Integrated Channel Estimation and Localization in ISAC With Spatially Distributed Targets: A Parametric Approach

Abstract

A fundamental task in integrated sensing and communication systems is channel estimation and localization, where sensing-related parameters are intrinsically embedded in the propagation channel and must be inferred from pilot-aided observations. However, most existing approaches rely on a point-target assumption, which becomes inadequate when sensing objects are spatially distributed and unresolved in angle, range, or velocity. In such scenarios, enforcing a point-target model fails to capture target extent information, resulting in biased parameter estimates and performance saturation even at high signal-to-noise ratios (SNRs). To address this limitation, we propose a compact parametric representation that unifies point-like and spatially distributed targets by augmenting conventional localization parameters with a set of spread parameters that explicitly characterize target extent. Based on this model, we develop a canonical polyadic decomposition-based estimator that exploits the amplitude–phase structure of spatial, temporal, and frequency steering responses to jointly estimate localization and spread parameters with reduced search dimensionality and inherent parameter pairing. Furthermore, we establish a performance benchmark by deriving the misspecified Cramér–Rao bound (MCRB) corresponding to model mismatch and comparing it with the correctly specified Cramér–Rao lower bound, thereby quantifying the fundamental performance loss incurred by neglecting target spread information or using an inaccurate spread distribution. Simulation results demonstrate that the proposed method consistently achieves improved accuracy and robustness across a wide range of SNRs and target spread conditions.