Normalization of a Fading Channel

In this paper we discuss the proper normalization of a fading channel model. Physically, radio channels correspond to passive circuits and follow the energy conservation law. The ratio of the received energy to the transmitted energy is the energy gain of the channel. The representative energy gain is defined as the average energy gain for a signal that is uniformly distributed in time, frequency and space. The major approaches for normalization include setting of either the average representative energy gain or the peak energy gain to unity. The peak energy gain of many fading models including Rayleigh fading is infinite, which is obviously impossible in a passive system where the peak energy gain should be less than or equal to unity. Our aim is to show that it is due to the normalization that in some cases the performance in a fading channel is better than in a nonfading channel.