Asymptotic statistics of mutual information for doubly correlated MIMO channels

In this paper, we derive the asymptotic statistics of mutual information for multiple-input multiple-output (MIMO) Rayleigh-fading channels in the presence of spatial fading correlation at both the transmitter and the receiver. We first introduce a class of asymptotic linear spectral statistics, called correlants, for a structured correlation matrix. The mean and variance of MIMO mutual information are then expressed in terms of the correlants of spatial correlation matrices in the asymptotic regime where the number of transmit and receive antennas tends to infinity. In particular, using Szego's theorem on the asymptotic eigenvalue distribution of Toeplitz matrices, we give examples for special classes of correlation matrices with Toeplitz structure-exponential (or Kac-Murdock-Szego), tridiagonal, and constant (or intraclass ) correlation matrices.

[1]  J. Pierce,et al.  Multiple Diversity with Nonindependent Fading , 1960, Proceedings of the IRE.

[2]  V. L. Girko,et al.  Thirty years of the Central Resolvent Law and three laws on the 1/n expansion for resolvent of random matrices , 2003 .

[3]  Björn E. Ottersten,et al.  Asymptotic eigenvalue distributions and capacity for MIMO channels under correlated fading , 2004, IEEE Transactions on Wireless Communications.

[4]  M. J. Gans,et al.  On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas , 1998, Wirel. Pers. Commun..

[5]  Hyundong Shin,et al.  Capacity of multiple-antenna fading channels: spatial fading correlation, double scattering, and keyhole , 2003, IEEE Trans. Inf. Theory.

[6]  Hyundong Shin,et al.  On the capacity of doubly correlated MIMO channels , 2005, IEEE Transactions on Wireless Communications.

[7]  Z. Bai.  METHODOLOGIES IN SPECTRAL ANALYSIS OF LARGE DIMENSIONAL RANDOM MATRICES , A REVIEW , 1999 .

[8]  S. Lang.  Complex Analysis , 1977 .

[9]  V. Marčenko,et al.  DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES , 1967 .

[10]  Moe Z. Win,et al.  On the capacity of spatially correlated MIMO Rayleigh-fading channels , 2003, IEEE Trans. Inf. Theory.

[11]  신현동.  Capacity and error exponents for multiple-input multiple-output wireless channels , 2004 .

[12]  Chen-Nee Chuah,et al.  Capacity scaling in MIMO Wireless systems under correlated fading , 2002, IEEE Trans. Inf. Theory.

[13]  Jack H. Winters,et al.  On the Capacity of Radio Communication Systems with Diversity in a Rayleigh Fading Environment , 1987, IEEE J. Sel. Areas Commun..

[14]  Helmut Bölcskei,et al.  Characterizing the statistical properties of mutual information in MIMO channels: insights into diversity-multiplexing tradeoff , 2002, Conference Record of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers, 2002..

[15]  U. Grenander,et al.  Toeplitz Forms And Their Applications , 1958 .

[16]  Emre Telatar,et al.  Capacity of Multi-antenna Gaussian Channels , 1999, Eur. Trans. Telecommun..

[17]  A. James.  Distributions of Matrix Variates and Latent Roots Derived from Normal Samples , 1964 .

[18]  Thomas L. Marzetta,et al.  Multiple-antenna channel hardening and its implications for rate feedback and scheduling , 2004, IEEE Transactions on Information Theory.

[19]  V. Girko.  A Refinement of the Central Limit Theorem for Random Determinants , 1998 .

[20]  Robert M. Gray,et al.  Toeplitz and Circulant Matrices: A Review , 2005, Found. Trends Commun. Inf. Theory.

[21]  Hyundong Shin,et al.  MIMO Diversity in the Presence of Double Scattering , 2005, IEEE Transactions on Information Theory.

[22]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[23]  Z. Bai,et al.  CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data , 2017, Statistical Papers.

[24]  Robert M. Gray,et al.  On the asymptotic eigenvalue distribution of Toeplitz matrices , 1972, IEEE Trans. Inf. Theory.

[25]  Aris L. Moustakas,et al.  MIMO capacity through correlated channels in the presence of correlated interferers and noise: a (not so) large N analysis , 2003, IEEE Trans. Inf. Theory.