Title: Super-resolution radar
Abstract: In this talk, we study the identification of a time-varying linear system whose response is a weighted superposition of time and frequency shifted versions of the input signal. This problem arises in a multitude of applications such as wireless communications and radar imaging. Due to practical constraints, the input signal has finite bandwidth B, and the received signal is observed over a finite time interval of length T only. This gives rise to a time and frequency resolution of 1/B and 1/T. We show that this resolution limit can be overcome, i.e., we can recover the exact (continuous) time-frequency shifts and the corresponding attenuation factors, by solving a convex optimization problem. This result holds provided that the distance between the time-frequency shifts is at least 2.37/B and 2.37/T, in time and frequency. Furthermore, this result allows the total number of time-frequency shifts to be linear (up to a log-factor) in BT, the dimensionality of the response of the system. More generally, we show that we can estimate the time-frequency components of a signal that is S-sparse in the continuous dictionary of time-frequency shifts of a random (window) function, from a number of measurements, that is linear (up to a log-factor) in S. We also discuss extensions of this theory to the localization of targets in MIMO radar.
Reinhard Heckel is a Postdoctoral researcher in the Department of Electrical Engineering and Computer Sciences at the University of California, Berkeley. Before that, he spent a year in the Cognitive Computing & Computational Sciences Department at IBM Research, Zurich. He completed his Ph.D. in August 2014 at ETH Zurich, Department of Information Technology and Electrical Engineering, advised by Helmut Bölcskei. In Fall 2013, he was a visiting Ph.D. student in the Statistics Department of Stanford University. Reinhard Heckel is interested in various topics in machine learning, mathematical signal processing, sparse signal recovery, and computational biology.