Dynamic Metasurface Antennas With Discrete Phase Shifts: Performance Analysis and Beamforming Methods

Dynamic metasurface antennas (DMAs), with their ability to manipulate electromagnetic waves using tunable metamaterial elements, provide a promising solution for beamforming in next-generation wireless communication systems. However, practical constraints, such as discrete phase shifts and the Lorentzian constraint, pose significant challenges for their optimization. This paper investigates the beamforming optimization problem in a downlink system where a base station (BS) equipped with a DMA operates under arbitrary discrete phase shift constraints. We propose two algorithms: the closest point projection (CPP) algorithm, which efficiently projects continuous-phase solutions onto discrete domains with lower complexity, and the optimal <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i>-phase beamforming (OMPB) algorithm, which is proven to achieve the globally optimal solution for discrete phase configurations. We derive closed-form expressions for the quantization performance loss and average signal-to-noise ratio (SNR). Our analysis reveals that the quantization-induced performance losses for 1-bit, 2-bit, and 3-bit uniform phase configurations are 3.74 dB, 0.87 dB, and 0.22 dB, respectively. Extensive Monte-Carlo simulations validate the theoretical analysis and demonstrate that the proposed methods achieve notable performance gains over traditional relaxation and random algorithms.