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

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 noncoherent 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.

Deep Learning for UL/DL Channel Calibration in Generic Massive MIMO Systems

“…Considering the linear TDD case of Sec. II-B, we compare the performance of the Argos [18] method and the Norm plus Phase Constraint First Coefficient (NPC FC-II) [19] method, as well as the method in [14] with that of the proposed DNN approach presented in Secs. III-B and III-C.…”

“…III-B and III-C. Moreover, we also report the CRB, which can be obtained in closed form following similar steps as in [19]. We have also investigated the calibration performance of the proposed DNN approach for generic nonlinear scenarios, for which no other method is available.…”

“…Then, the trained network is used to carry out the calibration task for yet unobserved channels. Compared with existing methods [18], [19] that are limited to linear UL/DL relationships, it is shown via simulations that our DNN design approaches the Cramér-Rao Bound (CRB). Moreover our DNN approach exhibits robust performance, even when the number of training sequences is limited.…”

“…As an improved method, [19] proposed a novel family of calibration schemes based on antenna grouping, which can greatly speed up the calibration process with respect to the classical approaches. In addition, some experimental data about the calibration coefficients were recently reported in [19], [20], giving an insight on how the impairments evolve in the time and frequency domains as well as with temperature. In the latter two papers, the hardware characteristics behind those coefficients were also discussed.…”

Relaying Systems With Reciprocity Mismatch: Impact Analysis and Calibration

“…To overcome the shortages, H. Wei et al presented the mutual coupling calibration, which utilized the strong mutual coupling effects among adjacent antennas rather than fading channels [24]. In [25], an over-the-air calibration framework was proposed based on some existing signal-space calibration schemes which were different special cases of antenna grouping schemes in the framework. To further relieve the impact of the reciprocity mismatch at the UE side, O.…”