  In this paper, the problem of optimal maximum likelihood detection in a
single user single-input multiple-output (SIMO) channel with phase noise at the
receiver is considered. The optimal detection rules under training are derived
for two operation modes, namely when the phase increments are fully correlated
among the $M$ receiver antennas (synchronous operation) and when they are
independent (non-synchronous operation). The phase noise increments are
parameterized by a very general distribution, which includes the Wiener phase
noise model as a special case. It is proven that phase noise creates a
symbol-error-rate (SER) floor for both operation modes. In the synchronous
operation this error floor is independent of $M$, while it goes to zero
exponentially with $M$ in the non-synchronous operation.
