Capacity Bounds and Low Complexity Transceiver Design for Double-Scattering MIMO Multiple Access Channels

We investigate the sum capacity and present low complexity transceiver designs for the multiple-input multiple-output (MIMO) multiple access channel (MAC) under a general class of fading, known as double-scattering. We assume that the receiver has perfect channel state information (CSI), while each transmitter only has access to its own statistical CSI. We show that the optimum transmit directions for each user coincide with the eigenvectors of the user´s own transmit spatial correlation matrix. We also derive new closed-form upper bounds on the sum capacity of the MIMO MAC under double-scattering, which are subsequently employed to obtain low complexity power allocation policies which are easy to compute, and require each user to know only their own channel statistics. Then, we establish beamforming optimality conditions for all users. Finally, we consider the case as the number of users becomes large, in which case we demonstrate that beamforming is asymptotically optimal.