Objectives For underwater acoustic (UWA) communication, the time-domain distortion of received baseband signal caused by residual Doppler frequency shift decreases the performance of channel equalizer especially in communication systems of long-frame data format. Digital phase-locked loop (DPLL) can compensate the phase difference between local carrier frequency and the received signal. However, the only DPLL cannot eliminate the time-domain extension of baseband signal, which will increase the timing error of detection symbols and lead to the re-divergence of equalizer after convergence. The real-time processing of UWA communication is limited to the computation complexity of receiver algorithm, a reasonable signal processing routine should be organized.

Methods We propose a Farrow interpolation based fractionally-spaced decision feedback equalizer (FFSDFE) to accomplish baseband signal recovery. A Farrow structure based interpolator is introduced into the operation loop and compensate the Doppler effect combined with DPLL. The Doppler factor is firstly estimated by fix frequency interval search, i.e. coarse Doppler factor, using fast Fourier transform method. Instant carrier phase error is calculated by equivalent phase discriminator with equalizer output error. The modified loop filter, with an additional integrate-dump step, smooths the phase error and gets the fine Doppler factor. The summary of Doppler factor estimators is utilized for signal interpolation, the time-domain extension or compression of baseband is mitigated in the same time. The fast recursive least squares (FRLS) algorithm, modified from stable fast transversal filter algorithm, is exploited for adaptive adaptation of fractionally-spaced decision feedback equalizer. The FRLS algorithm for FFSDFE reduces the computation complexity of recursive least squares from square relation to linear relation of equalizer length.

Results The results of simulations and lake trial show that: (1) The proposed scheme can endure the situation of fix Doppler factor, with 1 Hz residual Doppler frequency shift in the worst case after coarse search, and dynamic Doppler factor during one data frame in simulations. In addition, the bit error rate (BER) is reduced from 0.002 7 to 0 in fixed Doppler factor, and from 0.481 2 to 0.001 1 in dynamic Doppler factor. (2) The time cost of the Doppler processing procedure and three kinds of real-time equalization algorithms are measured in low-power consumption platform used in field environment. Different parameter configurations are made for different channel environment. (3) The performance of real-time UWA communication using the proposed scheme is tested by maximum 1 000 m lake trial in summer, and the BER of received signal attains to 7.95×10^-5 at 500 m and 3.03×10^-4 at 1 000 m which satisfy the engineering requirements.

Conclusions The proposed scheme is an engineering realization of real-time UWA communication system implementation, the BER performance is improved by combined structure of Farrow interpolator, modified DPLL and FSDFE. Hence, in the future work, we will concentrate on large-scale Doppler effect within frames and search for methods of further computation complexity reduction in order to tackle harsher UWA channel.