Optimal Interconnection for Massive MIMO Self-Calibration

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 acquired uplink (UL) CSI at the base station (BS). However, the mismatches in the radio frequency (RF) analog circuits among different antennas at the BS break the end-to-end UL and DL channel reciprocity. To avoid the severe performance degradation with massive MIMO, it is necessary to calibrate all the ℳ antennas at the BS to restore the end-to-end UL/DL channel reciprocity. In this paper, we examine 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. Basing on the derived results, we further prove that the star interconnection strategy is optimal for internal self-calibration due to its lowest CRLB. Numerical simulation results corroborate our theoretical analyses and results.