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

Jonathan Letessier Baptiste Vrigneau Phillipe Rostaing 1 Gilles Burel 1
1 Lab-STICC_UBO_CACS_COM
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance, UBO - Université de Brest
Abstract : Multiple-input multiple-output (MIMO) maxi-mum-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.
Keywords : Wishart matrix PDF largest eigenvalue Rayleigh fading channel MIMO maximum SNR MRT/MRC
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Journal articles
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https://hal.univ-brest.fr/hal-00395151
Contributor : Stéphane Azou <>
Submitted on : Monday, June 15, 2009 - 10:25:08 AM
Last modification on : Thursday, December 19, 2019 - 1:12:58 AM

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  • HAL Id : hal-00395151, version 1

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UNIV-BREST | CNRS | INSTITUT-TELECOM | LAB-STICC_UBO | LAB-STICC | ENIB | LAB-STICC_ENIB | IBNM

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Jonathan Letessier, Baptiste Vrigneau, Phillipe Rostaing, Gilles Burel. New Closed-Form of the Largest Eigenvalue PDF for Max-SNR MIMO System Performances. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Institute of Electronics, Information and Communication Engineers, 2008, E91-A (7), pp.1791-1796. ⟨hal-00395151⟩

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