# Phased Antenna-Array Synthesis Using Taylor-Series Expansion and Neural Networks
###### Abstract  
This paper presents a novel approach to synthesizing phased antenna arrays (PAAs) by combining Taylor-series expansion with neural networks (NNs), enhancing the PAA synthesis process for modern communication and radar systems. Synthesizing PAAs is crucial for these systems, offering versatile beamforming capabilities. Traditional methods often rely on complex analytical formulations or numerical optimizations, leading to suboptimal solutions or high computational costs. The proposed method uses Taylor-series expansion to derive analytical expressions for PAA radiation patterns and beamforming characteristics, simplifying the optimization process. Additionally, neural networks are employed to model the intricate relationships between PAA parameters and desired performance metrics, providing adaptive learning and real-time adjustments. A validation of the proposed method is performed on a dual-band 5G antenna, which exhibits marked resonances at 28.14 GHz and 37.88 GHz, with reflection coefficients of \(S_{11}=-19\) dB and \(S_{11}=-19.33\) dB, respectively. The integration of Taylor expansion with NNs offers improved efficiency, reduced computational complexity, and the ability to explore a broader design space. Simulation results and case studies demonstrate the effectiveness and applicability of the approach in practical scenarios. This work represents a significant advancement in PAA synthesis, showcasing the synergistic integration of mathematical modeling and artificial intelligence for optimized antenna design in modern communication and radar systems. Taylor; neural networks; radiation pattern; phased antenna array; beamforming; 5G +
Footnote †: journal: _Jet. of the IEEE Transactions on_  
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0 At its core, the [PERSON] method, founded on mathematical principles, provides engineers with a robust framework for approximating complex functions through series expansions. Within the context of antenna arrays, this method enables the manipulation of radiation patterns by fine-tuning polynomial coefficients, affording precise control over crucial parameters like beamwidth, sidelobe levels, and null steering [2; 3]. Complementing this mathematical prowess, neural networks harness their intrinsic learning capabilities to optimize these coefficients based on desired radiation patterns [4; 5]. Through iterative training processes, neural networks iteratively adjust the Taylor-series coefficients to minimize discrepancies between predicted and desired radiation patterns, refining their understanding with each iteration. This collaborative optimization process enables antenna arrays to achieve remarkable levels of performance across a myriad of applications. For instance, in beamforming, this integrated approach facilitates the precise steering of radiation beams towards specific directions while mitigating interference from undesired sources, enhancing signal quality and coverage. Furthermore, it enables the customization of radiation patterns to suit diverse application requirements, such as minimizing sidelobes for radar systems or optimizing coverage patterns for wireless communication networks [6; 7]. Unlike previous methods that treat analytical and machine learning techniques separately, this work introduces a hybrid synthesis framework where Taylor series-based excitation is used to guide and initialize a neural network model, resulting in enhanced optimization and interpretability. Additionally, in environments prone to interference, adaptive antenna arrays equipped with neural networks can dynamically adjust radiation patterns in real time to mitigate interference sources, ensuring robust performance even in challenging operating conditions.