Two receivers for maximum likelihood sequence detection of minimum shift keying over the Gaussian channel with unknown carrier phase

The first receiver is the suboptimum maximum likelihood soft decoder in which explicit recovery of the unknown carrier phase is not necessary and it leads to constant receiver complexity independent of data sequence length. The second receiver is the two-stage receiver which is of an estimator-detector structure. The first stage being the carrier phase estimator extracts the carrier phase information and feeds it to the second stage which is a Viterbi decoder. The carrier phase estimator is aided by a quadratic detector and also feedback from the Viterbi decoder. Both receivers achieve coherent performance if the carrier phase is relatively stable.