Asymptotic Analysis of Rayleigh Product Channels : A Free Probability Approach

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Zheng , Z , Wei , L , Speicher , R , Muller , R R , Hämäläinen , J & Corander , J 2017 , ' Asymptotic Analysis of Rayleigh Product Channels : A Free Probability Approach ' , IEEE Transactions on Information Theory , vol. 63 , no. 3 , pp. 1731-1745 . https://doi.org/10.1109/TIT.2016.2646699

Title: Asymptotic Analysis of Rayleigh Product Channels : A Free Probability Approach
Author: Zheng, Zhong; Wei, Lu; Speicher, Roland; Muller, Ralf R.; Hämäläinen, Jyri; Corander, Jukka
Other contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics


Date: 2017-03
Language: eng
Number of pages: 15
Belongs to series: IEEE Transactions on Information Theory
ISSN: 0018-9448
DOI: https://doi.org/10.1109/TIT.2016.2646699
URI: http://hdl.handle.net/10138/307118
Abstract: The Rayleigh product channel model is useful in capturing the performance degradation due to rank deficiency of MIMO channels. In this paper, such a performance degradation is investigated via the distribution of mutual information assuming the block fading channels and the uniform power transmission scheme. Using techniques of free probability theory, the asymptotic variance of mutual information is derived when the dimensions of the channel matrices approach infinity. In this asymptotic regime, the mutual information is rigorously proven to be Gaussian distributed. Using the obtained results, a fundamental tradeoff between multiplexing gain and diversity gain of Rayleigh product channels under the uniform power transmission can be characterized by the closed-form expression at any finite signal-to-noise ratio. Numerical results are provided to compare the outage performance between the Rayleigh product channels and the conventional Rayleigh MIMO channels.
Subject: Central limit theorem
finite-SNR diversity-multiplexing tradeoff
free probability theory
MIMO
mutual information
Rayleigh product channels
DIVERSITY-MULTIPLEXING TRADEOFF
DIMENSIONAL RANDOM MATRICES
SAMPLE COVARIANCE MATRICES
SCATTERING MIMO CHANNELS
LARGE N ANALYSIS
FADING CHANNELS
OUTAGE CAPACITY
CORRELATED RAYLEIGH
2ND-ORDER FREENESS
INFORMATION
113 Computer and information sciences
112 Statistics and probability
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