GMSK with differential phase detection in the satellite mobile channel

A formula is derived for the error probability of partial-response continuous-phase modulation (which contains Gaussian minimum shift keying (GMSK) as a special case) with N-b (N=1, 2) differential phase detection (DPD) for the satellite mobile channel, which contains as special cases the Gaussian and Rayleigh channels. In the satellite mobile channel, the input signal is the sum of a direct component, a diffuse component, and white Gaussian noise. The receiver is either with or without decision feedback, and the decision region is optimized for 2-b DPD to minimize the error probability. The error probability for GMSK is computed as a function of signal-to-noise ratio and other system or channel parameters (Doppler frequency, Gaussian filter bandwidth, ratio of powers in the direct and diffuse signal components, etc.). It is shown that decision feedback is more effective for GMSK with narrow bandwidth. The 2-b DPD is superior to the 1-b DPD for low Doppler frequencies and signal-to-noise ratios. For practical vehicle velocities and bit rates, a 2-b DPD with decision feedback outperforms all other analyzed schemes when the signal-to-noise ratio is low