Circuit-Compliant Optimization of Dynamic Metasurface Antennas for Near-Field Localization

This paper presents an optimization framework for near-field localization with Dynamic Metasurface Antenna (DMA) receivers. This metasurface technology offers enhanced angular and range resolution realizing efficient hybrid Analog and Digital (A/D) BeamForming (BF) with sub-wavelength-spaced metamaterials of tunable responses. However, the vast majority of the state-of-the-art DMA designs is based on an idealized model for their reception operation, which neglects several practical aspects, such as the inevitable mutual coupling among the densely deployed metamaterials within a given aperture. Capitalizing on a recent circuit-compliant active metasurface model, we present a novel mutual-coupling-aware framework for localization-optimized hybrid A/D BF weights at the reception DMA. To deal with the intrinsic complexity of the deployed model, we introduce first- and second-order approximations for the DMA analog BF matrix that enable efficient optimization, while maintaining accuracy. We derive the Cramér-Rao Bound for the user position estimation which serves as our design objective for the hybrid A/D BF matrices. Closed-form solutions for these matrices for both approximations are presented, whose validity is confirmed via numerical investigations. It is also demonstrated that the proposed DMA design outperforms state-of-the-art multi-antenna reception architectures optimized for the same localization objective.