Abstract
The phase shifter network (PSN) is 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, which constitute a three-way tensor. Having some signal sources transmit pilot signals from unknown directions, we make the phases switch across different gears and take the samples of the PSN output. We can then model the PSN calibration as a problem of maximum likelihood (ML) estimation of a three-way tensor, which 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).
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