A new performance bound for PAM-based CPM detectors

It is well understood that the pulse amplitude modulation (PAM) representation of continuous phase modulation (CPM) can lead to reduced-complexity detectors with near optimum performance. It has recently been shown that the PAM representation also extends to CPM schemes with multiple modulation indexes (multi-h CPM). In this paper, we present a detector for multi-h CPM which is based on the PAM representation. We also give an exact expression for the pairwise error probability for the entire class of PAM-based CPM detectors (single- and multi-h, optimal, and reduced-complexity) over the additive white Gaussian noise (AWGN) channel and show that this bound is tighter than the previously published bound for approximate PAM-based detectors. 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 especially useful in applications with greatly reduced trellis sizes. We give thorough examples of the analysis for different single- and multi-h signaling schemes. We also apply the new bound in comparing the performance of PAM-based detectors with other reduced-complexity detectors for CPM.