Phase-only synthesis of cosecant-squared patterns with reduced sidelobes in large planar arrays via physics-informed deep neural networks

This paper introduces a deep learning-based framework for phase-only synthesis of cosecant-squared (csc²) radiation patterns in planar antenna arrays with high efficiency and accuracy. The proposed method employs a physics-informed deep neural network (PIDNN), where the training process is guided by a loss function that enforces consistency between the desired and generated radiation patterns. By embedding physical constraints into the learning procedure, the model effectively achieves two critical objectives: suppression of sidelobe level (SLL) and minimization of ripples within the shaped beam region. To meet the target csc² profile under sidelobe constraints, only the phase excitations of the array elements are optimized, reducing the complexity of the problem. The performance of the proposed approach is evaluated against established optimization methods, including genetic algorithms (GA) and particle swarm optimization (PSO). Numerical and statistical analyses demonstrate that the PIDNN provides superior results in terms of pattern fidelity, loss function convergence, and computation time, particularly for large-scale planar arrays.

School of Computer Science and Technology, Shandong Xiehe University, Jinan, 250109, Shandong, China

Microwave Engineering Dept, Electronics Research Institute (ERI), Cairo, 11843, Egypt

The authors declare no competing interests.

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Sallam, T., Attiya, A.M. Phase-only synthesis of cosecant-squared patterns with reduced sidelobes in large planar arrays via physics-informed deep neural networks. Sci Rep (2026). https://doi.org/10.1038/s41598-026-58299-z

DOI: https://doi.org/10.1038/s41598-026-58299-z

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