On the Exact Outage Probability of 2×2 MIMO-MRC in Correlated Rician Fading

This paper addresses a classical problem in random matrix theory-finding the distribution of the maximum eigen-value of the correlated Wishart unitary ensemble. In particular, we derive a new exact expression for the cumulative distribution function (c.d. f.) of the maximum eigen-value of a 2 × 2 correlated non-central Wishart matrix with rank-l mean. By using this new result, we derive the exact outage probability of 2 × 2 multiple-input multiple-output maximum-ratio-combining (MIMO-MRC) in Rician fading with transmit correlation and a strong line-of-sight (LoS) component (rank-l channel mean). We also show that the outage performance is affected by the relative alignment of the eigen-spaces of the mean and correlation matrices. In general, when the LoS path aligns with the least eigenvector of the correlation matrix, in the high transmit signal-to-noise ratio (SNR) regime, the outage gradually improves with the increasing correlation. Moreover, we show that as K (Rician factor) grows large, the outage event can be approximately characterized by the c.d.f. of a certain Gaussian random variable.