Simple Approximation of Largest Eigenvalue Distribution in MIMO Channels Under Nakagami-Rice Fading

Shen SHA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A    No.9    pp.1862-1870
Publication Date: 2007/09/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.9.1862
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
MIMO,  eigenvalue,  Wishart matrix,  Nakagami-Rice fading,  Nakagami m fading,  maximum ratio combining,  

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This paper presents an approximation method of statistical distribution of the largest eigenvalue of i.i.d. (independent and identically distributed) MIMO (multiple input multiple output) channel correlation matrices under Nakagami-Rice fading environment. The equation is actually derived for MIMO Nakagami m fading channel which is known as a good approximation of Nakagami-Rice fading, hence it well approximates the curves of the largest eigenvalue distribution of noncentral Wishart matrices. In the proposed approximation method, MIMO MRC (maximal ratio combining) system is ascribed to SIMO space diversity theory with the same number of branches, and the statistical distribution becomes a monomial gamma distribution. As a result, the derived marginal density function does not contain any special functions, and has a simple monomial gamma form which is suitable for various calculations of performance indices. Through computer simulations, it is shown that the proposed approximation formula is effective and has a better precision than conventional method.