The output probability distribution of correlation receiver for GMSK signals

The formula of bit error rate(BER) for the performance analysis of Gaussian minimum shift keying(GMSK) system applying two-bit differential detection and decision feedback(DF) is derived. Using the formula of BER and the probability density function of sums of independent identical random variables, we analyse the error detection probability(EDP) and the missed detection probability(MDP) of correlation receiver. Numerical calculations show that the decision threshold is mainly determined by the MDP and the EDP with noise, not by the MDP and the EDP with orthogonal codes. They also show that the best range of normalized decision threshold is from 4 to 11 for receiving 16-bit walsh codes. The application of the probability distribution in the synchronous performance analysis of a frequency-hopping communication system verifies the theoretical investigation of correlation receiver.