Model-Aware Compressive Sensing with Applications to Channel Estimation in mmWave Systems

• Applicant: Professor Dr.-Ing. Wolfgang K. Utschick
• Subject Area: Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
• Term: from 2017 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 394803730

• Final Report Year: 2022

Final Report Abstract

In this project, we investigated CS problems with a focus on the case where the data of interest is constrained to lie in an infinite UoS. These kinds of problems appear, e.g., in the mmWave channel estimation context which we studied as our main application. In the first half of the project, we investigated how existing CS algorithms can be generalized to the infinite UoS constraint and we proposed different methods to take the constraint into account. Further, we proved both recovery guarantees and noise robustness bounds for the algorithms and we analyzed their MSE behavior. Moreover, we showed that random matrices are a suitable tool to produce sensing matrices with RIP properties which fit the infinite UoS setting. In the second half of the project, we focused on adapting, improving, and developing algorithms for the problem of channel estimation in mmWave communications systems. A main insight of early experiments was that databased algorithms are well suited for taking an infinite UoS constraint into account. For this reason, we first adapted an existing data-based algorithm to CS problems. On the one hand, we integrated the algorithm in the iterations of classical CS algorithms, on the other hand, we modified the data-based algorithm such that it can be applied to compressed observations. The adapted versions showed a convincing channel estimation performance. Thereafter, we developed a new channel estimation algorithm which can directly be applied to compressed observations. The algorithm turned out to be a very competitive channel estimator in all cases. Since CS algorithms typically use random sensing matrices—because random matrices have necessary recovery properties with high probability— many quantities in CS algorithms need to be recalculated whenever a new random sensing matrix is drawn. This can lead to computational complexity issues. We addressed this problem by developing a data-based method to design sensing matrices, which can be used instead of random matrices. The approach showed successes both in classical (finite) UoS settings as well as in infinite UoS settings and for different recovery algorithms. In particular, the matrices were observed to harmonize well with the newly developed channel estimation algorithm.

Publications

• A generalized hard thresholding pursuit on infinite unions of subspaces. In Proc. Int. ITG Workshop on Smart Antennas (WSA), pages 1–7, 2018
  Michael Koller, Thomas Wiese, and Wolfgang Utschick
  
• Machine learning for channel estimation from compressed measurements. In Proc. Int. Symp. on Wireless Commun. Syst. (ISWCS), pages 1–5, 2018
  Michael Koller, Christoph Hellings, Michael Knödlseder, Thomas Wiese, David Neumann, and Wolfgang Utschick
  
• MSE analysis of the projected gradient algorithm on unions of subspaces. In Proc. Int. ITG Workshop on Smart Antennas (WSA), pages 1–5, 2018
  Thomas Wiese, Kamel Shibli, and Wolfgang Utschick
  
• An asymptotically MSE-optimal estimator based on Gaussian mixture models. IEEE Trans. Signal Process., pages 1–14, 2022
  Michael Koller, Benedikt Fesl, Nurettin Turan, and Wolfgang Utschick
  
• An asymptotically optimal approximation of the conditional mean channel estimator based on Gaussian mixture models. In Proc. IEEE Int. Conf. Acoust., Speech, and Signal Process. (ICASSP), pages 5268–5272, 2022
  Michael Koller, Benedikt Fesl, Nurettin Turan, and Wolfgang Utschick
  
• Learning a compressive sensing matrix with structural constraints via maximum mean discrepancy optimization. Signal Process., page 108553, 2022
  Michael Koller and Wolfgang Utschick