<table>
<tr>
<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.CUBECube]] [[image:cad-ico.png | link=Building Geometrical Constructions in CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:static-ico.png | link=EM.Ferma]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]] </td>
<tr>
</table>
[[Image:Back_icon.png|30px]] '''[[A_Review_of_Maxwell%27s_Equations_%26_Computational_Electromagnetics_(CEM) | Back to Maxwell's Equations Page]]'''
== Physics-Based Propagation Channel Modeling ==
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.
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 angles. 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. The use of statistical models for prediction of fading effects is widely popular among communication system designers. These models are either based on measurement data or derived from simplistic analytical frameworks. The statistical models often exhibit considerable errors especially in areas having mixed building sizes. In such cases, one needs to perform a physics-based, site-specific analysis of the propagation environment to accurately identify and establish all the possible signal paths from the transmitter to the receiver. This involves an electromagnetic analysis of the scene with all of its geometrical and physical details.
Link budget analysis for a multipath channel is a challenging task due to the large size of the computational domains involved. Typical propagation scenes usually involve length scales on the order of thousands of wavelengths. To calculate the path loss between the transmitter and receiver, one must solve Maxwell's equations in an extremely large space. Full-wave numerical techniques like the Finite Difference Time Domain (FDTD) method, which require a fine discretization of the computational domain, are therefore impractical for solving large-scale propagation problems. The practical solution is to use asymptotic techniques such as SBR, which utilize analytical techniques over large distances rather than a brute force discretization of the entire computational domain. Such asymptotic techniques, of course, have to compromise modeling accuracy for computational efficiency.
[[EM.Terrano]] 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 of a ray tube expands as a function of the distance from the source. [[EM.Terrano]] 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.
== Free-Space Wave Propagation ==
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 θ and φ 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.
== Ray Reflection & Transmission in the Free Space and Inside Material Media ==
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>
<!--[[File:frml1.png]]-->
The reflected unit vectors are found as:
:<math> \mathbf{ \hat{u}_{\|}' = \hat{u}_{\perp}' \times \hat{k}' } </math>
<!--[[File:frml2.png]]-->
The transmitted unit vectors are found as:
:<math> \mathbf{ \hat{u}_{\|}^{\prime\prime} = \hat{u}_{\perp}^{\prime\prime} \times \hat{k}^{\prime\prime} } </math>
<!--[[File:frml3.png]]-->
where
:<math> \sin\theta^{\prime\prime} = \frac{k_1}{k_2}\sin\theta \text{ if } \sin\theta \le k_2/k_1</math>
<!--
[[File:frml4.png]]
[[File:frml5.png]]
-->
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>
<!--[[File:frml6.png]]-->
== Penetration through Thin Walls or Surfaces ==
<hr>
[[Image:Top_icon.png|48px30px]] '''[[#Maxwell's Equations in Differential Form Physics-Based_Propagation_Channel_Modeling | Back to the Top of the Page]]''' [[Image:Back_icon.png|30px]] '''[[A_Review_of_Maxwell%27s_Equations_%26_Computational_Electromagnetics_(CEM) | Back to Maxwell's Equations Page]]''' [[Image:Back_icon.png|30px]] '''[[EM.Terrano | Back to EM.Terrano Manual]]'''
[[Image:Back_icon.png|40px30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''