Unified performance analysis of suboptimum detection methods for multi-h CPM

It is well understood that the pulse amplitude modulation (PAM) representation of continuous phase modulation (CPM) can lead to reduced-complexity detection methods with near optimum performance. It has recently been shown that the PAM representation also extends to multi-h CPM schemes. In this paper we present a class of reduced-complexity detectors for multi-h CPM which are based on the PAM representation. We show that it is possible to achieve complexity savings greater than a factor of ten with these detectors in terms of trellis states and matched filtering requirements, in exchange for minor performance losses. We also give an exact expression for the pairwise error probability for these detectors over the additive white Gaussian noise (AWGN) channel. In arriving at this expression we show that PAM-based detectors for CPM are a special case of the broad class of mismatched CPM detectors. We also show that the metrics for PAM-based detectors accumulate distance in a different manner than metrics for other CPM detectors. These distance properties are particularly useful in this setting where the trellis size is greatly reduced. We give thorough examples of the analysis for two signaling formats: the multi-h satellite communication standard MIL-STD-188-181B and the advanced range telemetry (ARTM) multi-h CPM waveform.