The Second-Order Coding Rate of the MIMO Quasi-Static Rayleigh Fading Channel

Author

Hoydis, Jakob ; Couillet, Romain ; Piantanida, Pablo

Author_Institution

Bell Labs., Alcatel-Lucent, Nozay, France

Volume

61

Issue

12

fYear

2015

Firstpage

6591

Lastpage

6622

Abstract

The second-order coding rate of the multiple-input multiple-output (MIMO) quasi-static Rayleigh fading channel is studied. We tackle this problem via an information-spectrum approach and statistical bounds based on recent random matrix theory techniques. We derive a central limit theorem (CLT) to analyze the information density in the regime where the block length n and the number of transmit and receive antennas K and N, respectively, grow simultaneously large. This result leads to the characterization of closed-form upper and lower bounds on the optimal average error probability when the coding rate is within O(1/√(nK)) of the asymptotic capacity.

Keywords

MIMO communication; Rayleigh channels; matrix algebra; probability; statistical analysis; CLT; MIMO quasi-static Rayleigh fading channel; asymptotic capacity; central limit theorem; information-spectrum approach; multiple-input multiple-output quasi-static Rayleigh fading channel; optimal average error probability; random matrix theory techniques; second-order coding rate; statistical bounds; Capacity planning; Encoding; Error probability; Fading; MIMO; Manganese; Signal to noise ratio; Finite block-length; MIMO; block-fading channel; error probability; information spectrum; quasi-static fading channel; random matrix theory; second-order coding rate;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2015.2490066

Filename

7296644