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A Framework for Over-the-air Reciprocity Calibration for TDD Massive MIMO Systems

Xiwen Jiang, Alexis Decurninge, Kalyana Gopala, Florian Kaltenberger, Maxime Guillaud, Dirk Slock, Luc Deneire

TL;DR

This paper presents a novel family of calibration methods, based on antenna grouping, which improves accuracy and speeds up the calibration process compared to existing methods, and provides the Cramér–Rao bound as the performance evaluation benchmark and compares maximum likelihood and least squares estimators.

Abstract

One of the biggest challenges in operating massive multiple-input multiple-output systems is the acquisition of accurate channel state information at the transmitter. To take up this challenge, time division duplex is more favorable thanks to its channel reciprocity between downlink and uplink. However, while the propagation channel over the air is reciprocal, the radio-frequency front-ends in the transceivers are not. Therefore, calibration is required to compensate the RF hardware asymmetry. Although various over-the-air calibration methods exist to address the above problem, this paper offers a unified representation of these algorithms, providing a higher level view on the calibration problem, and introduces innovations on calibration methods. We present a novel family of calibration methods, based on antenna grouping, which improve accuracy and speed up the calibration process compared to existing methods. We then provide the Cramér-Rao bound as the performance evaluation benchmark and compare maximum likelihood and least squares estimators. We also differentiate between coherent and non-coherent accumulation of calibration measurements, and point out that enabling non-coherent accumulation allows the training to be spread in time, minimizing impact to the data service. Overall, these results have special value in allowing to design reciprocity calibration techniques that are both accurate and resource-effective.

A Framework for Over-the-air Reciprocity Calibration for TDD Massive MIMO Systems

TL;DR

This paper presents a novel family of calibration methods, based on antenna grouping, which improves accuracy and speeds up the calibration process compared to existing methods, and provides the Cramér–Rao bound as the performance evaluation benchmark and compares maximum likelihood and least squares estimators.

Abstract

One of the biggest challenges in operating massive multiple-input multiple-output systems is the acquisition of accurate channel state information at the transmitter. To take up this challenge, time division duplex is more favorable thanks to its channel reciprocity between downlink and uplink. However, while the propagation channel over the air is reciprocal, the radio-frequency front-ends in the transceivers are not. Therefore, calibration is required to compensate the RF hardware asymmetry. Although various over-the-air calibration methods exist to address the above problem, this paper offers a unified representation of these algorithms, providing a higher level view on the calibration problem, and introduces innovations on calibration methods. We present a novel family of calibration methods, based on antenna grouping, which improve accuracy and speed up the calibration process compared to existing methods. We then provide the Cramér-Rao bound as the performance evaluation benchmark and compare maximum likelihood and least squares estimators. We also differentiate between coherent and non-coherent accumulation of calibration measurements, and point out that enabling non-coherent accumulation allows the training to be spread in time, minimizing impact to the data service. Overall, these results have special value in allowing to design reciprocity calibration techniques that are both accurate and resource-effective.

Paper Structure

This paper contains 24 sections, 1 theorem, 45 equations, 10 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. OTA Reciprocity Calibration
  3. General OTA Calibration Framework
  4. Overview and signalling
  5. Parameter identifiability and pilot design
  6. LS calibration parameter estimation
  7. Existing calibration techniques
  8. Argos
  9. Methods based on successive single-antenna transmissions followed by joint estimation
  10. Avalanche
  11. Fast Calibration: optimal antenna grouping
  12. Optimal estimation and performance limits
  13. Cramér-Rao bound
  14. Maximum likelihood estimation
  15. Maximum likelihood vs. least squares
  16. ...and 9 more sections

Key Result

Lemma 1

Fix $K\geq 1$. Let us define an optimal grouping as the solution $G^*, L_1^*,\dots,L_{G^*}^*$ of then the optimal grouping corresponds to the case $L_1^*=\dots =L_{G^*}^*=1$ with $G^*=K$. The number of calibrated antennas is then equal to $\frac{1}{2}K(K-1)+1$.

Figures (10)

  • Figure 1: Reciprocity Model
  • Figure 2: Bi-directional transmission between antenna groups.
  • Figure 3: Argos calibration
  • Figure 4: Method of Rogalin et al. for reciprocity calibration. Not all links between elements are plotted.
  • Figure 5: Example of full Avalanche calibration with $7$ antennas partitioned into $4$ groups. Group $1$, $2$, $3$ have already been calibrated, and group $4$ is to be calibrated.
  • ...and 5 more figures

Theorems & Definitions (3)

  • Lemma 1
  • proof
  • proof