  We consider the multiple-input multiple-output (MIMO) communication channel
impaired by phase noises at both the transmitter and receiver. We focus on the
maximum likelihood (ML) detection problem for uncoded single-carrier
transmission. We derive an approximation of the likelihood function, based on
which we propose an efficient detection algorithm. The proposed algorithm,
named self-interference whitening (SIW), consists in 1) estimating the
self-interference caused by the phase noise perturbation, then 2) whitening the
said interference, and finally 3) detecting the transmitted vector. While the
exact ML solution is computationally intractable, we construct a
simulation-based lower bound on the error probability of ML detection.
Leveraging this lower bound, we perform extensive numerical experiments
demonstrating that SIW is, in most cases of interest, very close to optimal
with moderate phase noise. More importantly and perhaps surprisingly, such
near-ML performance can be achieved by applying only twice the nearest neighbor
detection algorithm. In this sense, our results reveal a striking fact: near-ML
detection of phase noise corrupted MIMO channels can be done as efficiently as
for conventional MIMO channels without phase noise.
