Super-Resolution Radar


Reinhard Heckel, Veniamin I. Morgenshtern, and Mahdi Soltanolkotabi


arXiv, Nov. 2014, submitted.

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In this paper 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 essentially solving a simple 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.

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Copyright Notice: © 2014 R. Heckel, V. I. Morgenshtern, and M. Soltanolkotabi.

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