Joint Unitary Triangularization for MIMO Networks

TL;DR

This paper introduces a joint unitary triangularization approach for MIMO networks that exploits interference and successive cancellation to improve capacity and distortion performance, enabling more efficient network modulation schemes.

Contribution

It derives conditions for shaping sub-channel gain ratios and applies them to develop capacity-achieving schemes and hybrid digital-analog methods for MIMO networks.

Findings

Practical capacity-achieving scheme using scalar codes and linear processing.

Existence of cases where hybrid digital-analog schemes optimize distortion.

Advantage of basis selection based on multiple links, termed 'network modulation'.

Abstract

This work considers communication networks where individual links can be described as MIMO channels. Unlike orthogonal modulation methods (such as the singular-value decomposition), we allow interference between sub-channels, which can be removed by the receivers via successive cancellation. The degrees of freedom earned by this relaxation are used for obtaining a basis which is simultaneously good for more than one link. Specifically, we derive necessary and sufficient conditions for shaping the ratio vector of sub-channel gains of two broadcast-channel receivers. We then apply this to two scenarios: First, in digital multicasting we present a practical capacity-achieving scheme which only uses scalar codes and linear processing. Then, we consider the joint source-channel problem of transmitting a Gaussian source over a two-user MIMO channel, where we show the existence of non-trivial cases, where the optimal distortion pair (which for high signal-to-noise ratios equals the optimal point-to-point distortions of the individual users) may be achieved by employing a hybrid digital-analog scheme over the induced equivalent channel. These scenarios demonstrate the advantage of choosing a modulation basis based upon multiple links in the network, thus we coin the approach "network modulation".