Power control and multiuser diversity in multiple access channels with two time-scale fading

We derive the optimal power control strategy to maximize the sum rate of a multiple access channel with two time-scale fading, where transmitters have access to each of the other users´ ´slow´ fading information and the statistics of the ´fast´ fading, but no knowledge of the instantaneous fast fading states. Assuming identical fast fading distributions for all users, it is found that the optimal strategy is to let at most one user transmit, with the user transmitting the one with the ´best´ slow fading condition. An example with users undergoing lognormal shadowing and Rayleigh fast fading is considered, and capacity comparisons are made. Simple sub-optimal power control schemes which provide close to optimal performance in certain favorable channel conditions are also proposed and analysed.