buildings made of the antenna array. However, keep in mind that any reasonable guess may still provide a good approximation without any significant error in the received ray dataconjoined cubic objects.

Receivers act as observables in a propagation scene. The objective of a SBR simulation is to calculate === Generating the far-zone electric fields and the total received power at the location of a receiver. In that sense, receivers indeed act as field observation points. You need to define at least one receiver in the scene before you can run a SBR simulation. You define the receivers of your scene by associating them with the base sets you have already defined in the project workspace. Unlike transmitters that usually one or few, a typical propagation scene may involve a large number of receivers. To generate a wireless coverage map, you need to define an array of points as your base set. Facet Mesh ===

To define a new Receiver Set, go You can view and examine the discretized version of your scene's objects as they are sent to the Observables section SBR simulation engine. You can adjust the mesh resolution and increase the geometric fidelity of discretization by creating more and finer triangular facets. On the Navigation Treeother hand, right click on you may want to reduce the '''Receivers''' item mesh complexity and select '''Insert Receiver.send to the SBR engine only a few coarse facets to model your buildings.The resolution of EM.Terrano''' A dialog opens up that contains a default name for s facet mesh generator is controlled by the new Receiver Set as well as a dropdown list labeled '''Select Radiator SetCell Edge Length'''. In this list you will see all the available base sets that you have already define in the project workspace. Select and designate the desired base set as the receiver set. Note that if the base set contains more than one point, all of them are designated as receivers. After defining a receiver set, the points change their color to the receiver colorparameter, which is yellow by defaultexpressed in project length units. The first element default mesh cell size of the set is represented by a larger ball of the same color indicating that it is the selected receiver in the scene100 units might be too large for non-flat objects. The Receiver Set Dialog is also used You may have to access individual receivers of the set for data visualization at the end of a simulationsmaller cell edge length in EM. At the end of an SBR simulationTerrano's Mesh Settings dialog, along with a lower curvature angle tolerance value to capture the button labeled &quot;Show Ray Data&quot; becomes enabled. Clicking this button opens the Ray Data Dialog, where you can see a list curvature of all the received rays at the selected receiver and their computed characteristicsyour curved structures adequately.

<table><tr><td> [[FileImage:PROP21(1)prop_manual-29.png]] [[File:PROP22|thumb|left|480px|EM.Terrano's mesh settings dialog.png]]</td></tr></table>

Figure 1[[Image: Info_icon.png|30px]] Click here to learn more about '''[[Propagation ModulePreparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'s Receiver dialog''.

<table><tr><td> [[FileImage:PMOM90UrbanCanyon2.png|thumb|[[Propagation Module]]'s Field Sensor dialog]]As an asymptotic electromagnetic field solver, left|640px|The facet mesh of the SBR simulation engine can compute the electric and magnetic field distributions buildings in a specified plane. In order to view these field distributions, you must first define field sensor observables before running the SBR simulationurban propagation scene generated by EM. To do that, right click on the Terrano'''Field Sensors''' item in the '''Observables''' section s Random City wizard with a cell edge length of the Navigation Tree and select '''Insert New Observable100m.]] </td></tr><tr><td> [[Image:UrbanCanyon3..'''. png|thumb|left|640px|The Field Sensor Dialog opens up. At the top facet mesh of the dialog and buildings in the section titled '''Sensor Plane Location''', first you need to set the plane of field calculationurban propagation scene generated by EM. In the dropdown box labeled Terrano'''Direction''', you have three options X, Y, and Z, representing the&quot;normals&quot; to the XY, YZ and ZX planes, respectively. The default direction is Z, i.e. XY plane parallel to the substrate layers. In the three boxes labeled '''Coordinates''', you set the coordinates s Random City wizard with a cell edge length of the center of the plane. Then, you specify the '''Size''' of the plane in project units, and finally set the '''Number of Samples''' along the two sides of the sensor plane. The larger the number of samples, the smoother the near field map will appear10m. ]] </td></tr></table>

In the section titled Output Settings, you can also select the field map type from two options: '''Confetti''' and '''Cone'''. The former produces an intensity plot for field amplitude and phase, while the latter generates a 3D vector plot. In the confetti case, you have an option to check the box labeled '''Data Interpolation''', which creates a smooth and blended (digitally filtered) map. In the cone case, you can set the size of the vector cones that represent the field direction. At the end of a sweep simulation, multiple field map are produced and added to the Navigation Tree. You can animate these maps. However, during the sweep only one field type is stored, either the E-field or H-field. You can choose the field type for multiple plots using the radio buttons == Running Ray Tracing Simulations in the section titled '''Field Display - Multiple Plots'''. The default choice is the E-fieldEM. Terrano ==

Once you close the Field Sensor dialog, its name is added under the '''Field Sensors''' node of the Navigation TreeEM. At the end Terrano provides a number of a SBR different simulation, the field sensor nodes in the Navigation Tree become populated by the magnitude and phase plots of the three vectorial components of the electric ('''E''') and magnetic ('''H''') field as well as the total electric and magnetic fields defined in the following manneror solver types:

:<math> \mathbf{|H_{tot}|} = \sqrt{|H_x|^2 + |H_y|^2 + |H_z|^2} </math><!--[[File:PMOM88The first three simulation types are described below. For a description of EM.Terrano's Radar Simulator, follow this link.png]]-->

=== Computing Radiation Patterns In Running a Single-Frequency SBR Analysis ===

Coming SoonIts main solver is the '''3D SBR Ray Tracer'''.Once you have set up your propagation scene in EM.Terrano and have defined sources/transmitters and observables/receivers for your scene, you are ready to run a SBR ray tracing simulation.You set the simulation mode in EM.Terrano's simulation run dialog. A single-frequency SBR analysis is a single-run simulation and the simplest type of ray tracing simulation in EM.Terrano. It involves the following steps:

In a typical SBR simulation, a ray is traced from the location of the source until it hits a scatterer. The <table><tr><td> [[SBR MethodImage:Terrano L1 Fig16.png|SBR methodthumb|left|480px|EM.Terrano's simulation run dialog.]] assumes that the ray hits either a flat facet of the scatterer or one of its edges. In the case of hitting a flat facet, the specular point is used to launch new reflected and transmitted rays. The surface of the facet is treated as an infinite dielectric medium interface, at which the reflection and transmission coefficients are calculated. In the case of hitting an edge, new diffracted rays are generated in the scene. However, only those who reach a nearby receiver in their line of sight are ever taken into account. In other words, diffractions are treated locally.</td></tr></table>

<table><tr><td> [[Image:PROP MAN10.png|thumb|left|550px|EM.Cube]]Terrano's [[Propagation Module]] allows you to draw any type of surface or solid CAD objects under impenetrable and penetrable surface groups. Some of these objects have flat faces such as boxes, pyramids, rectangle or triangle strips, etc. Some others contain curved surfaces or curved boundaries such as cylinders, cones, etc. All the non-flat surfaces have to be discretized in the form of a collection of smaller flat facets. [[EMoutput message window.Cube]] uses a triangular surface mesh generator to discretize the penetrable and impenetrable [[Surface Objects|surface objects]] of your propagation scene. This mesh generator is very similar to the ones used in [[EM.Cube]]'s two other modules: MoM3D and Physical Optics (PO). </td></tr></table>

You can build a variety of surface and [[Solid Objects|solid objects]] using [[EM.Cube]]'s native &quot;Curve&quot; CAD objects like lines, polylines, circles, etc. You can use tools like Extrude, Loft, Strip-Sweep, Pipe-Sweep, etc. to transform curves into surface or [[Solid Objects|solid objects]]. '''However, keep in mind that all the &quot;Curve&quot; CAD objects are ignored by === Changing the SBR mesh generator and are therefore not sent to the simulation engine.'''Engine Settings ===

=== Viewing There are a number of SBR Mesh ===simulation settings that can be accessed and changed from the Ray Tracing Engine Settings Dialog. To open this dialog, click the button labeled {{key|Settings}} on the right side of the '''Select Simulation or Solver Type''' drop-down list in the Run Dialog. EM.Terrano's SBR simulation engine allows you to separate the physical effects that are calculated during a ray tracing process. You can selectively enable or disable '''Reflection/Transmission''' and '''Edge Diffraction''' in the "Ray-Block Interactions" section of this dialog. By default, ray reflection and transmission and edge diffraction effects are enabled. Separating these effects sometimes help you better analyze your propagation scene and understand the impact of various blocks in the scene.

You can view and examine the discretized version EM.Terrano allows a finite number of your scene objects as they are sent to the SBR simulation engineray bounces for each original ray emanating from a transmitter. This is very important in situations that may involve resonance effects where rays get trapped among multiple surfaces and may bounce back and forth indefinitely. To view the mesh, click This is set using the box labeled &quot;'''MeshMax No. Ray Bounces''' [[File:mesh_tool&quot;, which has a default value of 10.png]] button Note that the maximum number of ray bounces directly affects the Simulate Toolbar or select computation time as well as the size of output simulation data files. This can become critical for indoor propagation scenes, where most of the rays undergo a large number of reflections. Two other parameters control the diffraction computations: '''Simulate &gt; Discretization &gt; Show MeshMax Wedge Angle''', or use the keyboard shortcut in degrees and '''Ctrl+MMin Edge Length'''. A triangular surface mesh of your physical structure appears in the project workspaceunits. In this case, [[EM.Cube]] enters it mesh view mode. You can perform view operations like rotate view, pan, zoom, etc. But you cannot select objects, or move The maximum wedge angle is the angle between two conjoined facets that is considered to make them almost flat or edit their propertiescoplanar with no diffraction effect. To get out The default value of the Mesh View and return to [[EMmaximum wedge angle is 170&deg;.Cube]]'s Normal View, press the '''Esc Key''' The minimum edge length is size of the keyboard, or click the Mesh button common edge between two conjoined facets that is considered as a mesh artifact and not a real diffracting edge. The default value of the Simulate Toolbar once again, or go to the Simulate Menu and deselect the '''Discretization &gt;''' '''Show Mesh''' itemminimum edge length is one project units.

You can adjust the mesh resolution and increase the geometric fidelity of discretization by creating more and finer triangular facets. On the other hand, you may want to reduce the mesh complexity and send to the SBR engine only a few coarse facets to model your buildings. To adjust the mesh resolution, open the Mesh Settings Dialog by clicking the '''Mesh Settings''' <table><tr><td> [[FileImage:mesh_settingsPROP MAN11.png]] button of the Simulate Toolbar or select '''Simulate &gt; Discretization &gt;''' '''Mesh Settings..|thumb|left|720px|EM.Terrano'''s SBR simulation engine settings dialog. This dialog provides a single [[parameters]]: '''Edge Length'''., which has a default value of 100 project units. If you are already in the Mesh View Mode and open the Mesh Settings Dialog, you can see the effect of changing the edge length using the '''Apply''' button. Click OK to close the dialog.</td></tr></table>

Note that unlike [[EMAs rays travel in the scene and bounce from surfaces, they lose their power, and their amplitudes gradually diminish.Cube]]'s other computational modules From a practical point of view, only rays that express the default mesh density based on have power levels above the wavelengthreceiver sensitivity can be effectively received. Therefore, all the resolution of the SBR mesh generator is expressed in project length unitsrays whose power levels fall below a specified power threshold are discarded. The '''Ray Power Threshold''' is specified in dBm and has a default edge length value of 100 units might be too large for non-flat objects150dBm. You may have to use a lower Keep in mind that the value to capture of this threshold directly affects the curvature accuracy of your curved structures adequatelythe simulation results as well as the size of the output data file.

[[File:prop_manualYou can also set the '''Ray Angular Resolution''' of the transmitter rays in degrees. By default, every transmitter emanates equi-29angular ray tubes at a resolution of 1 degree. Lower angular resolutions larger than 1° speed up the SBR simulation significantly, but they may compromise the accuracy. Higher angular resolutions less than 1° increase the accuracy of the simulating results, but they also increase the computation time. The SBR Engine Settings dialog also displays the '''Recommended Ray Angular Resolution''' in degrees in a grayed-out box. This number is calculated based on the overall extents of your computational domain as well as the SBR mesh resolution. To see this value, you have to generate the SBR mesh first. Keeping the angular resolution of your project above this threshold value makes sure that the small mesh facets at very large distances from the source would not miss any impinging ray tubes during the simulation.png]]

Figure 1: [[Propagation Module]]'s Mesh Settings dialogEM.Terrano gives a few more options for the ray tracing solution of your propagation problem. For instance, it allows you to exclude the direct line-of-sight (LOS) rays from the final solution. There is a check box for this purpose labeled "Exclude direct (LOS) rays from the solution", which is unchecked by default. EM.Terrano also allows you to superpose the received rays incoherently. In that case, the powers of individual ray are simply added to compute that total received power. This option in the check box labeled "Superpose rays incoherently" is disabled by default, too.

You It can use [[EM.Cube]]'s &quot;Polymesh&quot; tool to discretize solid and surface CAD objects. You can manually control be seen that if the mesh characteristics of polymesh objects including inserting new nodes on faces and edges or deleting existing nodes. In addition, [[EM.Cube]]ray's Solid Generator and Surface Generator tools create ploymesh solids and surfacesE-field is not normalized, respectively. Like tessellated object, polymesh objects are also considered as discretized objects by [[EM.Cube]] and they are not meshed again by the SBR mesh generatorcomputed ray power will correspond to that of a polarization matched isotropic receiver.

=== SBR Mesh Rules &amp; Considerations Polarimetric Channel Analysis ===

Coming SoonIn a 3D SBR simulation, a transmitter shoots a large number of rays in all directions.The electric fields of these rays are polarimetric and their strength and polarization are determined by the designated radiation pattern of the transmit antenna.The rays travel in the propagation scene and bounce from the ground and buildings or other scatterers or get diffracted at the building edges until they reach the location of the receivers. Each individual ray has its own vectorial electric field and power. The electric fields of the received rays are then superposed coherently and polarimetrically to compute the total field at the receiver locations. The designated radiation pattern of the receivers is then used to compute the total received power by each individual receiver.

In [[To perform a polarimatric channel characterization of your propagation scene, open EM.Cube]], buildings Terrano's Run Simulation dialog and all other CAD objects are initially created on select '''Channel Analyzer''' from the XY plane by defaultdrop-down list labeled '''Select Simulation or Solver Type'''. In other words, At the Z-coordinate end of the local coordinate system (LCS) of all blocks simulation, a large ray database is set to zero until you change themgenerated with two data files called "sbr_channel_matrix. As long as you use DAT" and "sbr_ray_path.DAT". The former file contains the global grounddelay, angles of arrival and departure and complex-valued elements of the channel matrix for all is fine as your buildings are seated on the ground. When your propagation scene has an irregular terrain, you want to place your buildings on the terrain individual rays that leave each transmitter and not buried under itarrive at each receiver. Buildings in [[EM.Cube]] are not adjusted to The latter file contains the terrain elevation automatically. You need to instruct [[EM.Cube]] to do sogeometric aspects of each ray such as hit point coordinates.

To update the building positions and adjust their elevation to the underlying terrain, right click on the '''Terrain''' item of the Navigation Tree and select '''Adjust Scene Elevation''' from the context menu. All the blocks in the scene are automatically elevated in the Z direction such that their bases sit on the terrain. In effect, all the blocks are translated along the global Z axis by proper amounts such that their local Z coordinate equals the Z=== The "Near Real-elevation of the underlying terrain object. This feature is particularly useful if you change the location of the terrain or import a new terrain after the blocks have been created.Time" Polarimatrix Solver ===

Note: You have to make sure After EM.Terrano's channel analyzer generates a ray database that characterizes your propagation channel polarimetrically for all the resolution combinations of your terraintransmitter and receiver locations, its fluctuation scale a ray tracing solution of the propagation problem can readily be found in almost real time by incorporating the effects of the radiation patterns of transmit and building dimensions are all comparablereceive antennas. OtherwiseThis is done using the '''Polarimatrix Solver''', on a highwhich is the third option of the drop-resolution, rapidly varying terrain, you will have buildings whose bottoms are down list labeled '''Select Simulation or Solver Type''' in contact with EM.Terrano's Run Simulation dialog. The results of the terrain only at a few points Polarimatrix and parts 3D SBR solvers must be identical from a theoretical point of them hang in view. However, there might be small discrepancies between the airtwo solutions due to roundoff errors.

[[File:prop_adjust1_tnUsing the Polarimatrix solver can lead to a significant reduction of the total simulation time in sweep simulations that involve a large number of transmitters and receivers.png|400px]] [[File:prop_adjust2_tnCertain simulation modes of EM.png|400px]]Terrano are intended for the Polarimatrix solver only as will be described in the next section.

=== Transmitters &amp; Receivers Above An Irregular Terrain EM.Terrano's Simulation Modes ===

In [[EM.Cube]], all the transmitters and receivers are tied up with point objects in the project workspace. These point objects are grouped and organized in base sets. When you move the point objects or change their coordinates, all of their associated transmitters or receivers immediately follow them to the new location. For example, you usually define Terrano provides a grid number of receivers using a base set different simulation modes that is made up of a uniformly spaced array of points and spread them in your scene. All of these receivers have the same height because their associated base points all have the same Z-coordinate. When your receivers are located above a flat terrain like the global ground, their Z-coordinates are equal to their height above the ground, as the terrain elevation is fixed and equal to zero everywhere. The same is true for transmitters, too. involve single or multiple simulation runs:

In many propagation modeling problems, your transmitters and receivers may be located above an irregular terrain with varying elevation across {| class="wikitable"|-! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Which Solver?! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[#Running a Single-Frequency SBR Analysis | Single-Frequency Analysis]]| style="width:180px;" | Simulates the propagation scene. In that case"As Is"| style="width:150px;" | SBR, you may want to place your transmitters or receivers Channel Analyzer, Polarimatrix, Radar Simulator| style="width:120px;" | Runs at a certain height above the underlying ground. The Zcenter frequency fc| style="width:300px;" | None|-coordinate of a transmitter or receiver is now | style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]| style="width:180px;" | Varies the sum operating frequency of the terrain elevation ray tracer | style="width:150px;" | SBR, Channel Analyzer, Polarimatrix, Radar Simulator| style="width:120px;" | Runs at the base point and the a specified height. set of frequency samples| style="width:300px;" | None|-| style="width:120px;" | [[EMParametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube| Parametric Sweep]] gives you | style="width:180px;" | Varies the option to adjust the transmitter and receiver sets to the terrain elevation. This is done for individual transmitter sets and individual receiver sets. At the top value(s) of the Transmitter Dialog there is a check box labeled &quotone or more project variables| style="width:150px;'''Adjust Tx Sets to Terrain Elevation'''&quot" | SBR| style="width:120px;. Similarly, " | Runs at the top center frequency fc| style="width:300px;" | Requires definition of sweep variables, works only with SBR solver as the Receiver Dialog there is a check box labeled &quotphysical scene may change during the sweep |-| style="width:120px;'''Adjust Rx Sets to Terrain Elevation'''&quot" | [[#Transmitter_Sweep | Transmitter Sweep]]| style="width:180px;. These boxes are unchecked by default. As a result, your transmitter sets " | Activates two or receiver sets coincide more transmitters sequentially with their associated base points only one transmitter broadcasting at each simulation run | style="width:150px;" | Polarimatrix| style="width:120px;" | Runs at the center frequency fc| style="width:300px;" | Requires at least two transmitters in the project workspace. If you check these boxes scene, works only with Polarimatrix solver and place a transmitter set or a receiver set above requires an irregular terrain, existing ray database|-| style="width:120px;" | [[#Rotational_Sweep | Rotational Sweep]]| style="width:180px;" | Rotates the transmitters or receivers are elevated from the location radiation pattern of their associated base points by the amount transmit antenna(s) sequentially to model beam steering | style="width:150px;" | Polarimatrix| style="width:120px;" | Runs at the center frequency fc| style="width:300px;" | Works only with Polarimatrix solver and requires an existing ray database|-| style="width:120px;" | [[#Mobile_Sweep | Mobile Sweep]]| style="width:180px;" | Considers one pair of terrain elevation as can be seen in active transmitter and receiver at each simulation run to model a mobile communication link| style="width:150px;" | Polarimatrix| style="width:120px;" | Runs at the figure below. center frequency fc| style="width:300px;" | Requires the same number of transmitters and receivers, works only with Polarimatrix solver and requires an existing ray database|}

To better understand why there are two separate sets of points Click on each item in the scene, note that a point array (CAD object) is used to create a uniformly spaced base set. The array object always preserves its grid topology as you move it around the scene. However, the transmitters or receivers associated with this point array object are elevated above the irregular terrain and no longer follow a strictly uniform grid. If you move the base set from its original position list to a new location, the base points' topology will stay intact, while the associated transmitters or receivers will be redistributed above the terrain based on their new elevationslearn more about each simulation mode.

[[File:prop_txrx1_tnYou set the simulation mode in EM.png|400px]] [[File:prop_txrx2_tnTerrano's simulation run dialog using the drop-down list labeled '''Simulation Mode'''. A single-frequency analysis is a single-run simulation. All the other simulation modes in the above list are considered multi-run simulations. In multi-run simulation modes, certain parameters are varied and a collection of simulation data files are generated. At the end of a sweep simulation, you can plot the output parameter results on 2D graphs or you can animate the 3D simulation data from the navigation tree.png|400px]]

Figure: Transmitters and receivers adjusted above an uneven terrain and their associated base sets{{Note| EM.Terrano's frequency sweep simulations are very fast because the geometrical optics (ray tracing) part of the simulation is frequency-independent.}}

== Running A SBR Simulation = Transmitter Sweep ===

[[When your propagation scene contains two or more transmitters, whether they all belong to the same transmitter set with the same radiation pattern or to different transmitter sets, EM.Cube]]'s [[Propagation Module]] offers three types Terrano assumes all to be coherent with respect to one another. In other words, synchronous transmitters are always assumed. The rays originating from all these transmitters are superposed coherently and vectorially at each receiver. In a transmitter sweep, on the other hand, EM.Terrano assumes only one transmitter broadcasting at a time. The result of ray tracing simulations:the sweep simulation is a number of received power coverage maps, each corresponding to a transmitter in the scene.

# Set You can rotate the unit 3D radiation patterns of project scene both the transmitters and receivers from the frequency property dialog of operationthe parent transmitter set or receiver set. Note that [[EM.Cube]]'s default project unit This is millimeterdone in advance before a SBR simulation starts. When working with You can define one or more of the [[Propagation Module]], pay attention to the project unit. Radio propagation problems usually require meter, mile rotation angles of a transmitter set or kilometer a receiver set as the project unitsweep variables and perform a parametric sweep simulation.# Create In that case, the blocks entire scene and draw the all of its buildings are discretized at the desired locations.# Keep the default ray domain each simulation run and accept the default global ground or change its material propertiesa complete physical SBR ray tracing simulation is carried out.# Define However, we know that the base sets (at least one for polarimetric characteristics of the transmitter and one for propagation channel are independent of the transmitter or receiver)antenna patterns or their rotation angles.# Define A rotational sweep allows you to rotate the radiation pattern of the transmitter and receiver(s) using about one of the available base setsthree principal axes sequentially.# Run This is equivalent to the SBR simulation enginesteering of the beam of the transmit antenna either mechanically or electronically.# Visualize The result of the sweep simulation is a number of received power coverage map and plot other datamaps, each corresponding to one of the angular samples. To run a rotational sweep, you must specify the rotation angle.

You can access the [[Propagation Module]]{{Note| EM.Terrano's run dialog by clicking rotational sweep works only with the '''Run''' [[File:run_icon.png]] button of the '''Simulate Toolbar''' or by selecting '''Simulate &gt; Run...''' or Polarimatrix Solver and requires an existing ray database previously generated using the keyboard shortcut '''Ctrl+R'''. When you click the '''Run''' button, a new window opens up that reports the different stages of the SBR simulation and indicates the progress of each stage. After the SBR simulation is successfully completed, a message pops up and prompts the completion of the processChannel Analyzer.}}

Figure 1: [[Propagation Module]]'s Simulation Run dialogIn a mobile sweep, each transmitter is paired with a receiver according to their indices in their parent sets. At each simulation run, only one (Tx, Rx) pair is considered to be active in the scene. As a result, the generated coverage map takes a different meaning implying the sequential movement of the transmitter and receiver pair along their corresponding paths. In other words, the set of point transmitters and the set of point receivers indeed represent the locations of a single transmitter and a single receiver at different instants of time. It is obvious that the total number of transmitters and total number of receivers in the scene must be equal. Otherwise, EM.Terrano will prompt an error message.

There are a number of SBR simulation settings that can be accessed and changed from the SBR Settings Dialog. To open this dialog, click the button labeled '''Settings''' on the right side of the '''Select Engine''' dropdown list in the Run Dialog. [[{{Note| EM.Cube]]Terrano's SBR simulation engine allows you to separate mobile sweep works only with the physical effects that are calculated during a Polarimatrix Solver and requires an existing ray tracing process. You can selectively enable or disable '''Ray Reflection''', '''Ray Transmission''' and '''Ray Diffraction'''. By default, all three effects are checked and included in the computations. Separating these effects sometimes help you better analyze your propagation scene and understand the impact of various blocks in database previously generated using the sceneChannel Analyzer.}}

[[EM.Cube]] requires === Investigating Propagation Effects Selectively One at a finite number of ray bounces for each original ray emanating from a transmitter. This is very important in situations that may involve resonance effects where rays get trapped among certain group of surfaces and may bounce back and forth indefinitely. This is set using the box labeled &quot;'''Max No. Ray Bounces'''&quot;, which has a default value of 10. Note that the maximum number of ray bounces directly affects the computation time as well as the size of output simulation data files. This can become critical for indoor propagation scenes, where most of the rays undergo a large number of reflections. Time ===

As rays travel in In a typical SBR ray tracing simulation, EM.Terrano includes all the scene propagation effects such as direct (LOS) rays, ray reflection and bounce from surfacestransmission, they lose their power and their amplitudes diminishedge diffractions. From a practical point At the end of viewa SBR simulation, only rays that have you can visualize the received power above coverage map of your propagation scene, which appears under the receiver sensitivity threshold can be effectively receivedset item in the navigation tree. Therefore, all The figure below shows the rays whose received power fall below coverage map of the random city scene with a specified power threshold are discarded. The '''Ray Power Threshold''' is specified in dBm vertically polarized half-wave dipole transmitter located 10m above the ground and has a default value large grid of vertically polarized half-100dBmwave dipole receivers placed 1. Keep in mind that 5m above the value of this threshold directly affects ground. The legend box shows the accuracy limits of the simulation results as well color map between -23dBm as the size of maximum and -150dB (the default receiver sensitivity value) as the output data fileminimum.

You can also set the '''Angular Resolution''' <table><tr><td> [[Image:UrbanCanyon10.png|thumb|left|640px|The received power coverage map of the random city scene with a dipole transmitter rays in degrees. By default, every transmitter emanates equi-angular ray tubes at a resolution of 1 degree. Lower angular resolutions larger than 1° speed up the SBR simulation significantly, but they may compromise the accuracy. Higher angular resolutions less than 1° increase the accuracy of the simulating results, but they also increase the computation time.]] </td></tr></table>

[[File:PROP13Sometime it is helpful to change the scale of the color map to better understand the dynamic range of the coverage map. If you double-click on the legend or right-click on the coverage map's name in the navigation tree and select '''Properties''', the Plot Settings dialog opens up. Select the '''User-Defined''' item and set the lower and upper bounds of color map as you wish.png]]

Figure 1: <table><tr><td> [[Propagation ModuleImage:UrbanCanyon15.png|thumb|left|480px|The plot settings dialog of the coverage map.]]'s SBR Engine Settings dialog</td></tr></table><table><tr><td> [[Image:UrbanCanyon16.png|thumb|left|640px|The received power coverage map of the random city scene with a user-defined color map scale between -80dBm and -20dBm.]] </td></tr></table>

If the associated radiator set is isotropic, so will be the transmitter set<table><tr><td> [[Image:UrbanCanyon14. By default, an isotropic transmitter has vertical polarizationpng|thumb|left|640px|EM. You can use the Terrano'''Polarization''' radio button to select one of the two options: '''Vertical''' or '''Horizontal'''. If the associated radiator set consists of '''Short Dipole''' or '''User Defined''' radiators, it is indicated in the transmitter property s simulation run dialog. In showing the case of a short dipole radiator, you can set a value check boxes for the dipole current in Amperescontrolling various propagation effects. The radiation resistance of a short dipole of length ''dl'' is given by:]] </td></tr></table>

<table><tr><td> [[Image:UrbanCanyon11.png|thumb|left|640px|The received power coverage map of the random city scene with direct LOS rays only.]] <math/td> R_r = 80\pi^2 \</tr><tr><td> [[Image:UrbanCanyon12.png|thumb|left( \frac{dl}{\lambda_0} \right)^2 |640px|The received power coverage map of the random city scene with reflected rays only.]] </mathtd><!--/tr><tr><td> [[FileImage:eqngr6UrbanCanyon13.png|thumb|left|640px|The received power coverage map of the random city scene with diffracted rays only.]]--</td></tr></table>

:<math> P_{rad} = \frac{1}{2} R_r |I_0|^2 = 40\pi^2 |I_0|^2 \left( \frac{dl}{\lambda_0} \right)^2 </math><!--[[File:shortdipole.png]]-->= The Ray Tracing Solvers' Output Simulation Data ===

For isotropic Both the SBR solver and user defined radiators you can set the '''Input Power''' and '''Phase''' Polarimatrix solver perform the same type of a transmitter set simulation but in Watts two different ways. The SBR solver discretizes the scene including all the buildings and degreesterrain, respectively. This can be accessed shoots a large number of rays from the '''Transmitter Chain''' dialog, which will be described in detail in transmitters and collects the next sectionrays at the receivers. The Polarimatrix solver does the same thing using an existing polarimetric ray database that has been previously generated using EM.Terrano's Channel Analyzer. It incorporates the effects of the radiation pattern patterns of the associated radiator set is normalized transmit and used receive antennas in conjunction with the input power value to create a weighted distribution of transmitted rayspolarimetric channel characteristics. In certain cases like hybrid simulations, you may want to use At the actual values end of a ray tracing simulation, all the far field to define polarimetric rays emanating from the transmitter power rather than a normalized radiation pattern. Note that the pattern (.RADs) file contains or other sources that are received by the value of total radiated power in its header. In this caseindividual receivers are computed, collected, check the box labeled '''&quot;Calculate Power From Radiation Pattern&quot;'''. This is calculated directly from the complex &theta; sorted and &phi; components of the far field saved into ASCII data by integrating them over the entire space (4&pi; solid angle)files. Note that this option is available only when From the radiator is of the User Defined type. When this box is checkedray data, the transmitter chain button is grayed out. By default, an isotropic transmitter emanates rays uniformly in all directions total electric field at the angular resolution specified by location of receivers as well as the usertotal received power are computed. A transmitter with a user defined associated radiator may represent a highly directional radiation pattern with The individual ray data include the main beam pointing in a certain direction. You can additionally force and limit field components of each ray, the ray'''Angular Extents''' s elevation and azimuth angles of rays to a certain solid angle around departure and arrival (departure from the transmitter. This is especially useful location and computationally efficient when arrival at the transmitter is on one side of the scenereceiver location), and all time delay of the scatterers and receivers are on received ray with respect to the other sidetransmitter. In this caseIf you specify the temperatures, there is no need to generate rays noise figure and transmission line losses in all directions. To limit the angular extents definition of raysthe receiver sets, define the Start noise power level and End values for both Theta signal-to-noise ratio (&theta;SNR) at each receiver are also calculated, and Phi so are the E_b/N₀ and bit error rate (&phi;BER) angles. The value of for the angular resolution of the rays can be changed from the Run Dialog as will be discussed laterselected digital modulation scheme.

In a regular SBR simulation, you have a transmitter and one or more arrays of receivers in your scene. At the end of the simulation, you can visualize the coverage map of the transmitter over the receiver sets. A coverage map shows the total '''Received Power''' by each of the receivers and is visualized as a color-coded intensity plot. You can visualize the coverage maps of individual receiver sets. At the end of a SBR simulation, each === Visualizing Field & Received Power Coverage Map is listed under the receiver set's name in the Navigation Tree. To display a coverage map, simply click on its entry in the Navigation Tree. The coverage map plot appears in the Main Window overlaid on the scene. A legend box on the right shows the color scale and units (dB). The 3-D coverage maps are displayed as horizontal confetti above the receivers. If the receivers are packed close to each other, you will see a continuous confetti map. If the receivers are far apart, you will see individual colored squares. You can also visualize coverage maps as colored 3-D cubes. This may be useful when you set up your receivers in a vertical arrangement or the scene has a highly uneven terrain. To change the type of coverage map visualization, open the receiver set's property dialog and select the desired option for '''Coverage Map: Confetti''' or '''Cube''' in the '''&quot;Visualization Options&quot;''' section of the dialog.Maps ===

[[File:prop_run11_tnIn wireless propagation modeling for communication system applications, the received power at the receiver location is more important than the field distributions.png|400px]] [[FileIn order to compute the received power, you need three pieces of information:prop_run12_tn.png|400px]]

Figure* '''Total Transmitted Power (EIRP)''': Received This requires knowledge of the baseband signal power coverage map, the transmitter chain parameters, the transmission characteristics of the transmission line connecting the transmitter circuit to the transmitting antenna and the radiation characteristics of the transmitting antenna.* '''Channel Path Loss''': (Left) confetti styleThis is computed through SBR simulation. * '''Receiver Properties''': This includes the radiation characteristics of the receiving antenna, the transmission characteristics of the transmission line connecting the receiving antenna to the receiver circuit and (Right) cube stylethe receiver chain parameters.

You can change In a simple link scenario, the settings of the coverage map by right clicking on its entry received power P_r in dBm is found from the Navigation Tree and selecting '''Properties...''' or by double-clicking on the legend box. In the Output Plot Settings dialog, you can choose from one of three Color Map optionsfollowing equation: '''Default''', '''Rainbow''' and '''Grayscale'''. The visualization plot uses default values for the color scale. In the section titled &quot;Limits&quot;, you can choose the radio button labeled '''User Defined'''. Then, you have to enter new values for the '''Lower''' and '''Upper''' Limits of the plot. You can also show or hide the Legend Box or change its '''Background''' and '''Foreground''' colors by clicking the buttons provided for this purpose.

<math> P_r [[File:prop_run4.pngdBm]= P_t [dBm]+ G_{TC} + G_{TA} - PL + G_{RA} + G_{RC} </math>

If you specify the noise-related parameters of your receiver set, the signal-to-noise ratios (SNR) is calculated at each receiver location: SNR === P_r - P_n, where P_n is the noise power level in dB. When planning, designing and deploying a communication system between points A and B, the link is considered to be closes and a connection established if the received signal power at the location of the receiver is above the noise power level by a certain threshold. In other words, the SNR at the receiver must be greater than a certain specified minimum SNR level. You specify (SNR)_min ss part of the definition of receiver chain in the Receiver Set dialog. In the "Visualization Options" section of this dialog, you can also check the check box labeled '''Generate Connectivity Map'''. This is a binary-level black-and-white map that displays connected receivers in white and disconnected receivers in black. At the end of an SBR simulation, the computed SNR is displayed in the Receiver Set dialog for the selected receiver. The Ray Data ===connectivity map is generated and added to the navigation tree underneath the received power coverage map node.

At the end of a an SBR simulation, each receiver receives a number of rays. Some receivers may not receive any rays at all. You you can visualize all the rays received by a certain field maps and receiver from the active transmitter power coverage map of the sceneyour receiver sets. To do this, right click A coverage map shows the total '''ReceiversReceived Power''' item by each of the Navigation Treereceivers and is visualized as a color-coded intensity plot. From Under each receiver set node in the context menu select '''Show Received Rays'''. All the rays navigation tree, a total of seven field maps together with a received by the currently selected receiver of the scene power coverage map are displayed in the sceneadded. The rays are identified by labels, are ordered by their power field maps include amplitude and have different colors phase plots for better visualization. You can display the rays for only one receiver at three X, Y, Z field components plus a time. The receiver set property dialog has a list of all the individual receivers belonging to that settotal electric field plot. To display the rays received by another receivera field or coverage map, you have to change simply click on its entry in the '''Selected Receiver''' navigation tree. The 3D plot appears in the receiver set's property dialogMain Window overlaid on your propagation scene. If you keep the mouse focus A legend box on this dropdown list the right shows the color scale and roll your mouse scroll wheel, you units (dB). The 3D coverage maps are displayed as horizontal confetti above the receivers. You can scan change the appearance of the selected receivers and move the rays maps from one receiver to the next in property dialog of the listreceiver set. To remove You can further customize the visualized rays from the scene, right click the Receivers item settings of the Navigation Tree again 3D field and from the context menu select '''Hide Received Rays'''coverage plots.

<table><tr><td>[[FileImage:prop_run5_tnAnnArbor Scene1.png|800pxthumb|left|640px|The downtown Ann Arbor propagation scene.]]</td></tr><tr><td>[[Image:AnnArbor Scene2.png|thumb|left|640px|The electric field distribution map of the Ann Arbor scene with vertical dipole transmitter and receivers.]]</td></tr><tr><td>[[Image:AnnArbor Scene3.png|thumb|left|640px|The received power coverage map of the Ann Arbor scene with vertical dipole transmitter and receivers.]]</td></tr><tr><td>[[Image:AnnArbor Scene4.png|thumb|left| 640px |The connectivity map of the Ann Arbor scene with SNR_min = 3dB with the basic color map option.]]</td></tr><tr><td>[[Image:AnnArbor Scene5.png|thumb|left| 640px |The connectivity map of the Ann Arbor scene with SNR_min = 20dB with the basic color map option.]]</td></tr></table>

Visualization of received rays at === Visualizing the location of Rays in the selected receiver.Scene ===

At the end of a SBR simulation, each receiver receives a number of rays. Some receivers may not receive any rays at all. You can visualize all the rays received by a certain receiver from the active transmitter of the scene. To do this, right click the '''Receivers''' item of the Navigation Tree. From the context menu select '''Show Received Rays'''. All the rays received by the currently selected receiver of the scene are displayed in the scene. The rays are identified by labels, are ordered by their power and have different colors for better visualization. You can display the rays for only one receiver at a time. The receiver set property dialog has a list of all the individual receivers belonging to that set. To display the rays received by another receiver, you have to change the '''Selected Receiver''' in the receiver set's property dialog. If you keep the mouse focus on this dropdown list and roll your mouse scroll wheel, you can scan the selected receivers and move the rays from one receiver to the next in the list. To remove the visualized rays from the scene, right click the Receivers item of the Navigation Tree again and from the context menu select '''Hide Received Rays'''. You can also view the ray [[parameters]] by opening the property dialog of a receiver set. By default, the first receiver of the set is always selected. You can select any other receiver from the drop-down list labeled '''Selected Receiver'''. If you click the button labeled '''Show Ray Data''', a new dialog opens up with a table that contains all the received rays at the selected receiver and their [[parameters]]:

{{Note: The |All the received rays are summed up coherently at the receiver. [[File:prop_run6_tn.png|800px]] Figure: Analyzing a selected ray from the ray data dialog. === Plotting Other Simulation Results === Besides visualizing the coverage map and received rays in the [[EM.Cube|EM.CUBE]]'s [[Propagation Module]], you can also plot the '''Path Loss''' of all the receivers belonging to a receiver set as well as vectorial manner at the '''Power Delay Profile''' of individual receivers. To plot these data, go the '''Observables''' section of the Navigation Tree and right click on the '''Receivers''' item. From the context menu, select '''Plot Path Loss''' or '''Plot Power Delay Profile''', respectively. The path loss data between the active transmitter and all the receivers belonging to a receiver set are plotted on a Cartesian graph. The horizontal axis of this graph represents the index of the receiver. Power Delay Profile is a bar chart that plots the power of individual rays received by the currently selected receiver versus their time delay. If there is a line of sight (LOS) between a transmitter and receiver, the LOS ray will have the smallest delay and therefore will appear first in the bar chart. Sometimes you may have several rays arriving at a receiver at the same time, i.e. all with the same delay, but with different power level. These will appear as stacked bars in the chartlocation.}}

You can also plot the path loss and power delay profile graphs and many others from <table><tr><td> [[EM.Cube|EM.CUBE]]'s data manager. You can open data manager by clicking the '''Data Manager''' [[FileImage:data_manager_iconUrbanCanyon18.png]] button |thumb|left|640px|Visualization of received rays at the '''Compute Toolbar''' or by selecting '''Compute [[File:larrow_tn.png]] Data Manager''' from the menu bar or by right clicking on the '''Data Manager''' item location of the Navigation Tree and selecting Open Data Manager... from the contextual menu or by using the keyboard shortcut '''Ctrl+D'''. In the Data manager Dialog, you will see a list of all the data files available for plotting. These include the theta and phi angles of arrival and departure of the selected receiver. You can select any data file by clicking and highlighting its '''ID''' in the random city scene.]] </td></tr></table and then clicking the '''Plot''' button.>

=== The Standard Output Data Files File ===

NEW LINEEach receiver line has the following information:

* Receiver NumberID* Receiver Base X, Y , Z Coordinatescoordinates* Receiver HeightTotal received power in dBm* Total number of received rays

NEW LINEEach rays line received by a receiver has the following information:

Number of Rays NEW LINE:* Ray Index* Ray NumberDelay in nsec

* Delay in nsec* Real(and imaginary parts of the three E<supsub>Vx</supsub>) &amp; Imag(, E^V)* Real(E^H) &amp; Imag(E^H)* Real('''E.e_Ry''') &amp; Imag(''', E.e_Rz''')components* Number of ray hit points * PowerCoordinates of individual hit points

The angles of arrival are the &theta; and &phi; angles of a received ray measured in degrees and are referenced in the local spherical coordinate systems centered at the location of the receiver. The angles of departure for a received ray are the &theta; and &phi; angles of the originating transmitter ray, measured in degrees and referenced in the local spherical coordinate systems centered at the location of the active transmitter, which eventually arrives at the receiver. The total time delay is measured in nanoseconds between t = 0 nsec at the time of launch from the transmitter location till being received at the receiver location. The last four columns show the real and imaginary parts of the received electric fields with vertical and horizontal polarizations, respectively. The complex field values are normalized in a way that when their magnitude is squared, it equals the received ray power. If the active transmitter is an isotropic radiator with either a vertical or horizontal polarization, then the field components corresponding to the other polarization will have zero entries in the output data file.

<table><tr><td> [[FileImage:prop_run8_tn.png|800pxthumb|left|720px|A typical SBR output data file.]]</td></tr></table>

By default, you run a single-frequency simulation The available data files in [[EM.Cube|EM.CUBE]]'s [[Propagation Module]]. You set the operational frequency "2D Data Files" tab of a SBR simulation in the project's '''Frequency Dialog''', which can be accessed in a number of waysData Manger include:

# By clicking the * '''FrequencyPath Loss''' [[File:freq_iconThe channel path loss is defined as PL = P_r - EIRP.png]] button The path loss data are stored in a file called "SBR_receiver_set_name_PATHLOSS.DAT" as a function of the '''Compute Toolbar'''receiver index. The path loss data make sense only if your receiver set has the default isotropic radiator.# By selecting * '''ComputePower Delay Profile''' [[File:larrow_tnThe delays of the individual rays received by the selected receiver with respect to the transmitter are expressed in ns and tabulated together with the power of each ray in the file "SBR_receiver_set_name_DELAY.png]]'''Frequency SettingsDAT"...''' You can plot these data from the Menu BarData Manager as a bar chart called the power delay profile.# Using The bars indeed correspond to the keyboard shortcut difference between the ray power in dBm and the minimum power threshold level in dBm, which makes them a positive quantity. * '''Ctrl+FAngles of Arrival'''.# By double clicking : These are the frequency section (box) Theta and Phi angles of the '''Status Bar'''individual rays received by the selected receiver and saved to the files "SBR_receiver_set_name_ThetaARRIVAL.<br /> ANG" and "SBR_receiver_set_name_PhiARRIVAL.ANG". You can plot them in the Data Manager in polar stem charts.

When you run a frequency or parametric sweep in [[File:prop_freqEM.pngTerrano]] , a tremendous amount of data may be generated. [[File:prop_run10EM.pngTerrano]]only stores the '''Received Power''', '''Path Loss''' and '''SNR''' of the selected receiverin ASCII data files called "PREC_i.DAT", "PL_i.DAT" and "SNR_i.DAT", where is the index of the receiver set in your scene. These quantities are tabulated vs. the sweep variable's samples. You can plot these files in EM.Grid.

(Left) Project[[Image:Info_icon.png|40px]] Click here to learn more about working with data filed and plotting graphs in [[EM.Cube]]'s frequency dialog and (Right) the frequency settings dialog'''[[Defining_Project_Observables_%26_Visualizing_Output_Data#The_Data_Manager | Data Manager]]'''.

You can also select the '''Frequency Sweep''' option in the '''Simulation Mode''' drop-down list of the '''Run Dialog'''<table><tr><td> [[Image:Terrano pathloss. Click the '''Settings...''' button on the right side of this dropdown list to open up the Frequency Settings Dialog. Based on the original values png|thumb|360px|Cartesian graph of the project center frequency and bandwidth, the '''Start Frequency''' and '''End Frequency''' have default valuespath loss. You can also change the '''Number of Samples'''. Once you click the '''Run''' button, ]] </td><td> [[EMImage:Terrano delay.Cubepng|EMthumb|360px|Bar graph of power delay profile.CUBE]] performs a frequency sweep by assigning each of the frequency samples as the current operational frequency and running the SBR simulation engine at that frequency</td></tr><tr><td> [[Image:Terrano ARR phi. All the simulation data at all frequency samples are saved into the output data files including &quot;SBR_results.RTOUT&quot;. After the completion png|thumb|360px|Polar stem graph of a frequency sweep simulation, as many coverage maps as the number Phi angle of frequency samples are generated and added to the Navigation Tree under the Receiver Set's entryarrival. You can click on each of the coverage maps corresponding to each of the frequency samples and visualize it in the project workspace. You can also animate the coverage maps. To do so, right click on the receiver set's name in the Navigation Tree and select ''']] </td><td> [[Animation]]''' from the contextual menuImage:Terrano ARR theta. The coverage maps start to animate by their order on the Navigation Tree. Once the entire list is displayed sequentially, it starts all over again from the beginning png|thumb|360px|Polar stem graph of the listTheta angle of arrival. During the [[animation]], the '''</td></tr><tr><td> [[Animation]] Controls''' dialog appears at the lower right corner of the screenImage:Terrano DEP phi. This dialog has a number png|thumb|360px|Polar stem graph of buttons for pause/resume, step forward/backward, and step to the end/start. The title Phi angle of each coverage map is shown in the box labeled '''Sample''' as it is displayed in the main windowdeparture. You can also change the speed of [[animation]]</td><td> [[Image:Terrano DEP theta. The default frame duration has a value png|thumb|360px|Polar stem graph of 300 (3x100) millisecondsTheta angle of departure. To stop the [[animation]], simply press the keyboard's '''Esc Key'''.</td></tr></table>

Multiple coverage maps on When you designate a "User Defined Antenna Pattern" as the Navigation Tree radiator type of a transmitter set or a receiver set, EM.Terrano copies the imported radiation pattern data file from its original folder to the current project folder. The name of the ".RAD" file is listed under the '''3D Data Files''' tab of the data manager. Sometimes it might be desired to visualize these radiation patterns in your propagation scene at the end actual location of the transmitter or receiver. To do so, you have to define a frequency sweep new '''Radiation Pattern''' observable in the navigation tree. The label of the new observable must be identical to the name of the ".RAD" data file. In addition, the Theta and starting an [[animation]] from Phi angle increments of the new radiation pattern observable (expressed in degrees) must be identical to the Theta and Phi angular resolutions of the imported pattern file. If all these conditions are met, then go to the '''Simulate Menu''' and select the item '''Update All 3D Visualization'''. The contents of the 3D radiation patterns are added to the navigation tree. Click on one of the radiation pattern items in the navigation tree and it will be displayed in the contextual menuscene.

<table><tr><td>[[FileImage:prop_run15_tnUrbanCanyon6.png|thumb|left|640px|The received power coverage map of the random city scene with a highly directional dipole array transmitter.]]</td></tr></table>

By Default, [[AnimationEM.Cube]] controls always visualizes the 3D radiation patterns at the origin of coordinates, i.e. at (0, 0, 0). This is because that radiation pattern data are computed in the standard spherical coordinate system centered at (0, 0, 0). The theta and phi components of the far-zone electric fields are defined with respect to the X, Y and Z axes of this system. When visualizing the 3D radiation pattern data in a propagation scene, it is more intuitive to display the pattern at the location of the transmitter or receiver. The Radiation Pattern dialog allows you to translate the pattern visualization to any arbitrary point in the project workspace. It also allows you to scale up or scale down the pattern visualization with respect to the background scene.

=== Running In the example shown above, the imported pattern data file is called "Dipole_Array1.RAD". Therefore, the label of the radiation pattern observable is chosen to be "Dipole_Array1". The theta and phi angle increments are both 1&deg; in this case. The radiation pattern has been elevated by 10m to be positioned at the location of the transmitter and a Parametric Sweep with SBR ===scaling factor of 0.3 has been used.

<table><tr><td>[[FileImage:prop_run24UrbanCanyon8.png|thumb|300pxleft|EM.CUBE's variable 640px|Setting the pattern parameters in the radiation pattern dialog.]]</td></tr></table><table><tr><td>[[Image:UrbanCanyon7.png|thumb|left|720px|Visualization of the 3D radiation pattern of the directional transmitter in the random city scene.]]</td></tr></table>

[[File:prop_run23There is an important catch to remember here.png|thumb|250px|Dialog When you define a radiation pattern observable for defining your project, EM.Terrano will attempt to compute the overall effective radiation pattern of the entire physical structure. However, in this case, you defined the radiation pattern observable merely for visualization purposes. To stop EM.Terrano from computing the actual radiation pattern of your entire scene, there is a check box in EM.Terrano's Ray Tracer Simulation Engine Settings dialog that is labeled '''Do not compute new variables]]radiation patterns'''. This box is checked by default, which means the actual radiation pattern of your entire scene will not be computed automatically. But you need to remember to uncheck this box if you ever need to compute a new radiation pattern using EM.Terrano's SBR solver as an asymptotic EM solver (see next section).

In <table><tr><td>[[EMImage:UrbanCanyon9.Cubepng|thumb|left|640px|EM.CUBE]], all the CAD object properties as well as certain source, material and mesh [[parameters]] can be assigned as [[variables]]Terrano's Run Simulation dialog. [[Variables]] are defined to control and vary the values of such [[parameters]] either for editing purposes or to run parametric sweep or [[optimization]]. Variable are defined using the '''[[Variables]] Dialog''', which can be accessed in the three ways:</td></tr></table>

# By clicking the '''[[Variables]]''' [[File:variable_icon.png]] button of the '''Compute Toolbar'''.# By selecting '''Compute''' [[File:larrow_tn.png]] '''[[Variables]]...''' from the Menu Bar.# == Using the keyboard shortcut '''Ctrl+B'''EM.Terrano as an Asymptotic Field Solver ==

The [[variables]] dialog is initially emptyLike every other electromagnetic solver, EM. To add a new variable, click the Terrano'''Add''' button to open up the '''Add Variable/Syntax Dialog'''. In this dialog you have to type in a name s SBR ray tracer requires an excitation source and one or more observables for the new variable and choose a typegeneration of simulation data. The default type is '''Uniformly Spaced Samples'''EM. You also need to specify the '''Start''', '''Stop''' Terrano offers several types of sources and '''Step''' values observables for the variablea SBR simulation. In You already learned about the figure below, transmitter set as a variable called &quot;Tx_Height&quot; is defined that varies between 2 source and 10 with equal steps of 2. This means the sample receiver set {2,4,6,8,10}. When you return to the [[variables]] dialog, the syntax of the new variable is shown as 2:10:2an observable. The last number in this syntax is always You can mix and match different source types and observable types depending on the variable step. In this example, this variable is going to be used to control the height requirements of the transmitter in a propagation sceneyour modeling problem.

Next, you have to attach the variable to the CAD object. In this case, the CAD object is the point object that represents the transmitter's radiator. To attach a variable to a CAD object, open the object's property dialog and type The available source types in the name of the variable as the value of a property or parameterEM. In this case, the variable Tx_Height is going to control the Z-Coordinate of the point object. Once the value of the object parameter is replaced by the name of an already defined variable, it is updated with the current value of that variable. In the case of a variable of &quot;Uniformly Spaced Samples&quot; type, the current value is the start value. This value will be incrementally varied during a parametric sweep simulation process. Note that a variable can take a fixed value or a discrete set of values, too. You can always open the [[variables]] dialog and change the value or syntax of any variable. To make a new or modified value effective, click the '''Apply''' button of the [[variables]] dialog. You can test the values by performing a '''Dry Run''' of the selected variable. This runs an [[animation]] of the project workspace as the value of the variable changes and all the related CAD objects Terrano are updated accordingly. Note that you can attach the same variable to more than one CAD object property or to the properties of different objects. You can also define multiple values or syntaxes to the same variable. To do so, open the '''Add Variable/Syntax Dialog''', and instead of typing in a new variable name, choose an existing variable name from the '''Name''' dropdown list. This will add a new value or syntax to the existing syntax(es) of the selected variable. When you return to the [[variables]] dialog, [[variables]] with more than one value or syntax will have a dropdown list in the '''Syntax''' column. You can choose any of these values or syntaxed at any time and make the change effective by clicking the '''Apply''' button.:

{| class="wikitable"|-! scope="col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:prop_run25transmitter_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Point Transmitter Set | Point Transmitter Set]]| style="width:250px;" | Modeling realsitic antennas & link budget calculations| style="width:250px;" | Requires to be associated with a base location point set|-| style="width:30px;" | [[File:hertz_src_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source | Hertzian Short Dipole]]| style="width:250px;" | Almost omni-directional physical radiator| style="width:250px;" | None, stand-alone source|-| style="width:30px;" | [[File:huyg_src_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source | Huygens Source]]| style="width:250px;" | Used for modeling equivalent sources imported from other [[EM.Cube]] modules | style="width:250px;" | None, stand-alone source imported from a Huygens surface data file|}

Replacing Click on each type to learn more about it in the value [[Glossary of a CAD object parameter with a variable nameEM.Cube's Materials, Sources, Devices & Other Physical Object Types]].

To run a parametric sweep, open the '''Run Dialog''' and select the '''Parametric Sweep''' option The available observables types in the '''Simulation Mode''' drop-down list. If you have not defined any [[variablesEM.Terrano]] in the project, the box in the '''are: {| class="wikitable"|-! scope="col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[VariablesFile:receiver_icon.png]]''' row before the '''View''' will be red| style="width:150px;" | [[Glossary of EM. You have Cube's Simulation Observables & Graph Types#Point Receiver Set | Point Receiver Set]]| style="width:250px;" | Generating received power coverage maps & link budget calculations| style="width:250px;" | Requires to turn it into green before you can run be associated with a simulation. By clicking the '''View''' button, you can open up the base location point set|-| style="width:30px;" | [[variablesFile:Distr Rx icon.png]] dialog from here. Once you click the '''Run''' button, | style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Distributed Receiver Set |EM.CUBEDistributed Receiver Set]] performs | style="width:250px;" | Computing received power at a parametric sweep receiver characterized by incrementally varying the values of all the defined Huygens surface data| style="width:250px;" | None, stand-alone source imported from a Huygens surface data file|-| style="width:30px;" | [[variablesFile:fieldsensor_icon.png]] from their start to stop values at the specified steps and updating all the related CAD objects. After the completion | style="width:150px;" | [[Glossary of a parametric sweep simulation, as many coverage maps as the total number of variable samples are generated and added to the Navigation Tree under the receiver setEM.Cube's entry. You can click on each of the coverage maps Simulation Observables & Graph Types#Near-Field Sensor Observable | Near-Field Sensor]]| style="width:250px;" | Generating electric and visualize it in the project workspace. You can also animate the coverage magnetic field distribution maps sequentially. To do so| style="width:250px;" | None, right click on the receiver set's name in the Navigation Tree and select '''stand-alone observable|-| style="width:30px;" | [[AnimationFile:farfield_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube''' from s Simulation Observables & Graph Types#Far-Field Radiation Pattern Observable | Far-Field Radiation Pattern]]| style="width:250px;" | Computing the contextual menu. To stop effective radiation pattern of a radiator in the presence of a large scattering scene | style="width:250px;" | None, stand-alone observable|-| style="width:30px;" | [[animationFile:huyg_surf_icon.png]], simply press the keyboard| style="width:150px;" | [[Glossary of EM.Cube's '''Esc Key'''Simulation Observables & Graph Types#Huygens Surface Observable | Huygens Surface]]| style="width:250px;" | Collecting tangential field data on a box to be used later as a Huygens source in other [[EM.Cube]] modules| style="width:250px;" | None, stand-alone observable|}

Click on each type to learn more about it in the [[File:prop_run26Glossary of EM.pngCube's Simulation Observables & Graph Types]]. When you define a far-field observable in EM.Terrano, a collection of invisible, isotropic receivers are placed on the surface of a large sphere that encircles your propagation scene and all of its geometric objects. These receivers are placed uniformly on the spherical surface at a spacing that is determined by your specified angular resolutions. In most cases, you need to define angular resolutions of at least 1&deg; or smaller. Note that this is different than the transmitter rays' angular resolution. You may have a large number of transmitted rays but not enough receivers to compute the effective radiation pattern at all azimuth and elevation angles. Also keep in mind that with 1&deg; Theta and Phi angle increments, you will have a total of 181 &times; 361 = 65,341 spherically placed receivers in your scene.

Choosing parametric sweep as the simulation mode in the run dialog. {{Note that one variable has been defined and | Computing radiation patterns using EM.Terrano's SBR solver typically takes much longer computation times than using [[EM.Cube|EM.CUBE]] is ready to run 's other computational modules.}} <table><tr><td> [[Image:SBR pattern.png|thumb|540px|Computed 3D radiation pattern of two vertical short dipole radiators placed 1m apart in the simulationfree space at 1GHz.]] </td></tr></table>

EM.Terrano's coverage maps display the received power at the location of all the receivers. The receivers together from a set/ensemble, which might be uniformly spaced or distributed across the propagation scene or may consist of randomly scattered radiators. Every coverage map shows the '''Mean''' and '''Standard Deviation''' of the scene received power for all the receivers involved. These information are displayed at the end bottom of a parametric sweep where the sweep variable is the transmitter heightcoverage map's legend box and are expressed in dB.

=== Statistical Analysis When you run either a frequency sweep or a parametric sweep simulation in EM.Terrano, you have the option to generate two additional coverage maps: one for the mean of Propagation Scene ===all the individual sample coverage maps and another for their standard deviation. To do so, in the '''Run Dialog''', check the box labeled '''&quot;Create Mean and Standard Deviation received power coverage maps&quot;'''. Note that the mean and standard deviation values displayed on the individual coverage maps correspond to the spatial statistics of the receivers in the scene, while the mean and standard deviation coverage maps show the statistics with respect to the frequency or other sweep variable sets at each point in the site. Also, note that both of the mean and standard deviation coverage maps have their own spatial mean and standard deviation values expressed in dB at the bottom of their legend box.

<table><tr><td> [[EMImage:PROP MAN12.Cubepng|thumb|left|480px|EM.CUBE]]Terrano's coverage maps display simulation run dialog showing frequency sweep as the received power at the location of all the receiverssimulation mode along with statistical analysis. The receivers together from a set]] </ensemble, which might be uniformly spaced or distributed across the propagation scene or may consist of randomly scattered radiators. Every coverage map shows the '''Mean''' and '''Standard Deviation''' of the received power for all the receivers involved. These information are displayed at the bottom of the coverage map's legend box and are expressed in dB.td></tr></table>

In the <table><tr><td> [[Propagation Module]], when you ran a sweep simulation (frequency, transmitter or parametric), you also have the option to generate two additional coverage mapsImage: one for the mean of all the individual sample coverage maps and another for their standard deviationUrbanCanyon4. To do so, in the '''Run Dialog''', check the box labeled '''&quot;Create Mean and Standard Deviation Coverage Maps&quot;'''. Note that the png|thumb|left|640px|The mean and standard deviation values displayed on the individual coverage maps correspond to map at the spatial statistics end of the receivers in the scene, while the mean and standard deviation coverage maps correspond to a frequency, transmitter or variable sets defined for the sweep simulation. Also, note that both of the mean and ]] </td></tr><tr><td> [[Image:UrbanCanyon5.png|thumb|left|640px|The standard deviation coverage maps have their own spatial mean and standard deviation values expressed in dB map at the bottom end of their legend boxa frequency sweep.]] </td></tr></table>

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