Reduced complexity detection methods for continuous phase modulation
Continuous phase modulation (CPM) is often plagued by high receiver complexity. One successful method of dealing with this is the well-known pulse amplitude modulation (PAM) representation of CPM, which was first proposed by Laurent. It is shown that the PAM representation also applies to multi-h CPM and ternary CPM, two previously unconsidered cases. In both cases it is shown that many PAM components may be required to exactly represent the signal. This is especially true of partial-response systems where the memory of the signal is long. Therefore, approximations are proposed which require only a limited number of terms.
These extensions of the PAM representation are used to construct reduced-complexity detectors for CPM. These are generalizations of the detector first proposed by Kaleh. These detectors can be used in an optimal configuration, or in a suboptimal reduced-complexity configuration. The PAM complexity-reduction principle is shown explicitly. An exact expression is given for the pairwise error probability for the entire class of PAM-based CPM detectors, not just the extended cases proposed herein. The analysis is performed for the additive white Gaussian noise (AWGN) channel. The performance bound that results from this pairwise error probability is shown to be tighter than a previously published bound for PAM-based CPM detectors. The analysis shows that PAM-based detectors are a special case of the broad class of mismatched CPM detectors. However, it is shown that the metrics for PAM-based detectors accumulate distance in a different manner than metrics for other mismatched and suboptimal detectors. These distance properties are especially useful in applications with greatly reduced trellis sizes.
The proposed detectors are included in two case studies. The first is for a multi-h CPM standard used in aeronautical telemetry. Many reduced-complexity detectors are studied in addition to PAM-based detectors. The second case study is for a ternary CPM known as shaped offset QPSK (SOQPSK). Here, the performance of serially concatenated coded SOQPSK is studied along with uncoded systems. It is shown that the coded systems achieve large gains over uncoded systems. However, the design proposed herein achieves these gains with less complexity than previously published designs.