Cell-free massive multiple-input multiple-output (MIMO) is a promising technology to address the requirements for higher spectral efficiency and energy efficiency in 6G networks. Downlink beamforming scheme, essential for mitigating multiuser interference and enhancing overall system performance, relies on the estimated uplink channel state information (CSI) in time-division duplex (TDD) mode exploiting channel reciprocity. However, hardware impairments render the bi-directional channel non-reciprocal. This paper focuses on channel calibration for cell-free massive MIMO systems, taking into account both radio frequency (RF) mismatches and nonlinear distortions. We derive the closed-form expression for downlink achievable rate within a specific calibration scheme. To address the calibration challenge, we introduce a novel conceptual model, in which the calibration vector is determined by optimizing the performance of the reference antenna. Expanding on this concept, we propose a novel digital twin (DT)-enabled approach to overcome the limitations in the conceptual model, where the DT model is established to perform calibration task by introducing DT services of virtual reference antennas. By exploiting this method, the calibration vector is computed utilizing the proposed alternating optimization algorithm within the DT model, obviating the need for deploying reference antennas in the real cell-free system, thereby reducing costs. The communication overheads and computation complexity for updating the calibration vector is proportional to the access point (AP) number. Simulation results demonstrate the significant improvement of system performance through channel calibration and verify the higher downlink throughput of our proposed DT-enabled calibration method compared to the existing calibration methods.
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