Lorentzian-Constrained Holographic Beamforming Optimization in Multi-user Networks with Dynamic Metasurface Antennas

TL;DR

The paper tackles resource allocation in DMA-aided multi-user downlink MISO systems under Lorentzian resonance constraints, aiming to minimize total transmit power while satisfying SINR targets. It introduces a unified Generalized Method of Lorentzian-Constrained Holography (GMLCH) framework to project unconstrained DMA weights onto Lorentzian circles and compares LCPH, LCEH, and LCUSH mappings, then proposes Adaptive Radius Lorentzian-Constrained Holography (ARLCH) to optimize both the Lorentzian diameter and the projection phases via alternating optimization. The approach uses SDP-based alternating optimization to jointly design digital precoders and DMA weights, enabling a flexible, platform-agnostic comparison of Lorentzian mappings and improved beamforming performance. Numerical results show ARLCH achieving over 20% transmit power reductions relative to benchmarks, with gains that grow with the number of users, approaching fully digital performance in favorable conditions. The work provides a practical, extensible framework for holographic beamforming in DMA networks with potential impact on energy-efficient 6G metasurface-enabled communications, and outlines avenues for hardware validation and learning-based extensions.

Abstract

Dynamic metasurface antennas (DMAs) are promising alternatives to fully digital (FD) architectures, enabling hybrid beamforming via low-cost reconfigurable metasurfaces. In DMAs, holographic beamforming is achieved through tunable elements by Lorentzian-constrained holography (LCH), significantly reducing the need for radio-frequency (RF) chains and analog circuitry. However, the Lorentzian constraints and limited RF chains introduce a trade-off between reduced system complexity and beamforming performance, especially in dense network scenarios. This paper addresses resource allocation in multi-user multiple-input-single-output (MISO) networks under the Signal-to-Interference-plus-Noise Ratio (SINR) constraints, aiming to minimize total transmit power. We propose a holographic beamforming algorithm based on the Generalized Method of Lorentzian-Constrained Holography (GMLCH), which optimizes DMA weights, yielding flexibility for using various LCH techniques to tackle the aforementioned trade-offs. Building upon GMLCH, we further propose a new algorithm i.e., Adaptive Radius Lorentzian Constrained Holography (ARLCH), which achieves optimization of DMA weights with additional degree of freedom in a greater optimization space, and provides lower transmitted power, while improving scalability for higher number of users. Numerical results show that ARLCH reduces power consumption by over 20\% compared to benchmarks, with increasing effectiveness as the number of users grows.

Figures (12)

• Figure 1: DMA aided Multi-user downlink MISO system.
• Figure 2: Mapping of ideal DMA weights onto the Lorentzian circle ($r=0.5$) via GMLCH, parameterized by $(x_\text{c}, y_\text{c})$. (a) GMLCH with any $(x_\text{c}, y_\text{c})$ (b) LCPH with $(x_\text{c}, y_\text{c}) = (0.0, 0.0)$, (c) LCEH with $(x_\text{c}, y_\text{c}) = (0.0, 0.5)$, and (d) LCUSH with $(x_\text{c}, y_\text{c}) = (0.0, 1.0)$.
• Figure 3: (a) Lorentzian mapping with various diameters ($D$). (b) Comparison of Lorentzian mapping with $D = 1.5$ against unitary Lorentzian mapping. (c) Final form of mapped weights in (b), where Lorentzian mapping with $D = 1.5$ is normalized to satisfy the unitary condition.
• Figure 4: Beamforming optimizations with different LCH techniques for $\delta = 30\,\text{dB}$, $K = 1$ and users located at $\rho = 0.5d_\text{F}$ and $\theta \in [0^\circ, 85^\circ]$. (a) Required transmit power versus user angle ($\theta$). (b) Transmit power relative to that of the FD case versus user angle ($\theta$).
• Figure 5: Optimized beamforming weights with various LCH methods in single user scenario with $\delta = 30\,\text{dB}$. (a) User position at $\rho=0.5d_\text{F}$, $\theta=50^\circ$. (b) User position at $\rho=0.5d_\text{F}$, $\theta=80^\circ$.

Theorems & Definitions (1)

• Lemma 1