Posterior Probability-Based Symbol Detection Algorithm for CPM in Underwater Acoustic Channels

The underwater acoustic (UWA) communication system is characterized by limited bandwidth, while continuous phase modulation (CPM) offers a constant envelope, improving power and spectrum utilization efficiency. However, severe inter-symbol interference (ISI) poses a significant challenge in CPM-based UWA communication. Traditional CPM frequency domain equalization (FDE) combined with simple phase detection neglects the inherent coding gain from CPM, leading to performance degradation. Although Viterbi detection provides high performance, its complexity makes it unsuitable for computationally constrained UWA systems. This paper proposes a symbol detection algorithm based on posterior probabilities combined with FDE (PS-FDE). PS-FDE improves CPM signal detection performance by effectively separating information, applying delay, and performing multiple rounds of information merging. Simulations using minimum shift keying (MSK) and Gaussian MSK signals demonstrate significant performance improvement in just a few iterations over UWA channels. A sea trial further validates the algorithm, showing a 15.83% reduction in bit error rate after three information mergings.