A Multi-Reference Calibration Method for Coherent Joint Transmission in Asynchronous Cell-Free Massive MIMO With Imperfect RF Chains

Cell–free massive multiple–input multiple–output (CF–mMIMO) has attracted significant research interest by leveraging coherent joint transmission (CJT) for achieving excellent performance. However, this performance is degraded by phase offsets arising from imperfect radio frequency (RF) chains and asynchronous reception. To significantly recover CJT performance with low calibration feedback overhead, we propose a multi-reference calibration method. Specifically, we first propose a multi-reference phase offset alignment mechanism that designates multiple service access points (APs) as reference APs, thereby eliminating feedback for self-referencing service APs and aligning phase offsets to a bounded range. Leveraging this mechanism, we formulate a reference AP selection optimization problem to balance CJT performance recovery and feedback overhead, and develop a matching-based algorithm to solve it. Simulation results show that compared to conventional single-reference methods, our method reduces feedback overhead by 45.6% while incurring only a 2.3% performance loss.