Transmit power allocation for Gaussian multiple access channels with diversity

Hanly and Tse (see Proc. 33rd Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, 1995), and also Cheng (see Proc. of IEEE Information Theory Workshop (ITW), p.36, Haifa, Israel, 1996) have generalized the results on the Gaussian multiple access channel to the case where flat fading occurs which can be tracked by both the receiver and transmitter. They distinguish two cases which they term Shannon and delay-limited capacity of that channel. With the Shannon capacity they refer to the case where the capacity region expected over the fading statistics is maximized for the constrained averaged sum power of all users. The practically more important so-called delay-limited capacity results from minimizing the sum energy of all users for fixed rates. In the article we focus on the second case. Instead of assuming a single receiver only we study the case of multiple receivers since in implemented systems diversity reception is used often. This can be caused e.g. by multiple receive antennas (receiver antenna diversity) for signal separation, or by multiple cell-site processing in cellular systems. Surprisingly, we show that some results which are valid for the case without diversity do not generalize to the diversity model