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

Multiband Spectrum Access: Great Promises for Future Cognitive Radio Networks

Cognitive radio has been widely considered as one of the prominent solutions to tackle the spectrum scarcity. While the majority of existing research has focused on single-band cognitive radio, multiband cognitive radio represents great promises towards implementing efficient cognitive networks compared to single-based networks. Multiband cognitive radio networks (MB-CRNs) are expected to significantly enhance the network's throughput and provide better channel maintenance by reducing handoff frequency. Nevertheless, the wideband front-end and the multiband spectrum access impose a number of challenges yet to overcome. This paper provides an in-depth analysis on the recent advancements in multiband spectrum sensing techniques, their limitations, and possible future directions to improve them. We study cooperative communications for MB-CRNs to tackle a fundamental limit on diversity and sampling. We also investigate several limits and tradeoffs of various design parameters for MB-CRNs. In addition, we explore the key MB-CRNs performance metrics that differ from the conventional metrics used for single-band based networks.Comment: 22 pages, 13 figures; published in the Proceedings of the IEEE Journal, Special Issue on Future Radio Spectrum Access, March 201

Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation

We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in two aspects: (i) we extend the formulation from real non-negative amplitude parameters to arbitrary complex ones, and (ii) we allow for mismatch between the manifold described by the parameters and its polar approximation. To quantify the improvements afforded by the proposed extensions, we evaluate six algorithms for estimation of parameters in sparse translation-invariant signals, exemplified with the time delay estimation problem. The evaluation is based on three performance metrics: estimator precision, sampling rate and computational complexity. We use compressive sensing with all the algorithms to lower the necessary sampling rate and show that it is still possible to attain good estimation precision and keep the computational complexity low. Our numerical experiments show that the proposed algorithms outperform existing approaches that either leverage polynomial interpolation or are based on a conversion to a frequency-estimation problem followed by a super-resolution algorithm. The algorithms studied here provide various tradeoffs between computational complexity, estimation precision, and necessary sampling rate. The work shows that compressive sensing for the class of sparse translation-invariant signals allows for a decrease in sampling rate and that the use of polar interpolation increases the estimation precision.Comment: 13 pages, 5 figures, to appear in IEEE Transactions on Signal Processing; minor edits and correction

Convolutional compressed sensing using deterministic sequences

This is the author's accepted manuscript (with working title "Semi-universal convolutional compressed sensing using (nearly) perfect sequences"). The final published article is available from the link below. Copyright @ 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, a new class of orthogonal circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier transform of a deterministic sequence with good autocorrelation. Both uniform recovery and non-uniform recovery of sparse signals are investigated, based on the coherence parameter of the proposed sensing matrices. Many examples of the sequences are investigated, particularly the Frank-Zadoff-Chu (FZC) sequence, the m-sequence and the Golay sequence. A salient feature of the proposed sensing matrices is that they can not only handle sparse signals in the time domain, but also those in the frequency and/or or discrete-cosine transform (DCT) domain