Sub-Nyquist Wideband Spectrum Sensing and Sharing

PhDThe rising popularity of wireless services resulting in spectrum shortage has motivated dynamic spectrum sharing to facilitate e cient usage of the underutilized spectrum. Wideband spectrum sensing is a critical functionality to enable dynamic spectrum access by enhancing the opportunities of exploring spectral holes, but entails a major implemen- tation challenge in compact commodity radios that have limited energy and computation capabilities. The sampling rates speci ed by the Shannon-Nyquist theorem impose great challenges both on the acquisition hardware and the subsequent storage and digital sig- nal processors. Sub-Nyquist sampling was thus motivated to sample wideband signals at rates far lower than the Nyquist rate, while still retaining the essential information in the underlying signals. This thesis proposes several algorithms for invoking sub-Nyquist sampling in wideband spectrum sensing. Speci cally, a sub-Nyquist wideband spectrum sensing algorithm is proposed that achieves wideband sensing independent of signal sparsity without sampling at full bandwidth by using the low-speed analog-to-digital converters based on sparse Fast Fourier Transform. To lower signal spectrum sparsity while maintaining the channel state information, the received signal is pre-processed through a proposed permutation and ltering algorithm. Additionally, a low-complexity sub-Nyquist wideband spectrum sensing scheme is proposed that locates occupied channels blindly by recovering the sig- nal support, based on the jointly sparse nature of multiband signals. Exploiting the common signal support shared among multiple secondary users, an e cient coopera- tive spectrum sensing scheme is developed, in which the energy consumption on signal acquisition, processing, and transmission is reduced with the detection performance guar- antee. To further reduce the computation complexity of wideband spectrum sensing, a hybrid framework of sub-Nyquist wideband spectrum sensing with geolocation database is explored. Prior channel information from geolocation database is utilized in the sens- ing process to reduce the processing requirements on the sensor nodes. The models of the proposed algorithms are derived and veri ed by numerical analyses and tested on both real-world and simulated TV white space signals

Compressive sensing spectral estimation for output-only structural system identification

In this paper a compressive sensing (CS), sub-Nyquist, non-uniform deterministic sampling technique is considered in conjunction with a computationally efficient power spectrum estimation approach for frequency domain output-only system identification of linear white noise excited structural systems. The adopted CS sensing spectral estimation approach assumes multi-band input random signals/stochastic processes without posing any signal sparsity requirements and therefore it is applicable to linear structures with arbitrary number of degrees of freedom and level of damping. Further, it applies directly to the sub-Nyquist (CS) measurements and, thus, it by-passes the computationally demanding signal reconstruction step from CS measurements. Numerical results pertaining to the acceleration response of a damped structure with closely-spaced natural frequencies are provided to demonstrate the effectiveness of the considered approach to provide reliable estimates of natural frequencies by means of the standard frequency domain peak-picking algorithm of operational modal analysis using up to 90% fewer measurements compared to the Nyquist rate sampled data. It is envisioned that this study will further familiarize the structural dynamics community with the potential of CS-based techniques for vibration-based structural health monitoring and condition assessment of engineering structures

A multi-sensor sub-Nyquist power spectrum blind sampling approach for low-power wireless sensors in operational modal analysis applications

A novel multi-sensor power spectrum blind sampling (PSBS) approach is proposed supporting low-power wireless sensor networks (WSN) for Operational Modal Analysis (OMA) applications. The developed approach relies on arrays of wireless sensors, employing deterministic non-uniform in time multi-coset sampling to acquire structural response acceleration signals at sub-Nyquist sampling rates, treated as realizations of stationary random processes without making any assumption about the average signal frequency content and spectral support. The acquired compressed measurements are transmitted to a central server and collectively processed via a PSBS technique, herein extended to the multi-sensor case, to estimate the power spectral density matrix of an underlying spatially correlated stationary response acceleration random process directly from the compressed measurements. Structural modal properties are then extracted through standard frequency domain decomposition (FDD). The efficacy of the proposed approach to resolve closely-spaced modes is numerically tested for various data compression levels using noisy response acceleration signals of a white-noise excited finite element model of a space truss as well as field-recorded acceleration time-histories of an instrumented bridge under operational loading. It is shown that accurate mode shapes based on the modal assurance criterion can be obtained from as low as 89% less measurements compared to conventional non-compressive FDD at Nyquist sampling rate. Further, significant gains in energy consumption and battery lifetime prolongation of the order of years are estimated, assuming wireless sensors operating on multi-coset sampling at different data compression levels. It is, therefore, concluded that the proposed PSBS approach could provide long-term structural health monitoring systems with low-maintenance cost once wireless sensors with multi-coset sampling capabilities become commercially available

Non-uniform sampling and reconstruction of multi-band signals and its application in wideband spectrum sensing of cognitive radio

Sampling theories lie at the heart of signal processing devices and communication systems. To accommodate high operating rates while retaining low computational cost, efficient analog-to digital (ADC) converters must be developed. Many of limitations encountered in current converters are due to a traditional assumption that the sampling state needs to acquire the data at the Nyquist rate, corresponding to twice the signal bandwidth. In this thesis a method of sampling far below the Nyquist rate for sparse spectrum multiband signals is investigated. The method is called periodic non-uniform sampling, and it is useful in a variety of applications such as data converters, sensor array imaging and image compression. Firstly, a model for the sampling system in the frequency domain is prepared. It relates the Fourier transform of observed compressed samples with the unknown spectrum of the signal. Next, the reconstruction process based on the topic of compressed sensing is provided. We show that the sampling parameters play an important role on the average sample ratio and the quality of the reconstructed signal. The concept of condition number and its effect on the reconstructed signal in the presence of noise is introduced, and a feasible approach for choosing a sample pattern with a low condition number is given. We distinguish between the cases of known spectrum and unknown spectrum signals respectively. One of the model parameters is determined by the signal band locations that in case of unknown spectrum signals should be estimated from sampled data. Therefore, we applied both subspace methods and non-linear least square methods for estimation of this parameter. We also used the information theoretic criteria (Akaike and MDL) and the exponential fitting test techniques for model order selection in this case

Novel Digital Alias-Free Signal Processing Approaches to FIR Filtering Estimation

This thesis aims at developing a new methodology of filtering continuous-time bandlimited signals and piecewise-continuous signals from their discrete-time samples. Unlike the existing state-of-the-art filters, my filters are not adversely affected by aliasing, allowing the designers to flexibly select the sampling rates of the processed signal to reach the required accuracy of signal filtering rather than meeting stiff and often demanding constraints imposed by the classical theory of digital signal processing (DSP). The impact of this thesis is cost reduction of alias-free sampling, filtering and other digital processing blocks, particularly when the processed signals have sparse and unknown spectral support. Novel approaches are proposed which can mitigate the negative effects of aliasing, thanks to the use of nonuniform random/pseudorandom sampling and processing algorithms. As such, the proposed approaches belong to the family of digital alias-free signal processing (DASP). Namely, three main approaches are considered: total random (ToRa), stratified (StSa) and antithetical stratified (AnSt) random sampling techniques. First, I introduce a finite impulse response (FIR) filter estimator for each of the three considered techniques. In addition, a generalised estimator that encompasses the three filter estimators is also proposed. Then, statistical properties of all estimators are investigated to assess their quality. Properties such as expected value, bias, variance, convergence rate, and consistency are all inspected and unveiled. Moreover, closed-form mathematical expression is devised for the variance of each single estimator. Furthermore, quality assessment of the proposed estimators is examined in two main cases related to the smoothness status of the filter convolution’s integrand function, \u1d454(\u1d461,\u1d70f)∶=\u1d465(\u1d70f)ℎ(\u1d461−\u1d70f), and its first two derivatives. The first main case is continuous and differentiable functions \u1d454(\u1d461,\u1d70f), \u1d454′(\u1d461,\u1d70f), and \u1d454′′(\u1d461,\u1d70f). Whereas in the second main case, I cover all possible instances where some/all of such functions are piecewise-continuous and involving a finite number of bounded discontinuities. Primarily obtained results prove that all considered filter estimators are unbiassed and consistent. Hence, variances of the estimators converge to zero after certain number of sample points. However, the convergence rate depends on the selected estimator and which case of smoothness is being considered. In the first case (i.e. continuous \u1d454(\u1d461,\u1d70f) and its derivatives), ToRa, StSa and AnSt filter estimators converge uniformly at rates of \u1d441−1, \u1d441−3, and \u1d441−5 respectively, where 2\u1d441 is the total number of sample points. More interestingly, in the second main case, the convergence rates of StSa and AnSt estimators are maintained even if there are some discontinuities in the first-order derivative (FOD) with respect to \u1d70f of \u1d454(\u1d461,\u1d70f) (for StSa estimator) or in the second-order derivative (SOD) with respect to \u1d70f of \u1d454(\u1d461,\u1d70f) (for AnSt). Whereas these rates drop to \u1d441−2 and \u1d441−4 (for StSa and AnSt, respectively) if the zero-order derivative (ZOD) (for StSa) and FOD (for AnSt) are piecewise-continuous. Finally, if the ZOD of \u1d454(\u1d461,\u1d70f) is piecewise-continuous, then the uniform convergence rate of the AnSt estimator further drops to \u1d441−2. For practical reasons, I also introduce the utilisation of the three estimators in a special situation where the input signal is pseudorandomly sampled from otherwise uniform and dense grid. An FIR filter model with an oversampled finite-duration impulse response, timely aligned with the grid, is proposed and meant to be stored in a lookup table of the implemented filter’s memory to save processing time. Then, a synchronised convolution sum operation is conducted to estimate the filter output. Finally, a new unequally spaced Lagrange interpolation-based rule is proposed. The so-called composite 3-nonuniform-sample (C3NS) rule is employed to estimate area under the curve (AUC) of an integrand function rather than the simple Rectangular rule. I then carry out comparisons for the convergence rates of different estimators based on the two interpolation rules. The proposed C3NS estimator outperforms other Rectangular rule estimators on the expense of higher computational complexity. Of course, this extra cost could only be justifiable for some specific applications where more accurate estimation is required

Compressive techniques for sub-Nyquist data acquisition & processing in vibration-based structural health monitoring of engineering structures

Vibration-based structural health monitoring (VSHM) is an automated method for assessing the integrity and performance of dynamically excited structures through processing of structural vibration response signals acquired by arrays of sensors. From a technological viewpoint, wireless sensor networks (WSNs) offer less obtrusive, more economical, and rapid VSHM deployments in civil structures compared to their tethered counterparts, especially in monitoring large-scale and geometrically complex structures. However, WSNs are constrained by certain practical issues related to local power supply at sensors and restrictions to the amount of wirelessly transmitted data due to increased power consumptions and bandwidth limitations in wireless communications. The primary objective of this thesis is to resolve the above issues by considering sub-Nyquist data acquisition and processing techniques that involve simultaneous signal acquisition and compression before transmission. This drastically reduces the sampling and transmission requirements leading to reduced power consumptions up to 85-90% compared to conventional approaches at Nyquist rate. Within this context, the current state-of-the-art VSHM approaches exploits the theory of compressive sensing (CS) to acquire structural responses at non-uniform random sub-Nyquist sampling schemes. By exploiting the sparse structure of the analysed signals in a known vector basis (i.e., non-zero signal coefficients), the original time-domain signals are reconstructed at the uniform Nyquist grid by solving an underdetermined optimisation problem subject to signal sparsity constraints. However, the CS sparse recovery is a computationally intensive problem that strongly depends on and is limited by the sparsity attributes of the measured signals on a pre-defined expansion basis. This sparsity information, though, is unknown in real-time VSHM deployments while it is adversely affected by noisy environments encountered in practice. To efficiently address the above limitations encountered in CS-based VSHM methods, this research study proposes three alternative approaches for energy-efficient VSHM using compressed structural response signals under ambient vibrations. The first approach aims to enhance the sparsity information of vibrating structural responses by considering their representation on the wavelet transform domain using various oscillatory functions with different frequency domain attributes. In this respect, a novel data-driven damage detection algorithm is developed herein, emerged as a fusion of the CS framework with the Relative Wavelet Entropy (RWE) damage index. By processing sparse signal coefficients on the harmonic wavelet transform for two comparative structural states (i.e., damage versus healthy state), CS-based RWE damage indices are retrieved from a significantly reduced number of wavelet coefficients without reconstructing structural responses in time-domain. The second approach involves a novel signal-agnostic sub-Nyquist spectral estimation method free from sparsity constraints, which is proposed herein as a viable alternative for power-efficient WSNs in VSHM applications. The developed method relies on Power Spectrum Blind Sampling (PSBS) techniques together with a deterministic multi-coset sampling pattern, capable to acquire stationary structural responses at sub-Nyquist rates without imposing sparsity conditions. Based on a network of wireless sensors operating on the same sampling pattern, auto/cross power-spectral density estimates are computed directly from compressed data by solving an overdetermined optimisation problem; thus, by-passing the computationally intensive signal reconstruction operations in time-domain. This innovative approach can be fused with standard operational modal analysis algorithms to estimate the inherent resonant frequencies and modal deflected shapes of structures under low-amplitude ambient vibrations with the minimum power, computational and memory requirements at the sensor, while outperforming pertinent CS-based approaches. Based on the extracted modal in formation, numerous data-driven damage detection strategies can be further employed to evaluate the condition of the monitored structures. The third approach of this thesis proposes a noise-immune damage detection method capable to capture small shifts in structural natural frequencies before and after a seismic event of low intensity using compressed acceleration data contaminated with broadband noise. This novel approach relies on a recently established sub-Nyquist pseudo-spectral estimation method which combines the deterministic co-prime sub-Nyquist sampling technique with the multiple signal classification (MUSIC) pseudo-spectrum estimator. This is also a signal-agnostic and signal reconstruction-free method that treats structural response signals as wide-sense stationary stochastic processes to retrieve, with very high resolution, auto-power spectral densities and structural natural frequency estimates directly from compressed data while filtering out additive broadband noise

Compressive Acquisition and Processing of Sparse Analog Signals

Since the advent of the first digital processing units, the importance of digital signal processing has been steadily rising. Today, most signal processing happens in the digital domain, requiring that analog signals be first sampled and digitized before any relevant data can be extracted from them. The recent explosion of the demands for data acquisition, storage and processing, however, has pushed the capabilities of conventional acquisition systems to their limits in many application areas. By offering an alternative view on the signal acquisition process, ideas from sparse signal processing and one of its main beneficiaries compressed sensing (CS), aim at alleviating some of these problems. In this thesis, we look into the ways the application of a compressive measurement kernel impacts the signal recovery performance and investigate methods to infer the current signal complexity from the compressive observations. We then study a particular application, namely that of sub-Nyquist sampling and processing of sparse analog multiband signals in spectral, angular and spatial domains.Seit dem Aufkommen der ersten digitalen Verarbeitungseinheiten hat die Bedeutung der digitalen Signalverarbeitung stetig zugenommen. Heutzutage findet die meiste Signalverarbeitung im digitalen Bereich statt, was erfordert, dass analoge Signale zuerst abgetastet und digitalisiert werden, bevor relevante Daten daraus extrahiert werden können. Jahrzehntelang hat die herkömmliche äquidistante Abtastung, die durch das Nyquist-Abtasttheorem bestimmt wird, zu diesem Zweck ein nahezu universelles Mittel bereitgestellt. Der kürzliche explosive Anstieg der Anforderungen an die Datenerfassung, -speicherung und -verarbeitung hat jedoch die Fähigkeiten herkömmlicher Erfassungssysteme in vielen Anwendungsbereichen an ihre Grenzen gebracht. Durch eine alternative Sichtweise auf den Signalerfassungsprozess können Ideen aus der sparse Signalverarbeitung und einer ihrer Hauptanwendungsgebiete, Compressed Sensing (CS), dazu beitragen, einige dieser Probleme zu mindern. Basierend auf der Annahme, dass der Informationsgehalt eines Signals oft viel geringer ist als was von der nativen Repräsentation vorgegeben, stellt CS ein alternatives Konzept für die Erfassung und Verarbeitung bereit, das versucht, die Abtastrate unter Beibehaltung des Signalinformationsgehalts zu reduzieren. In dieser Arbeit untersuchen wir einige der Grundlagen des endlichdimensionalen CSFrameworks und seine Verbindung mit Sub-Nyquist Abtastung und Verarbeitung von sparsen analogen Signalen. Obwohl es seit mehr als einem Jahrzehnt ein Schwerpunkt aktiver Forschung ist, gibt es noch erhebliche Lücken beim Verständnis der Auswirkungen von komprimierenden Ansätzen auf die Signalwiedergewinnung und die Verarbeitungsleistung, insbesondere bei rauschbehafteten Umgebungen und in Bezug auf praktische Messaufgaben. In dieser Dissertation untersuchen wir, wie sich die Anwendung eines komprimierenden Messkerns auf die Signal- und Rauschcharakteristiken auf die Signalrückgewinnungsleistung auswirkt. Wir erforschen auch Methoden, um die aktuelle Signal-Sparsity-Order aus den komprimierten Messungen abzuleiten, ohne auf die Nyquist-Raten-Verarbeitung zurückzugreifen, und zeigen den Vorteil, den sie für den Wiederherstellungsprozess bietet. Nachdem gehen wir zu einer speziellen Anwendung, nämlich der Sub-Nyquist-Abtastung und Verarbeitung von sparsen analogen Multibandsignalen. Innerhalb des Sub-Nyquist-Abtastung untersuchen wir drei verschiedene Multiband-Szenarien, die Multiband-Sensing in der spektralen, Winkel und räumlichen-Domäne einbeziehen.Since the advent of the first digital processing units, the importance of digital signal processing has been steadily rising. Today, most signal processing happens in the digital domain, requiring that analog signals be first sampled and digitized before any relevant data can be extracted from them. For decades, conventional uniform sampling that is governed by the Nyquist sampling theorem has provided an almost universal means to this end. The recent explosion of the demands for data acquisition, storage and processing, however, has pushed the capabilities of conventional acquisition systems to their limits in many application areas. By offering an alternative view on the signal acquisition process, ideas from sparse signal processing and one of its main beneficiaries compressed sensing (CS), have the potential to assist alleviating some of these problems. Building on the premise that the signal information rate is often much lower than what is dictated by its native representation, CS provides an alternative acquisition and processing framework that attempts to reduce the sampling rate while preserving the information content of the signal. In this thesis, we explore some of the basic foundations of the finite-dimensional CS framework and its connection to sub-Nyquist sampling and processing of sparse continuous analog signals with application to multiband sensing. Despite being a focus of active research for over a decade, there still remain signi_cant gaps in understanding the implications that compressive approaches have on the signal recovery and processing performance, especially against noisy settings and in relation to practical sampling problems. This dissertation aims at filling some of these gaps. More specifically, we look into the ways the application of a compressive measurement kernel impacts signal and noise characteristics and the relation it has to the signal recovery performance. We also investigate methods to infer the current complexity of the signal scene from the reduced-rate compressive observations without resorting to Nyquist-rate processing and show the advantage this knowledge offers to the recovery process. Having considered some of the universal aspects of compressive systems, we then move to studying a particular application, namely that of sub-Nyquist sampling and processing of sparse analog multiband signals. Within the sub-Nyquist sampling framework, we examine three different multiband scenarios that involve multiband sensing in spectral, angular and spatial domains. For each of them, we provide a sub-Nyquist receiver architecture, develop recovery methods and numerically evaluate their performance