Capacity and reliability function per fourth moment cost for WSSUSfading channels

摘要

This paper addresses the capacity of wide sense stationaryuncorrelated scattering (WSSUS) fading channels. Associated with a giveninput signal we define a quantity called the “fourthegy” ofthe signal, relative to a given WUSSUS channel. The name is inspired bythe fact that the measure is fourth order in the input signal amplitude.The fourthegy depends on the signal through its ambiguity function, andon the channel through a simple channel response function. The maximumpossible mutual information for the channel per unit fourthegy is found.Roughly speaking, the fourthegy is a sum over time and frequency bins ofthe local signal energy squared. The fourthegy-to-energy ratio ofdirect-sequence spread spectrum signals is inversely proportional to thebandwidth. Therefore, for such signals, the capacity per unit energy (orthe capacity per unit time for fixed power) tends to zero as thebandwidth increases. This does not happen to signals that are morebursty in time-frequency space, such as frequency-hopped signals orM-ary frequency shift keyed signals. A similar result was found byGallager and Medard (see Proc. International Symposium on InformationTheory'97 (ISIT), Ulm, Germany, p.471, 1997) for a less conventionalchannel model. Numerical evaluation of the bound shows it to beinformative only for rather large bandwidths