To Code or Not to Code Across Time: Space-Time Coding with Feedback

TL;DR

This paper investigates the impact of limited feedback on space-time coding in multi-antenna wireless systems, showing that simple beamforming is optimal at low feedback levels and becomes optimal for mutual information as feedback increases.

Contribution

It demonstrates the transition from beamforming to full space-time coding as feedback bits increase, providing insights for system design with limited feedback.

Findings

Beamforming maximizes average received SNR with few feedback bits.

Increasing feedback shifts optimality towards maximizing mutual information.

Low-complexity beamforming is effective both practically and information-theoretically.

Abstract

Space-time codes leverage the availability of multiple antennas to enhance the reliability of communication over wireless channels. While space-time codes have initially been designed with a focus on open-loop systems, recent technological advances have enabled the possibility of low-rate feedback from the receiver to the transmitter. The focus of this paper is on the implications of this feedback in a single-user multi-antenna system with a general model for spatial correlation. We assume a limited feedback model, that is, a coherent receiver and statistics along with B bits of quantized channel information at the transmitter. We study space-time coding with a family of linear dispersion (LD) codes that meet an additional orthogonality constraint so as to ensure low-complexity decoding. Our results show that, when the number of bits of feedback (B) is small, a space-time coding scheme that is equivalent to beamforming and does not code across time is optimal in a weak sense in that it maximizes the average received SNR. As B increases, this weak optimality transitions to optimality in a strong sense which is characterized by the maximization of the average mutual information. Thus, from a system designer's perspective, our work suggests that beamforming may not only be attractive from a low-complexity viewpoint, but also from an information-theoretic viewpoint.