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[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Terrano_Tutorial_Lessons Terrano_Documentation | EM.Terrano Tutorial Gateway]]'''

[[EM.Terrano]] 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.

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 in various environments. [[EM.Terrano]]’s 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 multi-core 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.

[[EM.Terrano]] is the ray tracing '''Propagation Module''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. EM.Teranno Terrano shares the 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.

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 model directional transmitters and receivers at the 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 [[EM.Illumina]].

[[EM.Terrano]]'s SBR simulation engine utilizes an intelligent ray tracing algorithm that is based on the concept of k-dimensional trees. A k-d tree is a space-partitioning data structure for organizing points in a k-dimensional space. k-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 might be a large number of rays emanating from the transmitter that may never hit any obstacles. For example, upward-looking rays in an urban propagation scene quickly exit the computational domain. Rays that hit obstacles on their path, on the 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 "field" 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 ε_r and electric conductivity σ. 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.

It is very important to keep in mind that SBR is an asymptotic electromagnetic analysis technique that is based on Geometrical Optics (GO) and the Uniform Theory of Diffraction (UTD). It is not a "full-wave" technique, and 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 much larger than the operating wavelength. Under this assumed regime, electromagnetic 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.

Import of shapefiles and STEP, IGES abnd and STL CAD model files for scene construction</li>

Python-based wizards for generation of parameterized multi-story office bulidings buildings and several terrain scene types</li>

Standard half-wave dipole transmitters and receivers orinted oriented along the principal axes</li>

Statistical analsyis analysis of the propagation scene</li> <li> Polarimetric channel characterization for MIMO analysis</li> <li> "Almost real-time" Polarimatrix solver using an existing ray database</li> <li> "Almost real-time" transmitter sweep using the Polarimatrix solver</li> <li> "Almost real-time" rotational sweep for modeling beam steering using the Polarimatrix solver</li>

Polarimetric channel characterization "Almost real-time" mobile sweep for MIMO analysis modeling mobile communications between Tx-Rx pairs along a mobile path using orthogonally polarized isotropic radiatorsthe Polarimatrix solver</li>

Color-coded intensity plots of polarimetric electric field distributionsLink connectivity maps (based on minimum required SNR and BER)</li>

Link connectivity maps (based on minimum required SNR)Color-coded intensity plots of polarimetric electric field distributions</li>

Incoming ray data analysis at each receiverincluding delay, angles of arrival and departure</li>

Power delay profileof the selected receiver</li> <li> Polar stem charts of angles of arrival and departure of the selected receiver</li>

A typical propagation scene in [[EM.Terrano]] consists of several elements. At a minimum, 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|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 of the 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.

A more complicated propagation scene usually contains several buildings, walls, or other kinds of scatterers and wave obstructing objects. You models model all of these elements by drawing geometric objects in the project workspace or by importing external CAD models. [[EM.Terrano]] does not organize the geometric 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:

! scope="col"| Block /Group Type

| style="width:250px200px;" | Ray reflection, ray diffraction

| style="width:250px200px;" | Ray reflection, ray diffraction, ray transmission through thin wallsin free space

| style="width:250px200px;" | Ray reflection, ray diffraction

| style="width:250px200px;" | Ray reflection, ray diffraction, ray transmission in and ray attenuation inside homogeneous material media

| style="width:250px200px;" | Either ray generation or ray reception

Impenetrable surfaces, penetrable surfaces, terrain surfaces and penetrable volumes represent all the objects that obstruct the propagation of electromagnetic waves (rays) in the free space. What differentiates them is the types of physical phenomena that are used to model their interaction with the impinging rays. [[EM.Terrano]] discretizes geometric objects into a number of flat facets. The field intensity, phase and power of the reflected and transmitted rays depend on the material properties of the obstructing facet. The 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 the obstructing objects such as buildings, walls, terrain, etc. behave in a similar way:

[[Image:PROP MAN2.png|thumb|left|720px|An urban propagation scene generated by EM.Terrano's "Random City" wizardand "Basic Link" wizards. It consists of 25 cubic brick buildings, one transmitter and a large two-dimensional array of receivers. ]]

In [[EM.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 objects listed under a particular group in the navigation tree share the same color, texture and material properties. Once a new block group has been created in the navigation tree, it becomes the "Active" group of the project workspace, which is always displayed in bold letters. You can draw new objects under the active node. Any block group can be made active by right-clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu.

It is recommended that you first create block groups, and then draw new objects under the active block group. However, if you start a new [[EM.Terrano]] project from scratch, 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 navigation tree to hold your new CAD object. You can always change the properties of a block group later by accessing its property dialog from the contextual menu. You can also delete a block group with all of its objects at any time.

{{Note|You can only import external CAD models (STEP, IGES, STL, DEM, etc.) only to the CubeCAD module. You can then transfer the imported objects from CubeCAD to [[EM.Terrano]].}}

You can move any geometric object or a selection of objects from one block group to another. You can also transfer objects among [[EM.Cube]]'s different modules. For example, you often need to move imported CAD models of terrain or buildings from CubeCAD to [[EM.Terrano]]. To transfer objects, first select them in the project workspace or select their names in the navigation tree. Then right-click on them and select <b>Move To &rarr; Module Name &rarr; Object Group</b> from the contextual menu. For example, if you want to move a selected object to a block group called "Terrain_1" in [[EM.Terrano]], then you have to select the menu item '''Move To &rarr; [[EM.Terrano]] &rarr; Terrain_1''' as shown in the figure below. Note that you can transfer several objects altogether using the keyboards's {{key|Ctrl}} or {{key|Shift}} keys to make multiple selections.

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 Elevation'''. 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.

== EM.Terrano's Ray Domain & Global Ground Environment ==

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 = 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.

Alternatively, you can use [[EM.Terrano]]'s '''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.

{{Note|To model a free-space propagation scene, you have to disable [[EM.Terrano]]'s default global ground.}}

[[Image:PROP4Global environ.png|thumb|left|480px720px|EM.Terrano's global ground settings Global Environment Settings dialog.]]

== Defining Point Transmitters &amp; Point Receivers for Your Propagation Scene ==

=== Defining a Transmitter Set The Nature of Transmitters & Receivers ===

Transmitters act as sources in a In EM.Terrano, transmitters and receivers are indeed point radiators used for transmitting and receiving signals at different locations of the propagation scene. A transmitter is From a geometric point radiator with a fully polarimetric radiation pattern defined over the entire 3D space in the standard spherical coordinate system. By defaultof view, [[EMboth transmitters and receivers are represented by point objects or point arrays.Terrano]] assumes that your transmitter is a vertically polarized half-wave resonant dipole antenna. This antenna has an almost omni-directional radiation pattern These are grouped as base locations in all azimuth directions. It also has radiation nulls along the axis "Physical Structure" section of the dipolenavigation tree. You can override the default As radiators, transmitters and receivers are defined by a radiator option and select any other kind of antenna type with a more complicated certain far-field radiation pattern. For this purpose, you have to import a radiation pattern data file to [[EM.Terrano]]. You can model any radiating structure using Consistent with [[EM.Cube]]'s other computational modules, [[EM.Tempo]]transmitters are categorizes as an excitation source, [[EMwhile receivers are categorized as a project observable.Picasso]]In other words, [[EM.Libera]] or [[EM.Illumina]], and a transmitter is used to generate a 3D radiation pattern data file for it. The far-field radiation patter data are stored electromagnetic waves that propagate in a specially formatted file with a &quot;'''the physical scene.RAD'''&quot; file extension. This file contains columns of spherical &phi; and &theta; angles as well as A receiver, on the real other hand, is used to compute the received fields and imaginary parts of the complexreceived signal power or signal-valued farto-zoned electric field components '''E_&theta;''' and '''E_&phi;'''noise ratio (SNR). The &theta;- For this reason, transmitters are defined and &phi;-components of listed under the far-zone electric field determine the polarization "Sources" sections of the transmitting radiatornavigation tree, while receivers are defined and listed under the "Observables" section.

{{Note|By default, [[EM.Terrano]] assume a vertical half-wave dipole provides three radiator types for your point transmitter set. The radiation pattern data file of this radiator is called "DPL_STD.RAD" and it is located in inside the "EMAG &rarr; Models" sub-folder under the Documents folder.}}sets:

A transmitter set always needs to be associated with an existing base location set in #Half-wave dipole oriented along one of the project workspace. Thereforethree principal axes#Two collocated, you cannot define a transmitter for your scene before drawing a point object under a base location set. orthogonally polarized, isotropic radiators #User defined (arbitrary) antenna with imported far-field radiation pattern

EM.Terrano also provides three radiator types for point receiver sets: #Half-wave dipole oriented along one of the three principal axes#Polarization-matched isotropic radiator#User defined (arbitrary) antenna with imported far-field radiation pattern The default transmitter and receiver radiator types are both vertical (Z-directed) half-wave dipoles.  There are three different ways to define a transmitter set or a receiver set: *By defining point objects or point arrays under physical base location sets in the navigation tree and then associating them with a transmitter or receiver set*Using Python commands emag_tx, emag_rx, emag_tx_array, emag_rx_array, emag_tx_line and emag_rx_line*Using the "Basic Link" wizard === Defining a Point Transmitter Set in the Formal Way === Transmitters 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: * Half-wave dipole* Orthogonally polarized isotropic radiators* User defined antenna pattern  By default, EM.Terrano assumes that your transmitter is a vertically polarized (Z-directed) resonant half-wave dipole antenna. This antenna has an almost omni-directional radiation pattern in all azimuth directions. It also has radiation nulls along the axis of the dipole. You can change the direction of the dipole and orient it along the X or Y axes using the provided drop-down list. The second choice of two orthogonally polarized isotropic radiators is an abstract source that is used for polarimetric channel characterization as will be discussed later.  You can override the default radiator option and select any other kind of antenna with a more complicated radiation pattern. For this purpose, you have to import a radiation pattern data file to EM.Terrano. You can model any radiating structure using [[EM.Cube]]'s other computational modules, [[EM.Tempo]], [[EM.Picasso]], [[EM.Libera]] or [[EM.Illumina]], and generate a 3D radiation pattern data file for it. The far-field radiation patter data are stored in a specially formatted file with a &quot;'''.RAD'''&quot; file extension. This file contains columns of spherical &phi; and &theta; angles as well as the real and imaginary parts of the complex-valued far-zone electric field components '''E_&theta;''' and '''E_&phi;'''. The &theta;- and &phi;-components of the far-zone electric field determine the polarization of the transmitting radiator.  {{Note|By default, EM.Terrano assumes a vertical half-wave dipole radiator for your point transmitter set.}} A transmitter set always needs to be associated with an existing base location set with one or more point objects in the project workspace. Therefore, you cannot define a transmitter for your scene before drawing a point object under a base location set.  [[Image:Info_icon.png|40px]] Click here to learn how to define a '''[[Glossary of EMGlossary_of_EM.Cube's Excitation Sources%27s_Materials,_Sources,_Devices_%26_Other_Physical_Object_Types#Transmitter Set Point_Transmitter_Set | Point Transmitter Set]]'''.

<td> [[Image:Terrano L1 Fig11.png|thumb|left|480px|The point transmitter set definition dialog.]] </td>

Once you define a new transmitter set, its name is added in the '''Transmitters''' section of the navigation tree. The color of all the base points associated with the newly defined transmitter set changes, and an additional little ball with the transmitter color (red by default) appears at the location of each associated base point. You can open the property dialog of the transmitter set and modify a number of parameters including the '''Baseband Source Power''' in Watts and the broadcast signal '''Phase''' in degrees. The default transmitter power level is 1W or 30dBm. There is also a check 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&deg; phase values as you wish. [[EM.Cube]]'s ".RAD" radiation pattern files usually contain the value of &quot;Total Radiated Power&quot; in their file header. This quantity is calculated based on the particular excitation mechanism that was used to generate the pattern file in the original [[EM.Cube]] module. When the "Use Custom Input Power" check box is unchecked, [[EM.Terrano]] will use the total radiated power value of the radiation file for the SBR simulation.

[[File:Terrano L1 Fig13NewTxProp.png|thumb|left|480px720px|The property dialog of a point transmitter set.]]

Your transmitter in EM.Teranno is indeed more sophisticated than a simple radiator. It consists of a basic "Super-Heterodyne Transmitter Chain" that starts contains a voltage source with a baseband/IF signal series source resistance, and ultimately ends in 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 a the basic super-heterodyne 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.

<td> [[File:Terrano L6 Fig13NewTxChain.png|thumb|left|720px|EM.Terrano's point transmitter chain dialog.]] </td>

=== Defining a Point Receiver Set in the Formal Way ===

Receivers act as observables in a propagation scene. The objective of a SBR simulation is to calculate the far-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. However, unlike the transmitter case, [[EM.Terrano]] assumes that your receiver, by default, is an isotropic gives you three options for the radiator. An isotropic radiator has associated with a perfect omni-directional radiation pattern in all azimuth and elevation directions. An isotropic radiator doesn't physically exist in the real world. But the assumption of a default, polarization-matched, isotropic receiver is a convenient choice to generate received power coverage maps of a propagation scene. You might also define a complicated radiation pattern for your point receiver set. In that case, you need to import a radiation pattern data file to [[EM.Terrano]]. Note that you can simply use the data file "DPL_STD.RAD" for that purpose, which is also used by [[EM.Terrano]] for the definition of the default vertical half-wave dipole transmitter. :

{{Note| [[EM.Terrano]] receivers, by default, are defined as polarization* Half-wave dipole* Polarization matched isotropic radiators.}}radiator* User defined antenna pattern

Similar to transmitter setsBy default, you define a EM.Terrano assumes that your receiver set by associating is a vertically polarized (Z-directed) resonant half-wave dipole antenna. You can change the direction of the dipole and orient it with an existing base location set in along the project workspace. A typical propagation scene contains one X or few transmitters but usually a large number of receiversY axes using the provided drop-down list. To generate An isotropic radiator has a wireless coverage mapperfect omni-directional radiation pattern in all azimuth and elevation directions. An isotropic radiator doesn't exist physically in the real world, you need to define an array of points but it can be used simply as your base location seta point in space to compute the electric field.

You may also define a complicated radiation pattern for your receiver set. In that case, you need to import a radiation pattern data file to EM.Terrano similar to the case of a transmitter set.  {{Note|By default, EM.Terrano assumes a vertical half-wave dipole radiator for your point receiver set.}} Similar 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. All the receivers belonging to the same receiver set have the same radiator type. A typical propagation scene contains one or few transmitters but usually a large number of receivers. To generate a wireless coverage map, you need to define an array of points as your base location set.  [[Image:Info_icon.png|40px]] Click here to learn how to define a '''[[Glossary of EMGlossary_of_EM.Cube's Simulation Observables%27s_Simulation_Observables_%26_Graph_Types#Receiver Set Point_Receiver_Set | Point Receiver Set]]'''.

<td> [[Image:Terrano L1 Fig12.png|thumb|left|480px|The point receiver set definition dialog.]] </td>

Once you define a new receiver set, its name is added in to the '''Receivers''' section of the navigation tree. The color of all the base points associated with the newly defined receiver set changes, and an additional little ball with the receiver color (yellow by default) appears at the location of each associated base point. You can open the property dialog of the receiver set and modify a number of parameters.

[[File:Terrano L1 Fig14NewRxProp.png|thumb|left|480px720px|The property dialog of a point receiver set.]]

If you choose the "user defined antenna" option for your receiver set, it will indeed consist consists of a basic "Super-Heterodyne Receiver Chain" that starts with contains a receive antenna, which is used connected via a segment of transmission line to capture the broadcast signal from the free space, and it ultimately ends low-noise amplifier (LNA) that is terminated in a baseband/IF signalmatched load. The receiverset's property dialog allows you to define a the basic super-heterodyne receiver chain. Click the {{key|Receiver Chain}} button of the Receiver Set dialog to open the receiver chain dialog. As shown in the figure below, you can specify the characteristics of the Low-Noise Amplifier (LNA), mixer such as its gain and baseband/IF amplifier including stage gains and impedance mismatch factors (IMF) noise figure in dB as well as the 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 '''Brightness Temperature''' as well as the temperature of the transmission line and the receiver's ambient temperature. The effective '''Receiver Bandwidth''' is assumed to be 100MHz, which you can change for the purpose of noise calculations. You also need to enter values for the '''Noise Figure''' of various active devices in the receiver chain. The Receive Chain dialog calculates and reports the "Noise Power" and "Total Receiver Chain Gain" based on your input. At the end of an SBR simulation, the receiver power and signal-noise ratio (SNR) of the selected receiver are calculated and they are reported in the receiver set dialog in dBm and dB, respectively. You can examine the properties of all the individual receivers and all the individual rays received by each receiver in your receiver set using the "Selected Element" drop-down list.

<td> [[File:Terrano L6 Fig15NewRxChain.png|thumb|left|720px|EM.Terrano's point receiver chain dialog.]] </td>

[[EM.Terrano]]'s Transmitter Set dialog and Receiver Set dialog both allow you to rotate an imported radiation pattern. In that case, you need to specify the '''Rotation''' angles in degrees about the X-, Y- and Z-axes. It is important to note that these rotations are performed sequentially and in the following 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.

<td> [[File:PROP22B.png|thumb|200px300px|The local coordinate system of a linear dipole antenna.]] </td><td> [[File:PROP22C.png|thumb|370px600px|Rotating the dipole antenna by +90&deg; about the local Y-axis.]] </td>

<td> [[File:PROP22D.png|thumb|600px720px|Rotating the dipole antenna by +90&deg; about the local X-axis and then by -45&deg; by the local Y-axis.]] </td>

When your transmitters or 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. In many propagation modeling problems, your transmitters and receivers may be located above an irregular terrain with varying elevation across the scene. In that case, you may want to place your transmitters or receivers at a certain height above the underlying ground. The Z-coordinate of a transmitter or receiver is now the sum of the terrain elevation at the base point and the specified height. [[EM.Terrano]] gives you 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 of the Transmitter Dialog there is a check box labeled &quot;'''Adjust Tx Sets to Terrain Elevation'''&quot;. Similarly, at the top of the Receiver Dialog there is a check box labeled &quot;'''Adjust Rx Sets to Terrain Elevation'''&quot;. 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 place a transmitter set or a receiver set above an irregular terrain, the transmitters or receivers are elevated from the location of their associated base points by the amount of terrain elevation as can be seen in the figure below.

== Using Discretizing the Propagation Scene in EM.Terrano as an Asymptotic Field Solver ==

Like every other electromagnetic solver, [[EM.Terrano]]'s SBR ray tracer requires an excitation source and one or more observables for the generation of simulation data. [[EM.Terrano]] offers several types of sources and observables for a SBR simulation. You already learned about the transmitter set as a source and the receiver set as an observable. === Why Do You can mix and match different source types and observable types depending on Need to Discretize the requirements of your modeling problem. Scene? ===

The available source types EM.Terrano's SBR solver uses a method known as Geometrical Optics (GO) in [[conjunction with the Uniform Theory of Diffraction (UTD) to trace the rays from their originating point at the source to the individual receiver locations. Rays may hit obstructing objects on their way and get reflected, diffracted or transmitted. EM.Terrano]] are:'s SBR solver can only handle diffraction off linear edges and reflection from and transmission through planar interfaces. When an incident ray hits the surface of the obstructing object, a local planar surface assumption is made at the specular point. The assumptions of linear edges and planar facets obviously work in the case of a scene with cubic buildings and a flat global ground.

{| class="wikitable"|-! scope="col"| Icon! scope="col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:transmitter_iconIn many practical scenarios, however, your buildings may have curved surfaces, or the terrain may be irregular.png]]| style="width:150px;" | [[Glossary EM.Terrano allows you to draw any type of surface or solid geometric objects such as cylinders, cones, etc. under impenetrable and penetrable surface groups or penetrable volumes. EM.CubeTerrano's Materials, Sourcesmesh generator creates a triangular surface mesh of all the objects in your propagation scene, Devices & Other Physical Object Types#Transmitter Set | Transmitter Set]]| style="width:250px;" | Modeling realsitic antennas & link budget calculations| style="width:250px;" | Requires to be associated with which is called a base location point set|-| style="width:30px;" | [[File:hertz_src_iconfacet mesh.png]]| style="width:150px;" | [[Glossary Even the walls of cubic buildings are meshed using triangular cells. This enables 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|}Terrano to properly discretize composite buildings made of conjoined cubic objects.

Click Unlike [[EM.Cube]]'s other computational modules, the density or resolution of EM.Terrano's surface mesh does not depend on each type to learn more about it the operating frequency and is not expressed in terms of the [[Glossary wavelength. The sole purpose of EM.CubeTerrano's Materialsfacet mesh is to discretize curved and irregular scatterers into flat facets and linear edges. Therefore, Sourcesgeometrical fidelity is the only criterion for the quality of a facet mesh. It is important to note that discretizing smooth objects using a triangular surface mesh typically creates a large number of small edges among the facets that are simply mesh artifacts and should not be considered as diffracting edges. For example, Devices & Other Physical Object Types]]each rectangular face of a cubic building is subdivided into four triangles along the two diagonals. The four internal edges lying inside the face are obviously not diffracting edges. A lot of subtleties like these must be taken into account by the SBR solver to run accurate and computationally efficient simulations.

=== Generating the Facet Mesh === You can view and examine the discretized version of your scene's objects as they are sent to the 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 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. The available observables resolution of EM.Terrano's facet mesh generator is controlled by the '''Cell Edge Length''' parameter, which is expressed in project length units. The default mesh cell size of 100 units might be too large for non-flat objects. You may have to set a smaller cell edge length in EM.Terrano's Mesh Settings dialog, along with a lower curvature angle tolerance value to capture the curvature of your curved structures adequately. <table><tr><td> [[Image:prop_manual-29.png|thumb|left|480px|EM.Terrano's mesh settings dialog.]] </td></tr></table> [[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''. [[Image:Info_icon.png|30px]] Click here to learn more about the properties of '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Facet_Mesh | EM.Terrano's Facet Mesh Generator]]'''. <table><tr><td> [[Image:UrbanCanyon2.png|thumb|left|640px|The facet mesh of the buildings in the urban propagation scene generated by EM.Terrano's Random City wizard with a cell edge length of 100m.]] </td></tr><tr><td> [[Image:UrbanCanyon3.png|thumb|left|640px|The facet mesh of the buildings in the urban propagation scene generated by EM.Terrano's Random City wizard with a cell edge length of 10m.]] </td></tr></table> == Running Ray Tracing Simulations in EM.Terrano == EM.Terrano provides a number of different simulation or solver types : * 3D Field Solver* SBR Channel Analyzer* Log-Haul Channel Analyzer* Communication Link Solver* Radar Link Solver The first three simulation types are described below. For a description of EM.Terrano's Radar Simulator, follow this link.  === Running a Single-Frequency SBR Analysis === Its 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: * Set the units of your project and the frequency of operation. Note that the default project unit is '''millimeter'''. Wireless propagation problems usually require meter, mile or kilometer as the project unit.* Create the blocks and draw the buildings at the desired locations.* Keep the default ray domain and accept the default global ground or change its material properties.* Define an excitation source and observables for your project.* If you intend to use transmitters and receivers in your scene, first define the required base sets and then define the transmitter and receiver sets based on them.* Run the SBR simulation engine.* Visualize the coverage map and plot other data. You can access EM.Terrano's Simulation Run dialog by clicking the '''Run''' [[File:run_icon.png]] button of the '''Simulate Toolbar''' or by selecting '''Simulate &rarr; Run...''' or using the keyboard shortcut {{key|Ctrl+R}}. When you click the {{key|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 process. <table><tr><td> [[Image:Terrano L1 Fig16.png|thumb|left|480px|EM.Terrano's simulation run dialog.]] </td></tr></table> <table><tr><td> [[Image:PROP MAN10.png|thumb|left|550px|EM.Terrano's output message window.]] </td></tr></table> === Changing the SBR Engine Settings === There area number of SBR 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. EM.Terrano allows 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 multiple 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. Two other parameters control the diffraction computations: '''Max Wedge Angle''' in degrees and '''Min Edge Length''' in project units. The maximum wedge angle is the angle between two conjoined facets that is considered to make them almost flat or coplanar with no diffraction effect. The default value of the maximum wedge angle is 170&deg;. The minimum edge length is size of the common edge between two conjoined facets that is considered as a mesh artifact and not a real diffracting edge. The default value of the minimum edge length is one project units.  <table><tr><td> [[Image:PROP MAN11.png|thumb|left|720px|EM.Terrano's SBR simulation engine settings dialog.]] </td></tr></table> As rays travel in the scene and bounce from surfaces, they lose their power, and their amplitudes gradually diminish. From a practical point of view, only rays that have power levels above the receiver sensitivity can be effectively received. Therefore, all the rays whose power levels fall below a specified power threshold are discarded. The '''Ray Power Threshold''' is specified in dBm and has a default value of -150dBm. Keep in mind that the value of this threshold directly affects the accuracy of the simulation results as well as the size of the output data file. You can also set the '''Ray Angular Resolution''' of the 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. 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. EM.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.  At the end of a ray tracing simulation, the electric field of each individual ray is computed and reported. By default, the actual received ray fields are reported, which are independent of the radiation pattern of the receive antennas. EM.Terrano provides a check box labeled "Normalize ray's E-field based on receiver pattern", which is unchecked by default. If this box is checked, the field of each ray is normalized so as to reflect that effect of the receiver antenna's radiation pattern. The received power of each ray is calculated from the following equation:  <math> P_{ray} = \frac{ | \mathbf{E_{norm}} |^2 }{2\eta_0} \frac{\lambda_0^2}{4\pi} </math> It can be seen that if the ray's E-field is not normalized, the computed ray power will correspond to that of a polarization matched isotropic receiver. === Polarimetric Channel Analysis === In 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. From a theoretical point of view, the radiation patterns of the transmit and receive antennas are independent of the propagation channel characteristics. For the given locations of the point transmitters and receivers, one can assume ideal isotropic radiators at these points and compute the polarimetric transfer function matrix of the propagation channel. This matrix relates the received electric field at each receiver location to the transmitted electric field at each transmitter location. In general, the vectorial electric field of each individual ray is expressed in the local standard spherical coordinate system at the transmitter and receiver locations. In other words, the polarimetric channel matrix expresses the '''E_&theta;''' and '''E_&phi;''' field components associated with each ray at the receiver location to its '''E_&theta;''' and '''E_&phi;''' field components at the transmitter location. Each ray has a delay and &theta; and &phi; angles of departure at the transmitter location and &theta; and &phi; angles of departure at the receiver location. To perform a polarimatric channel characterization of your propagation scene, open EM.Terrano's Run Simulation dialog and select '''Channel Analyzer''' from the drop-down list labeled '''Select Simulation or Solver Type'''. At the end of the simulation, a large ray database is generated with two data files called "sbr_channel_matrix.DAT" and "sbr_ray_path.DAT". The former file contains the delay, angles of arrival and departure and complex-valued elements of the channel matrix for all the individual rays that leave each transmitter and arrive at each receiver. The latter file contains the geometric aspects of each ray such as hit point coordinates. === The "Near Real-Time" Polarimatrix Solver === After EM.Terrano's channel analyzer generates a ray database that characterizes your propagation channel polarimetrically for all the combinations of transmitter and receiver locations, 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 receive antennas. This is done using the '''Polarimatrix Solver''', which is the third option of the drop-down list labeled '''Select Simulation or Solver Type''' in EM.Terrano's Run Simulation dialog. The results of the Polarimatrix and 3D SBR solvers must be identical from a theoretical point of view. However, there might be small discrepancies between the two solutions due to roundoff errors. Using 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. Certain simulation modes of EM.Terrano are intended for the Polarimatrix solver only as will be described in the next section.  {{Note| In order to use the Polarimatrix solver, you must first generate a ray database of your propagation scene using EM.Terrano's Channel Analyzer.}} === EM.Terrano's Simulation Modes === EM.Terrano provides a number of different simulation modes that involve single or multiple simulation runs:

! scope="col"| IconSimulation Mode! scope="col"| Source TypeUsage! scope="col"| ApplicationsWhich Solver?! scope="col"| Frequency

| style="width:30px120px;" | [[File:receiver_icon.png#Running a Single-Frequency SBR Analysis | Single-Frequency Analysis]]| style="width:150px180px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Receiver Set Simulates the propagation scene "As Is"| Receiver Set]]style="width:150px;" | SBR, Channel Analyzer, Polarimatrix, Radar Simulator| style="width:250px120px;" | Generating received power coverage maps & link budget calculationsRuns at the center frequency fc| style="width:250px300px;" | Requires to be associated with a base location point setNone

| style="width:30px120px;" | [[File:fieldsensor_iconParametric_Modeling_%26_Simulation_Modes_in_EM.pngCube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweep]]| style="width:150px180px;" | [[Glossary Varies the operating frequency of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor the ray tracer | Near-Field Sensor]]style="width:150px;" | SBR, Channel Analyzer, Polarimatrix, Radar Simulator| style="width:250px120px;" | Generating electric and magnetic field distribution mapsRuns at a specified set of frequency samples| style="width:250px300px;" | None, stand-alone observable

| style="width:30px120px;" | [[File:farfield_iconParametric_Modeling_%26_Simulation_Modes_in_EM.pngCube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]| style="width:150px180px;" | [[Glossary of EM.Cube'Varies the value(s Simulation Observables & Graph Types#Far-Field Radiation Pattern ) of one or more project variables| Far-Field Radiation Pattern]]style="width:150px;" | SBR| style="width:250px120px;" | Computing Runs at the effective radiation pattern of a radiator in the presence of a large scattering scene center frequency fc| style="width:250px300px;" | NoneRequires definition of sweep variables, stand-alone observableworks only with SBR solver as the physical scene may change during the sweep

| style="width:30px120px;" | [[File:huyg_surf_icon.png#Transmitter_Sweep | Transmitter Sweep]]| style="width:180px;" | Activates two or more transmitters sequentially with 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 scene, works only with Polarimatrix solver and requires an existing ray database|-| style="width:120px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Huygens Surface Rotational_Sweep | Huygens SurfaceRotational Sweep]]| style="width:250px180px;" | Collecting tangential field data on a box Rotates the radiation pattern of the transmit antenna(s) sequentially to be used later as a Huygens source in other 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;" | [[EM.Cube#Mobile_Sweep | Mobile Sweep]] modules| style="width:250px180px;" | NoneConsiders one pair of active transmitter and receiver at each simulation run to model a mobile communication link| style="width:150px;" | Polarimatrix| style="width:120px;" | Runs at the center frequency fc| style="width:300px;" | Requires the same number of transmitters and receivers, stand-alone observableworks only with Polarimatrix solver and requires an existing ray database

Click on each type item in the above list to learn more about it each simulation mode.  You set the simulation mode in EM.Terrano's simulation run dialog using the [[Glossary 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.  {{Note| EM.CubeTerrano's Simulation Observables & Graph Types]]frequency sweep simulations are very fast because the geometrical optics (ray tracing) part of the simulation is frequency-independent. }} === Transmitter Sweep === When you define a far-field observable in [[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.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 collection transmitter sweep, on the other hand, EM.Terrano assumes only one transmitter broadcasting at a time. The result of the sweep simulation is a number of invisiblereceived power coverage maps, isotropic each corresponding to a transmitter in the scene. {{Note| EM.Terrano's transmitter sweep works only with the Polarimatrix Solver and requires an existing ray database previously generated using the Channel Analyzer.}} === Rotational Sweep === You can rotate the 3D radiation patterns of both the transmitters and receivers are placed on from the surface property dialog of the parent transmitter set or receiver set. This is done in advance before a large sphere SBR simulation starts. You can define one or more of the rotation angles of a transmitter set or a receiver set as sweep variables and perform a parametric sweep simulation. In that encircles your propagation case, the entire scene and all of its geometric objects. These receivers buildings are placed uniformly on the spherical surface discretized at each simulation run and a spacing that complete physical SBR ray tracing simulation is determined by your specified angular resolutionscarried out. In most casesHowever, we know that the polarimetric characteristics of the propagation channel are independent of the transmitter or receiver antenna patterns or their rotation angles. A rotational sweep allows you need to define angular resolutions rotate the radiation pattern of at least 1&deg; the transmitter(s) about one of the three principal axes sequentially. This is equivalent to the steering of the beam of the transmit antenna either mechanically or smallerelectronically. The result of the sweep simulation is a number of received power coverage maps, each corresponding to one of the angular samples. To run a rotational sweep, you must specify the rotation angle. {{Note that this | EM.Terrano's rotational sweep works only with the Polarimatrix Solver and requires an existing ray database previously generated using the Channel Analyzer.}} === Mobile Sweep === In 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 than meaning implying the sequential movement of the transmitter rays' angular resolutionand receiver pair along their corresponding paths. You may have In other words, the set of point transmitters and the set of point receivers indeed represent the locations of a large single transmitter and a single receiver at different instants of time. It is obvious that the total number of transmitters and total number of transmitted rays but not enough receivers in the scene must be equal. Otherwise, EM.Terrano will prompt an error message. [[EM.Cube]] provides a '''Mobile Path Wizard''' that facilitates the creation of a transmitter set or a receiver set along a specified path. This path can be an existing nodal curve (polyline or NURBS curve) or an existing line objects. You can also import a sptial Cartesian data file containing the coordinates of the base location points. For more information, refer to compute [[Glossary_of_EM.Cube%27s_Wizards#Mobile_Path_Wizard | Mobile Path Wizard]]. {{Note| EM.Terrano's mobile sweep works only with the effective radiation pattern Polarimatrix Solver and requires an existing ray database previously generated using the Channel Analyzer.}} === Investigating Propagation Effects Selectively One at a Time === In a typical SBR ray tracing simulation, EM.Terrano includes all azimuth the propagation effects such as direct (LOS) rays, ray reflection and elevation angles. Also keep in mind that with 1&deg; Theta transmission, and Phi angle incrementsedge diffractions. At the end of a SBR simulation, you will have a total can visualize the received power coverage map of 181 &times; 361 = 65your propagation scene,341 spherically placed receivers which appears under the receiver set item in your the navigation tree. The figure below shows the received power coverage map of the random city scenewith a vertically polarized half-wave dipole transmitter located 10m above the ground and a large grid of vertically polarized half-wave dipole receivers placed 1.5m above the ground. The legend box shows the limits of the color map between -23dBm as the maximum and -150dB (the default receiver sensitivity value) as the minimum.

<td> [[Image:PROP18PUrbanCanyon10.png|thumb|450pxleft|Computed 3D radiation pattern 640px|The received power coverage map of two vertical short the random city scene with a dipole radiators placed 1m apart transmitter.]] </td></tr></table> Sometime 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 free space at 1GHznavigation 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. <table><tr><td> [[Image:UrbanCanyon15.png|thumb|left|480px|The plot settings dialog of the coverage map.]] </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> To better understand the various propagation effects, EM.Terrano allows you to enable or disable these effects selectively. This is done from the Ray Tracing Simulation Engine Settings dialog using the provided check boxes.  <table><tr><td> [[Image:UrbanCanyon14.png|thumb|left|640px|EM.Terrano's simulation run dialog showing the check boxes for controlling various propagation effects.]] </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.]] </td></tr><tr><td> [[Image:UrbanCanyon12.png|thumb|left|640px|The received power coverage map of the random city scene with reflected rays only.]] </td></tr><tr><td> [[Image:UrbanCanyon13.png|thumb|left|640px|The received power coverage map of the random city scene with diffracted rays only.]] </td>

== Working with EM.TerannoTerrano's Simulation Data ==

=== The SBR SolverRay Tracing Solvers's Output Simulation Data ===

Both the SBR solver and the Polarimatrix solver perform the same type of simulation but in two different ways. The SBR solver discretizes the scene including all the buildings and terrain, shoots a large number of rays from the transmitters and collects the rays 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 patterns of the transmit and receive antennas in conjunction with the polarimetric channel characteristics. At the end of an SBR a ray tracing simulation, all the polarimetric rays emanating from the transmitter(s) or other sources that are received by the individual receivers are computed, collected, sorted and savedinto ASCII data files. From the ray data, the total electric field at the location of receivers as well as the total received power are computed. The individual ray data include the field components of each ray, the ray's elevation and azimuth angles of departure and arrival (departure from the transmitter location and arrival at the receiver location), and time delay of the received ray with respect to the transmitter. If you specify the temperaturetemperatures, noise figure levels and transmission line losses in the definition of the receiver sets, the noise power level and signal-to-noise ratios ratio (SNR) at each receiver are also calculated, and so are the E_b/N₀ and bit error rate (BER) for the selected digital modulation scheme.

The In a simple link scenario, the received power P_r in dBm is found from the following equation:

where P_t is the baseband signal power in dBm at the transmitter, G_TC and G_RC are the total transmitter and receiver chain gains in dB, respectively, G_TA and G_RA are the total transmitting and receiving antenna gains in dB, respectively, and PL is the channel path loss in dB. Keep in mind that [[EM.Terrano]] is fully polarimetric. The transmitting and receiving antenna characteristics are specified through the imported radiation pattern files, which are part of the definition of the transmitters and receivers. In particular, the polarization mismatch losses are taken into account through the polarimetric SBR ray tracing analysis.

[[Image:Terrano L6 Fig4AnnArbor Scene1.png|thumb|left|640px|The downtown Ann Arbor propagation scene.]]

[[Image:Terrano L6 Fig16AAnnArbor Scene2.png|thumb|left|640px|The electric field distribution map of the Ann Arbor scene with super-heterodyne vertical dipole transmitter and receivers.]]

[[Image:Terrano L6 Fig16AnnArbor Scene3.png|thumb|left|640px|The received power coverage map of the Ann Arbor scene with super-heterodyne vertical dipole transmitter and receivers.]]

[[Image:Terrano L6 Fig17AnnArbor Scene4.png|thumb|left| 640px |The connectivity map of the Ann Arbor scene with SNR_min = 25dB 3dB with Rainbow 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.]]

[[Image:PROP12BUrbanCanyon17.png|thumb|left|480px720px|EM.Terrano's ray data dialogshowing a selected ray.]]

<td> [[Image:Terrano L6 Fig16BUrbanCanyon18.png|thumb|left|640px|Visualization of received rays at the location of a selected receiver in the downtown Ann Arbor random city scene.]] </td>

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

At the end of an SBR simulation, [[EM.Terrano]] writes a number of ASCII data files to your project folder. The main output data file is called "sbr_results.RTOUT". This file contains all the information about individual receivers and the [[parameters]] of each ray that is received by each individual receiver.

[[Image:Info_icon.png|40px]] Click here to learn more about working with data filed and plotting graphs in [[EM.Cube]]'s '''[[Data Visualization, Plotting & Processing in EM.CubeDefining_Project_Observables_%26_Visualizing_Output_Data#Organizing & Accessing Simulation Output Data Files in Data Manager The_Data_Manager | Data Manager]]'''.

<td> [[Image:PROP20ETerrano pathloss.png|thumb|350px360px|Cartesian graph of path loss.]] </td><td> [[Image:PROP20FTerrano delay.png|thumb|350px360px|Bar graph of power delay profile.]] </td>

<td> [[Image:PROP20GTerrano ARR phi.png|thumb|350px360px|Polar stem graph of Phi angle of arrival.]] </td><td> [[Image:PROP20HTerrano ARR theta.png|thumb|350px360px|Polar stem graph of Theta angle of arrival.]] </td></tr><tr><td> [[Image:Terrano DEP phi.png|thumb|360px|Polar stem graph of Phi angle of departure.]] </td><td> [[Image:Terrano DEP theta.png|thumb|360px|Polar stem graph of Theta angle of departure.]] </td>

== Discretizing = Visualizing 3D Radiation Patterns of Transmit and Receive Antennas in the Propagation Scene in EM.Terrano ===

=== Why Do You Need When you designate a "User Defined Antenna Pattern" as the radiator type of a transmitter set or a receiver set, EM.Terrano copies the imported radiation pattern data file from its original folder to Discretize the Scene? ===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 actual location of the transmitter or receiver. To do so, you have to define a 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 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 scene.

<table><tr><td>[[EM.Terrano]]'s SBR solver uses a method known as Geometrical Optics (GO) in conjunction with the Uniform Theory of Diffraction (UTD) to trace the rays from their originating point at the source to the individual receiver locations. Rays may hit obstructing objects on their way and get reflected, diffracted or transmitted. [[EM.Terrano]]'s SBR solver can only handle diffraction off linear edges and reflection from and transmission through planar interfaces. When an incident ray hits the surface of the obstructing object, a local planar surface assumption is made at the specular pointImage:UrbanCanyon6. png|thumb|left|640px|The assumptions received power coverage map of linear edges and planar facets are valid in in the case of a random city scene with cubic buildings and a flat global groundhighly directional dipole array transmitter. ]]</td></tr></table>

In many practical scenariosBy Default, however, your buildings may have curved surfaces, or the terrain may be irregular. [[EM.TerranoCube]] allows you to draw any type always visualizes the 3D radiation patterns at the origin of surface or solid geometric objects such as cylinders, conescoordinates, etci. under impenetrable and penetrable surface groups or penetrable volumese. [[EMat (0, 0, 0).Terrano]]'s mesh generator creates a triangular surface mesh 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 all the objects 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 your a propagation scene, which it is called a facet mesh. Even more intuitive to display the walls pattern at the location of cubic buildings are meshed using triangular cellsthe transmitter or receiver. This enables [[EMThe Radiation Pattern dialog allows you to translate the pattern visualization to any arbitrary point in the project workspace.Terrano]] It also allows you to properly discretize composite buildings made of conjoined cubic objectsscale up or scale down the pattern visualization with respect to the background scene.

Unlike [[EM.Cube]]'s other computational modulesIn the example shown above, the density or resolution of [[EM.Terrano]]'s surface mesh does not depend on the operating frequency and imported pattern data file is not expressed in terms of the wavelengthcalled "Dipole_Array1. The sole purpose of [[EM.Terrano]]'s facet mesh is to discretize curved and irregular scatterers into flat facets and linear edgesRAD". Therefore, geometrical fidelity is the only criterion for label of the quality of a facet mesh. It radiation pattern observable is important chosen to note that discretizing smooth objects using a triangular surface mesh typically creates a large number of small edges among the facets that are simply mesh artifacts and should not be considered as diffracting edges. For example, each rectangular face of a cubic building is subdivided into four triangles along the two diagonals"Dipole_Array1". The four internal edges lying inside the face theta and phi angle increments are obviously not diffracting edgesboth 1&deg; in this case. A lot of subtleties like these must be taken into account The radiation pattern has been elevated by the SBR solver 10m to run accurate and computationally efficient simulations.  === Generating be positioned at the SBR Mesh === You can view and examine the discretized version location of your scene objects as they are sent to the SBR simulation engine. You can adjust the mesh resolution transmitter 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. The resolution scaling factor of [[EM0.Terrano]]'s facet mesh generator is controlled by the '''Mesh Cell Size''' parameter, which is expressed in project length units. The default mesh cell size of 100 units might be too large for non-flat objects. You may have to set a smaller mesh cell size in [[EM.Terrano]]'s Mesh Settings dialog, along with a lower curvature angle tolerance value to capture the curvature of your curved structures adequately3 has been used.

<td> [[Image:prop_manual-29UrbanCanyon8.png|thumb|left|480px640px|EM.Terrano's mesh settings 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.]]

[[Image:Info_icon.png|40px]] Click There is an important catch to remember here . When you define a radiation pattern observable for your project, EM.Terrano will attempt to learn more about [[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 '''[[Glossary Do not compute new 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.CubeTerrano's Mesh Generators#Facet Mesh | Facet Mesh Generator]]'''SBR solver as an asymptotic EM solver (see next section).

<td> [[Image:PROP MAN9UrbanCanyon9.png|thumb|left|640px|The facet mesh of the buildings in the urban propagation scene generated by EM.Terrano's Random City wizardRun Simulation dialog.]] </td>

== Running SBR Simulations in Using EM.Terrano as an Asymptotic Field Solver ==

=== Like every other electromagnetic solver, EM.Terrano's SBR Simulation Types ===ray tracer requires an excitation source and one or more observables for the generation of simulation data. EM.Terrano offers several types of sources and observables for a SBR simulation. You already learned about the transmitter set as a source and the receiver set as an observable. You can mix and match different source types and observable types depending on the requirements of your modeling problem.

Once you have set up your propagation scene The available source types in [[EM.Terrano]] and have defined sources/transmitters and observables/receivers for your scene, you are ready to run a SBR ray tracing simulation. [[EM.Terrano]] offers thee simulation modes:

! scope="col"| Simulation ModeIcon! scope="col"| UsageSource Type! scope="col"| Number of Engine Runs! scope="col"| Frequency Applications

| style="width:120px30px;" | [[#Running a Single-Frequency SBR Analysis | Single-Frequency AnalysisFile:transmitter_icon.png]]| style="width:250px150px;" | Simulates the propagation scene "As Is"[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Point Transmitter Set | style="width:100px;" | Single runPoint Transmitter Set]]| style="width:150px250px;" | Runs at the center frequency fcModeling realsitic antennas & link budget calculations| style="width:100px250px;" | NoneRequires to be associated with a base location point set

| style="width:120px30px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EMFile:hertz_src_icon.Cube#Running_Frequency_Sweep_Simulations_in_EM.Cube | Frequency Sweeppng]]| style="width:250px150px;" | Varies the operating frequency [[Glossary of the ray tracer EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Hertzian Short Dipole Source | style="width:100px;" | Single ray tracing run, multiple frequency computations Hertzian Short Dipole]]| style="width:150px250px;" | Runs at a specified set of frequency samplesAlmost omni-directional physical radiator| style="width:100px250px;" | None, stand-alone source

| style="width:120px30px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EMFile:huyg_src_icon.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweeppng]]| style="width:250px150px;" | Varies the value(s) [[Glossary of one or more project variablesEM.Cube's Materials, Sources, Devices & Other Physical Object Types#Huygens Source | style="width:100px;" | Multiple runsHuygens Source]]| style="width:150px250px;" | Runs at the center frequency fcUsed for modeling equivalent sources imported from other [[EM.Cube]] modules | style="width:100px250px;" | None, stand-alone source imported from a Huygens surface data file

You set Click on each type to learn more about it in the simulation mode in [[Glossary of EM.Terrano]]Cube's simulation run dialog. A single-frequency analysis is a single-run simulation. The two other simulation modes in the above list are considered multi-run simulations. If you run a simulation without having defined any observablesMaterials, no data will be generated at the end of the simulation. In multi-run simulation modesSources, certain parameters are varied and a collection of simulation data files are generated. At the end of a sweep simulation, you can graph the simulation results in EM.Grid or you can animate the 3D simulation data from the navigation treeDevices & Other Physical Object Types]].

{{Note| The available observables types in [[EM.Terrano]]'s frequency sweep simulations are very fast because the geometrical optics (ray tracing) part of the simulation is frequency-independent.}}:

{| class="wikitable"|-! scope="col"| Icon! scope= Running "col"| Source Type! scope="col"| Applications! scope="col"| Restrictions|-| style="width:30px;" | [[File:receiver_icon.png]]| style="width:150px;" | [[Glossary of EM.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 be associated with a Singlebase location point set|-Frequency SBR Analysis | style="width:30px;" | [[File:Distr Rx icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Distributed Receiver Set | Distributed Receiver Set]]| style="width:250px;" | Computing received power at a receiver characterized by Huygens surface data| style="width:250px;" | None, stand-alone source imported from a Huygens surface data file|-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field Sensor Observable | Near-Field Sensor]]| style="width:250px;" | Generating electric and magnetic field distribution maps| style="width:250px;" | None, stand-alone observable|-| style="width:30px;" | [[File:farfield_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Far-Field Radiation Pattern Observable | Far-Field Radiation Pattern]]| style="width:250px;" | Computing the effective radiation pattern of a radiator in the presence of a large scattering scene | style="width:250px;" | None, stand-alone observable|-| style="width:30px;" | [[File:huyg_surf_icon.png]]| style="width:150px;" | [[Glossary of EM.Cube's 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|}

A single-frequency SBR analysis is the simplest Click on each type to learn more about it in the [[Glossary of ray tracing simulation and involves the following steps:EM.Cube's Simulation Observables & Graph Types]]. * Set When you define a far-field observable in EM.Terrano, a collection of invisible, isotropic receivers are placed on the units surface of a large sphere that encircles your project propagation scene and the frequency all of operationits geometric objects. Note These receivers are placed uniformly on the spherical surface at a spacing that the default project unit is '''millimeter'''determined by your specified angular resolutions. Wireless propagation problems usually require meterIn most cases, mile or kilometer as the project unit.* Create the blocks and draw the buildings at the desired locations.* Keep the default ray domain and accept the default global ground or change its material properties.* Define an excitation source and observables for your project.* If you intend need to use transmitters and receivers in your scene, first define the required base sets and then define the transmitter and receiver sets based on them.* Run the SBR simulation engine.* Visualize the coverage map and plot other data. You can access [[EM.Terrano]]'s Simulation Run dialog by clicking the '''Run''' [[File:run_icon.png]] button angular resolutions of the '''Simulate Toolbar''' or by selecting '''Simulate at least 1&gtdeg; Run..or smaller.Note that this is different than the transmitter rays''' or using the keyboard shortcut {{key|Ctrl+R}}angular resolution. When you click the {{key|Run}} button, You may have a new window opens up that reports the different stages large number of transmitted rays but not enough receivers to compute the SBR simulation effective radiation pattern at all azimuth and indicates the progress of each stageelevation angles. After the SBR simulation is successfully completedAlso keep in mind that with 1&deg; Theta and Phi angle increments, you will have a message pops up and prompts the completion total of the process181 &times; 361 = 65,341 spherically placed receivers in your scene.

<td> [[Image:Terrano L1 Fig16SBR pattern.png|thumb|left540px|480px|EM.Terrano's simulation run dialogComputed 3D radiation pattern of two vertical short dipole radiators placed 1m apart in the free space at 1GHz.]] </td>

<table><tr><td> [[Image:PROP MAN10.png|thumb|left|550px|EM.Terrano's output message window.]] </td></tr></table> === Changing the SBR Engine Settings === 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 {{key|Settings}} on the right side of the '''Select Engine''' 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, the reflection, transmission and edge diffraction effects are enabled and the terrain diffraction effects are disabled. Separating these effects sometimes help you better analyze your propagation scene and understand the impact of various blocks in the scene. [[EM.Terrano]] allows 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 multiple 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. Two other parameters control the diffraction computations: '''Max Wedge Angle''' in degrees and '''Min Edge Length''' in project units. The maximum wedge angle is the angle between two conjoined facets that is considered to make them almost flat or coplanar with no diffraction effect. The default value of the maximum wedge angle is 170&deg;. The minimum edge length is size of the common edge between two conjoined facets that is considered as a mesh artifact and not a real diffracting edge. The default value of the minimum edge length is 5 project units.  <table><tr><td> [[Image:PROP MAN11.png|thumb|left|480px|EM.Terrano's SBR simulation engine settings dialog.]] </td></tr></table> As rays travel in the scene and bounce from surfaces, they lose their power, and their amplitudes gradually diminish. From a practical point of view, only rays that have power levels above the receiver sensitivity threshold can be effectively received. Therefore, all the rays whose power levels fall below a specified power threshold are discarded. The '''Ray Power Threshold''' is specified in dBm and has a default value of -100dBm. Keep in mind that the value of this threshold directly affects the accuracy of the simulation results as well as the size of the output data file. You can also set the '''Angular Resolution''' of the 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. The SBR Engine Settings dialog also shows the required '''Minimum Angular Resolution''' in degrees in a greyed-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. === Statistical Analysis of Propagation Scene ===

[[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 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.

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 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 Coverage Mapsreceived 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.

[[Image:Terrano L4 Fig21UrbanCanyon4.png|thumb|left|640px|The mean coverage map at the end of a frequency sweep.]]

[[Image:Terrano L4 Fig22UrbanCanyon5.png|thumb|left|640px|The standard deviation coverage map at the end of a frequency sweep.]]

[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Terrano_Tutorial_Lessons Terrano_Documentation | EM.Terrano Tutorial Gateway]]'''