Sub-Nyquist Sampling for Active and Passive Cognitive Systems

sub nyquist plot
October, 05, 2016
Dept. of Electrical Engineering TechnionBack, Auditorium 1061
Deborah Cohen

In recent years, there has been an explosion of work to reduce sampling rates in a wide range of applications, when restrictions can be imposed on the signal using a priori information. In particular, the sparsity property of signals, expressed in diverse domains such as frequency, time or space, has been thoroughly investigated. In this work, we consider several examples in which sub-Nyquist sampling is possible without assuming any structure on the signal being sampled. This can be achieved due to the fact that we are not interested in direct recovery of the signal itself, but rather of some function of the signal. The first and main part of the talk is devoted to statistics recovery from low rate samples. In many signal processing and analysis applications, such as cognitive radio, spectrum sharing systems, machine learning, phaseless measurements, economics and financial time series analysis, second-order statistics suffice for the task at hand and estimation of the signal itself is unnecessary. While signal recovery from compressive measurements is an undetermined problem in the absence of a priori known structure, statistics recovery do not require additional assumptions on the signal, except for statistical models such as stationarity or cyclostationarity. In this work, we are interested in lower sampling rate bounds for second-order statistics recovery as well as practical sampling schemes design. Next, we consider sampling of a set of signals used for beamforming, where the beamformed signal has structure. In particular, we focus on radar signals. Radar processing aims at recovering several target parameters such as delay, Doppler frequency and azimuth in multiple input multiple output (MIMO) radar. Here, the structure exists only after processing and is expressed by the sparsity of the target scene. Again, we provide lower sampling rate bounds as well as practical target parameters recovery techniques. In both cases, we show that sampling at rates much lower than Nyquist is possible, despite the fact that no structure is assumed on the input signal. We illustrate these considerations on passive and active cognitive systems, cognitive radio and radar, respectively, and present practical hardware prototypes that demonstrate the theoretical concepts of this work.