The dirty MIMO multiple-access channel

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, which was shown to be optimal in the limit of high signal-to-noise ratios (SNRs), where the sum-capacity is dictated by the minimal ('bottleneck') channel gain. In the present work, 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, which 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 SNRs, under an equal rank assumption.