Frugal calibration of mutual coupling in large scale antenna array

In a time-division duplexing (TDD) system, the uplink (UL) and downlink (DL) channel reciprocity gets impaired due to the mismatches of the antenna radio frequency (RF) electronics. Meanwhile, in massive multiple-input multiple-output (MIMO), as the antenna elements are placed close to each other, the mutual coupling effects among the adjacent antennas also become pronounced. Different coupling matrices for transmission and reception also hurt the end-to-end UL/DL channel reciprocity. Aiming to restore the end-to-end channel reciprocity with a small amount of over-the-air (OTA) resources, we propose to estimate the gain mismatches of the RF electronics and the mutual coupling mismatches separately. Specifically, we rely on the pilot exchanges among the BS antennas and the symmetry of the antenna array to recover the transmit and receive gains of all the RF components. Unlike prior calibration works, our schemes can recover the off-diagonal elements in the calibration matrix as well. Our designs are also corroborated with numerical simulations.