Initial Excitation Estimation for DMAs via Amplitude-Only Measurements

Dynamic metasurface antennas (DMAs) enable energy-efficient implementations of massive multiple-input multiple-output (MIMO) systems by integrating a phase-shifting mechanism into the radiation elements. However, the unique hardware characteristics of DMAs, such as phase-amplitude coupling and limited phase-shifting capabilities, pose new challenges for excitation estimation. This paper presents two amplitude-only estimation methods tailored for DMAs. First, a Levenberg–Marquardt (LM) method-based estimator is developed, achieving accurate reconstruction under general DMA configurations via iterative optimization. To reduce complexity, a linear estimator is further introduced by reformulating the problem as a linear least-squares one, avoiding iteration while maintaining comparable performance in typical DMA scenarios, such as Lorentz-constrained or uniform-amplitude designs. To improve scalability in large-scale DMA systems, a group-based strategy is employed. Closed-form error expressions are also derived to theoretically characterize the estimation performance. The proposed methods are validated through both simulations and experiments on a dedicated testbed. The results demonstrate that the proposed methods achieve higher accuracy than the conventional approach under practical DMA constraints.