Quantization-Aware EE Optimization and SE-EE Tradeoff for MiLAC-Aided MU-MISO Beamforming

In large antenna arrays, hardware power consumption becomes a dominant design constraint, making energy efficiency (EE) a primary design objective alongside spectral efficiency (SE). Microwave linear analog computer (MiLAC)-aided beamforming, whose front end is a passive reciprocal stream-to-antenna network, emerges as a promising candidate to address this tradeoff by reducing the number of active radio-frequency chains to the stream number, at a moderate SE cost. Despite this promise, no EE optimization framework has been established for MiLAC-aided beamforming that accounts for digital-to-analog converter quantization noise and post-quantized transmit power. We fill this gap for downlink multiuser multiple-input single-output systems by formulating quantization-aware EE maximization over the MiLAC-feasible beamformer and characterizing the resulting SE-EE tradeoff. Three contributions follow. First, we prove a row-space optimality property of the effective MiLAC-aided beamformer, yielding an equivalent reduced-dimension reformulation whose complexity scales with the stream number rather than the antenna number. Second, we develop a low-complexity Dinkelbach-weighted minimum mean-square error algorithm aided by projected gradient descent that is guaranteed to converge to a stationary point. Third, we cast the SE-EE tradeoff as a multi-objective optimization problem and trace the tradeoff boundary via the weighted-sum method. An alternative reduced-dimension variable removes the bilinearity in the original parameterization, and an auxiliary-variable lift combined with successive convex approximation yields a convex per-iteration subproblem with guaranteed convergence. Numerical results on a DeepMIMO v4 deployment demonstrate that MiLAC-aided beamforming substantially improves EE over digital and hybrid benchmarks at a moderate SE cost. The tradeoff boundary analysis further shows that MiLAC-aided beamforming significantly expands the achievable SE-EE operating region relative to digital and hybrid architectures.