## 1 Introduction  
Conformal arrays can also be used in 5G applications to improve the performance and efficiency of wireless communication systems [1]. Indeed, 5G networks require a high density of small cells, which can be challenging to deploy in urban environments. Conformal arrays can help by providing compact and adaptable antennas that can be easily integrated into existing infrastructure, such as lamp posts or building facades. One of the main advantages of conformal arrays in 5G applications is their ability to provide directional coverage [2]. With beamforming capabilities, the arrays can steer the signal towards a specific area or user, increasing the signal strength and improving the overall network capacity. Conformal arrays are a type of antenna array that are designed to conform to the surface of a particular structure or platform, such as an aircraft, vehicle, or building. This means that instead of having a traditional flat or planar antenna array, the conformal array is shaped to fit the curvature of the structure it is mounted on, resulting in improved aerodynamics and reduced radar cross-section. Conformal arrays can use digital signal processing techniques to steer and shape the beam in multiple directions, even in real time. The combination of the conformal design and beamforming capabilities make these arrays well-suited for a variety of applications, including military and aerospace systems where high performance and low visibility are critical. They can also be used in commercial applications, such as for wireless communication or radar systems [3]. Antenna surface deformation significantly deteriorates the radiation performance of an antenna [4]. When an antenna is designed, its surface shape is carefully engineered to achieve specific radiation properties, such as beam pattern, polarization, and gain. Any deformation of the surface can cause changes in these properties, which can lead to a degradation of the antenna's performance. One common effect is the variation in the resonant frequency of antenna. This can occur when the deformation alters the physical measurements of the antenna, which in turn changes its resonant frequency. As a result, the antenna may no longer be optimized for the frequency at which it is intended to operate. Another effect of surface deformation is a change in the antenna's radiation pattern including sidelobe level (SSL) elevation, broadside beam divergence, nulls positioning alteration, and lower antenna gain. In order to moderate this surface deformation effect, it is important to include an adaptive pattern synthesis capability system in the antenna array, which can correct for the distortion and maintain the desired radiation pattern. This paper examines the impact of static deformation for several configuration of cylindrical and spherical structures of conformal array antenna, which is deformed from planar configuration. Radiation pattern synthesis in conformal array antennas is usually more complex as compared to planar arrays. This involves designing and optimizing the radiation pattern of the antenna to meet specific performance goals [5]. The radiation pattern describes the directional characteristics of the antenna's electromagnetic field, and the optimization process involves adjusting the position, orientation, and phase of the antenna elements to achieve the desired pattern. The main goal of synthesizing the array pattern in conformal arrays is to attain the desired radiation pattern through adjusting the mutual coupling effect, weight excitations, and polarization information of the array. In literature, a variety of methods and algorithms has been employed to resolve the synthesis problem for radiation pattern correction in conformal array antennas.