Iterative-detection–based time-domain adaptive decision feedback equalization for continuous phase modulation of underwater acoustic communication

Continuous phase modulation (CPM), which is widely used in aviation telemetry and satellite communications, may help improve the performance of underwater acoustic (UWA) communication systems owing to its high spectral and power efficiency. However, applying conventional frequency-domain equalization (FDE) algorithms to CPM signals over time-varying UWA channels considerably degrades performance. Moreover, time-domain equalization algorithms often rely on excessive approximations for symbol detection, compromising overall reception. This study presents an iterative-detection-based time-domain adaptive decision feedback equalization (ID-TDADFE) algorithm that tracks channel variations through symbol-by-symbol detection. The symbol detection in ID-TDADFE fully considers the inherent coding gain of CPM signals can be cascaded with an adaptive equalizer, and enhances symbol detection performance by utilizing joint probability estimation. Numerical simulations with minimum-shift keying (MSK) and Gaussian MSK signals demonstrated that ID-TDADFE significantly improved communication performance over a time-varying UWA channel within one or two iterations. In a sea trial for experimental verification, ID-TDADFE reduced bit errors by 45.08% and 51.8% in the first and second iterations, respectively, compared to FDE.