Channel Reciprocity Calibration for Hybrid Beamforming in Distributed MIMO Systems

Time Division Duplex (TDD)-based distributed massive MIMO systems are envisioned as candidate solution for the physical layer of 6G multi-antenna systems supporting cooperative hybrid beamforming that heavily relies on the obtained uplink channel estimates for efficient coherent downlink pre-coding. However, due to the hardware impairment between the transmitter and the receiver, full channel reciprocity does not hold between the downlink and uplink direction. Such reciprocity mismatch deteriorates the performance of mm-Wave hybrid beam-forming and has to be estimated and compensated for, to avoid performance degradation in the co-operative hybrid beamforming.In this paper, we address the channel reciprocity calibration between any two nodes at two levels. We decompose the problem into two sub-problems. In the first sub-problem, we calibrate the digital chain, i.e. obtain the mismatch coefficients of the (DAC/ADC) up to a constant scaling factor. In the second sub-problem, we obtain the (PA/LNA) mismatch coefficients. At each step, we formulate the channel reciprocity calibration as a least-square optimization problem that can efficiently be solved via conventional methods such as alternative optimization with high accuracy. Finally, we verify the performance of our channel reciprocity calibration approach through extensive numerical experiments.