Hybrid Adaptive Genetic Algorithm for Massive MIMO Beamforming: True Hybrid Precoding with MMSE Digital Stage

Millimetre-wave massive MIMO systems rely on hybrid analogue-digital precoding to keep RF hardware costs manageable without sacrificing spectral efficiency. Selecting the phase-shifter weights, however, poses a non-convex optimization problem that has no closed-form solution and resists gradient-based solvers because of the constant-modulus feasibility requirement. This paper proposes the Hybrid Adaptive Genetic Algorithm (HAGA), which extends a standard genetic algorithm with two targeted enhancements: a stagnation-triggered adaptive mutation schedule that guards against premature convergence, and a coordinate descent greedy refinement pass that sharpens individual solutions while honoring the constant-modulus constraint exactly, with no projection step required. The analogue beamformer produced by HAGA feeds a closed-form MMSE digital precoder, yielding a complete two-stage hybrid precoding pipeline. Evaluated on a 3GPP-like clustered mmWave channel (Nt = 64, NRF = 16, K = 8, 30 independent Monte Carlo trials), HAGA achieves a mean sum-rate of 38.82 bps/Hz, outperforming a plain GA by 22.6% and PSO by 47.9%. Both gains are statistically conclusive (p < 0.001, Mann-Whitney U; Cohen's d = 3.37 and d = 6.79, respectively). An ablation study shows that the greedy refinement drives virtually all of the improvement (d = 3.14, p < 0.001), while adaptive mutation alone contributes negligibly (d = 0.036, p = 0.44). Further experiments characterize phase quantization (3-bit retains 91.5% of the continuous-phase result), scalability with SNR, antenna count, user count, and RF-chain count, energy efficiency (2.05 bps/Hz/W under the Bjornson hardware model), and robustness to CSI estimation errors. All simulation code is released publicly to support reproducibility.