Constrained capacity and power allocation for MIMO Rayleigh fading channels

In this paper, we study the capacity of the multiple-input multiple-output (MIMO) fading channels with phase-shift keying (PSK) constellations. Assuming perfect channel state information (CSI) at the receiver, we derive an expression for the input-constrained capacity, and present an approximation method to estimate the constrained capacity. We also derive the optimal transmitter power allocation strategy that achieve this capacity gain under perfect CSI feedback. The transmitter can adapt its power to the current CSI to maximize the constrained capacity. Numerical results show that the proposed method can accurately estimate the capacity with less computation and the spatial power allocation becomes more important at low signal-to-noise ratio (SNR).