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In underwater acoustic signal processing, direction of arrival (DOA) estimation can provide important information for target tracking and localization. To address underdetermined wideband signal processing in underwater passive detection system, this paper proposes a novel underdetermined wideband DOA estimation method equipped with the nested array (NA) using focused atomic norm minimization (ANM), where the signal source number detection is accomplished by information theory criteria. In the proposed DOA estimation method, especially, after vectoring the covariance matrix of each frequency bin, each corresponding obtained vector is focused into the predefined frequency bin by focused matrix. Then, the collected averaged vector is considered as virtual array model, whose steering vector exhibits the Vandermonde structure in terms of the obtained virtual array geometries. Further, the new covariance matrix is recovered based on ANM by semi-definite programming (SDP), which utilizes the information of the Toeplitz structure. Finally, the Root-MUSIC algorithm is applied to estimate the DOAs. Simulation results show that the proposed method outperforms other underdetermined DOA estimation methods based on information theory in term of higher estimation accuracy.

In array signal processing, most existing direction-of-arrival (DOA) estimation methods fail to work given deficient snapshots. To solve this problem, this Letter proposes a novel wideband DOA estimation technique by utilising the sparse representation in terms of the low rank Toeplitz structure presented in uniform array geometries, followed by an enhanced MUSIC method. Specifically, each sub-band segment is first focused into the reference frequency band to collect the coherent covariance matrix even in the lack of sufficient samples. Then, the covariance matrix is denoised through a structure-based sparse reconstruction, which exploits the low rank Toeplitz structure. Finally, the DOAs is efficiently estimated via an enhanced MUSIC method. Simulation result confirms the efficacy of the proposed method that works well in MIMO and radar applications.

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