## 1 Introduction  
Recently, there has been an increasing need for the development of conformal arrays used in Unmanned Aerial Vehicles (UAVs) and vehicle platforms. When the conformal arrays are arranged on a curved platform shape, unlike planar arrays that require additional space for arrangement, the resistance to air can be reduced during movement, and RCS can be reduced by decreasing the protruding structure [1]. However, the electrical properties of conformal arrays change according to the curvature of the platform they are applied to, and when an array is curved, such as the noncollinear element arrangements in many common systems [2]. In some systems, nonlinearity occurs because conformal arrays must consider electrical properties in 3D space, unlike planar arrays located on the same plane.  
Several studies have been conducted on the phase calculation of the array factor to improve the electrical characteristics of the conformal arrays. The common array phase compensation of the vertical surface situation has been employed [3]. This study confirmed the S-parameter and radiation pattern by applying a \(4\times 4\) array to spherical platforms. A common array wide-angle scanning method has also been reported for vertical surface situations [4]. The authors performed beam scanning of up to 50\({}^{\circ}\) on conformal arrays. To improve the phase of the conformal arrays, the array factor was not calculated based on the location of the element, but the location was expressed as a location on the platform, considering the shape of the platform. However, each time the shape of the platform changes, the calculation formula must be changed (the equation for location calculation according to the shape of the platform appears differently every time).  
Herein, we propose a unified phase calculation method employing coordinates in three-dimensional (3D) space based on the phase composition method for common arraysthat include all the previous studies. Unlike previous studies that focused on specific platforms, this method applies to all random array grids and nonlinear arrays. Depending on the characteristics of a conformal array, beamforming through amplitude control is difficult. This differs from the case of widely used planar arrays based on the non-periodicity and additional coordinate axes. Amplitude tapering of conformal arrays has also been studied. Based on the elevation beam design method for airborne conformal arrays, the amplitude optimization has been studied for only one situation by optimizing the Bernstein polynomial [5]. In beam synthesis for conformal-array antennas with efficient tapering, the amplitude has been applied using the Least Square Method [6]. Conformal-array amplitude weight optimization has also been employed using the Bezier curve [7]. In addition, aperiodic and conformal arrays have been studied [8; 9; 10; 11; 12; 13; 14; 15; 16]. Previous studies on the amplitude application method for conformal arrays have shown aspects that do not consider phase-related parts and those that are applicable to only one case. We propose an amplitude tapering method that optimizes the above-described phase calculation method and Bernstein polynomials through Genetic Learning Particle Swarm Optimization (GLPSO) [17]. The performance of the proposed method is improved based on the array factor of conformal arrays, which is confirmed by CST simulations and MATLAB.  
The rest of the paper is arranged as follows. Pattern degradation improvement of conformal arrays and the array factor for nonplanar arrays are derived in Section 2.1 through phase compensation and verified in Section 2.2 by comparing the EM simulation and array factor calculations based on the derived array factor. In Section 2.3, we propose an amplitude tapering method to which the derived array factor could be applied. In Section 3, we verify the final array factor to which the proposed phase calculation and the amplitude tapering methods are applicable. Conclusions are presented in Section 4.