Optimal and suboptimal symbol-by-symbol demodulation of continuous phase modulated signals

In applications requiring soft-decision metrics, e.g., systems with interleaved coded modulation, symbol-by-symbol detection is preferred to sequence detection. This paper develops the optimum soft-output algorithm (OSA) for the demodulation of continuous phase modulated (CPM) signals. Since this optimum detector is computationally complex, a class of suboptimum symbol-by-symbol detectors, called the reduced state soft-output algorithm (RS-SOA) is developed. By varying certain parameters, the RS-SOA offers an effective tradeoff between performance and complexity, as measured by arithmetic operation count and the number of integrators required. Additionally, some simple complexity reduction schemes can be used in conjunction with the OSA and the RS-SOA. The properties of the OSA and the RS-SOA, and the various complexity reduction schemes are explored in an extensive simulation study