Approaching the Ergodic Capacity of the MIMO Channel with Lattice Codes

Abstract

Many aspects of lattice coding and decoding under time-varying multiple-antenna systems remain unexplored. This paper studies the achievable rates using lattice codes for the multiple-input- multiple-output (MIMO) point-to-point channel with ergodic fading and channel state information at the receiver. The proposed lattice coding scheme involves the use of decision regions that are universal for almost all realizations of a given fading distribution and hence providing a significant computational advantage over channel- matching decision regions. Under Rayleigh fading, the rates achieved are within a constant gap to the ergodic capacity. The gap is also shown to diminish as the number of receive antennas increases, implying the asymptotic optimality of lattice codes even at finite signal-to-noise ratio (SNR).