Changes

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Every wireless communication system involves a transmitter that transmits some sort of signal (voice, video, data, etc.), 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 to the location 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. In a free-space line-of-sight (LOS) communication system, the signal propagates directly from the transmitter to the receiver without encountering any obstacles (scatterers). Free-space line-of-sight channels are ideal scenarios that can typically be used to model aerial or space communication system applications.

A receiver may receive a large number of rays: direct line-of-sight rays from the transmitter, 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 power, delay and angles of arrival, which are the spherical coordinate angles &theta; and &phi; of the incoming ray. The actual signal received and detected by the receiver is the superposition of all these rays with different power levels and different time delays. Most of the time, you will be interested 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.

The incident, reflected and transmitted rays are each characterized by a triplet of unit vectors:

:<math> \mathbf{ \hat{u}_{\|} = \hat{u}_{\perp} \times \hat{k} } </math>

The reflected unit vectors are found as:

:<math> \mathbf{ \hat{u}_{\|}' = \hat{u}_{\perp}' \times \hat{k}' } </math>

The transmitted unit vectors are found as:

:<math> \mathbf{ \hat{u}_{\|}^{\prime\prime} = \hat{u}_{\perp}^{\prime\prime} \times \hat{k}^{\prime\prime} } </math>

where

:<math> \sin\theta^{\prime\prime} = \frac{k_1}{k_2}\sin\theta \text{ if } \sin\theta \le k_2/k_1</math>

The reflection coefficients at the interface are calculated for the two parallel and perpendicular polarizations as:

:<math> R_{\perp} = \frac { \eta_2(\mathbf{ \hat{k} \cdot \hat{n} }) - \eta_1(\mathbf{ \hat{k}^{\prime\prime} \cdot \hat{n} }) } { \eta_2(\mathbf{ \hat{k} \cdot \hat{n} }) + \eta_1(\mathbf{ \hat{k}^{\prime\prime} \cdot \hat{n} }) } = \frac{\eta_2 / \cos\theta^{\prime\prime} - \eta_1 / \cos\theta} {\eta_2 / \cos\theta^{\prime\prime} + \eta_1 / \cos\theta} = \frac{Z_{2\perp} - Z_{1\perp}} {Z_{2\perp} + Z_{1\perp}} </math>

== Penetration through Thin Walls or Surfaces ==

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