Optimality of beamforming condition for multiple antenna systems with mean feedback

The necessary and sufficient condition for beamforming optimality for multiple-input multiple output (MIMO) systems with mean feedback has been derived and thoroughly investigated in this article. The condition is an inequality that contains parameters of the number of antennas, transmission power, and the singular values of channel mean matrix. When the beamforming optimality condition is satisfied, the Shannon capacity of MIMO system can be achieved by beamforming and hence scalar codes can therefore be used to achieve the maximum capacity. The channel is modeled as the sum of a scattering matrix of i.i.d zero mean, unit variance complex Gaussian random variables, and a mean matrix having its rank r ≥ 1. The beamforming condition inequality performance versus system parameters of signal-to-noise ratio and Ricean factor have thoroughly been investigated by numerical results. Computer simulations show that the beamforming strategy can be adopted on a relatively relaxed beamforming condition without the loss of capacity performance.