Compressed Sensing for spherical near- to far-field transformation (CoSSTra)

• Applicants: Professor Dr.-Ing. Dirk Heberling; Professor Dr. Rudolf Mathar
• Subject Area: Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
• Term: from 2016 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 314196459

• Final Report Year: 2020

Final Report Abstract

The contributions of this project are given as the theoretical perspective of the application of CS techniques to SNF and some practical implementations. The construction of a sensing matrix from spherical harmonics and Wigner D-functions is a core of this project. First of all, considering random sampling to construct a matrix can be proven to satisfy the RIP condition. Second of all, from an application perspective, a class of equiangular type sampling patterns is proven analytically and numerically inappropriate for CS application. Furthermore, a sampling strategy to construct a low coherence sensing matrix from spherical harmonics and Wigner D-functions has been proposed. It is numerically shown that these sampling patterns deliver a better recovery performance than other well-known sampling patterns. Surprisingly, this sampling pattern also outperforms random sampling schemes in terms of SMCs reconstruction and far-field radiation pattern. It has been verified that the proposed sampling pattern can be implemented in real measurements. Additionally, it is shown that the measurement time can be significantly reduced. Furthermore, by application of the technique known as pointwise probe correction, the derived theory can be extended to other arbitrary geometries. This enables, e.g., the application of the proposed sampling to the acquisition with systems optimized for geometries other than spherical, such as the cylindrical one. However, compressed measurements suffer from additional problems due to the lack of redundancy of the measurements. Most additional effects can be modelled as contributing to BM. The effect of aliasing is especially heightened and critical for environmental reflections occurring outside of the measurement sphere, which forces measuring in a shielded environment for adequate performance. For future direction related to the SNF, it is possible to extend the result to the phaseless measurements problem. It is discussed numerically, that the reduction in the number of measurements compared to the classical method is feasible. A lot of open questions related to this problem remain, such as the condition of the sensing matrix, the number of measurements to have recovery guarantee, as well as sampling strategies to construct the sensing matrices. Therefore, the authors deem further research based on the results of this project and in the direction of phaseless SNF as promising.

Publications

• "Sparse recovery in Wigner-D basis expansion". In: Signal and Information Processing (GlobalSIP), 2016 IEEE Global Conference on. IEEE. 2016, pp. 287-291
  Arya Bangun, Arash Behboodi, and Rudolf Mathar
  
• "Radiation center estimation from near-field data using a direct and an iterative approach". In: 2017 Antenna Measurement Techniques Association Symposium (AMTA). IEEE. 2017, pp. 1-6
  Cosme Culotta-López, Kui Wu, and Dirk Heberling
  
• "A Compressed Sampling for Spherical Near-Field Measurements". In: 2018 40th (AMTA). Williamsburg Virginia, USA, 2018
  Cosme Culotta-López, Dirk Heberling, Arya Bangun, Arash Behboodi, and Rudolf Mathar
  
• "Coherence bounds for Sensing Matrices in Spherical Harmonics Expansion". In: IEEE ICASSP'18. Calgary, Canada: IEEE, Apr. 2018
  Arya Bangun, Arash Behboodi, and Rudolf Mathar
  
• "A Modified Minimum-Coherence Sampling for Fast Spherical Near-Field Measurements". In: 13th European Conference on Antennas and Propagation (EUCAP 2019) (EuCAP 2019). IEEE. Krakow, Poland, 2019
  Cosme Culotta-López, Arya Bangun, Arash Behboodi, Rudolf Mathar, and Dirk Heberling
  
• "Fast Spherical Near-Field Measurements on Arbitrary Surfaces by Application of Pointwise Probe Correction to Compressed Sampling Schemes". In: 2019 41st Antenna Measurement Techniques Association Symposium (AMTA). San Diego, California, USA, 2019
  Cosme Culotta-López and Dirk Heberling
  
• "On Phaseless Spherical Near-Field Antenna Measurements". In: 13th European Conference on Antennas and Propagation (EUCAP 2019) (EuCAP 2019). IEEE. Krakow, Poland, 2019
  Arya Bangun, Cosme Culotta-López, Arash Behboodi, Rudolf Mathar, and Dirk Heberling
  
• "Signal Recovery from Phaseless Measurements of Spherical Harmonics Expansion". In: 2019 27th European Signal Processing Conference (EUSIPCO) (EUSIPCO 2019). IEEE. A Coruna, Spain, 2019
  Arya Bangun, Arash Behboodi, and Rudolf Mathar