Reduced Complexity Detectors for Continuous Phase Modulation Based on a Signal Space Approach

Optimum detectors for CPM use in general a large number of filters in order to calculate the optimum metrics. In this paper, we propose correlation detectors that calculate its metrics in a subspace of the signal space. The subspace is selected such that the asymptotic error performance is optimized for the given dimensionality. We focus on noncoherent detectors but show also some results for coherent detectors. The subspace metric calculation is combined with previously published reduced complexity decoding algorithms such as the SAN(B) and RSSD algorithms. Optimum subspace correlation detectors with different number of filters are found for both binary and quaternary CPM schemes. Their error performance on an AWGN channel is derived analytically through the use of a minimum Euclidean distance approach and is also simulated through the symbol error probability. Comparison is done with the optimum detectors. A close agreement between minimum distance and simulated symbol error probability is found for all considered detectors. We find that in most cases only 4 to 6 matched filters are needed in order to obtain a performance that is close to optimum. This corresponds to at least a five‐fold reduction in number of filters and with the reduced complexity search algorithms for making symbol decisions this leads to a dramatic reduction in overall complexity.