Performance Improvement of the Catastrophic CPM Scheme with New Split-Merged MNSED

Abstract

Continuous phase modulation (CPM) is a very attractive digital modulation scheme, with constant envelope feature and high efficiency in meeting the power and bandwidth requirements. CPM signals with pairs of input sequences that differ in an infinite number of positions and map into pairs of transmitted signals with finite Euclidean distance (ED) are called catastrophic. In the CPM scheme, data sequences that have the catastrophic property are called the catastrophic sequences; they are periodic difference data patterns. The catastrophic sequences are usually with shorter length of the merger. The corresponding minimum normalized squared ED (MNSED) is smaller and below the distance bound. Two important CPM schemes, viz., LREC and LRC schemes, are known to be catastrophic for most cases; they have poor overall power and bandwidth performance. In the literatures, it has been shown that the probability of generating such catastrophic sequences are negligible, therefore, the asymptotic error performance (AEP) of those well-known catastrophic CPM schemes evaluated with the corresponding MNSED, over AWGN channels, might be too negative or pessimistic. To deal with this problem in AWGN channel, this paper presents a new split-merged MNSED and provide criteria to explore which conventional catastrophic CPM scheme could increase the length of mergers with split-merged non-periodic events, effectively. For comparison, we investigate the exact power and bandwidth performance for LREC and LRC CPM for the same bandwidth occupancy. Computer simulation results verify that the AEP evaluating with the split-merged MNSED could achieve up to 3dB gain over the conventional approach.