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1. Non-Uniform Wavelet Sampling for RF Analog-to-Information Conversion

   https://doi.org/10.1109/TCSI.2017.2729779  

   Pelissier, Michael ; Studer, Christoph ( August 2017 , IEEE Transactions on Circuits and Systems I: Regular Papers)

   Feature extraction, such as spectral occupancy, interferer energy and type, or direction-of-arrival, from wideband radio-frequency (RF) signals finds use in a growing number of applications as it enhances RF transceivers with cognitive abilities and enables parameter tuning of traditional RF chains. In power and cost limited applications, e.g., for sensor nodes in the Internet of Things, wideband RF feature extraction with conventional, Nyquist-rate analog-to-digital converters is infeasible. However, the structure of many RF features (such as signal sparsity) enables the use of compressive sensing (CS) techniques that acquire such signals at sub-Nyquist rates; while such CS-based analog-to-information (A2I) converters have the potential to enable low-cost and energy-efficient wideband RF sensing, they suffer from a variety of real-world limitations, such as noise folding, low sensitivity, aliasing, and limited flexibility. This paper proposes a novel CS-based A2I architecture called non-uniform wavelet sampling. Our solution extracts a carefully-selected subset of wavelet coefficients directly in the RF domain, which mitigates the main issues of existing A2I converter architectures. For multi-band RF signals, we propose a specialized variant called non-uniform wavelet bandpass sampling (NUWBS), which further improves sensitivity and reduces hardware complexity by leveraging the multi-band signal structure. We use simulations to demonstrate that NUWBSmore »approaches the theoretical performance limits of ℓ₁-norm-based sparse signal recovery. We investigate hardware-design aspects and show ASIC measurement results for the wavelet generation stage, which highlight the efficacy of NUWBS for a broad range of RF feature extraction tasks in cost- and power-limited applications.« less
2. Mean Field Analysis of Sparse Reconstruction with Correlated Variables.

   Ramezanali, Mohammad ; Mitra, Partha P ; Sengupta, Anirvan M. ( January 2016 , Eusipco)

   Sparse reconstruction algorithms aim to retrieve high-dimensional sparse signals from a limited number of measurements. A common example is LASSO or Basis Pursuit where sparsity is enforced using an `1-penalty together with a cost function ||y − Hx||_2^2. For random design matrices H, a sharp phase transition boundary separates the ‘good’ parameter region where error-free recovery of a sufficiently sparse signal is possible and a ‘bad’ regime where the recovery fails. However, theoretical analysis of phase transition boundary of the correlated variables case lags behind that of uncorrelated variables. Here we use replica trick from statistical physics to show that when an Ndimensional signal x is K-sparse and H is M × N dimensional with the covariance E[H_{ia}H_{jb}] = 1 M C_{ij}D_{ab}, with all D_{aa} = 1, the perfect recovery occurs at M ∼ ψ_K(D)K log(N/M) in the very sparse limit, where ψ_K(D) ≥ 1, indicating need for more observations for the same degree of sparsity.
3. Projected Nesterov's proximal-gradient signal recovery from compressive poisson measurements

   https://doi.org/10.1109/acssc.2015.7421393  

   Gu, Renliang ; Dogandzic, Aleksandar ( November 2015 , Proc. 49th Asilomar Conference on Signals, Systems and Computers)

   We develop a projected Nesterov’s proximal-gradient (PNPG) scheme for reconstructing sparse signals from compressive Poisson-distributed measurements with the mean signal intensity that follows an affine model with known intercept. The objective function to be minimized is a sum of convex data fidelity (negative log-likelihood (NLL)) and regularization terms. We apply sparse signal regularization where the signal belongs to a nonempty closed convex set within the domain of the NLL and signal sparsity is imposed using total-variation (TV) penalty. We present analytical upper bounds on the regularization tuning constant. The proposed PNPG method employs projected Nesterov’s acceleration step, function restart, and an adaptive step-size selection scheme that aims at obtaining a good local majorizing function of the NLL and reducing the time spent backtracking. We establish O(k⁻²) convergence of the PNPG method with step-size backtracking only and no restart. Numerical examples demonstrate the performance of the PNPG method.
4. NUWBS: Non-Uniform Wavelet Bandpass Sampling for Compressive RF Feature Acquisition

   Pelissier, Michael ; Studer, Chrsitoph ( June 2017 , Signal Processing with Adaptive Sparse Structured Representations (SPARS) workshop)

   Feature extraction from wideband radio-frequency (RF) signals, such as spectral activity, interferer energy and type, or direction- of-arrival, finds use in a growing number of applications. Compressive sensing (CS)-based analog-to-information (A2I) converters enable the design of inexpensive and energy-efficient wideband RF sensing solutions for such applications. However, most A2I architectures suffer from a variety of real-world impairments. We propose a novel A2I architecture, referred to as non-uniform wavelet bandpass sampling (NUWBS). Our architecture extracts a carefully-tuned subset of wavelet coefficients directly in the RF domain, which mitigates the main issues of most existing A2I converters. We use simulations to show that NUWBS approaches the performance limits of l1-norm-based sparse signal recovery.
5. Structured Signal Recovery from Non-linear and Heavy-tailed Measurements

   https://doi.org/10.1109/TIT.2018.2842216  

   Goldstein, Larry ; Minsker, Stanislav ; Wei, Xiaohan ( May 2018 , IEEE Transactions on Information Theory)

   We study high-dimensional signal recovery from non-linear measurements with design vectors having elliptically symmetric distribution. Special attention is devoted to the situation when the unknown signal belongs to a set of low statistical complexity, while both the measurements and the design vectors are heavy-tailed. We propose and analyze a new estimator that adapts to the structure of the problem, while being robust both to the possible model misspecification characterized by arbitrary non-linearity of the measurements as well as to data corruption modeled by the heavy-tailed distributions. Moreover, this estimator has low computational complexity. Our results are expressed in the form of exponential concentration inequalities for the error of the proposed estimator. On the technical side, our proofs rely on the generic chaining methods, and illustrate the power of this approach for statistical applications. Theory is supported by numerical experiments demonstrating that our estimator outperforms existing alternatives when data is heavy-tailed.