Joint Location and Velocity Estimation and Fundamental CRLB Analysis for Cell-Free MIMO-ISAC

Abstract

This paper presents a fundamental performance analysis of joint location and velocity estimation in a cell-free (CF) MIMO integrated sensing and communication (ISAC) system. Unlike prior studies that primarily rely on continuous-time signal models, we consider a more practical and challenging scenario in the discrete-time digital domain. Based on the discrete received signal, we first formulate a logarithmic likelihood function (LLF) for both single- and multiple-target sensing under deterministic, unknown, and spatially varying radar cross-section (RCS) models. Building upon the proposed LLF framework, closed-form Cramér-Rao lower bounds (CRLBs) for joint location and velocity estimation are derived. These CRLBs can serve as a fundamental performance metric to guide CF MIMO-ISAC system design. To enhance tractability, we also develop a class of simplified closed-form CRLBs, referred to as approximate CRLBs, along with a rigorous analysis of the conditions under which they remain accurate. Furthermore, we investigate how the sampling rate, squared effective bandwidth, and time width influence CRLB performance. For a multiple-target scenario, the concepts of safety distance and safety velocity are introduced to characterize the conditions under which the CRLBs converge to their single-target counterparts. Extensive simulations using orthogonal frequency division multiplexing (OFDM) and orthogonal chirp division multiplexing (OCDM) validate the theoretical findings and provide practical insights for CF MIMO-ISAC system design.