TY - JOUR
T1 - Asymptotic analysis of Rayleigh product channels
T2 - A free probability approach
AU - Zheng, Zhong
AU - Wei, Lu
AU - Speicher, Roland
AU - Müller, Ralf R.
AU - Hämäläinen, Jyri
AU - Corander, Jukka
PY - 2017/3/1
Y1 - 2017/3/1
N2 - 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.
AB - 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.
KW - Central limit theorem
KW - Finite-SNR diversity-multiplexing tradeoff
KW - Free probability theory
KW - MIMO
KW - Mutual information
KW - Rayleigh product channels
UR - http://www.scopus.com/inward/record.url?scp=85013378481&partnerID=8YFLogxK
U2 - 10.1109/TIT.2016.2646699
DO - 10.1109/TIT.2016.2646699
M3 - Article
AN - SCOPUS:85013378481
SN - 0018-9448
VL - 63
SP - 1731
EP - 1745
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 3
M1 - 7802604
ER -