Machine-learning nonstationary noise out of gravitational-wave detectors

Signal extraction out of background noise is a common challenge in high-precision physics experiments, where the measurement output is often a continuous data stream. To improve the signal-to-noise ratio of the detection, witness sensors are often used to independently measure background noises and subtract them from the main signal. If the noise coupling is linear and stationary, optimal techniques already exist and are routinely implemented in many experiments. However, when the noise coupling is nonstationary, linear techniques often fail or are suboptimal. Inspired by the properties of the background noise in gravitational wave detectors, this work develops a novel algorithm to efficiently characterize and remove nonstationary noise couplings, provided there exist witnesses of the noise source and of the modulation. In this work, the algorithm is described in its most general formulation, and its efficiency is demonstrated with examples from the data of the Advanced LIGO gravitational-wave observatory, where we could obtain an improvement of the detector gravitational-wave reach without introducing any bias on the source parameter estimation

Adaptive polynomial filters

Journal ArticleWhile linear filter are useful in a large number of applications and relatively simple from conceptual and implementational view points. there are many practical situations that require nonlinear processing of the signals involved. This article explains adaptive nonlinear filters equipped with polynomial models of nonlinearity. The polynomial systems considered are those nonlinear systems whose output signals can be related to the input signals through a truncated Volterra series expansion, or a recursive nonlinear difference equation. The Volterra series expansion can model a large class of nonlinear systems and is attractive in filtering applications because the expansion is a linear combination of nonlinear functions of the input signal. The basic ideas behind the development of gradient and recursive least-squares adaptive Volterra filters are first discussed. followed by adaptive algorithms using system models involving recursive nonlinear difference equations. Such systems are attractive because they may be able to approximate many nonlinear systems with great parsimony in the use pf coefficients. Also discussed are current research trends and new results and problem areas associated with these nonlinear filters. A lattice structure for polynomial models is also described

Various nonlinear models and their identification, equalization and linearization

System identification is a pre-requisite to analysis of a dynamic system and design of an appropriate controller for improving its performance. The more accurate the mathematical model identified for a system, the more effective will be the controller designed for it. The identification of nonlinear systems is a topic which has received considerable attention over the last two decades. Generally speaking, when it is difficult to model practical systems by mathematical analysis method, system identification may be an efficient way to overcome the shortage of mechanism analysis method. The goal of the modeling is to find a simple and efficient model which is in accord with the practical system. In many cases, linear models are not suitable to present these systems and nonlinear models have to be considered. Since there are nonlinear effects in practical systems, e.g. harmonic generation, intermediation, desensitization, gain expansion and chaos, we can infer that most control systems are nonlinear. Nonlinear models are more widely used in practice, because most phenomena are nonlinear in nature. Indeed, for many dynamic systems the use of nonlinear models is often of great interest and generally characterizes adequately physical processes over their whole operating range. Thus, accuracy and performance of the control law increase significantly. Therefore, nonlinear system modeling is much more important than linear system identification. We will deal with various nonlinear models and their processing

Method and system for training dynamic nonlinear adaptive filters which have embedded memory

Described herein is a method and system for training nonlinear adaptive filters (or neural networks) which have embedded memory. Such memory can arise in a multi-layer finite impulse response (FIR) architecture, or an infinite impulse response (IIR) architecture. We focus on filter architectures with separate linear dynamic components and static nonlinear components. Such filters can be structured so as to restrict their degrees of computational freedom based on a priori knowledge about the dynamic operation to be emulated. The method is detailed for an FIR architecture which consists of linear FIR filters together with nonlinear generalized single layer subnets. For the IIR case, we extend the methodology to a general nonlinear architecture which uses feedback. For these dynamic architectures, we describe how one can apply optimization techniques which make updates closer to the Newton direction than those of a steepest descent method, such as backpropagation. We detail a novel adaptive modified Gauss-Newton optimization technique, which uses an adaptive learning rate to determine both the magnitude and direction of update steps. For a wide range of adaptive filtering applications, the new training algorithm converges faster and to a smaller value of cost than both steepest-descent methods such as backpropagation-through-time, and standard quasi-Newton methods. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system 5, as well as a nonlinear amplifier 6

Machine-learning nonstationary noise out of gravitational-wave detectors

Signal extraction out of background noise is a common challenge in high-precision physics experiments, where the measurement output is often a continuous data stream. To improve the signal-to-noise ratio of the detection, witness sensors are often used to independently measure background noises and subtract them from the main signal. If the noise coupling is linear and stationary, optimal techniques already exist and are routinely implemented in many experiments. However, when the noise coupling is nonstationary, linear techniques often fail or are suboptimal. Inspired by the properties of the background noise in gravitational wave detectors, this work develops a novel algorithm to efficiently characterize and remove nonstationary noise couplings, provided there exist witnesses of the noise source and of the modulation. In this work, the algorithm is described in its most general formulation, and its efficiency is demonstrated with examples from the data of the Advanced LIGO gravitational-wave observatory, where we could obtain an improvement of the detector gravitational-wave reach without introducing any bias on the source parameter estimation

Multi Look-Up Table Digital Predistortion for RF Power Amplifier Linearization

Premi extraordinari doctorat curs 2007-2008, àmbit d’Enginyeria de les TICAquesta Tesi Doctoral se centra en el disseny d'un nou linealitzador de Predistorsió Digital (Digital Predistortion - DPD) capaç de compensar la dinàmica i els efectes no lineals introduïts pels Amplificadors de Potència (Power Amplifiers - PAs). Un dels trets més rellevants d'aquest nou predistorsionador digital i adaptatiu consisteix en ser deduïble a partir d'un model de PA anomenat Nonlinear Auto-Regressive Moving Average (NARMA). A més, la seva arquitectura multi-LUT (multi-Taula) permet la implementació en un dispositiu Field Programmable Gate Array (FPGA).La funció de predistorsió es realitza en banda base, per tant, és independent de la banda freqüencial on es durà a terme l'amplificació del senyal de RF, el que pot resultar útil si tenim en compte escenaris multibanda o reconfigurables. D'altra banda, el fet que aquest DPD tingui en compte els efectes de memòria introduïts pel PA, representa una clara millora de les prestacions aconseguides per un simple DPD sense memòria. En comparació amb d'altres DPDs basats en models més computacionalment complexos, com és el cas de les xarxes neuronals amb memòria (Time-Delayed Neural Networks - TDNN), la estructura recursiva del DPD proposat permet reduir el nombre de LUTs necessàries per compensar els efectes de memòria del PA. A més, la seva estructura multi-LUT permet l'escalabilitat, és a dir, activar or desactivar les LUTs que formen el DPD en funció de la dinàmica que presenti el PA.En una primera aproximació al disseny del DPD, és necessari identificar el model NARMA del PA. Un dels majors avantatges que presenta el model NARMA és la seva capacitat per trobar un compromís entre la fidelitat en l'estimació del PA i la complexitat computacional introduïda. Per reforçar aquest compromís, l' ús d'algoritmes heurístics de cerca, com són el Simulated Annealing o els Genetic Algorithms, s'utilitzen per trobar els retards que millor caracteritzen la memòria del PA i per tant, permeten la reducció del nombre de coeficients necessaris per caracteritzar-la. Tot i així, la naturalesa recursiva del model NARMA comporta que, de cara a garantir l'estabilitat final del DPD, cal dur a terme un estudi previ sobre l'estabilitat del model.Una vegada s'ha obtingut el model NARMA del PA i s'ha verificat l'estabilitat d'aquest, es procedeix a l'obtenció de la funció de predistorsió a través del mètode d'identificació predictiu. Aquest mètode es basa en la continua identificació del model NARMA del PA i posteriorment, a partir del model obtingut, es força al PA perquè es comporti de manera lineal. Per poder implementar la funció de predistorsió en la FPGA, cal primer expressar-la en forma de combinacions en paral·lel i cascada de les anomenades Cel·les Bàsiques de Predistorsió (BPCs), que són les unitats fonamentals que composen el DPD. Una BPC està formada per un multiplicador complex, un port RAM dual que actua com a LUT (taula de registres) i un calculador d'adreces. Les LUTs s'omplen tenint en compte una distribució uniforme dels continguts i l'indexat d'aquestes es duu a terme mitjançant el mòdul de l'envoltant del senyal. Finalment, l'adaptació del DPD consisteix en monitoritzar els senyals d'entrada i sortida del PA i anar duent a terme actualitzacions periòdiques del contingut de les LUTs que formen les BPCs. El procés d'adaptació del contingut de les LUTs es pot dur a terme en la mateixa FPGA encarregada de fer la funció de predistorsió, o de manera alternativa, pot ser duta a terme per un dispositiu extern (com per exemple un DSP - Digital Signal Processor) en una escala de temps més relaxada. Per validar l'exposició teòrica i provar el bon funcionalment del DPD proposat en aquesta Tesi, es proporcionen resultats tant de simulació com experimentals que reflecteixen els objectius assolits en la linealització del PA. A més, certes qüestions derivades de la implementació pràctica, tals com el consum de potència o la eficiència del PA, són també tractades amb detall.This Ph.D. thesis addresses the design of a new Digital Predistortion (DPD) linearizer capable to compensate the unwanted nonlinear and dynamic behavior of power amplifiers (PAs). The distinctive characteristic of this new adaptive DPD is its deduction from a Nonlinear Auto Regressive Moving Average (NARMA) PA behavioral model and its particular multi look-up table (LUT) architecture that allows its implementation in a Field Programmable Gate Array (FPGA) device.The DPD linearizer presented in this thesis operates at baseband, thus becoming independent on the final RF frequency band and making it suitable for multiband or reconfigurable scenarios. Moreover, the proposed DPD takes into account PA memory effects compensation which representsan step forward in overcoming classical limitations of memoryless predistorters. Compared to more computational complex DPDs with dynamic compensation, such Time-Delayed Neural Networks (TDNN), this new DPD takes advantage of the recursive nature of the NARMA structure to relax the number of LUTs required to compensate memory effects in PAs. Furthermore, its parallel multi-LUT architecture is scalable, that is, permits enabling or disabling the contribution of specific LUTs depending on the dynamics presented by a particular PA.In a first approach, it is necessary to identify a NARMA PA behavioral model. The extraction of PA behavioral models for DPD linearization purposes is carried out by means of input and output complex envelope signal observations. One of the major advantages of the NARMA structure regards its capacity to deal with the existing trade-off between computational complexity and accuracy in PA behavioral modeling. To reinforce this compromise, heuristic search algorithms such the Simulated Annealing or Genetic Algorithms are utilized to find the best sparse delays that permit accurately reproducing the PA nonlinear dynamic behavior. However, due to the recursive nature of the NARMA model, an stability test becomes a previous requisite before advancing towards DPD linearization.Once the PA model is identified and its stability verified, the DPD function is extracted applying a predictive predistortion method. This identification method relies just on the PA NARMA model and consists in adaptively forcing the PA to behave as a linear device. Focusing in the DPD implementation, it is possible to map the predistortion function in a FPGA, but to fulfill this objective it is first necessary to express the predistortion function as a combined set of LUTs.In order to store the DPD function into a FPGA, it has to be stated in terms of parallel and cascade Basic Predistortion Cells (BPCs), which are the fundamental building blocks of the NARMA based DPD. A BPC is formed by a complex multiplier, a dual port RAM memory block acting as LUT and an address calculator. The LUT contents are filled following an uniform spacing procedure and its indexing is performed with the amplitude (modulus) of the signal's envelope.Finally, the DPD adaptation consists in monitoring the input-output data and performing frequent updates of the LUT contents that conform the BPCs. This adaptation process can be carried out in the same FPGA in charge of performing the DPD function, or alternatively can be performed by an external device (i.e. a DSP device) in a different time-scale than real-time operation.To support all the theoretical design and to prove the linearization performance achieved by this new DPD, simulation and experimental results are provided. Moreover, some issues derived from practical experimentation, such as power consumption and efficiency, are also reported and discussed within this thesis.Award-winningPostprint (published version

ADAPTIVE AND NONLINEAR SIGNAL PROCESSING

1996/1997X Ciclo1967Versione digitalizzata della tesi di dottorato cartacea

Nonlinear processing of non-Gaussian stochastic and chaotic deterministic time series

It is often assumed that interference or noise signals are Gaussian stochastic processes. Gaussian noise models are appealing as they usually result in noise suppression algorithms that are simple: i.e. linear and closed form. However, such linear techniques may be sub-optimal when the noise process is either a non-Gaussian stochastic process or a chaotic deterministic process. In the event of encountering such noise processes, improvements in noise suppression, relative to the performance of linear methods, may be achievable using nonlinear signal processing techniques. The application of interest for this thesis is maritime surveillance radar, where the main source of interference, termed sea clutter, is widely accepted to be a non-Gaussian stochastic process at high resolutions and/or at low grazing angles. However, evidence has been presented during the last decade which suggests that sea clutter may be better modelled as a chaotic deterministic process. While the debate over which model is more suitable continues, this thesis investigates whether nonlinear processing techniques can be used to improve the performance of maritime surveillance radar, relative to the performance achievable using linear techniques. Linear and nonlinear prediction of chaotic signals, sea clutter data sets, and stochastic surrogate clutter data sets is carried out. Volterra series filter networks and radial basis function networks are used to implement nonlinear predictors. A novel structure for a forward-backward nonlinear predictor, using a radial basis function network, is presented. Prediction results provide evidence to support the view that sea clutter is better modelled as a stochastic process, rather than as a chaotic process. The clutter data sets are shown to have linear predictor functions. Linear and nonlinear predictors are used as the basis of target detection algorithms. The performance of these predictor-detectors, against backgrounds of sea clutter data and against a background of chaotic noise data is evaluated. The detection results show that linear predictor-detectors perform as well as, or better than, nonlinear predictor-detectors against the non-Gaussian clutter backgrounds considered in this thesis, whilst the reverse is true for a background of chaotic noise. An existing, nonlinear inverse, noise cancellation technique, referred to as Broomhead’s filtering technique in this thesis, is re-investigated using a sine wave corrupted by broadband chaotic noise. It is demonstrated that significant improvements can be obtained using this nonlinear inverse technique, relative to results obtained using linear alternatives, despite recent work which suggested otherwise. A novel bandstop filtering approach is applied to Broomhead’s filtering method, which allows the technique to be applied to the cancellation of signals with a band of interest greater than that of a sine wave. This modified Broomhead filtering technique is shown to cancel broadband chaotic noise from a narrowband Gaussian signal better than alternative linear methods. The modified Broomhead filtering technique is shown to only perform as well as, o

Blind identification of bilinear systems

Journal ArticleAbstract-This paper is concerned with the blind identification of a class of bilinear systems excited by non-Gaussian higher order white noise. The matrix of coefficients of mixed input-output terms of the bilinear system model is assumed to be triangular in this work. Under the additional assumption that the system output is corrupted by Gaussian measurement noise, we derive an exact parameter estimation procedure based on the output cumulants of orders up to four. Results of the simulation experiments presented in the paper demonstrate the validity and usefulness of our approach