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

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.