The Constrained Capacity of Single and Multiuser Channels with Unknown Fading

This work presents a general technique to compute tight upper and lower bounds on the constrained capacity of both the point to point and multiuser Rayleigh flat fading channel with no channel state information (CSI) at the transmitter or the receiver. The paper begins by proving that the optimal input distribution for the point-to-point fading channel must have uniform i.i.d phase and therefore, for constant envelope transmitters, the only design parameter is the density of the driving constellation. The paper then presents plots of the (essentially coincident) upper and lower bounds on the constrained capacity for BPSK,QPSK and 8-PSK inputs as a function of SNR for the point to point channel. These allow the designer to judge the benefits of different channel alphabet choices and to compare the efficiency of the final coding system with the capacity of this channel and modulation alphabet combination. The paper then goes on to extend these methods to multiuser fading channels.