On the Capacity of Large-MIMO Block-Fading Channels

TL;DR

This paper determines the capacity of large-MIMO block-fading channels in noncoherent settings, showing that traditional modulation schemes are suboptimal at high SNR and introducing a new capacity-achieving input distribution.

Contribution

It proves that unitary space-time modulation is not optimal for large-MIMO channels at high SNR and introduces Beta-variate space-time modulation as the optimal input, settling a long-standing conjecture.

Findings

BSTM outperforms USTM with up to 13% higher rate at practical SNRs.

USTM is not capacity-achieving when antennas exceed channel coherence time.

The paper confirms a conjecture by Zheng & Tse (2002).

Abstract

We characterize the capacity of Rayleigh block-fading multiple-input multiple-output (MIMO) channels in the noncoherent setting where transmitter and receiver have no a priori knowledge of the realizations of the fading channel. We prove that unitary space-time modulation (USTM) is not capacity-achieving in the high signal-to-noise ratio (SNR) regime when the total number of antennas exceeds the coherence time of the fading channel (expressed in multiples of the symbol duration), a situation that is relevant for MIMO systems with large antenna arrays (large-MIMO systems). This result settles a conjecture by Zheng & Tse (2002) in the affirmative. The capacity-achieving input signal, which we refer to as Beta-variate space-time modulation (BSTM), turns out to be the product of a unitary isotropically distributed random matrix, and a diagonal matrix whose nonzero entries are distributed as the square-root of the eigenvalues of a Beta-distributed random matrix of appropriate size. Numerical results illustrate that using BSTM instead of USTM in large-MIMO systems yields a rate gain as large as 13% for SNR values of practical interest.