Reciprocity Calibration of Dual-Antenna Repeaters via MMSE Estimation

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.

💡 Research Summary

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This paper addresses the reciprocity calibration problem in time‑division duplex (TDD) massive MIMO systems when a dual‑antenna repeater is introduced between two antenna arrays (denoted A and B). In conventional TDD calibration, the uplink and downlink channels are assumed reciprocal apart from the transceiver hardware, and calibration methods such as relative calibration or over‑the‑air bidirectional pilots rely on a single‑hop channel model. The presence of a repeater, however, adds forward and reverse gains (α and β) that are generally non‑reciprocal, as well as additional transmit‑receive (TX/RX) chain mismatches at the repeater and at each antenna element. Consequently, the effective end‑to‑end channel consists of a direct component G and a repeater‑assisted component α g hᵀ (forward) and β h gᵀ (reverse), together with diagonal hardware response matrices T_A, R_A, T_B, R_B. All these quantities are unknown.

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