Reduced Complexity Sequence Detection of Continuous Phase Modulation Represented as the Linear Superposition of Amplitude Modulated Pulses

The Laurent decomposition expresses any binary single-h CPM waveform as the summation of a finite number of pulse amplitude modulated components, and this result has been useful in the development of a class of reduced complexity CPM detection schemes. In a recent generalization, it has been shown that a similar finite-term amplitude modulation expansion exists for all variants of CPM, regardless of signal complexity, with the important distinction that the amplitude modulated pulses are, generally, data-dependent. Furthermore, it has been shown that most of the signal power is typically concentrated in the first 1-2 principle components of the expansion, which suggests a possible reduction in receiver complexity viz. the optimal maximum likelihood sequence detector. In this paper, we investigate the bit error rate (BER) performance of a maximum likelihood sequence detector when the incoming signal is matched to the data-dependent pulse modulation components found in this new signal representation. Numerical results suggest that there is a negligible decrease in performance between the optimal conventional matched filter receiver and a reduced complexity, sub-optimal scheme that only uses the first 1-2 (principle) signal components in the construction of the matched filter bank.