Information Theory of Underspread WSSUS Channels

In this chapter, we are interested in the ultimate limit on the rate of reliable communication over Rayleigh-fading channels that satisfy the wide-sense stationary (WSS) and uncorrelated scattering (US) assumptions and are underspread [Bel63, Ken69]. Therefore, the natural setting is an information-theoretic one, and the performance metric is channel capacity [CT91, Gal68]. The family of Rayleigh-fading underspread WSSUS channels (reviewed in Chapter 1) constitutes a good model for real-world wireless channels: their stochastic properties, like amplitude and phase distributions match channel measurement results [SB07,Sch09]. The Rayleigh-fading and the WSSUS assumptions imply that the stochastic properties of the channel are fully described by a two-dimensional power spectral density (PSD) function, often referred to as scattering function [Bel63]. The underspread assumption implies that the scattering function is highly concentrated in the delay-Doppler plane. To analyze wireless channels with information-theoretic tools, a system model, not just a channel model, needs to be specified. A system model is more comprehensive than a channel model because it defines, among other parameters, the transmit-power constraints and the channel knowledge available at the transmitter and the receiver. The choice of a