Frequency domain direct adaptive turbo equalization based on block least mean square for underwater acoustic communications

•A frequency domain block adaptive decision feedback equalizer (FD-ADFE) is proposed for rapid time-varying UWA channels.•The FD-ADFE is extended to the coded system and proposed a new adaptive turbo equalization implemented in frequency domain (FDDA-TEQ).•The performance of the proposed scheme is superior to existing turbo equalization schemes and is proved by the data collected in real-world underwater experiments.