Unified Spatial Diversity Combining and Power Allocation for CDMA Systems in Multiple Time-Scale Fading Channels ∗ Junshan Zhang, † Edwin K. P. Chong ‡ , Ioannis Kontoyiannis § January 29, 2001 Abstract In a mobile wireless system, fading effects can be classified into large-scale (long-term) effects and small-scale (short-term) effects. We use transmission power control to compensate for large-scale fading and exploit receiver antenna (space) diversity to combat small-scale fading. We show that the interferences across the antennas are jointly Gaussian in a large system, and then characterize the signal-to-interference ratio (SIR) for both independent and correlated (across the antennas) small-scale fading cases. Our results show that when each user’s small- scale fading effects are independent across the antennas, there is a clear separation between the gains of transmission power control and diversity combining, and the two gains are additive (in decibels). When each user’s small-scale fading effects are correlated across the antennas, we observe that in general the gains of transmission power control and diversity combining are coupled. However, when the noise level diminishes to zero, using maximum ratio combining (MRC) “decouples” the gains and achieves the same diversity gain as in the independent case. We then characterize the Pareto-optimal (minimum) transmission power allocation for the cases of perfect and noisy knowledge of the desired user’s large-scale fading effects. We find that using antenna diversity leads to significant gains for the transmission power. Index Terms: CDMA, power control, space diversity, maximum ratio combining, selection combining, large-scale fading, small-scale fading, MMSE. 1 Introduction In a mobile radio communication system, signal fading may severely degrade the system perfor- mance, and is a dominant source of impairment. Fading arises from randomly-delayed scattering, reflecting, and diffracting of electromagnetic waves in a random medium. According to their time scales, fading effects can be classified into two categories (as has been verified experimentally [14, ∗ J. Zhang and E. Chong were supported in part by the National Science Foundation through grant ECS-9501652. † Junshan Zhang is with the Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287- 7206 (junshan.zhang@asu.edu). ‡ Edwin K. P. Chong is with the School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907 (echong@ecn.purdue.edu). § Ioannis Kontoyiannis is with the Department of Statistics, Purdue University, West Lafayette, IN 47907 (yian- nis@stat.purdue.edu). 1