Differential detection of partial response continuous phase modulation with index 0.5

The author presents a method for the design of an MMSE (minimum mean-squared error) optimum receiver filter for the differentially coherent detection of CPM (continuous phase modulation) with modulation index 0.5. The receiver filter is equivalent to the cascade of a matched filter and an equalizer, to reduce inherent intersymbol interference (ISI). The performance can be improved when the delay between signals, multiplied by the differential detector, is increased from one to M bit time intervals. This decreases the effect of noise correlation, and consequently decreases the bit error probability. It is shown that performance degradation with respect to that of the differential binary phase-shift keying system is due to inherent ISI contained in the signal and also due 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 signal is used for illustration