Detection error probabilities in noncoherent channels

This paper presents performance bounds for block-based detection of PAM and QAM transmitted over non-coherent channels. Such channels give rise to inherent detection ambiguities since multiple possible transmit sequences can have the same likelihood. The number of ambiguous sequences is a function of the block length. In this paper, we derive the probability of detection error in terms of a Dedekind zeta function of the block length, for infinite-sized constellations and zero noise. We also provide expressions for finite constellations which can be evaluated in polynomial time with the constellation size, as opposed to checking all possible sequences