## 5 Conclusions  
In conclusion, this research paper has presented a comprehensive sensitivity study of mmWave antenna arrays to structural distortion phenomena, utilizing a novel coupled structural-electromagnetic statistical concept. Structural error in an array causes elements of the array to be random, thereby affecting antenna array performance. This effect has been modeled, analyzed, and compared with parameters taken from systematic distortion plus random samples of errors. The random error causes unpredictable antenna electromechanical performance, particularly the sidelobe levels as compared to the beamwidth and antenna gain. Parameters obtained from the proposed model show higher accuracy than the random sample errors. The performance of the coupled structure electromagnetic statistical model is nearly the same as the performance average of the large random samples. The proposed method was validated or benchmarked via the popular HFSS software, and good agreement was observed. By considering the coupled effects of structural and electromagnetic phenomena, engineers and researchers can develop robust antenna array designs that are resilient to structural distortions and environmental variations. Therefore, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Performance** & **Sample 1** & **Sample 2** & **Sample 3** & **Statistical Random Error** \\ \hline \hline \multicolumn{5}{c}{Boresight pointing (\({}^{\circ}\))} \\ \(\phi=0^{\circ}\) & \(+0.09\) & \(+0.23\) & \(-0.22\) & \(+0.25\) \\ \(\phi=90^{\circ}\) & \(-0.21\) & \(+0.23\) & \(+0.28\) & \(+0.31\) \\ Beam width (\({}^{\circ}\)) & \(\phi=0^{\circ}\) & \(+0.12\) & \(+0.20\) & \(+0.23\) & \(+0.25\) \\ \(\phi=90^{\circ}\) & \(+0.17\) & \(+0.30\) & \(+0.23\) & \(+0.33\) \\ Gain loss (dB) & \(-1.99\) & \(-2.44\) & \(-1.78\) & \(-2.14\) \\ First SLL (dB) & & & & \\ \(\phi=0^{\circ}\) & \(+0.45\) & \(+0.31\) & \(+0.31\) & \(+0.03\) \\ \(\phi=90^{\circ}\) & \(+0.53\) & \(+1.54\) & \(+1.96\) & \(+0.03\) \\ Second SLL (dB) & & & & \\ \(\phi=0^{\circ}\) & \(-0.41\) & \(-1.22\) & \(-0.09\) & \(-0.64\) \\ \(\phi=90^{\circ}\) & \(+0.82\) & \(-0.13\) & \(-1.52\) & \(-0.89\) \\ Third SLL (dB) & & & & \\ \(\phi=0^{\circ}\) & \(+0.52\) & \(-3.82\) & \(+1.14\) & \(-0.41\) \\ \(\phi=90^{\circ}\) & \(-1.31\) & \(+0.17\) & \(+0.57\) & \(-0.41\) \\ Fourth SLL (dB) & & & & \\ \(\phi=0^{\circ}\) & \(+1.65\) & \(-0.23\) & \(-4.54\) & \(-0.24\) \\ \(\phi=90^{\circ}\) & \(-0.81\) & \(+1.15\) & \(-0.43\) & \(-0.24\) \\ Fifth SLL (dB) & & & & \\ \(\phi=0^{\circ}\) & \(-0.76\) & \(-0.43\) & \(+0.44\) & \(-0.11\) \\ \(\phi=90^{\circ}\) & \(-2.72\) & \(-1.78\) & \(+1.12\) & \(-0.12\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance parameters with various random error samples and systematic distortion (+ implies right hand side of \(\theta=0^{\circ}\) and \(-\) means left hand side of \(\theta=0^{\circ}\)). the model provides guidance towards the determination of the optimal performance-driven structure tolerance. Looking ahead, future research directions may involve the development of advanced modeling techniques to capture the dynamic interactions between structural dynamics, electromagnetic fields, and environmental factors in mmWave antenna arrays. Additionally, experimental validation and field trials are essential to validate the effectiveness of proposed mitigation strategies and ensure the practical applicability of our findings in real-world scenarios. Overall, the insights gained from this study contribute to the advancement of mmWave communication technology, offering valuable guidance for the design, deployment, and optimization of next-generation wireless networks. By addressing the challenges posed by structural distortions at mmWave frequencies, we can unlock the full potential of mmWave technology and pave the way for the seamless integration of high-speed, reliable, and resilient wireless communication systems in the era of 5G and beyond. Conceptualization, O.J.F. ; methodology, O.J.F. and T.S. ; software, T.S. ; validation, O.J.F. and T.S.