  We address quantum $M$-ary phase-shift keyed (PSK) communication channels in
the presence of phase diffusion, and analyze the use of probabilistic noiseless
linear amplifiers (NLA) to enhance performance of coherent signals. We consider
both static and dynamical phase diffusion and assess the performances of the
channel for ideal and realistic phase receivers. Our results show that NLA
employed at the stage of signal preparations is a useful resource, especially
in the regime of weak signals. We also discuss the interplay between the use of
NLA, and the memory effects occurring with dynamical noise, in determining the
capacity of the channel.
