# Phased Antenna-Array Synthesis Using Taylor-Series Expansion and Neural Networks
## 6 Conclusions  
In conclusion, this paper has presented a novel methodology for the synthesis of phased antenna arrays (PAAs) by combining Taylor-series expansion with neural networks (NNs), achieving notable improvements over traditional techniques. Taylor expansion offers an analytical foundation that simplifies the optimization process by approximating complex radiation behaviors using polynomial expressions. This enables the derivation of more efficient and accurate formulations for beamforming and radiation characteristics. The neural network component complements this by learning the nonlinear relationships between design parameters and target performance metrics, allowing for adaptive tuning and real-time adjustment. The main contributions of this work include the following: (i) the integration of Taylor -series modeling with neural network refinement, (ii) simulation-based validation on a realistic millimeter-wave array, and (iii) performance improvements in sidelobe control and computational efficiency compared to traditional techniques. The proposed method was validated through simulations and an electromagnetic analysis of a 16-element linear array operating at millimeter-wave frequencies (28.14 GHz and 37.88 GHz), ensuring relevance to 5G and 6G use cases. The simulation results demonstrate that the hybrid Taylor-NN framework reduces computational complexity, enhances adaptability, and enables broader design-space exploration. The validation confirms the method's practical potential for the design of efficient antenna arrays in advanced communication and radar systems. It is worth noting that, although experimental measurements were not included in the current study, the simulation framework was built upon detailed electromagnetic modeling using realistic substrate and layout parameters. Future investigations may involve hardware prototyping and empirical validation as part of an extended deployment-oriented study. While the current work focused on uniform linear arrays, we acknowledge its present limitations in addressing more complex configurations such as conformal or sparse geometries, which are prevalent in aerospace and vehicular applications. Future extensions will target these scenarios by incorporating non-linear geometries, generalized position encoding, and data-driven training strategies. This work marks a significant advancement in phased antenna array synthesis, highlighting the benefits of integrating analytical modeling with artificial intelligence to enable robust and flexible antenna design. By integrating scalability, adaptability, and extensibility into the design pipeline, the proposed approach provides a promising solution to modern challenges in wireless communication and radar engineering. Although experimental measurements are not included in the current study, the simulation framework is built upon detailed electromagnetic modeling using realistic substrate and layout parameters. Future investigations may involve hardware prototyping and empirical validation as part of an extended deployment-oriented study. **Author Contributions:** Conceptualization, A.K., R.K. and R.G. ; methodology J.F. and I.E.G. ; software, A.K., R.G. and W.A. ; validation, I.E.G. and J.F. ; formal analysis, L.B.A. ; investigation, L.L. ; resources I.E.G. ; data curation, A.K. and R.G. ; writing--original draft preparation, A.K. and R.G. writing review and editing, L.B.A. and I.E.G. ; visualization, R.G. and R.K.; supervision, L.B.A. ; project administration. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by Umm Al-Qura University, Saudi Arabia, Grant Number 25 UQU4361156 GSSR03. The APC was funded by Umm Al-Qura University. **Data Availability Statement:** The data supporting the findings of this study are available within the article. Further inquiries can be directed to the corresponding authors. **Conflicts of Interest:** The authors declare no conflicts of interest.