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Funding Information: This research was supported in part by the National Natural Science Foundation of China under Grant No. 61901136, the National Key Research and Development Program of China under Grant No. 2021YFC2801204, the Ph.D. Student Research and Innovation Fund of the Fundamental Research Funds for the Central Universities under Grant No. 3072021GIP0507, and the China Scholarship Council under Grant No. 202006680029. The authors would like to thank the Acoustic Research Laboratory of the National University of Singapore for providing the snapping shrimp noise. The authors also thank Mandar Chitre, the head of the Acoustic Research Laboratory, for his helpful comments to improve the manuscript. Publisher Copyright: © 2022 Acoustical Society of America. Detecting the presence or absence of a known signal is an important aspect of underwater acoustic (UWA) communications as it is a vital first step to process the received data. The influence of impulsive noise and multipath propagation on detection are both considered in this paper. Many robust detectors have been designed to cope with impulsive noise, but they tend to ignore the impact of multipath propagation, which may decrease the detection probability. To emphasize the role of multipath channel, we propose two-stage detection methods. In the first stage, the channel is estimated based on robust orthogonal matching pursuit, while in the second stage, detectors that use the channel estimation from the first stage, namely augmented log-likelihood ratio detector and augmented pseudo-correlation detector, are developed. The former detector is parametric and the latter one is non-parametric. The improved performance is demonstrated in simulated multipath channel and actual UWA channel with both simulated noiseand recorded snapping shrimp noise, indicating that the proposed detectors are resistant to impulsive noise. It is also shown that the use of multipath information helps to improve the detection performance.

A so‐called worst‐case‐based robust adaptive beamforming approach has been proposed a few years ago. This approach has been followed up by a number of works, which significantly improved the implementation issues. Recently, two new approaches have been developed: the probability constrained based and sequential quadratic programing based approaches. The probability constraint based design requires the distortionless response constraint to be kept with a certain selected probability, while the worst‐case‐based design requires this constraint to be kept for the worst‐case operational conditions. The sequential quadratic programing based approach uses the iterative estimation of the signal steering vector and, therefore, is significantly different from two two aforementioned designs. In this paper, we overview, analyze, and compare all the aforementioned approaches to robust adaptive beamforming design.