Transmitter Optimization and Beamforming Optimality Conditions for Double-Scattering MIMO Channels

We investigate the capacity of a general class of MIMO channels, known as double-scattering channels. Our results assume perfect channel state information (CSI) at the receiver and statistical CSI at the transmitter. We first derive the optimal capacity-achieving signaling directions, and show that they correspond to the eigenvectors of the transmit spatial correlation matrix. We then derive new simple closed-form power allocation policies which are shown to yield negligible capacity loss compared with the optimal power allocation policy, without requiring complicated numerical optimization methods to compute. Finally we derive a necessary and sufficient condition for which a beamforming approach (i.e. rank-1 transmission) achieves the ergodic capacity.