On the role of the input power constraint in the beamforming optimality range in TIMO channels

In this paper, the effect of the input power constraint on the beamforming optimality range in Gaussian two-input multiple-output (TIMO) channels is explored. The obtained results, using standard Lagrangian formulation, determine explicitly the range of the input SNR for which rank-1 signaling (beamforming) is optimal in TIMO channels for both the common power constraint and the individual power constraint cases. Moreover, the obtained results are extended to random TIMO channels, with channel state information at the receiver only, using the Jensen's upper bound on the mutual information.