In wireless communications, a communication channel includes channel coefficients such as gain and phase factors as well as noise factors. For the one-tap linear model, we assume that the channel coefficients and the noise signal are given as $ h $ and $ n $, respectively. Then, the received signal at the receiver is represented as

$ r = P h x + n $

where $ x $ is the transmission signal at the transmitter and $ P $ is the transmission power.

Rayleigh Fading ChannelEdit

When a fading model of given wireless channel can be represented as Rayleigh distribution, we model both the complex channel coefficient $ h $ and the noise signal $ n $ are normalized Gaussian random variable, i.e., distributed with $ N(0,1) $.