## 5 Conclusions  
UWA communication is one of the fundamental requirements for underwater positioning, navigation and timing networks. As for the single-carrier UWA communication, the continuous carrier phase observation from the receiver loop has the potential to provide high-precision location information in the future, just like the Beidou Navigation Satellite System. The UWA channel suffers formidable interferences caused by the underwater environment and physical acoustic characteristics. So, in this paper, we investigated the robust turbo receiving scheme of single-carrier UWA communication under harsh shallow-water channel environments, and the critical conclusions are summarized as follows:  
1. For time-varying UWA channels, the Doppler effect should be finely compensated to guarantee the stability of UWA communication. We concentrated on the fine Doppler estimation and compensation because of the low Doppler estimation accuracy demand of signal synchronization. The proposed anti-Doppler module embeds an interpolator with Farrow structure into the DPLL; thus, the cumulative timing error will be eliminated in time. To couple the ADM and equalizer effectively, we introduced the integral-zeroing module to smooth the noisy phase error. The controlling parameters of the ADM are calculated according to the output of the loop filter. Owing to the adjustable interpolator in cooperation with the DPLL, the time-scale distortion caused by the dynamic Doppler effect can be alleviated. The proposed anti-Doppler module achieves available noise reduction in phase detection, and the field lake trial verifies the reliability and robustness of the proposed scheme in time-varying UWA communication situations. 2. To satisfy the cluster-sparse UWA channel, we considered a system transmission model with grouped multipaths. The excellent performance of the PRLS algorithm has been confirmed for sparse identification. To accelerate the convergence speed and accomplish a reduction in steady-state error, we exploited the hybrid norm regularization to rebuild the cost function of the adaptive algorithm. Combined with the proportional updating mechanism, the so-called \(\ell_{p,q}\)-PRLS algorithm was obtained to settle the cluster-sparse problems. Experiments have shown that the resulting \(\ell_{2,0}\)-PRLS algorithm presents performance superiority over existing PRLS-type algorithms in specific channels. The main drawback of the proposed adaptive algorithm is the process of parameter configuration. 3. Turbo equalization or turbo receiver is the appropriate implementation structure to reduce the troublesome ISI for single-carrier UWA communication systems. We utilized the SIC filter to solve the noncausal interference of the channel, and the SIC should only be applied after the extrinsic soft symbols of the decoder are obtained. The improved soft FS-SE is exploited to constitute the SISO equalizer in the turbo receiver structure. To eliminate the error propagation of the feedback equalizer further, the VTRM technology is employed in our proposed VSTD-TEQ scheme. We considered that the bidirectional received baseband signals are approximatively independently identically distributed, and the experiment result demonstrated that the cross-correlation coefficient of the bidirectional input reduces along with the growth of the fractionally spaced order. In particular, the cross-correlation coefficient is approximately only 0.1, while the fractionally spaced order is 1/8,which verifies the rationality of the bidirectional structure. Therefore, the proposed scheme is a suitable receiving implementation for fast time-varying UWA channels. The results of the simulations and the lake trial demonstrate that the proposed scheme achieves obvious MMSE and BER performance improvement over existing similar schemes. Conceptualization, Z.H. and P.J. ; methodology, W.T. ; software, D.Z. ; validation, Z.H., W.T. and D.Z. ; formal analysis, Z.H. ; investigation, P.J. ; resources, W.T. ; data curation, W.T. ; writing--original draft preparation, Z.H.