Analysis and Approximation of Statistical Distribution of Eigenvalues in i.i.d. MIMO Channels under Rayleigh Fading

Shen SHA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A    No.10    pp.2808-2817
Publication Date: 2008/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.10.2808
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Communication Theory
MIMO,  eigenvalue,  Wishart matrix,  gamma approximation,  space diversity,  maximal ratio combining,  

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In multiple input multiple output (MIMO) communication systems, eigenvalues of channel correlation matrices play an essential role for the performance analysis, and particularly the investigation about their behavior under time-variant environment ruled by a certain statistics is an important problem. This paper first gives the theoretical expressions for the marginal distributions of all the ordered eigenvalues of MIMO correlation matrices under i.i.d. (independent and identically distributed) Rayleigh fading environment. Then, an approximation method of those marginal distributions is presented: We show that the theory of SIMO space diversity using maximal ratio combining (MRC) is applicable to the approximation of statistical distributions of all eigenvalues in MIMO systems with the same number of diversity branches. The derived approximation has a monomial form suitable for the calculation of various performance measures utilized in MIMO systems. Through computer simulations, the effectiveness of the proposed method is demonstrated.