Sub-Nyquist Sampling: Bridging Theory and Practice

Sampling theory encompasses all aspects related to the conversion of continuous-time signals to discrete streams of numbers. The famous Shannon-Nyquist theorem has become a landmark in the development of digital signal processing. In modern applications, an increasingly number of functions is being pushed forward to sophisticated software algorithms, leaving only those delicate finely-tuned tasks for the circuit level. In this paper, we review sampling strategies which target reduction of the ADC rate below Nyquist. Our survey covers classic works from the early 50's of the previous century through recent publications from the past several years. The prime focus is bridging theory and practice, that is to pinpoint the potential of sub-Nyquist strategies to emerge from the math to the hardware. In that spirit, we integrate contemporary theoretical viewpoints, which study signal modeling in a union of subspaces, together with a taste of practical aspects, namely how the avant-garde modalities boil down to concrete signal processing systems. Our hope is that this presentation style will attract the interest of both researchers and engineers in the hope of promoting the sub-Nyquist premise into practical applications, and encouraging further research into this exciting new frontier.Comment: 48 pages, 18 figures, to appear in IEEE Signal Processing Magazin

Spectral Compressive Sensing with Model Selection

The performance of existing approaches to the recovery of frequency-sparse signals from compressed measurements is limited by the coherence of required sparsity dictionaries and the discretization of frequency parameter space. In this paper, we adopt a parametric joint recovery-estimation method based on model selection in spectral compressive sensing. Numerical experiments show that our approach outperforms most state-of-the-art spectral CS recovery approaches in fidelity, tolerance to noise and computation efficiency.Comment: 5 pages, 2 figures, 1 table, published in ICASSP 201

Reducing the Computational Complexity of Reconstruction in Compressed Sensing Nonuniform Sampling

Publication in the conference proceedings of EUSIPCO, Marrakech, Morocco, 201

Discrete Electronic Warfare Signal Processing using Compressed Sensing Based on Random Modulator Pre-Integrator

Electronic warfare receiver works in the wide electromagnetic spectrum in dense radar signal environment. Current trends in radar systems are ultra wideband and low probability of intercept radar technology. Detection of signals from various radar stations is a concern. Performance and probability of intercept are mainly dependent on high speed ADC technology. The sampling and reconstruction functions have to be optimized to capture incoming signals at the receiver to extract characteristics of the radar signal. The compressive sampling of the input signal with orthonormal base vectors, projecting the basis in the union of subspaces and recovery through convex optimisation techniques is the current traditional approach. Modern trends in signal processing suggest the random modulator pre-integrator (RMPI), which sample the input signal at information rate non-adaptively and recovery by the processing of discrete and finite vectors. Analysis of RMPI theory, application to EW receiver, simulation and recovery of EW receiver signals are discussed

Technical Report: Compressive Temporal Higher Order Cyclostationary Statistics

The application of nonlinear transformations to a cyclostationary signal for the purpose of revealing hidden periodicities has proven to be useful for applications requiring signal selectivity and noise tolerance. The fact that the hidden periodicities, referred to as cyclic moments, are often compressible in the Fourier domain motivates the use of compressive sensing (CS) as an efficient acquisition protocol for capturing such signals. In this work, we consider the class of Temporal Higher Order Cyclostationary Statistics (THOCS) estimators when CS is used to acquire the cyclostationary signal assuming compressible cyclic moments in the Fourier domain. We develop a theoretical framework for estimating THOCS using the low-rate nonuniform sampling protocol from CS and illustrate the performance of this framework using simulated data