The Dirty MIMO Multiple-Access Channel

TL;DR

This paper extends the scalar dirty MAC to MIMO systems, showing that a specific matrix decomposition yields optimal high-SNR rates and applying this to physical-layer network coding in MIMO relay channels.

Contribution

It introduces a MIMO dirty MAC model, analyzes optimal matrix decompositions for structured coding, and applies findings to MIMO relay network coding.

Findings

Decomposition with equal diagonal elements is optimal at high SNR.

Structured coding outperforms i.i.d. codes in high interference regimes.

Extension of decomposition approach to multiple transmitters.

Abstract

In the scalar dirty multiple-access channel, in addition to Gaussian noise, two additive interference signals are present, each known non-causally to a single transmitter. It was shown by Philosof et al. that for strong interferences, an i.i.d. ensemble of codes does not achieve the capacity region. Rather, a structured-codes approach was presented, that was shown to be optimal in the limit of high signal-to-noise ratios, where the sum-capacity is dictated by the minimal ("bottleneck") channel gain. In this paper, we consider the multiple-input multiple-output (MIMO) variant of this setting. In order to incorporate structured codes in this case, one can utilize matrix decompositions that transform the channel into effective parallel scalar dirty multiple-access channels. This approach however suffers from a "bottleneck" effect for each effective scalar channel and therefore the achievable rates strongly depend on the chosen decomposition. It is shown that a recently proposed decomposition, where the diagonals of the effective channel matrices are equal up to a scaling factor, is optimal at high signal-to-noise ratios, under an equal rank assumption. This approach is then extended to any number of transmitters. Finally, an application to physical-layer network coding for the MIMO two-way relay channel is presented.