Enhancing Phased-Array Radiation Pattern Synthesis with a Hybrid Complex-Valued Deep Learning

Phased antenna arrays are essential for millimeter-wave (mmWave) communications in 5G/6G systems, enabling adaptive beamforming and precise radiation pattern control. Traditional array synthesis methods rely on analytical techniques or iterative optimization algorithms that are computationally intensive and often too slow for real-time applications. This paper presents a novel hybrid deep neural network (DNN) architecture that incorporates complex-valued neural network (CVNN) processing for rapid synthesis of phased array radiation patterns. Unlike conventional real-valued DNNs that treat amplitude and phase as separate outputs, our approach employs a CVNN output layer to directly predict complex excitations, naturally capturing the coupled amplitude-phase relationships inherent in electromagnetic wave phenomena. We trained and validated the model on an 8-element uniform linear array operating at 28 GHz, using 8000 electromagnetic simulations generated in CST Microwave Studio.  

The network accepts a desired radiation pattern (181 angular samples covering 0°–180°) as input and outputs the complex excitations for seven array elements (with one reference element fixed). Experimental results across three challenging beamforming scenarios—main-beam steering with shaped sidelobes, aggressive sidelobe suppression (target: -30 dB), and broad beam shaping—demonstrate that the DNN-CVNN consistently outperforms a baseline real-valued DNN. The hybrid model achieves sidelobe levels 15-20 dB better than the baseline, maintains sub-degree beam-pointing accuracy, and produces smooth, physically realizable excitation distributions. CST-validated patterns confirm that the learned weights directly correspond to accurate far-field radiation, with the DNN-CVNN achieving pattern synthesis in milliseconds compared to hours required by traditional optimization methods. These results establish complex-valued neural networks as a powerful and practical tool for real-time adaptive beamforming in next-generation wireless communication systems.

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