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stochastic Analysis of the Signed LMS algorithms for Cyclostationary White Gaussian Inputs

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2017年第7期65卷 1673-1684页

作者： Eweda, Eweda Bershad, Neil J. C4 Adv Solut Abu Dhabi 43269 U Arab Emirates Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA 92660 USA

This paper studies the stochastic behavior of the signed variants of the LMS algorithm for a system identification framework when the input signal is a cyclostationary white Gaussian process. Three algorithms are studied: the signed regressor, the signed error, and the sign-sign algorithms. The input cyclostationary signal is modeled by a white Gaussian random process with periodically time-varying power. The system parameters vary according to a random-walk. Mathematical models are derived for the mean and mean-square-deviation behavior of the adaptive weights with the input cyclostationarity. These models are used to derive new results concerning the performance of the algorithms. Some of these results are surprising. Monte Carlo simulations of the three algorithms provide strong support for the theory.

关键词： Adaptive Filters Analysis Signed LMS algorithms stochastic algorithms

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A switched variable step size NLMS adaptive filter

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DIGITAL SIGNAL PROCESSING 2020年 101卷 102730-000页

作者： Bershad, Neil J. Bermudez, Jose C. M. Univ Calif Irvine Dept Elect & Comp Engn Irvine CA 92717 USA Univ Fed Santa Catarina Dept Elect & Elect Engn Florianopolis SC Brazil Catholic Univ Pelotas UCPel Pelotas Grad Program Elect Engn & Comp Pelotas RS Brazil

This paper studies the statistical behavior of a switched variable step size Normalized Least Mean Square adaptive filter. The purpose of the switching is to obtain a Normalized Least Mean Square adaptive filter combination with fast convergence and small steady-state mean-square weight deviation (MSD). Previous works studied variable step-size Least Mean Square (LMS) and Normalized Mean Square (NLMS) adaptive filters using a measured quantity (say instantaneous squared error) in a nonlinear recursion for varying the step size. Here, it is proposed to avoid the nonlinear recursion in a novel way that is based upon a simple physical premise: For several practical applications, what is required is a faster initial convergence rate phase, followed by a slower convergence rate period that allows for a desired steady-state performance. The fast NLMS transient behavior is obtained with a fixed step size. After convergence, the step size is reduced to a smaller value to satisfy a desired tradeoff between the second transient and the desired steady-state MSD. Thus, during the first transient, the Switched VSS-NLMS adaptive weights will converge faster or as fast as any VSS-NLMS algorithm. Of course, during the second phase, some variable step size algorithms may eventually outperform the Switched VSS-NLMS algorithm. However, in many cases, this can be a small price to pay in exchange for the theoretical and computational simplicity. No new theory is needed to predict the behavior of the nonlinear recursion for the step size. Furthermore, the analytical theory for the MSD of the new scheme is well-known. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Adaptive filters Variable step-size NLMS algorithm stochastic algorithms

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stochastic analysis of soft limiters in the LMS algorithm for stationary white Gaussian inputs-A unified theory

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SIGNAL PROCESSING 2018年 142卷 27-35页

作者： Bershad, Neil J. Eweda, Eweda Bermudez, Jose C. M. Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA 92660 USA Adv Solut C4 Abu Dhabi U Arab Emirates Univ Fed Santa Catarina Dept Elect & Elect Engn BR-88040970 Florianopolis SC Brazil

The effects of saturation-type nonlinearities on the input and the error in the weight update equation for LMS adaptation are investigated for a stationary white Gaussian data model for system identification. Nonlinear recursions are derived for the transient and steady-state weight first and second moments that include the effect of soft limiters on both the input and the error driving the algorithm. By varying a single parameter of the soft limiter, a general theory is presented that is applicable to LMS, soft limiting of the input, error or both and sign-sign LMS. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Adaptive filters Analysis LMS type algorithms stochastic algorithms

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Adaptive modulation for MU-MIMO-OFDM systems in Underlay Cognitive Radio Networks

Adaptive modulation for MU-MIMO-OFDM systems in Underlay Cog...

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USNC-URSI Radio Science Meeting / IEEE International Symposium on Antennas and Propagation (AP-S)

作者： Labdaoui, Rym Ghanem, Khalida Nedil, Mourad Ettoumi, Fatiha Youcef

ISBN: (纸本)9781728106922

In this paper, a modified rate quantization algorithm for multi-user multiple-input-multiple-output-orthogonal frequency division multiplexing (MU-MIMO-OFDM) cognitive architectures is proposed. Targeting to fulfill the requirements of 5G communications systems and beyond, while keeping a low complexity degree, we first adapt the sub-channel transmit power and spectral efficiency in the spatial and temporal domains under transmit power and instantaneous bit error rate (BER) constraints. We then use a stochastic algorithm to maximize the rate and transmit power of each secondary user (SU) over the spatial eigen-channels of the corresponding subcarrier MIMO channel, under the constraints of average power budget and probability of interference. It is shown that the proposed scheme outperforms the extended rounding-off (SR) alternative, for the entire SNR range.

关键词： Multi-user MIMO-OFDM systems stochastic algorithms CSI imperfections Adaptive modulation

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Study of the Number Recognition algorithms Efficiency After a Reduction of the Characteristic Space Using Typical Testors

Study of the Number Recognition Algorithms Efficiency After ...

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World Conference on Information Systems and Technologies (WorldCIST)

作者： Muenala, Kuntur Ibarra-Fiallo, Julio Intriago-Pazmino, Monserrate Univ San Francisco Quito Colegio Ciencias & Ingn Cumbaya Ecuador Escuela Politec Nacl Dept Informat & Ciencias Comp Quito Ecuador

ISBN: (纸本)9783030161804;9783030161811

The present work studies an application of typical testors to reduce the space of characteristics used as inputs in statistical models to recognize a manuscript digit from its corresponding binary image. The fundamentals of typical testors are described, and the use of logistic and multilogistic regression models in the predictions. Images from the public database of the Semeion Research Center of Sciences of Communication are used. Adequate prediction results were achieved in a reduced space of characteristics.

关键词： Typical testor Number recognition algorithm stochastic algorithms Logistic regression

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Brief Announcement: A Local stochastic Algorithm for Separation in Heterogeneous Self-Organizing Particle Systems 18

Brief Announcement: A Local Stochastic Algorithm for Separat...

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37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC)

作者： Cannon, Sarah Daymude, Joshua J. Gokmen, Cem Randall, Dana Richa, Andrea W. Georgia Inst Technol Atlanta GA 30332 USA Arizona State Univ Tempe AZ USA

ISBN: (纸本)9781450357951

We investigate stochastic, distributed algorithms that can accomplish separation and integration behaviors in self-organizing particle systems, an abstraction of programmable matter. These particle systems are composed of individual computational units known as particles that have limited memory, strictly local communication abilities, and modest computational power, and which collectively solve system-wide problems of movement and coordination. In this work, we extend the usual notion of a particle system to treat heterogeneous systems by considering particles of different colors. We present a fully distributed, asynchronous, stochastic algorithm for separation, where the particle system self-organizes into segregated color classes using only local information about each particle's preference for being near others of the same color. Conversely, by simply changing the particles' preferences, the color classes become well-integrated. We rigorously analyze the convergence of our distributed, stochastic algorithm and prove that under certain conditions separation occurs. We also present simulations demonstrating our algorithm achieves both separation and integration.

关键词： Programmable matter self-organization separation distributed algorithms stochastic algorithms

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stochastic QUANTUM INFORMATION PROCESSING, WITH APPLICATIONS TO BLIND QUANTUM SYSTEM IDENTIFICATION AND SOURCE SEPARATION 28

STOCHASTIC QUANTUM INFORMATION PROCESSING, WITH APPLICATIONS...

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IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP)

作者： Deville, Y. Deville, A. Univ Toulouse UPS CNRS CNESOMPIRAP F-31400 Toulouse France Aix Marseille Univ IM2NP CNRS UMR 7334 F-13397 Marseille France

ISBN: (纸本)9781538654774

Many methods for processing classical or quantum data are based on estimating some parameters, e.g. those of adaptive filters, artificial neural networks (including deep learning approaches), blind source separation systems or quantum gates. For classical signals, these methods include stochastic algorithms, such as stochastic gradient descent. We here first introduce a partly related, general, type of stochastic algorithms for quantum data and we prove the asymptotic efficiency of the proposed estimator. We then show the attractiveness of this stochastic approach for the quantum version of blind multiple-input multiple-output system identification and blind source separation: the resulting model estimation methods can operate with a single copy of each considered quantum state, whereas the previous methods require many copies of the same (unknown) states to be available and are thus "less blind". Numerical tests show that good performance is obtained with 10(4) such quantum states.

关键词： stochastic algorithms blind adaptation blind MIMO system identification / process tomography and inversion blind source separation quantum information processing

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Approximate inference in Bayesian networks: Parameterized complexity results

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2018年 93卷 119-131页

作者： Kwisthout, Johan Radboud Univ Nijmegen Donders Inst Brain Cognit & Behav Montessorilaan 3 NL-6525 HR Nijmegen Netherlands

Computing posterior and marginal probabilities constitutes the backbone of almost all inferences in Bayesian networks. These computations are known to be intractable in general, both to compute exactly and to approximate (e.g., by sampling algorithms). While it is well known under what constraints exact computation can be rendered tractable (viz., bounding tree-width of the moralized network and bounding the cardinality of the variables) it is less known under what constraints approximate Bayesian inference can be tractable. Here, we extend the existing formal framework of fixed-error randomized tractability (a randomized analogue of fixed-parameter tractability), and use it to address this problem, both by re-interpreting known results from the literature and by providing some additional new results, including results on fixed parameter tractable de-randomization of approximate inference. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Approximate inference Sampling Bayesian networks Parameterized complexity stochastic algorithms De-randomization

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Performance of soft limiters in the LMS algorithm for cyclostationary white Gaussian inputs

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SIGNAL PROCESSING 2018年 152卷 197-205页

作者： Bershad, Neil J. Eweda, Eweda Bermudez, Jose C. M. Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA 92660 USA C4 Adv Solut Abu Dhabi U Arab Emirates Univ Fed Santa Catarina Dept Elect & Elect Engn BR-88040970 Florianopolis SC Brazil

The analysis of saturation-type nonlinearities on the input and the error in the weight update equation for LMS adaptation were obtained for a stationary white Gaussian data model in [28] for system identification. Here the input signal is modeled by a cyclostationary white Gaussian random process with periodically time-varying power. The system parameters vary according to a random-walk. Using the previous analysis results, nonlinear recursions are presented for the transient and steady-state weight first and second moments that include the effect of the soft limiters. Monte Carlo simulations of the algorithms provide strong support for the theory. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Adaptive filters Analysis Signed LMS algorithms stochastic algorithms

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Discretization of processes at stopping times and Uncertainty quantification of stochastic approximation limits

Discretization of processes at stopping times and Uncertaint...

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作者： Uladzislau Stazhynski Ecole Polytechnique

学位级别：博士

This thesis consists of two parts. The first part is devoted to the problems of Brow- nian semimartingales discretization based on stop- ping times. We start with the study of the optimal discretization for stochastic integrals. In this context we establish an almost sure lower bound on the renormalized quadra- tic variation of the error and provide a sequence of stopping times which are asymptotically optimal, wi- thout the non-degeneracy assumption. Also we esta- blish an optimal discretization strategy which is com- pletely adaptive to the model. Further we study statistical fluctuations of the discreti- zation errors by showing Central Limit Theorems for general sequences of stopping times. The class of discretization grids is quite large and the limit distri- bution is given explicitly. The results are proved in the multidimensional case both for the process and for the discretization error. We apply these results to the problem of parametric statistical inference for diffusion processes based on observations at general stopping times. The second part is devoted to the problem of un- certainty quantification for stochastic approximation li- mits. In our framework the limit is defined as the zero of a function given by an expectation and typically re- presents the solution to some stochastic optimization problem. The expectation is related to a random va- riable for which the distribution is supposed to depend on an uncertain parameter (Bayesian point of view). Thereby the limit of the algorithm depends on this pa- rameter and is also uncertain. We introduce an algo- rithm called USA (Uncertainty for stochastic Approxi- mation) to efficiently calculate the chaos expansion coefficients of the limit as a function of the uncertain parameter. The convergence and the L 2 -convergence rate of the USA are analysed.

关键词： stochastic processes discretization optimization stopping times uncertainty quantification stochastic algorithms

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