Reciprocity Calibration for Massive MIMO: Proposal, Modeling and Validation

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.Comment: Submitted to IEEE Transactions on Wireless Communications, 21/Feb/201

On the Impact of Antenna Array Geometry on Indoor Wideband Massive MIMO Networks

Multi-user massive multiple-input-multiple-output (massive MIMO) will play a key role in future wireless communication networks. Since spatial channel diversity is the fundamental merit of this technique, high channel correlation may significantly restrict its abilities. This study investigates the impact of channel correlation on a prototyped massive MIMO network with the objective to identify an antenna array geometry which has reduced mutual coupling and channel correlation. To this end, a highly efficient directional wideband single antenna element was designed for the antenna arrays and the user equipments (UEs). The designed array geometry is tested in an experimental indoor wideband massive MIMO setup. Important system parameters, such as channel correlation, power delay profile, and average received power from the UEs, are studied by analyzing the measured channel data. Furthermore, system-level simulations and network capacity calculations are performed based on the measured channel data to evaluate the performance of the prototyped antenna arrays. A regular array was also fabricated and used for benchmarking comparison. Moreover, a power control algorithm is introduced for the uplink, which was shown to improve the network capacity by up to 3 dB. The results demonstrate that the introduced antenna array outperforms the uniform antenna array in terms of mutual coupling and channel capacity

Hierarchical-Absolute Reciprocity Calibration for Millimeter-wave Hybrid Beamforming Systems

In time-division duplexing (TDD) millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems, the reciprocity mismatch severely degrades the performance of the hybrid beamforming (HBF). In this work, to mitigate the detrimental effect of the reciprocity mismatch, we investigate reciprocity calibration for the mmWave-HBF system with a fully-connected phase shifter network. To reduce the overhead and computational complexity of reciprocity calibration, we first decouple digital radio frequency (RF) chains and analog RF chains with beamforming design. Then, the entire calibration problem of the HBF system is equivalently decomposed into two subproblems corresponding to the digital-chain calibration and analog-chain calibration. To solve the calibration problems efficiently, a closed-form solution to the digital-chain calibration problem is derived, while an iterative-alternating optimization algorithm for the analog-chain calibration problem is proposed. To measure the performance of the proposed algorithm, we derive the Cram\'er-Rao lower bound on the errors in estimating mismatch coefficients. The results reveal that the estimation errors of mismatch coefficients of digital and analog chains are uncorrelated, and that the mismatch coefficients of receive digital chains can be estimated perfectly. Simulation results are presented to validate the analytical results and to show the performance of the proposed calibration approach

Analysis and Mitigation of Channel Non-Reciprocity in TDD MIMO Systems

The ever-growing demands for higher number of connected devices as well as higher data rates and more energy efficient wireless communications have necessitated the use of new technical solutions. One of the main enablers in this respect is Multiple-Input Multiple-Output (MIMO) systems in which transmitting and receiving sides are equipped with multiple antennas. Such systems need precise information of the MIMO radio channel available at the transmitter side to reach their full potential. Owing to the reciprocity of uplink and downlink channels in Time Division Duplexing (TDD) systems, Base Stations (BSs) may acquire the required channel state information for downlink transmission by processing the received uplink pilots. However, such reciprocity only applies to the physical propagation channels and does not take into consideration the so-called observable or effective uplink and downlink channels which also include the possible non-reciprocal behavior of the involved transceiver circuits and antenna systems. This thesis focuses on the channel non-reciprocity problem in TDD MIMO systems due to mismatches in Frequency Response (FR) and mutual coupling of transmitting and receiving chains of transceivers and associated antenna systems. The emphasis in the work and developments is placed on multi-user MIMO precoded downlink transmission. In this respect, the harmful impacts of channel non-reciprocity on the performance of such downlink transmission are analyzed. Additionally, non-reciprocity mitigation methods are developed seeking to reclaim TDD reciprocity and thus to avoid the involved performance degradations. Firstly, the focus is on the small-scale MIMO systems where BSs are equipped with relatively limited number of antennas, say in the order of 4 to 8. The provided analysis on Zero-Forcing (ZF) and eigen-based precoding schemes in single-cell scenario shows that both schemes experience considerable performance degradations in the presence of FR and mutual coupling mismatches. Whereas, in general, the system performance is more sensitive to i) non-reciprocity sources in the BS transceiver; and ii) mutual coupling mismatches. Then, assuming reasonably good antenna isolation, an Over-The-Air (OTA) pilot-based algorithm is proposed to efficiently mitigate the BS transceiver non-reciprocity. The numerical results indicate high accuracy in estimating the BS transceiver non- reciprocity parameters as well as considerable improvement in the performance of the system. In multi-cell scenario, both centralized and decentralized precoding approaches are covered while the focus is on the impacts of FR mismatches of UE transceivers. The how that there is severe degradation in the performance of decentralized precoding while centralized precoding is immune to such channel non-reciprocity impacts. Secondly, the so-called massive MIMO systems are considered in which the number of antennas in the BS side is increased with an order of magnitude or more. Based on the detailed developed signal models, closed-form analytical expressions are first provided for effective signal-to-interference-plus-noise ratios of both ZF and maximum ratio transmission precoding schemes. The analysis covers the joint impacts of channel non-reciprocity and imperfect uplink channel estimation and shows that while both precoding schemes suffer from channel non-reciprocity impacts, ZF is more sensitive to such non-idealities. Next, a concept and an algorithm are proposed, involving UE side measurements and processing, to be deployed in the UE side to efficiently estimate the level of BS transceiver non-reciprocity. This enables the UEs to inform the BS about the optimum time to perform channel non-reciprocity mitigation round and thus improves the spectral efficiency. Finally, in order to mitigate channel non-reciprocity in massive MIMO systems, an efficient iterative OTA pilot-based algorithm is proposed which estimates and mitigates transceiver non-reciprocity impacts in both BS and UE sides. Compared to the state-of-the-art methods, the simulation results indicate substantial improvements in system spectral efficiency when the proposed method is being used. Overall, the analyses provided in this thesis can be used as valuable tools to better understand practical TDD MIMO systems which can be very helpful in designing such systems. Furthermore, the channel non-reciprocity mitigation methods proposed in this thesis can be deployed in practical TDD MIMO syst channel reciprocity and thus significantly increase the spectral efficiency