## 1 Introduction  
Millimeter-wave (mmWave) communication systems have emerged as a key technology for meeting the ever-increasing demand for high-speed wireless connectivity in the era of 5G and beyond. Operating at frequencies above 30 GHz, mmWave systems offer abundant spectrum resources and the potential for multi-gigabit data rates, promising revolutionary advancements in wireless communication networks. Central to the success of mmWave technology are antenna arrays, which enable beamforming, spatial multiplexing, and enhanced spectral efficiency. However, the performance of mmWave antenna arrays can be significantly influenced by structural distortions, such as mechanical deformations and environmental conditions, which may alter the antenna's radiation characteristics and beamforming capabilities. Traditional design approaches often neglect the coupled effects of structural dynamics and electromagnetic behavior, leading to suboptimal performance and reliability issues in practical deployments [1; 2; 3; 4]. In [3], the influence of environmental factors is investigated, such as temperature variations and wind-induced vibrations, on the performance of mmWave antenna arrays. The findings revealed that thermal expansion and mechanical vibrations can lead to deviations in beam steering and the degradation of antenna gain, underscoring the need for robust antenna designs capable of withstanding environmental uncertainties. Therefore, there is a critical need for comprehensive sensitivity studies to assess the impact of structural distortion on the performance of mmWave antenna arrays. Antenna arrays with high detection and tracking capacity are multifunctional, highly reliable, and have been employed in different applications [1; 2; 3]. With the development of technological advancements, there is a high demand for correct and accurate design mechanisms and array optimization. The beamwidth, gain, sidelobe, and boresight pointing accuracy of the antenna are the determinants of the performances of array antennas [3]. Also, random errors emanated from fabrication/manufacturing, assembling procedure, and structural/mechanical deformation are caused by vibration, impact force, and high thermal power, which results in the displacement of elements and consequently affects the performance of the antenna, such as higher sidelobe level, gain loss, inaccurate boresight pointing, and beamwidth broadening [4; 5; 6; 7]. The effect is more serious at a higher frequency of operation and will be more in the implementation process of future 5G technology (i.e., at mmWave). The analysis of the requirements for next-generation wireless communication systems to meet future applications highlights the need for higher transmission speeds and very low latency as critical aspects. While precise standards are yet to be established, the ambitious goals identified for 5G and beyond wireless systems include the following: fast data transfer rates; aiming for 1 TB per second download speed; wide bandwidth availability; improved coverage; almost zero latency (approximately 0.1 ms); increased overall data traffic and number of connected users; reduced energy consumption; and the capability of connecting intelligence rather than just objects through the use of Artificial Intelligence [8; 9]. The combination of systematic distortion and random position error causes random element positioning which results in degraded electromagnetic performance of the array [10; 11; 12; 13; 14]. It causes shortened communication distance and low resistance to interference, which severely limits high performance actualization of antenna arrays. Hence, structural errors or deformation limits the realization of desired antenna array performance. So, deeply exploring the relationship between structural error and EM performance of antenna arrays in the presence of random element positioning is necessary [15; 16]. There are some previous studies that concentrate on the impact of mechanical distortion and random position error on array performance.