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This paper addresses one of the classical problems in random matrix theory--finding the distribution of the maximum eigenvalue of the correlated Wishartunitary ensemble. In particular, we derive a new exact expression for thecumulative distribution function (c.d.f.) of the maximum eigenvalue of a$2\times 2$ correlated non-central Wishart matrix with rank-$1$ mean. By usingthis new result, we derive an exact analytical expression for the outageprobability of $2\times 2$ multiple-input multiple-outputmaximum-ratio-combining (MIMO-MRC) in Rician fading with transmit correlationand a strong line-of-sight (LoS) component (rank-$1$ channel mean). We alsoshow that the outage performance is affected by the relative alignment of theeigen-spaces of the mean and correlation matrices. In general, when the LoSpath aligns with the least eigenvector of the correlation matrix, in the {\ithigh} transmit signal-to-noise ratio (SNR) regime, the outage graduallyimproves with the increasing correlation. Moreover, we show that as $K$ (Ricianfactor) grows large, the outage event can be approximately characterized by thec.d.f. of a certain Gaussian random variable.

Outage Analysis of $2\times2 $ MIMO-MRC in Correlated Rician Fading