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New ClosedForm of the Largest Eigenvalue PDF for MaxSNR MIMO System Performances
Jonathan LETESSIER Baptiste VRIGNEAU Philippe ROSTAING Gilles BUREL
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E91A
No.7
pp.17911796 Publication Date: 2008/07/01
Online ISSN: 17451337
DOI: 10.1093/ietfec/e91a.7.1791
Print ISSN: 09168508 Type of Manuscript: PAPER Category: Communication Theory and Signals Keyword: Wishart matrix, PDF, largest eigenvalue, Rayleigh fading channel, MIMO, maximum SNR, MRT/MRC,
Full Text: PDF(295.9KB)>>
Summary:
Multipleinput multipleoutput (MIMO) maximumSNR (maxSNR) 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 closedform 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 formallywritten closedform 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 maxSNR.

