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Bounded Component Analysis (BCA) has recently been introduced as an alternative linear decomposition scheme. In this approach the boundedness property of sources is exploited to replace the usual independence assumption with a weaker assumption, which enables development of methods to separate both independent and dependent components from their mixtures. This paper positions total output range minimization based blind source separation approach as a BCA method for the separation of uncorrelated sources. It is shown that the global minimizers of the corresponding optimization problem are the perfect separators. Furthermore, a stationary point analysis for the corresponding algorithms based on symmetrical orthogonalization is provided. The main result of this analysis is that the range minimization based parallel BCA algorithm and the kurtosis maximization based Independent Component Analysis algorithm have related set of identified stationary points. [ABSTRACT FROM PUBLISHER]

The discrete complex image method (DCIM) has been well-established and widely employed as a tool to compute spatial-domain Green's functions in planar multilayered media. Although the use of the DCIM in conjunction with the method of moments has been quite satisfactory for the efficient analysis of printed structures in layered media, it has not been considered much as a legitimate tool for commercial applications. Up until recently, there has been mainly two reasons for the reluctance of its acceptance in commercial products: the lack of a proper error criterion in the spatial domain and the manual selection of the order of images. As the former shortcoming has recently been eliminated by establishing a proper error criterion in the spatial domain, this paper intends to propose a viable solution for the latter problem, i.e., for the choice of the number of images. Note that, thus far, this choice has been based on the number of significant singular values obtained as a by-product of the method, which is neither rigorous, nor optimum in any sense, and renders it nonrobust and unreliable. As a remedy for this remaining shortcoming, a model selection approach known as minimum description length (MDL) has been introduced into the algorithm of the DCIM with success. The MDL approach, exploiting the regularities in the data, selects the order of the model based on the tradeoff between the quality of fitting and complexity of the model. [ABSTRACT FROM AUTHOR]

In this paper, we consider mixture approaches that adaptively combine outputs of several parallel running adaptive algorithms. These parallel units can be considered as diversity branches that can be exploited to improve the overall performance. We study various mixture structures where the final output is constructed as the weighted linear combination of the outputs of several constituent filters. Although the mixture structure is linear, the combination weights can be updated in a highly nonlinear manner to minimize the final estimation error such as in Singer and Feder 1999; Arenas-Garcia, Figueiras-Vidal, and Sayed 2006; Lopes, Satorius, and Sayed 2006; Bershad, Bermudez, and Tourneret 2008; and Silva and Nascimento 2008. We distinguish mixture approaches that are convex combinations (where the linear mixture weights are constrained to be nonnegative and sum up to one) [Singer and Feder 1999; Arenas-Garcia, Figueiras-Vidal, and Sayed 2006], affine combinations (where the linear mixture weights are constrained to sum up to one) [Bershad, Bermudez, and Tourneret 2008] and, finally, unconstrained linear combinations of constituent filters [Kozat and Singer 2000]. We investigate mixture structures with respect to their final mean-square error (MSE) and tracking performance in the steady state for stationary and certain nonstationary data, respectively. We demonstrate that these mixture approaches can greatly improve over the performance of the constituent filters. Our analysis is also generic such that it can be applied to inhomogeneous mixtures of constituent adaptive branches with possibly different structures, adaptation methods or having different filter lengths. [ABSTRACT FROM AUTHOR]

Recently an instantaneous blind source separation (BSS) approach that exploits the bounded magnitude structure of digital communications signals has been introduced. In this paper, we introduce a deflationary adaptive algorithm based on this criterion and provide its convergence analysis. We show that the resulting algorithm is convergent to one of the globally optimal points that correspond to perfect separation. The simulation examples related to the separation of digital communication signals are provided to illustrate the convergence and the performance of the algorithm [ABSTRACT FROM PUBLISHER]

We propose a novel blind equalization method based on subgradient search over a convex cost surface. This is an alternative to the existing iterative blind equalization approaches such as the Constant Modulus Algorithm (CMA), which often suffer from the convergence problems caused by their nonconvex cost functions. The proposed method is an iterative algorithm called SubGradient based Blind Algorithm (SGBA) for both real and complex constellations, with a very simple update rule. It is based on the minimization of the l∞ norm of the equalizer output under a linear constraint on the equalizer coefficients using subgradient iterations. The algorithm has a nice convergence behavior attributed to the convex l∞ cost surface as well as the step size selection rules associated with the subgradient search. We illustrate the performance of the algorithm using examples with both complex and real constellations, where we show that the proposed algorithm's convergence is less sensitive to initial point selection, and a fast convergence behavior can be achieved with a judicious selection of step sizes. Furthermore, the amount of data required for the training of the equalizer is significantly lower than most of the existing schemes. [ABSTRACT FROM AUTHOR]

We approach the multiple input multiple output (MIMO) decision feedback equalization (DFE) problem in digital communications from an H∞ estimation point of view. Using the standard (and simplifying) assumption that all previous decisions are correct, we obtain an explicit parameterization of all H∞ optimal DFEs. In particular, we show that, under the above assumption, minimum mean square error (MMSE) DFEs are H∞ optimal. The H∞ approach also suggests a method for dealing with errors in previous decisions. [ABSTRACT FROM AUTHOR]

In this paper, we consider model combination methods for adaptive filtering that perform unbiased estimation. In this widely studied framework, two adaptive filters are run in parallel, each producing unbiased estimates of an underlying linear model. The outputs of these two filters are combined using another adaptive algorithm to yield the final output of the system. Overall, we require that the final algorithm produce an unbiased estimate of the underlying model. We later specialize this framework where we combine one filter using the least-mean squares (LMS) update and the other filter using the least-mean fourth (LMF) update to decrease cross correlation in between the outputs and improve the overall performance. We study the steady-state performance of previously introduced methods as well as novel combination algorithms for stationary and nonstationary data. These algorithms use stochastic gradient updates instead of the variable transformations used in previous approaches. We explicitly provide steady-state analysis for both stationary and nonstationary environments. We also demonstrate close agreement with the introduced results and the simulations, and show for this specific combination, more than 2 dB gains in terms of excess mean square error with respect to the best constituent filter in the simulations. [ABSTRACT FROM AUTHOR]