This paper proposes a novel Bayesian reciprocity calibration method that consistently ensures uplink and downlink channel reciprocity in repeater-assisted multiple-input multiple-output (MIMO) systems. The proposed algorithm is formulated under the minimum mean-square error (MMSE) criterion. Its Bayesian framework incorporates complete statistical knowledge of the signal model, noise, and prior distributions, enabling a coherent design that achieves both low computational complexity and high calibration accuracy. To further enhance phase alignment accuracy, which is critical for calibration tasks, we develop a von Mises denoiser that exploits the fact that the target parameters lie on the circle in the complex plane. Simulation results demonstrate that the proposed MMSE algorithm achieves substantially improved estimation accuracy compared with conventional deterministic non-linear least-squares (NLS) methods, while maintaining comparable computational complexity. Furthermore, the proposed method exhibits remarkably fast convergence, making it well suited for practical implementation.

翻译：本文提出了一种新颖的贝叶斯互易性校准方法，可在中继辅助的多输入多输出（MIMO）系统中持续确保上下行信道的互易性。所提算法基于最小均方误差（MMSE）准则构建。其贝叶斯框架整合了信号模型、噪声及先验分布的完整统计知识，实现了一种兼具低计算复杂度与高校准精度的连贯设计。为了进一步提升对校准任务至关重要的相位对准精度，我们开发了一种冯·米塞斯去噪器，该去噪器利用了目标参数位于复平面单位圆上的特性。仿真结果表明，与传统的确定性非线性最小二乘（NLS）方法相比，所提出的MMSE算法在保持相当计算复杂度的同时，显著提高了估计精度。此外，所提方法展现出极快的收敛速度，使其非常适合于实际部署。