2018/11/16 by Prathapasinghe Dharmawansa, Dharmawansa, Prathapasinghe, Kumara Kahatapitiya +5
Computer Science · Engineering · Mathematics · #15B52 #62H10 #Advanced Wireless Communication Technologies #FOS: Computer and information sciences #FOS: Electrical engineering #Information Theory (cs.IT) #Random Matrices and Applications #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #cs.IT #eess.SP #electronic engineering #information engineering #math.IT #msc:15B52 #msc:62H10
paper · pdf · doi:10.48550/arxiv.1811.06712
7 pages
arxiv created 2018/11/16 · openalex publication_date 2018/11/16 · arxiv updated 2018/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper addresses one of the classical problems in random matrix theory-- finding the distribution of the maximum eigenvalue 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 eigenvalue of a 2× 2 correlated non-central Wishart matrix with rank-1 mean. By using this new result, we derive an exact analytical expression for the 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-1 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 \it 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.