A Hybrid HHO–CMA-ES Framework for Unified Linear Antenna Array Synthesis and Beamforming Optimization in 5G/6G Wireless Networks

Beamforming for linear antenna arrays (LAAs) has become a critical research topic in advanced 5G and emerging 6G wireless communication systems due to the increasing demand for high spectral efficiency, interference mitigation, and enhanced radiation performance. This paper proposes an enhanced hybrid optimization framework based on Harris Hawks Optimization integrated with the Covariance Matrix Adaptation Evolution Strategy (HHO–CMA-ES) for unified LAA synthesis. The proposed approach simultaneously optimizes excitation amplitudes, phase shifts, and inter-element positions to achieve substantial peak sidelobe level (PSLL) reduction while preserving desirable beam characteristics. The optimization performance of the proposed method is systematically evaluated against several widely used metaheuristic algorithms, including the Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Whale Optimization Algorithm (WOA), Flower Pollination Algorithm (FPA), and conventional Harris Hawks Optimization (HHO), under identical simulation conditions. Simulation results obtained for a 20-element LAA demonstrate the superior effectiveness of the proposed HHO–CMA-ES framework across multiple optimization scenarios. In amplitude-only optimization, the proposed method achieves a PSLL of −41.746 dB, corresponding to an improvement of approximately 29.3% compared with WOA and more than 88% relative to GA. For amplitude–phase optimization, HHO–CMA-ES improves PSLL by nearly 21% compared with WOA. In the amplitude–position scenario, the proposed approach achieves the best performance with a PSLL of −44.54 dB, yielding an approximately 63% improvement over PSO and more than 111% over GA. Furthermore, the proposed framework exhibits faster convergence, improved solution stability, and enhanced beamforming robustness, confirming its suitability for high-dimensional antenna synthesis problems in future 5G/6G communication systems.