Reciprocity Calibration for Massive MIMO: Proposal, Modeling and Validation

TL;DR

This paper introduces a mutual coupling based calibration method for massive MIMO systems, utilizing an EM algorithm for improved accuracy, validated through experiments and modeling of calibration errors across frequency.

Contribution

The paper proposes a novel EM-based calibration algorithm for massive MIMO that outperforms existing methods and is applicable to both co-located and distributed systems.

Findings

The EM algorithm achieves lower MSE and higher sum-rate capacity.

Experimental validation confirms the effectiveness of the calibration method.

A frequency-dependent model of calibration error is developed and validated.

Abstract

This paper presents a mutual coupling based calibration method for time-division-duplex massive MIMO systems, which enables downlink precoding based on uplink channel estimates. The entire calibration procedure is carried out solely at the base station (BS) side by sounding all BS antenna pairs. An Expectation-Maximization (EM) algorithm is derived, which processes the measured channels in order to estimate calibration coefficients. The EM algorithm outperforms current state-of-the-art narrow-band calibration schemes in a mean squared error (MSE) and sum-rate capacity sense. Like its predecessors, the EM algorithm is general in the sense that it is not only suitable to calibrate a co-located massive MIMO BS, but also very suitable for calibrating multiple BSs in distributed MIMO systems. The proposed method is validated with experimental evidence obtained from a massive MIMO testbed. In addition, we address the estimated narrow-band calibration coefficients as a stochastic process across frequency, and study the subspace of this process based on measurement data. With the insights of this study, we propose an estimator which exploits the structure of the process in order to reduce the calibration error across frequency. A model for the calibration error is also proposed based on the asymptotic properties of the estimator, and is validated with measurement results.