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Partial response continuous phase modulation (CPM) gives constant envelope digital modulation schemes with excellent power spectra. Both narrow main lobe and low spectral tails can be achieved. When these signals are detected in an optimum coherent maximum likelihood sequence detector (Viterbi detector), power efficient schemes can also be designed, sometimes at the expense of receiver complexity. This paper describes a general class of simple Viterbi detectors with reduced complexity compared to the optimum case. The key idea is that the approximate receiver is based on a less complex CPM scheme than the transmitted scheme. The asymptotically optimum reduced-complexity receiver is found for a variety of transmitted schemes and various complexity reduction factors, for a specific class of receivers and modulation indexes. A new distance measure is introduced for the performance analysis. Smooth schemes based on raised cosine pulses are analyzed and simulated for the case of simplified reception. A graceful performance degradation occurs with the reduction of complexity.