CENIIT project: Adaptive linearization of electronic devices

Project leader: Martin Enqvist
PhD student: Ylva Jung

Background and industrial motivation

During the last decades, there has been a strong industrial trend towards high-performance electronics with low power consumption. For example, the rapid growth of the number of mobile communication devices during the last twenty years has created a huge market for small-sized power-efficient transmitters and receivers with key components such as analog-to-digital converters (ADCs) and power amplifiers (PAs).

In some cases, the design of power-efficient ADCs and PAs comes with a price, namely that the resulting device might exhibit a nonlinear and possibly also dynamic behavior that reduces its usefulness in communication applications. One way to circumvent this problem is to apply signal processing techniques for ADC error correction and PA predistortion. The main idea in these techniques is to compensate for the nonlinear and dynamic behavior of the ADC or PA by applying a nonlinear filter to the output or input signal, respectively. In order to design such a filter, a model is typically needed. In many cases, this model does not have to reflect the actual physical properties of the device. Instead, more simple, generic models, known as black-box models are often used to capture and compensate for the dominating nonlinear and dynamic properties of the devices.

Estimation of black-box models has been studied for many years in several adjacent research communities. For example, it is a central concept in the field of system identification within the automatic control community. Control design is often done using approximate models that capture only the main characteristics of the system. This indicates that system identification methods for estimation of approximate models originally developed for control design purposes can be useful also for other applications, such as linearization of electronic devices. One class of models that has been studied extensively within the system identification field is block-oriented models, which are cascade, and sometimes also parallel, combinations of static nonlinear and dynamic linear submodels. Two relatively simple examples are Hammerstein and Wiener models, which each contains one nonlinear and one linear submodel. Recently, there has been an increased research activity on this topic and a number of new methods have been proposed.

Block-oriented model structures have been used for amplifier predistortion in several publications and will be investigated also in the present project. Other approaches to amplifier predistortion include Volterra series, NFIR models and look-up tables . The use of phase-only predistortion seems particularly interesting for the outphasing amplifiers that will be one of the applications in the present project.

Furthermore, the available approaches to ADC error correction include the use of Kautz-Volterra models, which are related to parallel Wiener models, and Volterra series, but also other types of models.

Project description

Both ADC error correction and PA predistortion involve the application of an inverse model of the device in series with the actual hardware. The main objective of this research project is to investigate how approximate nonlinear inverse models can be estimated efficiently from input-output data using system identification methods for the purpose of ADC error correction and PA predistortion. Some research topics that will be studied are:

• Suitable model structures: There exist general nonlinear black-box model structures that can be used to model large classes of nonlinear systems, but in case there is some a priori knowledge about the system characteristics it is usually better to use a model structure with similar properties. The present project will be carried out in close cooperation with hardware designers, and it should therefore be possible to select specialized model structures that fit the particular hardware structure. In particular, it seems interesting to investigate the properties of state-of-the-art ADCs from a model structure point of view, with the tradeoff between simplicity and accuracy in mind. Furthermore, the static models for outphasing PAs that have been used in Fritzin et al. (2011) will be extended in order to capture also some dynamic properties of the PAs.
• Problem reformulations: In many cases, estimation of nonlinear models involve solving nonconvex optimization problems, which can be challenging and lead to suboptimal model estimates. Hence, it is interesting to try to rewrite nonconvex problems into convex ones. For example, this has turned out to be possible in the case of static models of outphasing PAs and will be investigated also for other models and ADCs. However, the reformulation might also have some drawbacks. For example, an initial nonlinear transformation of data can lead to a new problem formulation that is easier to solve from an optimization point of view, but which contains less common features such as non-additive noise.
• Adaptive error correction and predistortion: Many electronic devices are time-varying and thus impossible to model perfectly using a time-invariant model. For example, the time variations can be due to temperature changes or aging hardware. In order to achieve accurate ADC error correction and PA predistortion over longer time frames, adaptive estimation and correction methods will be investigated. For example, recursive formulations of the system identification methods will be developed for some of the model structures that are used. Since the investigated systems are nonlinear, this can be referred to as adaptive linearization.

Research environment and industrial cooperation

The research in this project will be performed at the Division of Automatic control at Linköping University. There are around 50 researchers (including PhD students) in this research group and the research topics include control applications, system identification, sensor fusion, optimization and industrial robotics.

The project will be performed in close cooperation with researchers from the Integrated circuits and systems research group. They design state-of-the-art integrated circuits and have already developed and manufactured some of the PAs and ADCs that will be studied in this project. Furthermore, the lab equipment that will be necessary for this project is already available at the Integrated circuits and systems research group.

Furthermore, a couple of researchers at Ericsson have agreed to act as industrial advisors in this project.

Visions and plans

The vision for this project is to establish a platform for long-term cooperation between more hardware-oriented researchers and the system identification researchers in the Automatic control group at the Department of Electrical Engineering at Linköping University. The long-term goal is to be able to combine novel hardware solutions with accurate and reliable correction and predistortion techniques in order to be able to develop state-of-the-art devices with low power consumption and high accuracy. The plan is to perform this within the existing Automatic control group, in order for this project to be able to benefit from the research there on adjacent application areas.

Initially, the plan is to investigate dynamic nonlinear predistortion of an outphasing PA as well as static error correction for a recently developed ADC. After three years, the vision is to have developed these methods further and to have made at least one of them adaptive in order to be able to follow a time-varying system.

Project status

Several results concerning outphasing PA predistortion have been obtained in the project with the least-squares reformulation of the problem as the most significant one. This approach was published in IEEE TCAS-I in 2013. Furthermore, some general results concerning estimation of inverse models have also been obtained and published in two conference articles in 2013 and 2015. One Licentiate's thesis has also been written in the project. In parallel, there have been related activities about sensor-to-sensor system identification, dynamic networks and block-oriented systems, which have resulted in two journal papers and 11 conference papers.

Publications

• D. Ho and M. Enqvist. On the equivalence of forward and inverse IV estimators with application to quadcopter modeling. In Proceedings of the 18th IFAC Symposium on System Identification, pages 951-956, Stockholm, Sweden, July 2018. (Related publication)
• D. Ho, J. Linder, G. Hendeby, and M. Enqvist. Vertical modeling of a quadcopter for mass estimation and diagnosis purposes. In Proceedings of the Workshop on Research, Education and Development on Unmanned Aerial Systems (RED-UAS), pages 192-197, Linköping, Sweden, October 2017. (Related publication)
• J. Linder and M. Enqvist. Identification and prediction in dynamic networks with unobservable nodes. In Proceedings of the 20th IFAC World Congress, Toulouse, France, July 2017. (Related publication)
• D. Ho, J. Linder, G. Hendeby, and M. Enqvist. Mass estimation of a quadcopter using IMU data. In Proceedings of the 2017 International Conference on Unmanned Aircraft Systems (ICUAS), pages 1260-1266, Miami, Florida, June 2017. (Related publication)
• J. Linder and M. Enqvist. Identification of systems with unknown inputs using indirect input measurements. International Journal of Control, 90(4):729-745, 2017. (Related publication)
• J. Escobar and M. Enqvist. Instrumental variables and LSM in continuous-time parameter estimation. ESAIM: Control, Optimisation and Calculus of Variations, 23(2):427-442, 2017. (Related publication)
• Y. Jung and M. Enqvist. On estimation of approximate inverse models of block-oriented systems. In Proceedings of the 17th IFAC Symposium on System Identification, pages 1226-1231, Beijing, China, October 2015.
• J. Linder and M. Enqvist. On indirect input measurements. In Proceedings of the 17th IFAC Symposium on System Identification, pages 104-109, Beijing, China, October 2015. (Related publication)
• J. Linder, M. Enqvist, T. I. Fossen, T. A. Johansen, and F. Gustafsson. Online estimation of ship's mass and center of mass using inertial measurements. In Proceedings of the 10th IFAC Conference on Manoeuvring and Control of Marine Craft, Copenhagen, Denmark, August 2015. (Related publication)
• J. Linder, M. Enqvist, T. I. Fossen, T. A. Johansen, and F. Gustafsson. Modeling for IMU-based online estimation of a ship's mass and center of mass. In Proceedings of the 10th IFAC Conference on Manoeuvring and Control of Marine Craft, Copenhagen, Denmark, August 2015. (Related publication)
• J. Linder, M. Enqvist, and F. Gustafsson. A closed-Loop instrumental variable approach to mass and center of mass estimation using IMU data. In Proceedings of the 53rd IEEE Conference on Decision and Control, pages 283-289, Los Angeles, California, December 2014. (Related publication)
• M. Sadeghi Reineh, M. Enqvist, and F. Gustafsson. IMU-based vehicle load estimation under normal driving conditions. In Proceedings of the 53rd IEEE Conference on Decision and Control, pages 3376-3381, Los Angeles, California, December 2014. (Related publication)
• J. Linder, M. Enqvist, F. Gustafsson, and J. Sjöberg. Identifiability of physical parameters in systems with limited sensors. In Proceedings of the 19th IFAC World Congress, pages 6454-6459, Cape Town, South Africa, August 2014. (Related publication)
• M. Sadeghi Reineh, M. Enqvist, and F. Gustafsson. Detection of roof load for automotive safety systems. In Proceedings of the 52nd IEEE Conference on Decision and Control, pages 2840-2845, Florence, Italy, December 2013. (Related publication)
• Y. Jung and M. Enqvist. Estimating models of inverse systems. In Proceedings of the 52nd IEEE Conference on Decision and Control, pages 7143-7148, Florence, Italy, December 2013.
• Y. Jung. Estimation of Inverse Models Applied to Power Amplifier Predistortion. Licentiate's thesis no. 1605, Department of Electrical Engineering, Linköping University, Linköping, Sweden, 2013.
• Y. Jung, J. Fritzin, M. Enqvist, and A. Alvandpour. Least-squares phase predistortion of a +30 dBm class-D outphasing RF PA in 65 nm CMOS. IEEE Transactions on Circuits and Systems-Part I: Regular Papers, 60(7):1915-1928, 2013.
• J. Fritzin, Y. Jung, P. N. Landin, P. Händel, M. Enqvist, and A. Alvandpour. Phase predistortion of a class-D outphasing RF amplifier in 90nm CMOS. IEEE Transactions on Circuits and Systems - Part II: Express Briefs, 58(10):642-646, 2011. (Related publication published prior to this project.)