# 7.1 Physical Model for the Wireless Channel

The propagation problem should be afforded by solving the Maxwell's equation with the boundary conditions on buildings, ground, vehicles, sea, etc. Boundary conditions should be specified at least with accuracy of the order of the wavelength λ, where λf = c, f being the transmitted frequency and c 3 · 10^{8}ms^{−1} the propagation speed. In the case of mobile cellular communications, f 1GHz = 10^{9}Hz so that λ 3 · 10^{−1}m. Since describing the boundary conditions with such an accuracy is a formidable problem, a simplified approach is used to afford the propagation problem in the wireless channel (Gallagher 2008).

## 7.1.1 Assumptions on the Propagation Channel

In the sequel, the following assumptions on the propagation channel are made.

The transmitter (TX) is located in the origin of the (x, y, z) axis system (TX reference system). The receiver (RX) is located in *P* ≡ (*r, θ, ψ*) (spherical coordinates with respect to TX reference system) where the electric and magnetic fields are *e*(*P*, t) and *h*(*P*, t), respectively. Free-space propagation and far field (r > λ) conditions are satisfied. Thus e is orthogonal to *h*, both *e* and *h* are orthogonal to the propagation ...