## 1 Introduction  
Estimation of the direction-of-arrival (DoA) is an important and basic challenge in signal processing, such as source separation, spatial filtering, etc. It has applications in mobile communications systems, military surveillance, sonar, radar, and vehicular technology. The knowledge of the DoA of an incoming signal by the receiving antenna is employed to localize the locations of the analogous sources. It improves the adaptive beamforming of the receiving radiation pattern for system sensitivity enhancement in the required directions of signals and reduces unwanted interference. DoAs ensure that antennas provide the best beam in the direction of the required users, and null in the directions of interferences, consequently improving the fidelity of the base stations and mobile stations [1; 2; 3; 4; 5; 6]. Hence, estimating the DoA of electromagnetic (EM) waves that impinge antenna arrays is important for effective mobile communication. Spherical antenna array (SAA) (as shown in Figure 1) is an important configuration when obtaining an array with isotropic characteristics [1; 3]. Estimating both the horizontal and vertical angle of arrivals requires a 3D antenna array configuration. An antenna array structure that samples EM waves in such a way that they can be described and defined in spherical harmonics (SH) domain is of interest, because this description makes it possible to analyze EM waves at the same resolution in all directions using approaches that are not dependent on the particular geometry of the array [1; 7]. The SAA has applications in aerospace, spacecraft, and vehicular technology, which are critical in the military and other industrial areas. Different DoA estimation approaches for use in the SH domain have been reported in the literature [3; 4; 5; 6; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17]. Some of the most popular approaches include the multiple signal classification (MUSIC) approach [3], estimation of signal parameters through rotational invariance technique (ESPRIT) technique [5; 6; 7; 8; 9], beamforming, and the maximum likelihood (ML) methods [4; 15]. These methods have been considered and used for arrays of antenna with arbitrary structures and generate accurate DoA estimates [18; 19]. Other methods include the MUSIC group delay [4], the steered response power with phase transform (SRP-PHAT) methods [20], generalized cross-correlation (GCC) method [21], adaptive eigenvalue decomposition method [22], 1-D MUSIC [23] approach, and order aware algorithm [24]. MUSIC has been considered for spherical structures in the near-field [19; 22; 23; 24]; this is named MUSIC-SH. As a result of MUSIC-SH's sensitivity to distortions in the multipath scenario, [PERSON] [25] proposed an alternative method called direct path dominance (DPD). In the near-field, the mode strength is a function of source range, which is not known a priori. Therefore, DPD can only be measured in the time dimension, and for this reason, the MUSIC-SH-DPD uses higher frames [25]. When applying the near-field frequency smoothing, source normalization that depends on this range is required. Hence,  
Figure 1: Spherical antenna array from computer simulation technology (CST) software. (**a**) lateral view and (**b**) aerial view [3]. Average element spacing is 0.76\(\lambda_{0}\), dome radius is 1.85\(\lambda_{0}\), and the number of rings is 4. The SAA has effective isotropic radiated power (EIRP) to support the link. the remaining DoA estimation technique, decomposed into the spherical domain, is the minimum variance distortionless response [26]. Other parameter estimate methods can be found in the literature, such as the SAGE algorithm [27] and Butler matrices [28]. Different DoA estimation approaches to planar and linear array configurations have been presented earlier. Due to the merits of SAA, various approaches that employed SAA are under consideration at present. For example, MUSIC and ESPRIT have been analyzed using spherical harmonics [22; 23; 24], and a comprehensive comparison is presented in [19].