Interconnection Strategies for Self-Calibration of Large Scale Antenna Arrays

In time-division duplexing (TDD) systems, massive multiple-input multiple-output (MIMO) relies on the channel reciprocity to obtain the downlink (DL) channel state information (CSI) with the uplink (UL) CSI. In practice, the mismatches in the radio frequency (RF) analog circuits among different antennas at the base station (BS) break the end-to-end UL and DL channel reciprocity. Antenna calibration is necessary to avoid the severe performance degradation with massive MIMO. Many calibration schemes are available to compensate the RF gain mismatches and restore the channel reciprocity in TDD massive MIMO systems. In this paper, we focus on the internal self-calibration scheme where different BS antennas are interconnected via hardware transmission lines. First, we study the resulting calibration performance for an arbitrary interconnection strategy. Next, we obtain closed-form Cramer-Rao lower bound (CRLB) expressions for each interconnection strategy at the BS with only (M-1) transmission lines and M denotes the total number of BS antennas. Basing on the derived results, we further prove that the star interconnection strategy is optimal for internal self-calibration due to its lowest CRLB. In addition, we also put forward efficient recursive algorithms to derive the corresponding maximum-likelihood (ML) estimates of all the calibration coefficients. Numerical simulation results are also included to corroborate our theoretical analyses and results.