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

This paper investigates joint location and velocity estimation, along with their fundamental performance bounds analysis, in a cell-free multi-input multi-output (MIMO) integrated sensing and communication (ISAC) system. First, unlike existing studies that derive likelihood functions for target parameter estimation using continuous received signals, we formulate the maximum likelihood estimation (MLE) for radar sensing based on discrete received signals at a given sampling rate. Second, leveraging the proposed MLEs, we derive closed-form Cramer-Rao lower bounds (CRLBs) for joint location and velocity estimation in both single-target and multiple-target scenarios. Third, to enhance computational efficiency, we propose approximate CRLBs and conduct an in-depth accuracy analysis. Additionally, we thoroughly examine the impact of sampling rate, squared effective bandwidth, and time width on CRLB performance. For multiple-target scenarios, the concepts of safety distance and safety velocity are introduced to characterize conditions under which the CRLBs for multiple targets converge to their single target counterparts. Finally, extensive simulations are conducted to verify the accuracy of the proposed CRLBs and the theoretical results using state-of-the-art waveforms, namely orthogonal frequency division multiplexing (OFDM) and orthogonal chirp division multiplexing (OCDM).