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

arXiv: https://arxiv.org/abs/2604.24538 · HTML: https://mlsanity.com/paper/2604.24538/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 47 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Builds on (most cited first, 20 of 20)

- [On the Road to 6G: Visions, Requirements, Key Technologies and Testbeds](https://mlsanity.com/paper/2302.14536/) (2023)
- [Stacked Intelligent Metasurfaces for Efficient Holographic MIMO Communications in 6G](https://mlsanity.com/paper/2305.08079/) (2023)
- [Optimal Design of Energy-Efficient Multi-User MIMO Systems: Is Massive MIMO the Answer?](https://mlsanity.com/paper/1403.6150/) (2014)
- [Energy Efficiency Maximization Precoding for Quantized Massive MIMO Systems](https://mlsanity.com/paper/2108.03048/) (2021)
- [Rate-Splitting Multiple Access for Multi-antenna Downlink Communication Systems: Spectral and Energy Efficiency Tradeoff](https://mlsanity.com/paper/2001.03206/) (2020)
- [Modeling and Architecture Design of Reconfigurable Intelligent Surfaces Using Scattering Parameter Network Analysis](https://mlsanity.com/paper/2011.11362/) (2020)
- [Enabling 6G Performance in the Upper Mid-Band by Transitioning From Massive to Gigantic MIMO](https://mlsanity.com/paper/2407.05630/) (2024)
- [Discrete-Value Group and Fully Connected Architectures for Beyond Diagonal Reconfigurable Intelligent Surfaces](https://mlsanity.com/paper/2110.00077/) (2021)
- [Reconfigurable Intelligent Surface: Power Consumption Modeling and Practical Measurement Validation](https://mlsanity.com/paper/2211.00323/) (2022)
- [Analog Computing for Signal Processing and Communications -- Part I: Computing with Microwave Networks](https://mlsanity.com/paper/2504.06790/) (2025)
- [Analog Computing for Signal Processing and Communications -- Part II: Toward Gigantic MIMO Beamforming](https://mlsanity.com/paper/2504.07477/) (2025)
- [Lossy Beyond Diagonal Reconfigurable Intelligent Surfaces: Modeling and Optimization](https://mlsanity.com/paper/2504.19744/) (2025)
- [MIMO Systems Aided by Microwave Linear Analog Computers: Capacity-Achieving Architectures with Reduced Circuit Complexity](https://mlsanity.com/paper/2506.15052/) (2025)
- [Energy Efficiency Maximization of Massive MIMO Communications With Dynamic Metasurface Antennas](https://mlsanity.com/paper/2106.09442/) (2021)
- [Capacity of MIMO Systems Aided by Microwave Linear Analog Computers (MiLACs)](https://mlsanity.com/paper/2506.05983/) (2025)
- [On the Performance of Lossless Reciprocal MiLAC Architectures in Multi-User Networks](https://mlsanity.com/paper/2601.01834/) (2026)
- [Microwave Linear Analog Computer (MiLAC)-aided Multiuser MISO: Fundamental Limits and Beamforming Design](https://mlsanity.com/paper/2601.10060/) (2026)
- [Channel Estimation in MIMO Systems Aided by Microwave Linear Analog Computers (MiLACs)](https://mlsanity.com/paper/2601.11438/) (2026)
- [Physics-Compliant Modeling and Optimization of MIMO Systems Aided by Microwave Linear Analog Computers](https://mlsanity.com/paper/2602.19379/) (2026)
- [Analog Computing with Hybrid Couplers and Phase Shifters](https://mlsanity.com/paper/2603.24604/) (2026)

## Abstract (arXiv)

In large antenna arrays, hardware power consumption becomes a dominant design constraint, making energy efficiency (EE) a first-class objective alongside spectral efficiency (SE). Microwave linear analog computer (MiLAC)-aided beamforming, whose front end is a passive reciprocal stream-to-antenna network, addresses this tension by reducing the active radio-frequency chain count 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 (MU-MISO) 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 problem and trace its Pareto boundary via a weighted-sum method that combines an alternative reduced-dimension coordinate with auxiliary-variable successive convex approximation, yielding convex per-iteration subproblems with guaranteed convergence. Numerical results on a DeepMIMO v4 deployment show MiLAC-aided beamforming substantially improves EE over digital and hybrid benchmarks at a moderate SE cost and significantly expands the achievable SE-EE operating region.