Electromagnetics-Compliant Optimization of Dynamic Metasurface Antennas for Bistatic Sensing

Dynamic Metasurface Antennas (DMAs) are recently attracting considerable research interests due to their potential to enable low-cost, reconfigurable, and highly scalable antenna array architectures for next generation wireless systems. However, most of the existing literature relies on idealized models for the DMA operation, often overlooking critical structural and physical constraints inherent to their constituent metamaterials. In this paper, leveraging a recently proposed model for this antenna architecture incorporating physically consistent modeling of mutual coupling and waveguide propagation losses, we optimize DMA-based transmission for bistatic sensing. A tractable approximation for the DMA response is first presented, which enables efficient optimization of the dynamically reconfigurable Lorentzian-constrained responses of the array's metamaterials. In particular, we formulate a robust beamforming optimization problem with the objective to minimize the worst-case position error bound, in the presence of spatial uncertainties for the environment's scatterers as well as synchronization uncertainties at the analog combining multi-antenna receiver. To address the resulting high computational complexity due to the possibly excessive number of metamaterial-based antennas and their operation constraints, two low complexity beamforming design approaches are presented that perform offline searching over a novel beam codebook. The accuracy of all presented DMA designs is assessed by means of Monte Carlo simulations for various system parameters, confirming that accurately modeling mutual coupling is essential for maintaining increased localization performance. It is also shown that, even under positioning and synchronization uncertainties, the proposed designs yield accuracy comparable to their fully digital and analog counterparts, while adhering to the structural DMA constraints.