Reciprocity Calibration of Dual-Antenna Repeaters

TL;DR

This paper addresses non-reciprocity in dual-antenna repeaters by introducing a reciprocity calibration method that estimates the ratio $\beta/\alpha$ of forward to reverse repeater gains. A nonlinear least-squares framework is developed, with variables $\boldsymbol{H}$, $\boldsymbol{A}$, $\boldsymbol{B}$, $\boldsymbol{Z}$ and $\gamma=\beta/\alpha$, and solved via a basic NLS algorithm and an enhanced alternating-optimization variant to approach the global optimum. Numerical results demonstrate the approach can yield consistent estimates and improve accuracy at higher SNR, while variations cover practical deployment scenarios such as pre-calibrated arrays, on/off measurements, and simultaneous calibration of multiple repeaters using structured phase patterns. The practical impact is enabling repeaters to act as transparent, reciprocal components of the propagation environment, thereby enabling reciprocity-based beamforming and improved coverage for disadvantaged users in multiuser MIMO systems.

Abstract

We present a reciprocity calibration method for dual-antenna repeaters in wireless networks. The method uses bi-directional measurements between two network nodes, A and B, where for each bi-directional measurement, the repeaters are configured in different states. The nodes A and B could be two access points in a distributed MIMO system, or they could be a base station and a mobile user terminal, for example. From the calibration measurements, the differences between the repeaters' forward and reverse gains are estimated. The repeaters are then (re-)configured to compensate for these differences such that the repeaters appear, transparently to the network, as reciprocal components of the propagation environment, enabling reciprocity-based beamforming in the network.

Figures (2)

• Figure 1: Two antenna arrays, A and B, and a repeater (R). By definition, ${\boldsymbol{G}}$ is the propagation channel from A to B with R turned off. Radio channels are represented by solid lines ($-$) and repeater gains by dashed lines ($--$).
• Figure 2: Root-mean-square-error of $\hat{\gamma}$.