Performance evaluation of the factor Graph CPM phase discriminator decoder with canonical messages and modulo mean updates

The paper addresses the CPM class of the modulation passing through the parametric channel with the factor graph decoding inherently coping with the channel parameter. The combination of the discrete channel symbols with continuous valued channel parameter leads generally to complex mixture densities difficult to cope in the sum-product algorithm message updates in the factor graph. We attack the problem by, first, performing the factor graph operations in phase-space domain, and, second, by defining proper canonical densities described by a limited set of parameters. We derive proper factor and variable node update rules respecting the modulo 2*pi nature of the phase operations. We evaluate the error rate performance and compare it against the brute-force marginalization rules.