Distributed Compression Method for Channel Calibration in Cell-Free MIMO ISAC Systems

This paper investigates the challenge of acquiring channel state information at the transmitter (CSIT) in cell-free massive multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) systems operating in time-division duplex (TDD) mode. Although channel state information at the receiver (CSIR) is readily obtainable and CSIT is typically assumed to be its transpose, imperfections in the radio frequency (RF) chains disrupt this reciprocity. Focusing on this issue, we establish the necessary and sufficient conditions characterizing RF chain imperfections and their impact on system performance in a simplified scenario, underscoring the criticality of channel calibration. To address this challenge, a distributed source coding (DSC)-based calibration framework is proposed, leveraging the multiplexing of the sensing task to eliminate any additional communication overhead. This framework comprises a distributed compression scheme at each slave access point (AP) and a joint aggregation scheme at the central process unit (CPU). To validate the proposed DSC-based calibration framework, we analytically derive the performance gap relative to the fully collaborated approach. Building on this, a novel data-driven DSC-based deep learning method is proposed to address channel calibration without requiring clean labels. Numerical results demonstrate significant improvement in calibration performance achieved by our proposed method compared to existing calibration methods, approaching the performance of the fully collaborated method.