On the optimum processing gain for a hybrid DS/FFH‐CDMA cellular system over Rayleigh fading channels

The optimization between the processing gain and the theoretically achievable average channel capacity per user (in the Shannon sense) of a constant total system's allocated bandwidth hybrid direct sequence/fast frequency hopping code‐division multiple‐access (DS/FFH‐CDMA) cellular system, when operating in a Rayleigh fading environment, is presented. Then, the spectral efficiency, expressed in (bits/s/Hz), is estimated in terms of the achievable average channel capacity per user, during the operation over a broadcast cellular time‐varying link, and leads to a simple theoretical novel‐closed‐form expression for the optimal processing gain value based on the maximization of the achieved spectral efficiency. The final expression derived can be useful for the practical design of a DS/FFH‐CDMA cellular system and for an initial quantitative analysis since it relates to the optimal processing gain applied and all system's parameters. Finally, numerical results are presented to illustrate and prove the validity of the presented analysis. Copyright © 2011 John Wiley & Sons, Ltd.