Optimum processing gain for a hybrid direct sequence/slow frequency hopping code division multiple access cellular system over Rayleigh fading channels: the direct sequence/slow frequency hopping code division multiple access case

Abstract

In this paper, the optimum value of the processing gain of a hybrid direct sequence/slow frequency hopping code division multiple access cellular system, when operating in a Rayleigh fading environment, is examined. The optimization is based on the maximization of the average spectral efficiency achieved, expressed in bits per second per Hertz, which is estimated in terms of the achievable average channel capacity (in the Shannon–Hartley theorem sense) per user during the operation over a broadcast cellular time-varying link. The analysis leads to a simple theoretical novel closed-form expression for the optimal processing gain that is related with the system's parameters but becomes independent of hopping frequencies assigned to each system's cell. Finally, the expression derived can be useful for the practical design of a direct sequence/slow frequency hopping code division multiple access cellular system and for an initial quantitative analysis. Numerical results are presented to illustrate the presented analysis. Copyright © 2011 John Wiley & Sons, Ltd.