CDMA Systems With Correlated Spatial Diversity: A Generalized Resource Pooling Result

This correspondence analyzes the behavior of code-division multiple-access (CDMA) systems with correlated spatial diversity. The users transmit to one or more antenna arrays. The centralized receiver employs a linear multiuser detector. We derive the performance of a large system with random spreading sequences and weak assumptions on the flat-fading channel gains—the fading may be correlated and contain line-of-sight components. We show that, as the number of users and the spreading factor grow large with fixed ratio, the performance of the system is fully characterized by a square matrix with size equal to the number of receiving antennas and multiuser efficiencies are not identical for all users. Our general result includes the analysis of CDMA systems with spatial diversity discussed by Hanly and Tse ('01) for independent channel gains in case of both micro-diversity and macro-diversity and provides a rigorous proof for the macro-diversity case missing in their work. We also show that to any scenario with correlated Rayleigh fading, there exists a macro-diversity scenario with independent Rayleigh fading which is characterized by the same signal-to-interference-and-noise ratio (SINR). Furthermore, sufficient conditions are given which force the multiuser efficiencies of all users to become identical also in case of statistically dependent channel gains.