New Closed-Form of the Largest Eigenvalue PDF for Max-SNR MIMO System Performances

Jonathan LETESSIER  Baptiste VRIGNEAU  Philippe ROSTAING  Gilles BUREL  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.7   pp.1791-1796
Publication Date: 2008/07/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.7.1791
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Communication Theory and Signals
Wishart matrix,  PDF,  largest eigenvalue,  Rayleigh fading channel,  MIMO,  maximum SNR,  MRT/MRC,  

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Multiple-input multiple-output (MIMO) maximum-SNR (max-SNR) system employs the maximum ratio combiner (MRC) at the receiver side and the maximum ratio transmitter (MRT) at the transmitter side. Its performances highly depend on MIMO channel characteristics, which vary according to both the number of antennas and their distribution between the transmitter and receiver sides. By using the decomposition of the ordered Wishart distribution in the uncorrelated Rayleigh case, we derived a closed-form expression of the largest eigenvalue probability density function (PDF). The final result yields to an expression form of the PDF where polynomials are multiplied by exponentials; it is worth underlining that, though this form had been previously observed for given couples of antennas, to date no formally-written closed-form was available in the literature for an arbitrary couple. Then, this new expression permits one to quickly and easily get the well known largest eigenvalue PDF and use it to determine the binary error probability (BEP) of the max-SNR.