Fundamental Limits for Near-Field Sensing -- Part II: Wide-Band Systems

TL;DR

This paper establishes fundamental estimation limits for wide-band near-field sensing systems with large antenna arrays, accounting for frequency-dependent effects and parameter coupling, providing theoretical bounds and design insights.

Contribution

It derives the Cramér-Rao bounds for joint target parameter estimation in wide-band near-field sensing, extending previous work to include wide-band effects and practical system modeling.

Findings

CRBs validate the theoretical limits across various scenarios

Wide-band effects significantly influence estimation accuracy

Design insights on bandwidth, array size, and integration time

Abstract

Near-field sensing with extremely large-scale antenna arrays (ELAAs) in practical 6G systems is expected to operate over broad bandwidths, where delay, Doppler, and spatial effects become tightly coupled across frequency. The purpose of this and the companion paper (Part I) is to develop the unified Cram'er--Rao bounds (CRBs) for sensing systems spanning from far-field to near-field, and narrow-band to wide-band. This paper (Part II) derives fundamental estimation limits for a wide-band near-field sensing systems employing orthogonal frequency-division multiplexing signaling over a coherent processing interval. We establish an exact near-field wide-band signal model that captures frequency-dependent propagation, spherical-wave geometry, and the intrinsic coupling between target location and motion parameters across subcarriers and slow time. Similar as Part I using the Slepian--Bangs formulation, we derive the wide-band Fisher information matrix and the CRBs for joint estimation of target position, velocity, and radar cross-section, and we show how wide-band information aggregates across orthogonal subcarriers. We further develop tractable far-field and near-field approximations which provide design-level insights into the roles of bandwidth, coherent integration length, and array aperture, and clarify when wide-band effects. Simulation results validate the derived CRBs and its approximations, demonstrating close agreement with the analytical scaling laws across representative ranges, bandwidths, and array configurations.