Normalization of Linear Vector Channels

Abstract

In this paper we study the normalization of mathematical models of linear vector channels. The ratio of the received energy to the transmitted energy is the energy gain of the channel. All physical systems follow an energy conservation law which implies that the energy gain of the channel is less than or equal to one. The major approaches for normalization include setting of either the average energy gain or the peak energy gain to unity. The peak energy gain of many mathematical fading models is infinite and those models cannot be normalized by the peak energy gain. We propose a new approach to normalization where the mathematical channel model is guaranteed to represent a physical system with a predefined probability. We show that the proper normalization of the mathematical model and the selection of the correct performance measure are of paramount importance in comparative performance analysis of adaptive transmission systems.