Ph.D Thesis

Ph.D StudentCohen Deborah
SubjectStructure-Free Compressive Sampling
Sub-Nyquist Sampling for Passive and Active
Cognitive systems
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROF. Yonina Eldar
Full Thesis textFull thesis text - English Version


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 is possible 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 part of the thesis is devoted to statistics recovery from low rate samples. In many signal processing and analysis applications, such as cognitive radio (CR), 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 focus on CR applications and derive lower sampling rate bounds for second-order statistics recovery as well as practical sampling schemes design.

Next, we consider parameter estimation problems, where the goal is not to recover the signal itself but rather parameters embodied into it. In particular, we focus on radar signals. Radar processing aims at recovering several target parameters such as range, velocity and azimuth in multiple input multiple output (MIMO) radar. Here, the received signal is an amplitude-scaled and time and frequency-shifted version of a known transmitted pulse. We exploit the sparsity of the target scene to recover their parameters from low rate samples. We next turn to joint carrier frequency and direction of arrival (DOA) estimation of several communication transmissions. In this case, the received signal is unknown. In both scenarios, we provide lower sampling rate bounds as well as practical parameters recovery techniques and show that the number of required samples for this task is a function of the number of degrees of freedom, namely the number of unknown parameters.

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. Finally, we show that analog compression may have an impact beyond reducing sampling and processing rates and enable technology otherwise challenging, such as communication and radar spectrum sharing.