## 2 Introduction  
In wireless communication systems, antennas are the most important components. High directivity, narrow beam width, low sidelobes, point-to-point, and preferred coverage pattern characteristics are desired features of antenna array beamforming. Beamforming combines signals from array elements of an array antenna system after multiplying signals from each antenna ele ment with a given weight [1]. The use of adaptive beamforming techniques enables signals to be steered in any anticipated direction electrically rather than mechanically [2]. Nowadays, the antenna array is also vastly used in the semiconductor field [3]. While linear arrays experience a low sidelobe level (SLL), considering high gain main lobe and narrow beamwidth in any given direction [4], circular antenna arrays are ideal configurations as their main lobe can steer all azimuth directions without changing their bandwidth [5], where the inter-element distance produces an unwanted mutual coupling effect. A unique structure known as a concentric multi-ring array with adequate inter-element spacing is implemented to reduce this problem. It has been used in applications including direction-of-arrival estimation, as well as in narrowband and broadband beamforming [6]. Concentric circular antenna array (CCAA) has the ability of all-azimuth scanning, and the beam pattern retains circularly symmetric in this configuration, which is invariant for 360\({}^{\circ}\) of azimuthal coverage [4]. In the presence of high and low noise conditions, the performance of circular and concentric circular antenna arrays is investigated using the DOA estimation technique [7]. The efficiency of this algorithm is compared with that of the optimal technique, while other robust techniques are ignored. A method for analyzing the performance of space-time adaptive processing (STAP) based on a diversely polarized antenna (DPA) array is proposed [8], with the proposed method providing a better clutter suppression performance and carrying a quasi-convex form. Any mismatch between steering directions and the actual signal causes degradation of the antenna array performance. Different loading methods can be used to solve the mismatch problem and make the device more robust. The array of the time samples is taken into account in the DOA frequency scheme using a single-stage problem [9], and the design of a smart antenna system and its monitoring strategy are briefly outlined in [10]. There are also two new approaches, called unscented transform (UT) and principal component analysis, that are briefly explored, considering the mutual coupling effect [11]. Additionally, compressive antenna arrays are addressed briefly to determine the narrowband direction of arrival (DOA) out of the larger aperture, as well as a small amount of hardware difficulty [12]. However, as FDL can detect and attenuate the interference signal, the drawbacks of the conventional technique are addressed in terms of interference detection for a CCAA beamformer [13]. Indeed, the authors of [14] provide a brief overview of existing robust algorithms for various array geometries. A technique named the optimal diagonal loading (ODL) technique for the CCAA system increases the output power by 28.12 dB and 8.624 dB at 2\({}^{\circ}\) disparity [15]. The normalized output power of the proposed structure is improved to \(-\)61.044 dB, \(-\)2.1 dB and \(-\)1.410 dB, respectively, by employing several robust techniques such as FDL, ODL, and VDL [16]. In comparison to the CCAA standard capon beamformer (CSB), robust SCB, and existing novel loading technique, the proposed robust CCAA beamformer improved the output power 28.9 dB, 9.34 dB, and 1.63 dB at 10 disparity angle [17]. A maximum flatness gain bandwidth of 80 nm (1525-1605 nm) and average gain level of 22.5 dB are obtained at a small input signal power of \(-\)25 dBm and optimum pump power values [18]. For the antenna array mentioned above, there are still a few areas where the SLL and beam width can be improved.