Differentially coherent detection of binary partial response continuous phase modulation with index 0.5

The performance of binary partial response continuous phase modulation (with index 0.5) using a differentially coherent receiver depends on the choice of the receiver filter. An optimum MMSE design method for this filter is presented. The receiver filter is equivalent to the cascade of a matched filter and an equalizer in order to reduce inherent intersymbol interference (ISI). It is shown that performance degradation with respect to that of the differential binary phase shift keying (BPSK) system is due to inherent ISI contained in the signal and also to noise enhancement and correlation caused by the receiver filter. The bit error probability on the Gaussian channel is calculated by assuming that ISI is Gaussian. The Gaussian minimum shift keying (MSK) signal is used for illustration