On an Achievable Rate of Large Rayleigh Block-Fading MIMO Channels with No CSI

TL;DR

This paper analyzes the achievable rates of large MIMO Rayleigh block-fading channels without CSI, showing that minimal pilot information suffices and that successive decoding can outperform traditional methods, especially at low-to-moderate SNRs.

Contribution

It provides new analytical formulas for achievable rates using the replica method, improving existing capacity bounds and highlighting the effectiveness of SD schemes without CSI.

Findings

Negligible pilot information maximizes achievable rates in large systems.

The derived bounds outperform previous lower bounds on capacity.

SD schemes offer significant gains in low-to-moderate SNR regimes.

Abstract

Training-based transmission over Rayleigh block-fading multiple-input multiple-output (MIMO) channels is investigated. As a training method a combination of a pilot-assisted scheme and a biased signaling scheme is considered. The achievable rates of successive decoding (SD) receivers based on the linear minimum mean-squared error (LMMSE) channel estimation are analyzed in the large-system limit, by using the replica method under the assumption of replica symmetry. It is shown that negligible pilot information is best in terms of the achievable rates of the SD receivers in the large-system limit. The obtained analytical formulas of the achievable rates can improve the existing lower bound on the capacity of the MIMO channel with no channel state information (CSI), derived by Hassibi and Hochwald, for all signal-to-noise ratios (SNRs). The comparison between the obtained bound and a high SNR approximation of the channel capacity, derived by Zheng and Tse, implies that the high SNR approximation is unreliable unless quite high SNR is considered. Energy efficiency in the low SNR regime is also investigated in terms of the power per information bit required for reliable communication. The required minimum power is shown to be achieved at a positive rate for the SD receiver with no CSI, whereas it is achieved in the zero-rate limit for the case of perfect CSI available at the receiver. Moreover, numerical simulations imply that the presented large-system analysis can provide a good approximation for not so large systems. The results in this paper imply that SD schemes can provide a significant performance gain in the low-to-moderate SNR regimes, compared to conventional receivers based on one-shot channel estimation.