  We consider multiple-input multiple-output (MIMO) transmit beamforming
systems with maximum ratio combining (MRC) receivers. The operating environment
is Rayleigh-fading with both transmit and receive spatial correlation. We
present exact expressions for the probability density function (p.d.f.) of the
output signal-to-noise ratio (SNR), as well as the system outage probability.
The results are based on explicit closed-form expressions which we derive for
the p.d.f. and c.d.f. of the maximum eigenvalue of double-correlated complex
Wishart matrices. For systems with two antennas at either the transmitter or
the receiver, we also derive exact closed-form expressions for the symbol error
rate (SER). The new expressions are used to prove that MIMO-MRC achieves the
maximum available spatial diversity order, and to demonstrate the effect of
spatial correlation. The analysis is validated through comparison with
Monte-Carlo simulations.
