On the Beamforming Optimality Range in TIMO Channels with Common and Individual Input Power Constraints

In this letter, the effect of the input power constraint on the beamforming optimality range in Gaussian two-input multiple-output (TIMO) channels is investigated. The obtained expressions, using standard Lagrangian formulation, determine explicitly the range of the input signal-to-noise ratio (SNR) for which beamforming (rank-1 signaling) is optimal for 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.