Performance of generalised AMF receivers for continuous phase modulation

Partial-response continuous phase modulation (CPM) signals can in many cases yield power spectra with narrow mainlobe and also low sidelobes. The optimum receiver for these signals is sometimes complex. In the paper the idea of using a smaller signal set in the receiver than used by the transmitter is considered. This is done by means of using a generalised average matched filter (AMF) receiver. Only coherent detection of signals transmitted over an additive white Gaussian noise channel is considered. The multiple-symbol AMF receiver can be implemented with fewer filters than the optimum receiver. These receivers are analysed for various partial-response CPM signals. The analysis is done under the assumption of error-free filter and phase updating. A Euclidean distance for mismatched signal sets is used to give the symbol error probability for large signal/noise ratios conditioned on error-free updating. Under the above assumptions, it is shown that the multiple-symbol AMF receiver performs equally well as the optimum receiver for schemes with low modulation indices and also for large modulation indices for some schemes. This is the case both for binary and quarternary schemes. A simple updatiing method is also simulated.