Beamforming Capacity Optimization for MISO Systems with Both Mean and Covariance Feedback

The beamforming capacity optimization problem in MISO systems, when the transmitter has both mean and covariance feedback of the channel, has been tackled only with the SNR maximization approach, which is known to give a sub-optimal solution. Numerical solutions of the full rank input covariance matrix, presented in the literature, are capable of tracking the beamforming vector only if it is the optimal capacity achieving solution. In this paper, we solve the beamforming capacity optimization problem by following an analytical approach that projects the beamforming vector on an orthonormal basis defined by the eigenvectors of the channel covariance matrix. The proposed formulation reduces the complexity of calculating the solution and provides intuition into the problem itself. In particular, we express the necessary conditions for beamforming capacity maximization as a system of two equations, which can be solved numerically very efficiently using the secant method. Surprisingly, our indicative numerical results for the 2 x 1 and 10 x 1 MISO systems, showed that for some cases the performance gain through beamforming capacity optimization compared to the SNR maximization approach can reach 0.4 bps/Hz. This means that the SNR maximization solution deviates considerably from the optimal beamforming vector. Finally, the optimality of the SNR maximization solution is also examined.