Alper T. Erdogan

Steady-State MSE Performance Analysis of Mixture Approaches to Adaptive Filtering

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.

On linear H∞ equalization of communication channels

As an alternative to existing techniques and algorithms, we investigate the merit of the H/sup /spl infin// approach to the linear equalization of communication channels. We first give the formulation of all causal H/sup /spl infin// equalizers using the results of and then look at the finite delay ease. We compare the risk-sensitive H/sup /spl infin// equalizer with the MMSE equalizer with respect to both the average and the worst-case BER performances and illustrate the improvement due to the use of the H/sup /spl infin// equalizer.

A simple geometric blind source separation method for bounded magnitude sources

A novel blind source separation approach and the corresponding adaptive algorithm is presented. It is assumed that the observation mixture is obtained through an unknown memoryless linear mapping of independent and bounded magnitude sources. We further assume an initial adaptive prewhitening of the original observation vector which transforms it into a white vector with the same dimension as the original source vector. Our approach is centered around the basic geometric fact that, under a certain boundedness assumption, the unitary mapping which transforms the whitening output vector into an independent vector has the minimum value of maximum (real component) magnitude output over the ensemble of all output components. Therefore, the related criterion is the minimization of the infinity norm of the real component of the unitary separators output over all possible output combinations. For the minimization of the corresponding nondifferentiable cost function, we propose the use of subgradient optimization methods to obtain a low complexity iterative adaptive solution. The resulting algorithm is fairly intuitive and simple, and provides a low complexity solution especially to a class of multiuser digital communications problems. We provide examples at the end of this paper to illustrate the performance of our algorithm.

MIMO decision feedback equalization from an H i perspective

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

Fast and low complexity blind equalization via subgradient projections

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/sub /spl infin// 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/sub /spl infin// 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 algorithms 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.

MIMO Linear Equalization With an

In this paper, we study the problem of linearly equalizing the multiple-input multiple-output (MIMO) communications channels from an

H^infty

H^infty

Criterion

point of view.

On robust signal reconstruction in noisy filter banks

H^infty

FIR H ∞ equalization

estimation theory has been recently introduced as a method for designing filters that have acceptable performance in the face of model uncertainty and lack of statistical information on the exogenous signals. In this paper, we obtain a closed-form solution to the square MIMO linear