Spanning Tree Method for Over-the-Air Channel Calibration in 6G Cell-Free Massive MIMO

Cell-free massive multiple-input multiple-output (MIMO) is an attractive network in 6G communications that significantly increases the spectral efficiency. Operating in time-division duplex (TDD) mode, the downlink beamforming is achieved by the estimated uplink channel, which is equal to the downlink channel due to the property of channel reciprocity. However, the involvement of different radio frequency (RF) gains in transceiver antennas renders the whole channel non-reciprocal. Therefore, it is of great necessity to calibrate the bi-directional channel. In this paper, we focus on the issue of over-the-air channel calibration in cell-free system. Taking a toy scenario as an example, we examine the performance differences between the calibration methods of 'Direct Process' and 'Indirect Process'. A novel low-cost calibration method based on spanning tree model is proposed specifically for this distributed AP scenario, where a calibration tree is established to calculate calibration coefficients. Numerical results manifest that higher accuracy of our method is achieved compared to the existing calibration methods in the literatures. Our method is less sensitive to the location of master AP compared to Argos, and practical applications under the impact of phase noise show the priority of our method compared to LS method.