On optimal design and applications of linear transforms

Linear transforms are encountered in many fields of applied science and engineering. In the past, conventional block transforms provided acceptable answers to different practical problems. But now, under increasing competitive pressures, with the growing reservoir of theory and a corresponding development of computing facilities, a real demand has been created for methods that systematically improve performance. As a result the past two decades have seen the explosive growth of a class of linear transform theory known as multiresolution signal decomposition. The goal of this work is to design and apply these advanced signal processing techniques to several different problems. The optimal design of subband filter banks is considered first. Several design examples are presented for M-band filter banks. Conventional design approaches are found to present problems when the number of constraints increases. A novel optimization method is proposed using a step-by-step design of a hierarchical subband tree. This method is shown to possess performance improvements in applications such as subband image coding. The subband tree structuring is then discussed and generalized algorithms are presented. Next, the attention is focused on the interference excision problem in direct sequence spread spectrum (DSSS) communications. The analytical and experimental performance of the DSSS receiver employing excision are presented. Different excision techniques are evaluated and ranked along with the proposed adaptive subband transform-based excises. The robustness of the considered methods is investigated for either time-localized or frequency-localized interferers. A domain switchable excision algorithm is also presented. Finally, sonic of the ideas associated with the interference excision problem are utilized in the spectral shaping of a particular biological signal, namely heart rate variability. The improvements for the spectral shaping process are shown for time-frequency analysis. In general, this dissertation demonstrates the proliferation of new tools for digital signal processing

Adaptive Interference Mitigation in GPS Receivers

Satellite navigation systems (GNSS) are among the most complex radio-navigation systems, providing positioning, navigation, and timing (PNT) information. A growing number of public sector and commercial applications rely on the GNSS PNT service to support business growth, technical development, and the day-to-day operation of technology and socioeconomic systems. As GNSS signals have inherent limitations, they are highly vulnerable to intentional and unintentional interference. GNSS signals have spectral power densities far below ambient thermal noise. Consequently, GNSS receivers must meet high standards of reliability and integrity to be used within a broad spectrum of applications. GNSS receivers must employ effective interference mitigation techniques to ensure robust, accurate, and reliable PNT service. This research aims to evaluate the effectiveness of the Adaptive Notch Filter (ANF), a precorrelation mitigation technique that can be used to excise Continuous Wave Interference (CWI), hop-frequency and chirp-type interferences from GPS L1 signals. To mitigate unwanted interference, state-of-the-art ANFs typically adjust a single parameter, the notch centre frequency, and zeros are constrained extremely close to unity. Because of this, the notch centre frequency converges slowly to the target frequency. During this slow converge period, interference leaks into the acquisition block, thus sabotaging the operation of the acquisition block. Furthermore, if the CWI continuously hops within the GPS L1 in-band region, the subsequent interference frequency is locked onto after a delay, which means constant interference occurs in the receiver throughout the delay period. This research contributes to the field of interference mitigation at GNSS's receiver end using adaptive signal processing, predominately for GPS. This research can be divided into three stages. I first designed, modelled and developed a Simulink-based GPS L1 signal simulator, providing a homogenous test signal for existing and proposed interference mitigation algorithms. Simulink-based GPS L1 signal simulator provided great flexibility to change various parameters to generate GPS L1 signal under different conditions, e.g. Doppler Shift, code phase delay and amount of propagation degradation. Furthermore, I modelled three acquisition schemes for GPS signals and tested GPS L1 signals acquisition via coherent and non-coherent integration methods. As a next step, I modelled different types of interference signals precisely and implemented and evaluated existing adaptive notch filters in MATLAB in terms of Carrier to Noise Density (\u1d436/\u1d4410), Signal to Noise Ratio (SNR), Peak Degradation Metric, and Mean Square Error (MSE) at the output of the acquisition module in order to create benchmarks. Finally, I designed, developed and implemented a novel algorithm that simultaneously adapts both coefficients in lattice-based ANF. Mathematically, I derived the full-gradient term for the notch's bandwidth parameter adaptation and developed a framework for simultaneously adapting both coefficients of a lattice-based adaptive notch filter. I evaluated the performance of existing and proposed interference mitigation techniques under different types of interference signals. Moreover, I critically analysed different internal signals within the ANF structure in order to develop a new threshold parameter that resets the notch bandwidth at the start of each subsequent interference frequency. As a result, I further reduce the complexity of the structural implementation of lattice-based ANF, allowing for efficient hardware realisation and lower computational costs. It is concluded from extensive simulation results that the proposed fully adaptive lattice-based provides better interference mitigation performance and superior convergence properties to target frequency compared to traditional ANF algorithms. It is demonstrated that by employing the proposed algorithm, a receiver is able to operate with a higher dynamic range of JNR than is possible with existing methods. This research also presents the design and MATLAB implementation of a parameterisable Complex Adaptive Notch Filer (CANF). Present analysis on higher order CANF for detecting and mitigating various types of interference for complex baseband GPS L1 signals. In the end, further research was conducted to suppress interference in the GPS L1 signal by exploiting autocorrelation properties and discarding some portion of the main lobe of the GPS L1 signal. It is shown that by removing 30% spectrum of the main lobe, either from left, right, or centre, the GPS L1 signal is still acquirable

Interference Mitigation and Localization Based on Time-Frequency Analysis for Navigation Satellite Systems

Interference Mitigation and Localization Based on Time-Frequency Analysis for Navigation Satellite SystemsNowadays, the operation of global navigation satellite systems (GNSS) is imperative across a multitude of applications worldwide. The increasing reliance on accurate positioning and timing information has made more serious than ever the consequences of possible service outages in the satellite navigation systems. Among others, interference is regarded as the primary threat to their operation. Due the recent proliferation of portable interferers, notably jammers, it has now become common for GNSS receivers to endure simultaneous attacks from multiple sources of interference, which are likely spatially distributed and transmit different modulations. To the best knowledge of the author, the present dissertation is the first publication to investigate the use of the S-transform (ST) to devise countermeasures to interference. The original contributions in this context are mainly: • the formulation of a complexity-scalable ST implementable in real time as a bank of filters; • a method for characterizing and localizing multiple in-car jammers through interference snapshots that are collected by separate receivers and analysed with a clever use of the ST; • a preliminary assessment of novel methods for mitigating generic interference at the receiver end by means the ST and more computationally efficient variants of the transform. Besides GNSSs, the countermeasures to interference proposed are equivalently applicable to protect any direct-sequence spread spectrum (DS-SS) communication

Radio transients: Surveys and Techniques

I present two pilot surveys and a range of new algorithms to aid in planning and implementing wide-field radio surveys for transient and variable sources. The first pilot survey is a blind survey for transient and variable radio sources with the Molonglo Observatory Synthesis Telescope at 843~MHz. This survey discovered 53 highly variable sources and 15 transient sources and determined surface densities of 0.268 \unit{deg^{-2}} for variable sources and 1.3 \times 10^{-2} \unit{deg^{-2}} for transient sources, with associated timescales of between one day and three years. I also propose two new techniques which were developed for this survey. The first technique provides a post-imaging calibration for image gain. The second technique is a statistical method for verifying whether flux error measurements agree with the scatter in light curves over a population of sources. I also describe a follow-up survey for prompt radio emission from gamma ray bursts (GRBs) at 1.4~GHz. This survey used a single-dish telescope to automatically slew to a GRB position within 2~min of the gamma ray trigger and performed single-pulse, repeating and low-time resolution searches for variability. This survey discovered single, dispersed pulses following two long GRBs, which are possibly related to the delayed formation of a black hole at the centre of the GRBs. The high-time resolution measurements from this survey are some of the most constraining limits on prompt radio emission from GRBs to date. I also present two efficient new algorithms for detecting dispersed radio emission in interferometric data: the Chirpolator and the Chimageator. These two techniques excel in the regime of sparse arrays, where they both require substantially lower data rates, and the Chirpolator requires a much lower post-integrator operation rate than the existing algorithms. These techniques are well matched to future supercomputing architectures, where the arithmetic capability is outstripping the bandwidth capa! bility, and are therefore suitable for use by interferometer-based fast transient surveys. The surveys and techniques described in this thesis will have immediate application to upcoming surveys with the next generation of wide-field radio telescopes, such as the two transients surveys proposed for the Australian Square Kilometre Array Pathfinder

Radio frequency interference detection and mitigation techniques for navigation and Earth observation

Radio-Frequency Interference (RFI) signals are undesired signals that degrade or disrupt the performance of a wireless receiver. RFI signals can be troublesome for any receiver, but they are especially threatening for applications that use very low power signals. This is the case of applications that rely on the Global Navigation Satellite Systems (GNSS), or passive microwave remote sensing applications such as Microwave Radiometry (MWR) and GNSS-Reflectometry (GNSS-R). In order to solve the problem of RFI, RFI-countermeasures are under development. This PhD thesis is devoted to the design, implementation and test of innovative RFI-countermeasures in the fields of MWR and GNSS. In the part devoted to RFI-countermeasures for MWR applications, first, this PhD thesis completes the development of the MERITXELL instrument. The MERITXELL is a multi-frequency total-power radiometer conceived to be an outstanding platform to perform detection, characterization, and localization of RFI signals at the most common MWR imaging bands up to 92 GHz. Moreover, a novel RFI mitigation technique is proposed for MWR: the Multiresolution Fourier Transform (MFT). An assessment of the performance of the MFT has been carried out by comparison with other time-frequency mitigation techniques. According to the results, the MFT technique is a good trade-off solution among all other techniques since it can mitigate efficiently all kinds of RFI signals under evaluation. In the part devoted to RFI-countermeasures for GNSS and GNSS-R applications, first, a system for RFI detection and localization at GNSS bands is proposed. This system is able to detect RFI signals at the L1 band with a sensitivity of -108 dBm at full-band, and of -135 dBm for continuous wave and chirp-like signals when using the averaged spectrum technique. Besides, the Generalized Spectral Separation Coefficient (GSSC) is proposed as a figure of merit to evaluate the Signal-to-Noise Ratio (SNR) degradation in the Delay-Doppler Maps (DDMs) due to the external RFI effect. Furthermore, the FENIX system has been conceived as an innovative system for RFI detection and mitigation and anti-jamming for GNSS and GNSS-R applications. FENIX uses the MFT blanking as a pre-correlation excision tool to perform the mitigation. In addition, FENIX has been designed to be cross-GNSS compatible and RFI-independent. The principles of operation of the MFT blanking algorithm are assessed and compared with other techniques for GNSS signals. Its performance as a mitigation tool is proven using GNSS-R data samples from a real airborne campaign. After that, the main building blocks of the patented architecture of FENIX have been described. The FENIX architecture has been implemented in three real-time prototypes. Moreover, a simulator named FENIX-Sim allows for testing its performance under different jamming scenarios. The real-time performance of FENIX prototype has been tested using different setups. First, a customized VNA has been built in order to measure the transfer function of FENIX in the presence of several representative RFI/jamming signals. The results show how the power transfer function adapts itself to mitigate the RFI/jamming signal. Moreover, several real-time tests with GNSS receivers have been performed using GPS L1 C/A, GPS L2C, and Galileo E1OS. The results show that FENIX provides an extra resilience against RFI and jamming signals up to 30 dB. Furthermore, FENIX is tested using a real GNSS timing setup. Under nominal conditions, when no RFI/jamming signal is present, a small additional jitter on the order of 2-4 ns is introduced in the system. Besides, a maximum bias of 45 ns has been measured under strong jamming conditions (-30 dBm), which is acceptable for current timing systems requiring accuracy levels of 100 ns. Finally, the design of a backup system for GNSS in tracking applications that require high reliability against RFI and jamming attacks is proposed.Les interferències de radiofreqüència (RFI) són senyals no desitjades que degraden o interrompen el funcionament dels receptors sense fils. Les RFI poden suposar un problema per qualsevol receptor, però són especialment amenaçadores per les a aplicacions que fan servir senyals de molt baixa potència. Aquest és el cas de les aplicacions que depenen dels sistemes mundials de navegació per satèl·lit (GNSS) o de les aplicacions de teledetecció passiva de microones, com la radiometria de microones (MWR) i la reflectometria GNSS (GNSS-R). Per combatre aquest problema, sistemes anti-RFI s'estan desenvolupament actualment. Aquesta tesi doctoral està dedicada al disseny, la implementació i el test de sistemes anti-RFI innovadors en els camps de MWR i GNSS. A la part dedicada als sistemes anti-RFI en MWR, aquesta tesi doctoral completa el desenvolupament de l'instrument MERITXELL. El MERITXELL és un radiòmetre multifreqüència concebut com una plataforma excepcional per la detecció, caracterització i localització de RFI a les bandes de MWR més utilitzades per sota dels 92 GHz. A més a més, es proposa una nova tècnica de mitigació de RFI per MWR: la Transformada de Fourier amb Multiresolució (MFT). El funcionament de la MFT s'ha comparat amb el d'altres tècniques de mitigació en els dominis del temps i la freqüència. D'acord amb els resultats obtinguts, la MFT és una bona solució de compromís entre les altres tècniques, ja que pot mitigar de manera eficient tots els tipus de senyals RFI considerats. A la part dedicada als sistemes anti-RFI en GNSS i GNSS-R, primer es proposa un sistema per a la detecció i localització de RFI a les bandes GNSS. Aquest sistema és capaç de detectar senyals RFI a la banda L1 amb una sensibilitat de -108 dBm a tota la banda, i de -135 dBm per a senyals d'ona contínua i chirp fen un mitjana de l'espectre. A més a més, el Coeficient de Separació Espectral Generalitzada (GSSC) es proposa com una mesura per avaluar la degradació de la relació senyal a soroll (SNR) en els Mapes de Delay-Doppler (DDM) a causa del impacte de les RFI. La major contribució d'aquesta tesi doctoral és el sistema FENIX. FENIX és un sistema innovador de detecció i mitigació de RFI i inhibidors de freqüència per aplicacions GNSS i GNSS-R. FENIX utilitza la MFT per eliminar la interferència abans del procés de correlació amb el codi GNSS independentment del tipus de RFI. L'algoritme de mitigació de FENIX s'ha avaluat i comparat amb altres tècniques i els principals components de la seva arquitectura patentada es descriuen. Finalment, un simulador anomenat FENIX-Sim permet avaluar el seu rendiment en diferents escenaris d'interferència. El funcionament en temps real del prototip FENIX ha estat provat utilitzant diferents mètodes. En primer lloc, s'ha creat un analitzador de xarxes per a mesurar la funció de transferència del FENIX en presència de diverses RFI representatives. Els resultats mostren com la funció de transferència s'adapta per mitigar el senyal interferent. A més a més, s'han realitzat diferents proves en temps real amb receptors GNSS compatibles amb els senyals GPS L1 C/A, GPS L2C i Galileo E1OS. Els resultats mostren que FENIX proporciona una resistència addicional contra les RFI i els senyals dels inhibidors de freqüència de fins a 30 dB. A més a més, FENIX s'ha provat amb un sistema comercial de temporització basat en GNSS. En condicions nominals, sense RFI, FENIX introdueix un petit error addicional de tan sols 2-4 ns. Per contra, el biaix màxim mesurat en condicions d'alta interferència (-30 dBm) és de 45 ns, el qual és acceptable per als sistemes de temporització actuals que requereixen nivells de precisió d'uns 100 ns. Finalment, es proposa el disseny d'un sistema robust de seguiment, complementari als GNSS, per a aplicacions que requereixen alta fiabilitat contra RFI.Postprint (published version

Proceedings of the Fall 1995 Advanced Digital Communication Systems

Coordinated Science Laboratory was formerly known as Control Systems Laborator

Gigahertz Bandwidth and Nanosecond Timescales: New Frontiers in Radio Astronomy Through Peak Performance Signal Processing

Abstract In the past decade, there has been a revolution in radio-astronomy signal processing. High bandwidth receivers coupled with fast ADCs have enabled the collection of tremendous instantaneous bandwidth, but streaming computational resources are struggling to catch up and serve these new capabilities. As a consequence, there is a need for novel signal processing algorithms capable of maximizing these resources. This thesis responds to the demand by presenting FPGA implementations of a Polyphase Filter Bank which are an order of magnitude more efficient than previous algorithms while exhibiting similar noise performance. These algorithms are showcased together alongside a broadband RF front-end in Starburst: a 5 GHz instantaneous bandwidth two-element interferometer, the first broadband digital sideband separating astronomical interferometer.  Starburst technology has been applied to three instruments to date. Abstract Wielding tremendous computational power and precisely calibrated hardware, low frequency radio telescope arrays have potential greatly exceeding their current applications.  This thesis presents new modes for low frequency radio-telescopes, dramatically extending their original capabilities.  A microsecond-scale time/frequency mode empowered the Owens Valley Long Wavelength Array to inspect not just the radio sky by enabling the testing of novel imaging techniques and detecting overhead beacon satellites, but also the terrestrial neighborhood, allowing for the characterization and mitigation of nearby sources of radio frequency interference (RFI).  This characterization led to insights prompting a nanosecond-scale observing mode to be developed, opening new avenues in high energy astrophysics, specifically related to the radio frequency detection of ultra-high energy cosmic rays and neutrinos. Abstract Measurement of the flux spectrum, composition, and origin of the highest energy cosmic ray events is a lofty goal in high energy astrophysics. One of the most powerful new windows has been the detection of associated extensive air showers at radio frequencies. However, all current ground-based systems must trigger off an expensive and insensitive external source such as particle detectors - making detection of the rare, high energy events uneconomical.  Attempts to make a direct detection in radio-only data have been unsuccessful despite numerous efforts. The problem is even more severe in the case of radio detection of ultra-high energy neutrino events, which cannot rely on in-situ particle detectors as a triggering mechanism. This thesis combines the aforementioned nanosecond-scale observing mode with real-time, on-FPGA RFI mitigation and sophisticated offline post-processing.  The resulting system has produced the first successful ground based detection of cosmic rays using only radio instruments. Design and measurements of cosmic ray detections are discussed, as well as recommendations for future cosmic ray experiments.  The presented future designs allow for another order of magnitude improvement in both sensitivity and output data-rate, paving the way for the economical ground-based detection of the highest energy neutrinos.</p