# Phased Antenna-Array Synthesis Using Taylor-Series Expansion and Neural Networks
## 5 Neural Networks for Synthesis and Optimization of Antenna Arrays
### Benefits of the Taylor-Neural Network Architecture  
The integration of Taylor-series phase synthesis with neural network optimization offers a powerful solution to improve antenna array performance. This hybrid approach effectively reduces sidelobe levels, shapes the main beam, and enhances overall directivity. While the Taylor method provides a mathematically grounded initial phase distribution, it faces limitations in handling practical constraints such as irregular element spacing or varying antenna geometries. Neural networks complement this by learning from data and adapting to complex design conditions, including those affected by environmental factors or hardware imperfections. Compared to traditional methods like genetic algorithms (GAs) or particle swarm optimization (PSO), neural networks require less computational time once trained and can rapidly adjust excitation parameters to meet performance targets. Moreover, their ability to generalize allows them to be used across different array configurations, including MIMO antennas, radar systems, and satellite platforms, making the approach versatile and scalable. The hybrid Taylor-neural network approach can be summarized as follows:  
\[\Phi_{\text{opt}}(\theta)=f\left(\sum_{k=0}^{M}a_{k}(\theta-\theta_{0})^{k}; \mathbf{W},b\right) \tag{19}\]  
where  
* \(\Phi_{\text{opt}}(\theta)\) is the optimized phase distribution;
* \(f\) represents the neural network optimization function;
* \(\mathbf{W}\) and \(b\) are the weights and biases of the neural network;
* \(a_{k}\) are the Taylor-series coefficients for phase distribution. The Taylor-neural network architecture provides a robust framework for optimizing antenna array designs, combining the mathematical precision of the Taylor method with the adaptability and learning power of neural networks. This hybrid approach enables efficient, high-performance antenna array synthesis capable of meeting the stringent demands of modern communication systems. The Taylor method for antenna array synthesis is a well-established approach used to optimize the distribution of the array's element amplitudes in order to achieve a desired radiation pattern, such as minimizing side lobes while maintaining the main lobe characteristics. This method involves solving an optimization problem to determine the appropriate excitation levels for each element in the array, ensuring that the synthesized radiation pattern meets specific requirements. The Taylor method is widely used for controlling side lobe levels in antenna arrays, providing a smooth, continuous pattern that reduces interference from unwanted directions. When applying neural networks to this problem, the Taylor method can be combined with machine learning techniques to enhance the process of optimizing the antenna array design. In this context, neural networks can learn from a dataset that includes different configurations of antenna arrays and their corresponding radiation patterns. The neural network is trained to recognize the relationship between the array's excitation parameters and the resulting radiation pattern, improving its ability to predict and optimize array designs. The dataset used for training typically contains both the array configurations (as input features) and their associated radiation patterns (as target outputs). Through this approach, the neural network can generalize and efficiently identify optimal solutions for antenna array synthesis, reducing the computational cost and time required compared to traditional methods. In essence, by using the Taylor method as a dataset, neural networks can become an effective tool for synthesizing antenna arrays, automating the design process, and optimizing performance in terms of radiation pattern control and interference management. Table 3 compares various neural network training algorithms and their performance characteristics. The Levenberg-Marquardt (LM) algorithm is known for its high convergence rate, making it efficient in reaching an optimal solution quickly.