## 1 Introduction
By linear transformation of the solution vector, the weighted LASSO method [20] imposes certain structural constraint on the solution vector to achieve efficient processing of spatially extended sources (e.g., underwater embedded objects in acoustic imaging [21]). The total variation norm regularization method [22] for DOA estimation of spatially extended sources can be seen as a special case of the weighted LASSO method, which uses the band matrix to realize the linear transformation of the solution vector, so that the solution vector has block sparsity [19; 23]. Besides, using the information contained in the covariance matrix, the sparse spectrum fitting (SpSF) algorithm [24] first performs a vectorization operation on the covariance matrix, and then fits the estimated covariance matrix and the ideal covariance matrix under the \(l_{2}\)-norm. At the same time, considering the sparsity of the source, \(l_{1}\)-norm penalization is imposed on the source strength vector. However, SpSF algorithm is based on the assumption that ambient noise is white Gaussian noise. Therefore, [PERSON], [PERSON], and [PERSON] proposed the directional noise field sparse spectrum fitting (DN-SpSF) algorithm [25], which uses the slowly varying characteristics of the noise spectral density function to derive the general expression of the covariance matrix of underwater directional ambient noise, and takes an optimization process similar to the SpSF algorithm. The naturally occurring ambient noise in the ocean is generally considered to be a nuisance [1; 26]. Therefore, one of the purposes of the sonar signal processing algorithms is to distinguish the desired signal from the ambient noise and suppress the ambient noise as much as possible. However, recent studies have shown that ocean ambient noise actually contains a lot of useful information [27; 28], and could be used for the underwater imaging [26], the geoacoustic inversion [29; 30], and the determination of seabed sub-bottom layer profile [31; 32; 33]. A similar situation is that when the presumed steering vector is mismatched with the actual steering vector, MVDR-based beamformers exhibit a so-called signal self-cancellation phenomenon, that is, the signal of interest is erroneously treated as interference, thereby being greatly suppressed. Therefore, signal self-cancellation is commonly regarded as a nuisance, and the existing related algorithms are intended to reduce the effect of signal self-cancellation. To the best of our knowledge, there is currently no research on how to use the information containedin the signal self-cancellation phenomenon. Therefore, this paper does not take signal self-cancellation as a troublesome thing, but explores the potential information behind the signal self-cancellation phenomenon and uses it to achieve high-precision DOA estimation of underwater acoustic sources. The main contributions of this paper are: (1) Treating the signal self-cancellation problem of the MVDR-based beamformers from a new perspective, that is, although for the MVDR-based beamformers, signal self-cancellation is a nuisance, it also contains favorable information and can be used for DOA estimation of underwater acoustic sources. (2) A novel unit circle mapping method is proposed, which effectively correlates the signal self-cancellation and the beam response curves by uniformly mapping all beam response sample values in the direction interval to a unit circle. (3) DOA estimation performance of the proposed method is analyzed in the underwater acoustic propagation simulation environment, and the performance comparisons with existing DOA methods is also completed.