Cram\'er-Rao Bound Optimization for Near-Field Sensing with Continuous-Aperture Arrays

TL;DR

This paper introduces a CRB optimization framework for near-field sensing using continuous-aperture arrays, demonstrating significant performance improvements over traditional discrete arrays through a novel gradient descent method.

Contribution

It develops a CRB-based optimization approach for CAPAs, deriving the optimal source current structure and proposing a low-complexity SMGD algorithm for enhanced near-field sensing.

Findings

CAPAs outperform SPDAs with tenfold sensing performance improvement.

The SMGD method effectively minimizes CRB with reduced computational complexity.

The proposed framework exploits full spatial degrees of freedom for improved target localization.

Abstract

A Cram\'er-Rao bound (CRB) optimization framework for near-field sensing (NISE) with continuous-aperture arrays (CAPAs) is proposed. In contrast to conventional spatially discrete arrays (SPDAs), CAPAs emit electromagnetic (EM) probing signals through continuous source currents for target sensing, thereby exploiting the full spatial degrees of freedom (DoFs). The maximum likelihood estimation (MLE) method for estimating target locations in the near-field region is developed. To evaluate the NISE performance with CAPAs, the CRB for estimating target locations is derived based on continuous transmit and receive array responses of CAPAs. Subsequently, a CRB minimization problem is formulated to optimize the continuous source current of CAPAs. This results in a non-convex, integral-based functional optimization problem. To address this challenge, the optimal structure of the source current is derived and proven to be spanned by a series of basis functions determined by the system geometry. To solve the CRB minimization problem, a low-complexity subspace manifold gradient descent (SMGD) method is proposed, leveraging the derived optimal structure of the source current. Our simulation results validate the effectiveness of the proposed SMGD method and further demonstrate that i)~the proposed SMGD method can effectively solve the CRB minimization problem with reduced computational complexity, and ii)~CAPA achieves a tenfold improvement in sensing performance compared to its SPDA counterpart, due to full exploitation of spatial DoFs.