Fundamental Sensing Limits of 6G Cooperative MIMO-ISAC Networks: Joint Position-Velocity CRLB and Decoupling Analysis

Yanpeng Su, Norman Franchi, Maximilian Lübke

This paper presents a Cramér-Rao lower bound (CRLB)-based performance bound analysis of cooperative multiple-input multiple-output (MIMO) integrated sensing and communications (ISAC) networks. We first show the CRLB transformation of the signal-level parameters to the state parameters (position and velocity) in cooperative ISAC networks. Unlike existing studies that primarily ignored coupling between position and velocity in the Fisher information matrix (FIM), we derive the full FIM and the corresponding exact CRLB. Particularly, the results of multi-monostatic sensing, multi-bistatic sensing, and their hybrid are discussed. Addressing the complexity and tractability, we simplify the FIM and CRLB by excluding the coupling terms between the position and velocity, and provide a criterion for determining whether the simplification is valid. The simplified CRLB benefits from low computational complexity and provides a tractable and reliable performance metric for optimization problems such as resource allocation and beamforming. Finally, the position and velocity CRLBs and the simplification-induced error are examined in the simulation. The results demonstrate that the simplified CRLB can be applied in general cases. Based on the simulation results, the impact of resource and geometric parameters on position and velocity error bounds, and the validity of the simplified CRLBs is explained through the corresponding CRLB expressions.