Simple noncoherent CPM receivers by PAM decomposition and MMSE equalization

Conventional differential detection and energy detection offer poor performances for demodulating continuous phase modulated (CPM) signal because of inherent inter-symbol interference (ISI). Based on the pulse amplitude modulation (PAM) decomposition of CPM signal, the binary CPM with any non-integer modulation index can be interpreted as a linear modulation with differentially encoded pseudo-symbols or equivalently as a modulation scheme with two overlapped waveforms to carry information bits. By combining the equalization of ISI with the design of the receiver filters under the minimum mean square error (MMSE) criterion, the equalized differential detection and equalized energy detection for binary CPM signal demonstrate significant performance improvements while maintaining the same simple receiver structures as the conventional ones. Through theoretical analysis, a closed-form formula is derived to efficiently evaluate the bit error probabilities of the proposed noncoherent receivers. Simulation results using minimum shift keying (MSK) and Gaussian frequency shift keying (GFSK) with BT = 0.5, h = 0.34 are also provided to conform with the performance improvements.