Performance analysis of adaptive filters equipped with the dual sign algorithm

Journal ArticleAdaptive filters equipped with the sign algorithm are attractive in many applications because of their computational simplicity. Unfortunately, their slow speed of convergence is a major limitation. The dual sign algorithm (DSA) is a means by which the convergence speed can be increased without overly degrading the steady-state performance and with a minimal amount of additional computational complexity. This paper presents a convergence analysis for adaptive filters equipped with the dual sign algorithm. Previous analyses of the dual sign algorithm were based on two assumptions: 1) the input sequence to the adaptive filter is white; 2) the behavior for the DSA is such that it switches from an adaptive filter equipped with the sign algorithm with a relatively large convergence constant to another one with a smaller convergence constant a certain amount of the after the filter is initialized. Both these restrictions are removed for Gaussian input signals in our analysis. A simulation example that shows good match between theoretical and empirical results is also presented in this paper

An Efficient Framework For Fast Computer Aided Design of Microwave Circuits Based on the Higher-Order 3D Finite-Element Method

In this paper, an efficient computational framework for the full-wave design by optimization of complex microwave passive devices, such as antennas, filters, and multiplexers, is described. The framework consists of a computational engine, a 3D object modeler, and a graphical user interface. The computational engine, which is based on a finite element method with curvilinear higher-order tetrahedral elements, is coupled with built-in or external gradient-based optimization procedures. For speed, a model order reduction technique is used and the gradient computation is achieved by perturbation with geometry deformation, processed on the level of the individual mesh nodes. To maximize performance, the framework is targeted to multicore CPU architectures and its extended version can also use multiple GPUs. To illustrate the accuracy and high efficiency of the framework, we provide examples of simulations of a dielectric resonator antenna and full-wave design by optimization of two diplexers involving tens of unknowns, and show that the design can be completed within the duration of a few simulations using industry-standard FEM solvers. The accuracy of the design is confirmed by measurements

Stochastic gradient adaptive filters with gradient adaptive step sizes

Journal ArticleThis paper presents two adaptive step-size gradient adaptive filters. The step sizes are changed using a gradient descent algorithm designed to minimize the squared estimation error. The first algorithm uses the same step-size sequence for all the filter coefficients whereas the second algorithm uses different step-size sequences for different adaptive filter coefficients. An analytical performance analysis of the first algorithm is also presented in the paper. Analyses and experiments indicate that (1) the algorithms have fast convergence rates and small misadjustment errors; and (2) in nonstationary environments, the algorithms tend to adjust the step sizes so as to give close to the best possible performance. Several simulation examples demonstrating the good properties of the adaptive filters are also presented in the paper

Extension of Wirtinger's Calculus to Reproducing Kernel Hilbert Spaces and the Complex Kernel LMS

Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space. However, so far, the emphasis has been on batch techniques. It is only recently, that online techniques have been considered in the context of adaptive signal processing tasks. Moreover, these efforts have only been focussed on real valued data sequences. To the best of our knowledge, no adaptive kernel-based strategy has been developed, so far, for complex valued signals. Furthermore, although the real reproducing kernels are used in an increasing number of machine learning problems, complex kernels have not, yet, been used, in spite of their potential interest in applications that deal with complex signals, with Communications being a typical example. In this paper, we present a general framework to attack the problem of adaptive filtering of complex signals, using either real reproducing kernels, taking advantage of a technique called \textit{complexification} of real RKHSs, or complex reproducing kernels, highlighting the use of the complex gaussian kernel. In order to derive gradients of operators that need to be defined on the associated complex RKHSs, we employ the powerful tool of Wirtinger's Calculus, which has recently attracted attention in the signal processing community. To this end, in this paper, the notion of Wirtinger's calculus is extended, for the first time, to include complex RKHSs and use it to derive several realizations of the Complex Kernel Least-Mean-Square (CKLMS) algorithm. Experiments verify that the CKLMS offers significant performance improvements over several linear and nonlinear algorithms, when dealing with nonlinearities.Comment: 15 pages (double column), preprint of article accepted in IEEE Trans. Sig. Pro

On the Performance Analysis of a Class of Transform-domain NLMS Algorithms with Gaussian Inputs and Mixture Gaussian Additive Noise Environment

This paper studies the convergence performance of the transform domain normalized least mean square (TDNLMS) algorithm with general nonlinearity and the transform domain normalized least mean M-estimate (TDNLMM) algorithm in Gaussian inputs and additive Gaussian and impulsive noise environment. The TDNLMM algorithm, which is derived from robust M-estimation, has the advantage of improved performance over the conventional TDNLMS algorithm in combating impulsive noises. Using Price's theorem and its extension, the above algorithms can be treated in a single framework respectively for Gaussian and impulsive noise environments. Further, by introducing new special integral functions, related expectations can be evaluated so as to obtain decoupled difference equations which describe the mean and mean square behaviors of the TDNLMS and TDNLMM algorithms. These analytical results reveal the advantages of the TDNLMM algorithm in impulsive noise environment, and are in good agreement with computer simulation results. © 2010 The Author(s).published_or_final_versionSpringer Open Choice, 21 Feb 201

Distributed and adaptive location identification system for mobile devices

Indoor location identification and navigation need to be as simple, seamless, and ubiquitous as its outdoor GPS-based counterpart is. It would be of great convenience to the mobile user to be able to continue navigating seamlessly as he or she moves from a GPS-clear outdoor environment into an indoor environment or a GPS-obstructed outdoor environment such as a tunnel or forest. Existing infrastructure-based indoor localization systems lack such capability, on top of potentially facing several critical technical challenges such as increased cost of installation, centralization, lack of reliability, poor localization accuracy, poor adaptation to the dynamics of the surrounding environment, latency, system-level and computational complexities, repetitive labor-intensive parameter tuning, and user privacy. To this end, this paper presents a novel mechanism with the potential to overcome most (if not all) of the abovementioned challenges. The proposed mechanism is simple, distributed, adaptive, collaborative, and cost-effective. Based on the proposed algorithm, a mobile blind device can potentially utilize, as GPS-like reference nodes, either in-range location-aware compatible mobile devices or preinstalled low-cost infrastructure-less location-aware beacon nodes. The proposed approach is model-based and calibration-free that uses the received signal strength to periodically and collaboratively measure and update the radio frequency characteristics of the operating environment to estimate the distances to the reference nodes. Trilateration is then used by the blind device to identify its own location, similar to that used in the GPS-based system. Simulation and empirical testing ascertained that the proposed approach can potentially be the core of future indoor and GPS-obstructed environments