GRU-Based Beam Pattern Synthesis for Optimized Uniform Linear Antenna Arrays

This study presents a deep learning-based framework for beam pattern synthesis in optimized uniform linear antenna arrays, combining Differential Evolution–based pre-optimization with recurrent neural network (RNN) modeling. Radiation patterns are first generated to satisfy sidelobe suppression and directivity constraints and are then used to train recurrent models that learn the mapping between radiation patterns and complex excitation parameters. A formal mathematical formulation of the Simple RNN, Gated Recurrent Unit (GRU), and Long Short-Term Memory (LSTM) architectures is provided, together with a per–time-step computational cost analysis based on dominant matrix–vector multiplications. A comparative evaluation under identical training conditions shows that gated architectures significantly outperform the standard RNN. Although the LSTM achieves the lowest prediction errors, the GRU attains comparable performance with reduced structural complexity. Beam pattern synthesis experiments for unseen steering directions demonstrate accurate reconstruction of main lobe alignment, sidelobe levels (approximately −12 to −13 dB), and directivity values close to 8 dB. The floating-point operations (FLOPs) analysis indicates that the GRU requires fewer dominant operations per time step than the LSTM, potentially reducing computational cost and energy consumption in resource-constrained beamforming applications.