Analytical Mathematical Expression for the Channel Capacity of a Power and Rate Simultaneous Adaptive Cellular DS/FFH-CDMA Systemin a Rayleigh Fading Channel

In this paper, an accurate theoretical analysis for the achievable average channel capacity (in the Shannon sense) per user of a hybrid cellular direct-sequence/fast frequency hopping code-division multiple-access (DS/FFH-CDMA) system operating in a Rayleigh fading environment is presented. The analysis covers the downlink operation and leads to the derivation of an exact mathematical expression between the normalized average channel capacity available to each system’s user, under simultaneous optimal power and rate adaptation and the system’s parameters, as the number of hops per bit, the processing gain applied, the number of users per cell and the received signal-tonoise power ratio over the signal bandwidth. Finally, numerical results are presented to illustrate the proposed mathematical analysis. Keywords—Shannon capacity, adaptive systems, codedivision multiple access, fading channels.