Robust estimation in flat fading channels under bounded channel uncertainties

Abstract

Cataloged from PDF version of article.We investigate channel equalization problem for time-varying flat fading channels under bounded\ud channel uncertainties. We analyze three robust methods to estimate an unknown signal transmitted\ud through a time-varying flat fading channel. These methods are based on minimizing certain meansquare\ud error criteria that incorporate the channel uncertainties into their problem formulations instead of\ud directly using the inaccurate channel information that is available. We present closed-form solutions to\ud the channel equalization problems for each method and for both zero mean and nonzero mean signals.\ud We illustrate the performances of the equalization methods through simulations.\ud © 2013 Elsevier Inc. All rights reserved

Robust least squares methods under bounded data uncertainties

“…In this paper, we investigate estimation of an unknown deterministic signal that is observed through a deterministic data matrix under additive noise, which models a wide range of problems in signal processing applications [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In this framework, the data matrix and the output vector are not exactly known, however, estimates for both of them as well as uncertainty bounds on the estimates are given [2,8,[15][16][17][18][19]]. Since the model parameters are not known exactly, the performances of the classical LS estimators may significantly degrade, especially when the perturbations on the data matrix and the output vector are relatively high [9,15,16,[20][21][22].…”

“…In all these methods, LS estimators under worst case perturbations are introduced to achieve robustness. However, due to this conservative problem formulation, in many practical applications, these approaches yield unsatisfactory performances [2,8,18,[28][29][30].…”

“…In order to counterbalance this conservative nature of the robust LS methods [9], we propose a novel robust LS approach that minimizes a worst case "regret" that is defined as the difference between the squared residual error and the smallest attainable squared residual error with an LS estimator [2,8,18,[28][29][30]. By this regret formulation, we seek a linear estimator whose performance is as close as possible to that of the optimal estimator for all possible perturbations on the data matrix and the output vector.…”

“…Our main goal in proposing the minimax regret formulation is to provide a trade-off between the robust LS methods tuned to the worst possible data parameters (under the uncertainty bounds) and the optimal LS estimator tuned to the underlying unknown model parameters. Minimax regret approaches have been presented in signal processing literature to alleviate the pessimistic nature of the worst case optimization methods [2,8,18,[28][29][30]. In [18,29], linear minimax regret estimators are introduced to minimize the mean squared error (MSE) under imperfect knowledge of channel statistics and true parameters, respectively.…”

“…In [28], a minimum mean squared error (MMSE) estimation technique under imperfect channel and data knowledge is investigated. In [2], these robust estimation methods are extended to flat fading channels to perform channel equalization. These methods are shown to provide a better average performance compared to the minimax estimators, whereas under large perturbations the robustness of the minimax estimators are superior to these competitive methods.…”