Closed-form expressions for the outage and ergodic Shannon capacity of MIMO MRC systems

Transmit-beamforming (TB) over multiple-input multiple-output (MIMO) fading channels steers the transmit power in the receiver´s direction, so as to maximize the output signal-to-noise ratio (SNR) after maximal ratio combining (MRC) at the receiver. This letter proposes a simple algorithm that allows evaluating an exact and tractable expression for the probability density function of the SNR at the output of the TB receiver, subject to Rayleigh fading. The latter enables the derivation of closed-form expressions for the outage and ergodic capacity of MIMO MRC systems under Rayleigh fading, thereby avoiding the need for time-consuming numerical integrations or Monte Carlo simulations.