Feedback Acquisition and Reconstruction of Spectrum-Sparse Signals by Predictive Level Comparisons

In this letter, we propose a sparsity promoting feedback acquisition and reconstruction scheme for sensing, encoding and subsequent reconstruction of spectrally sparse signals. In the proposed scheme, the spectral components are estimated utilizing a sparsity-promoting, sliding-window algorithm in a feedback loop. Utilizing the estimated spectral components, a level signal is predicted and sign measurements of the prediction error are acquired. The sparsity promoting algorithm can then estimate the spectral components iteratively from the sign measurements. Unlike many batch-based Compressive Sensing (CS) algorithms, our proposed algorithm gradually estimates and follows slow changes in the sparse components utilizing a sliding-window technique. We also consider the scenario in which possible flipping errors in the sign bits propagate along iterations (due to the feedback loop) during reconstruction. We propose an iterative error correction algorithm to cope with this error propagation phenomenon considering a binary-sparse occurrence model on the error sequence. Simulation results show effective performance of the proposed scheme in comparison with the literature

Xampling: Signal Acquisition and Processing in Union of Subspaces

We introduce Xampling, a unified framework for signal acquisition and processing of signals in a union of subspaces. The main functions of this framework are two. Analog compression that narrows down the input bandwidth prior to sampling with commercial devices. A nonlinear algorithm then detects the input subspace prior to conventional signal processing. A representative union model of spectrally-sparse signals serves as a test-case to study these Xampling functions. We adopt three metrics for the choice of analog compression: robustness to model mismatch, required hardware accuracy and software complexities. We conduct a comprehensive comparison between two sub-Nyquist acquisition strategies for spectrally-sparse signals, the random demodulator and the modulated wideband converter (MWC), in terms of these metrics and draw operative conclusions regarding the choice of analog compression. We then address lowrate signal processing and develop an algorithm for that purpose that enables convenient signal processing at sub-Nyquist rates from samples obtained by the MWC. We conclude by showing that a variety of other sampling approaches for different union classes fit nicely into our framework.Comment: 16 pages, 9 figures, submitted to IEEE for possible publicatio

Improved Random Demodulator for Compressed Sensing Applications

The advances in the field of signal processing have led to the continuous increase in the bandwidth of signals. Sampling these signals becomes harder and harder due to the increased bandwidth. This brings in need for a complex high rate ADCs to meet the Nyquist rate which is the minimum rate to avoid aliasing. For a given increase in bandwidth, there has to be a corresponding increase in the sampling rate of ADC. This might not be possible in the near future at the current rate of increase in bandwidth. Hence, there is a need to replace the current Nyquist rate sampling method by a process that relaxes the requirements but still keeps the quality of signal reconstruction good . Compressed sensing is a new technique in the field of signal acquisition. Compressed sensing allows a signal to be acquired below Nyquist rate if the signal is sparse in a given domain. Compressed sensing makes possible to acquire sparse signals at rates below Nyquist rate. Signals like audio and images are sparse and can be sampled at a rate below the Nyquist rate. The random demodulator (RD) is a hardware architecture that is used to implement compressed sensing. A direct implementation of compressed sensing in hardware requires several copies of the RD. To reduce the complexity fewer RDs can be used. Usage of fewer RDs comes at the cost of decreased signal reconstruction performance. The contribution of this thesis is about improving the efficiency of RD. First contribution of this thesis involves proposing a new RD architecture that improves signal reconstruction quality using a post-acquisition randomization step. The second contribution of this thesis is to develop a hardware platform for compressed sensing using field programmable analog arrays (FPAAs) and field programmable gate arrays (FPGAs). This platform can be used to test new architectures of RD in hardware

The Pros and Cons of Compressive Sensing for Wideband Signal Acquisition: Noise Folding vs. Dynamic Range

Compressive sensing (CS) exploits the sparsity present in many signals to reduce the number of measurements needed for digital acquisition. With this reduction would come, in theory, commensurate reductions in the size, weight, power consumption, and/or monetary cost of both signal sensors and any associated communication links. This paper examines the use of CS in the design of a wideband radio receiver in a noisy environment. We formulate the problem statement for such a receiver and establish a reasonable set of requirements that a receiver should meet to be practically useful. We then evaluate the performance of a CS-based receiver in two ways: via a theoretical analysis of its expected performance, with a particular emphasis on noise and dynamic range, and via simulations that compare the CS receiver against the performance expected from a conventional implementation. On the one hand, we show that CS-based systems that aim to reduce the number of acquired measurements are somewhat sensitive to signal noise, exhibiting a 3dB SNR loss per octave of subsampling, which parallels the classic noise-folding phenomenon. On the other hand, we demonstrate that since they sample at a lower rate, CS-based systems can potentially attain a significantly larger dynamic range. Hence, we conclude that while a CS-based system has inherent limitations that do impose some restrictions on its potential applications, it also has attributes that make it highly desirable in a number of important practical settings

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

Fully-passive switched-capacitor techniques for high performance SAR ADC design

In recent years, SAR ADC becomes more and more popular in various low-power applications such as wireless sensors and low energy radios due to its circuit simplicity, high power efficiency, and scaling compatibility. However, its speed is limited by its successive approximation procedures and its power efficiency greatly reduces with the ADC resolution going beyond 10 bit. To address these issues, this thesis proposes to embed two techniques: 1) compressive sensing (CS) and 2) noise shaping (NS) to a conventional SAR ADC. The realization of both techniques are based on fully-passive switched-capacitor techniques. CS is a recently emerging sampling paradigm, stating that the sparsity of a signal can be exploited to reduce the ADC sampling rate below the Nyquist rate. Different from conventional CS frameworks which require dedicated analog CS encoders, this thesis proposes a fully-passive CS-SAR ADC architecture which only requires minor modification to a conventional SAR ADC. Two chips are fabricated in a 0.13 µm process to prove the concept. One chip is a single-channel CS-SAR ADC which can reduce the ADC conversion rate by 4 times, thus reducing the ADC power by 4 times. In many wireless sensing applications, multiple ADCs are commonly required to sense multi-channel signals such as multi-lead ECG sensing and parallel neural recording. Therefore, the other chip is a multi-channel CS-SAR ADC which can simultaneously convert 4-channel signals with a sampling rate of one channel’s Nyquist rate. At 0.8 V and 1 MS/s, both chips achieve an effective Walden FoM of around 5 fJ/conversion-step. This thesis also proposes a novel NS SAR ADC architecture that is simple, robust and low power for high-resolution applications. Compared to conventional ∆Σ ADCs, it replaces the power-hungry active integrator with a passive integrator which only requires one switch and two capacitors. Compared to previous 1st-order NS SAR ADC works, it achieves the best NS performance and can be easily extended to 2nd-order. A 1st-order 10-bit NS SAR ADC is fabricated in a 0.13 µm process. Through NS, SNDR increases by 6 dB with OSR doubled, achieving a 12- bit ENOB at OSR = 8. An improved version of a 2nd-order 9-bit NS SAR ADC is designed and simulated in a 40 nm process. The SNDR increases by 10 dB with OSR doubled, achieving a 14-bit ENOB at OSR = 16. At a bandwidth of 312.5 kHz, the Schreier FoM is 181 dB and the Walden FoM is 12.5 fJ/conversion-step, proving that the proposed NS SAR ADC architecture can achieve high resolution and high power efficiency simultaneously.Electrical and Computer Engineerin

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

Structured Compressed Sensing Using Deterministic Sequences

The problem of estimating sparse signals based on incomplete set of noiseless or noisy measurements has been investigated for a long time from different perspec- tives. In this dissertation, after the review of the theory of compressed sensing (CS) and existing structured sensing matrices, a new class of convolutional sensing matri- ces based on deterministic sequences are developed in the first part. The proposed matrices can achieve a near optimal bound with O(K log(N)) measurements for non-uniform recovery. Not only are they able to approximate compressible signals in the time domain, but they can also recover sparse signals in the frequency and discrete cosine transform domain. The candidates of the deterministic sequences include maximum length sequence (or called m-sequence), Golay's complementary sequence and Legendre sequence etc., which will be investigated respectively. In the second part, Golay-paired Hadamard matrices are introduced as structured sensing matrices, which are constructed from the Hadamard matrix, followed by diagonal Golay sequences. The properties and performances are analyzed in the following. Their strong structures ensure special isometry properties, and make them be easier applicable to hardware potentially. Finally, we exploit novel CS principles successfully in a few real applications, including radar imaging and dis- tributed source coding. The performance and the effectiveness of each scenario are verified in both theory and simulations