Mismatch Analysis and Cooperative Calibration of Array Beam Patterns for ISAC Systems

Integrated sensing and communication (ISAC) is a key technology for enabling a wide range of applications in future wireless systems. However, the sensing performance is often degraded by model mismatches caused by geometric errors (e.g., position and orientation) and hardware impairments (e.g., mutual coupling and amplifier non-linearity). This paper focuses on the angle estimation performance with antenna arrays and tackles the critical challenge of array beam pattern calibration for ISAC systems. To assess calibration quality from a sensing perspective, a novel performance metric that accounts for angle estimation error, rather than beam pattern similarity, is proposed and incorporated into a differentiable loss function. Additionally, a cooperative calibration framework is introduced, allowing multiple user equipments to iteratively optimize the beam pattern based on the proposed loss functions and local data, and collaboratively update global calibration parameters. The proposed models and algorithms are validated using real-world beam pattern measurements collected in an anechoic chamber. Experimental results show that the angle estimation error can be reduced from {$\textbf{1.01}^\circ$} to $\textbf{0.11}^\circ$ in 2D calibration scenarios, and from $\textbf{5.19}^\circ$ to $\textbf{0.86}^\circ$ in 3D calibration ones.