Coding for the discretely phase ambiguous additive white Gaussian channel

Communication over the additive white Gaussian channel, subject to a discrete phase ambiguity at the receiver, is considered. When this phase ambiguity is considered as a discretely distributed random variable, the channel is termed the acoherent additive white Gaussian (AAWG) channel. It is shown that the optimum decoder for the AAWG channel is not practically implementable and a suboptimum decoder that is asymptotically optimum at high signal-to-noise ratio is developed. The low signal-to-noise ratio performance of the suboptimum decoder is also examined. By considering the structural possibilities for this decoder, it is shown that one implementation leads to rotationally invariant codes. Other implementations, based on a rotationally disjoint property, lead to a variety of solutions that offer a general framework for communication over this channel. Some of these solutions use a parallel receiver configuration. Various solutions are compared in terms of implementation and performance