Transmitter Optimization and Optimality of Beamforming for MIMO Systems in the Presence of Double Scattering

In this paper, we consider a general family of MIMO channels known as double scattering channels, which encompass a variety of propagation environments from independent and identically distributed Rayleigh to degenerate Keyhole or pinhole cases by embracing both rank-deficiency and spatial correlation effects. We investigate the optimal transmit strategy of a single-user MIMO systems with channel statistical information feedback in the presence of double scattering. We show that transmitting in the direction of the eigenvectors of the transmit correlation matrix is the optimal transmission strategy under the criteria of maximizing the ergodic capacity. In addition to this, the power allocation problem is studied and a necessary and sufficient condition for optimality of beamforming is derived.