Ph.D Thesis

Ph.D StudentMishali Moshe
SubjectSampling and Processing of Structured Signals at Sub-Nyquist
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROF. Yonina Eldar
Full Thesis textFull thesis text - English Version


This dissertation develops practical sub-Nyquist sampling strategies for multiband signals with band locations that are a-priori unknown, as well as for broader classes of structured signals. We begin by establishing a general mathematical framework for rate reduction and efficient reconstruction, by mapping a given acquisition scheme to an infinite set of underdetermined linear systems possessing jointly-sparse solution vectors. We construct a finite-dimensional optimization program from the measurements and prove its solution indicates the nonzero location set. The values are then computed using standard least squares. Utilizing this framework for multiband sampling, we design a periodic nonuniform grid whose corresponding linear system determines the spectral support. In practice, however, realizing a nonuniform grid with existing technology effectively requires devices with Nyquist-rate bandwidths. To circumvent analog bandwidth limitations, we develop the modulated wideband converter (MWC) system which allows implementation with existing low rate and low analog bandwidth sampling devices. A digital algorithm we provide creates a seamless interface to conventional processing methods at sub-Nyquist rates. This thesis also reports on a circuit work in which we manufactured a four-channel MWC board-level prototype. Results of hardware experiments verify a dynamic range of input powers up to 50 dB and affirm accurate reconstruction of 2 GHz Nyquist-bandwidth inputs from sampling at rate as low as 280 MHz. To the best of our knowledge, this is the first wideband hardware accomplishing minimal sub-Nyquist rates without knowledge of the carrier positions.

We generalize the approach to an abstract model of signals lying in a union of subspaces. A polynomial-time reconstruction method from generalized samples with provable error guarantees is proposed for a finite union of finite dimensions and well structured subspaces. In order to treat the more challenging case with infiniteness in either union or subspace cardinalities, we introduce a functional architecture, referred to as Xampling, of five blocks and show that Xampling is sufficiently general to capture a variety of sampling strategies for union applications. We summarize in a more hardware-oriented viewpoint, suggesting spectrum sensing in cognitive radio mobiles as a potential application for our theoretical and practical results.