Unified spatial diversity combining and power allocation for CDMA systems in multiple time-scale fading channels

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 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 "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.