Phase shifter networks (PSN) are now widely used in multi-input multi-output (MIMO) systems for various purposes, from hybrid beamforming to strong interference mitigation. These applications require the phases of the PSN elements to be precisely calibrated, but the phase deviations always exist in practice. This paper proposes a novel over-the-air (OTA) approach to estimate the deviations of the phase shifters at each gear. Having some signal sources transmit pilot signals from unknown directions, we make the phases of the PSN shift across different gears and take the samples of the PSN output. Then the maximum likelihood (ML) estimation of the PSN errors which constitutes a three-way tensor, can be solved effectively by an iterative algorithm. The simulation results verify the effectiveness of the proposed algorithm and show that the root mean square errors (RMSEs) of the phase estimates can closely approach the Cramer Rao Bounds (CRBs).

中文翻译：

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混合 MIMO 系统移相器网络的无线校准


移相器网络 (PSN) 现在广泛用于多输入多输出 (MIMO) 系统，用于各种目的，从混合波束成形到强干扰抑制。这些应用需要对PSN元件的相位进行精确校准，但在实际应用中相位偏差始终存在。本文提出了一种新颖的无线（OTA）方法来估计每个档位移相器的偏差。让一些信号源从未知方向传输导频信号，我们使 PSN 的相位在不同档位之间移动，并采集 PSN 输出的样本。然后，构成三路张量的PSN误差的最大似然（ML）估计可以通过迭代算法有效地求解。仿真结果验证了该算法的有效性，并表明相位估计的均方根误差（RMSE）可以接近克拉默饶界（CRB）。