Multiple symbol noncoherent detection of GMSK

This paper studies the problem of noncoherent detection of Gaussian minimum shift keying (GMSK). Particular attention is focussed on the popular case of BT=0.25, but the concepts presented apply to other cases as well in addition to the general case of continuous phase frequency shift keying (CPFSK). The optimum noncoherent detector is shown to consist of a bank of matched filters followed by a sequence estimator. The metric which must be optimized by the sequence estimator is explicitly given. A simple approximation is introduced which allows the number of matched filters to be reduced from 16 to 3 for GMSK (BT=0.25). A suboptimal metric is introduced which is interpreted as an N-symbol differential detection metric. Based on this metric, a receiver structure is then presented which uses the Viterbi algorithm with a 2 ^N state trellis to perform the sequence estimation. Simulation results indicate that it is possible to obtain performance within 1 dB of optimum coherent detection on either a Gaussian noise or a slowly Rayleigh fading channel with the N=4 symbol differential detector