MIMO Broadcast Channels with Block Diagonalization and Finite Rate Feedback

TL;DR

This paper analyzes the impact of limited feedback on block diagonalization in MIMO broadcast channels, showing that linear scaling of feedback bits with SNR maintains near-capacity performance, and compares vector and scalar quantization schemes.

Contribution

It quantifies throughput loss due to finite feedback in block diagonalization and demonstrates that linear feedback scaling with SNR preserves performance, including a simple scalar quantization scheme.

Findings

Feedback bits must scale linearly with SNR to prevent interference.

Scalar quantization achieves similar scaling as vector quantization.

Limited feedback causes quantifiable throughput loss that can be mitigated by increased feedback.

Abstract

Block diagonalization is a linear precoding technique for the multiple antenna broadcast (downlink) channel that involves transmission of multiple data streams to each receiver such that no multi-user interference is experienced at any of the receivers. This low-complexity scheme operates only a few dB away from capacity but does require very accurate channel knowledge at the transmitter, which can be very difficult to obtain in fading scenarios. We consider a limited feedback system where each receiver knows its channel perfectly, but the transmitter is only provided with a finite number of channel feedback bits from each receiver. Using a random vector quantization argument, we quantify the throughput loss due to imperfect channel knowledge as a function of the feedback level. The quality of channel knowledge must improve proportional to the SNR in order to prevent interference-limitations, and we show that scaling the number of feedback bits linearly with the system SNR is sufficient to maintain a bounded rate loss. Finally, we investigate a simple scalar quantization scheme that is seen to achieve the same scaling behavior as vector quantization.