###### Abstract
Hence, DPD is measured in the dimension of time; as such, SH-DPD-MUSIC utilizes higher frames [1]. If near-field frequency smoothing is applied, then a range dependent source normalization is a requirement. Therefore, other DoA estimation methods are broken down into the SH domain, which is the minimum variance distortionless response (MVDR) [8]. At present, different methods for DoA estimation employ a spatial covariance matrix [5; 11; 18; 19; 22; 23; 24]. For instance, the steer response power map generated by MVDR (minimum variance distortionless response) beamformer rejects background noise optimally for all look directions through the adjustment of the beam pattern based on the MUSIC and spatial covariance matrix [25], which decomposes the spatial covariance matrix into noise and signal subspaces. The MVDR beamformer comes up as the error in the placement of beam pattern loss. MUSIC, based on the linear dependency of the reflections  
Figure 1: A connected 64-element SAA in anechoic chamber [8]. on the direct path signals, implies the covariance matrix rank is made smaller and the division between the noise and signal subspaces may be prone to errors. The generally established mutual coupling correction approaches for antenna arrays are classified into two classes. The first class deals with the compensation of or calibration of mutual coupling in decoupled network design and antenna array design. In the second class, the mutual coupling is corrected by solving the mutual coupling matrix (MCM) via array signal processing and analysis of electromagnetics (EM) [25]. The implementation of the first approach is more challenging in engineering. The approach is based on the analysis of EM, such as the S-scattering parameter technique, and open-circuit voltage techniques are only applied to transmit mode arrays. The full-wave approach and reception of the mutual impedance approach require larger measurement data, and the steps involved are complicated. From the perspective of array signal processing, the blind calibration approach uses an MCM banded symmetric Toeplitz structure. Mutual coupling calibration can be achieved using matrix transformation or separation of the mutual coupling coefficient. The blind calibration approach, when combined with the estimation algorithm, simultaneously estimates mutual coupling parameters and DoAs [26]. Motivated by the sparse representation method [26; 27], spherical sparse signal processing has drawn attention recently. For instance, [28; 29], studied sparse recovery for random sampling in the SH domain. In [30; 31], sparse Bayesian learning techniques for DoA estimations were developed in the SH domain. This sparse Bayesian learning technique could exhibit better performance than the \(\ell_{1}\) norm dependent ones [27], and they have slow rates of convergence. In addition, grid mismatch issues degrade the aforementioned sparsity-dependent methods. Dealing with this issue, research has been conducted to remove the grid modeling error [32]. Lately, a unified scheme was developed for the representation of sparse signals on the infinite or finite dimensional dictionary in [33]. It leads to the gridless sparse recovery technique by resolving the optimization problem on the convex hull of an atomic set that is recognized as atomic norm minimization (ANM). Particularly, atoms that are described by complex exponentials, Candes and Fernandez-Granda depict that bandlimited signals are recoverable provided the low-rate samples frequency separation condition is ensured [34]. According to theory, the ANM method is extended to multidimensional frequency models [35; 36; 37], prior knowledge [38], multi-measurement vectors [39] and covariance matrix scenarios [40; 41; 42] for DoA estimation and gridless signal recovery. Conversely, the traditional ANM techniques are based on the array manifold's Vandermonde structure, and therefore applicable only to linear/rectangular arrays.