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Machine Learning for Signal Processing, 2009. MLSP 2012. IEEE International Workshop on; 01/2012
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ABSTRACT: Widely linear filters play an important role in signal processing applications where the circularity properties on the complex data do not hold. They are able to achieve smaller mean-square error (MSE) than linear complex filters, but at a significantly higher computational cost. In this paper, we propose a modified version of widely linear filters with a reduced computational complexity. In the proposed version, the data vector is real, being constituted by the real and imaginary parts of the complex data separately. We prove that the new scheme achieves the same minimum MSE of standard widely linear estimators. We exemplify this idea for the least-mean squares (LMS) algorithm and also for the recursive least-squares (RLS) algorithm.
Wireless Communication Systems (ISWCS), 2010 7th International Symposium on; 10/2010
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ABSTRACT: In this paper, we propose an approach to the transient and steady-state analysis of the affine combination of one fast and one slow adaptive filters. The theoretical models are based on expressions for the excess mean-square error (EMSE) and cross-EMSE of the component filters, which allows their application to different combinations of algorithms, such as least mean-squares (LMS), normalized LMS (NLMS), and constant modulus algorithm (CMA), considering white or colored inputs and stationary or nonstationary environments. Since the desired universal behavior of the combination depends on the correct estimation of the mixing parameter at every instant, its adaptation is also taken into account in the transient analysis. Furthermore, we propose normalized algorithms for the adaptation of the mixing parameter that exhibit good performance. Good agreement between analysis and simulation results is always observed.
IEEE Transactions on Signal Processing 09/2010; · 2.63 Impact Factor
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ABSTRACT: Combinations of adaptive filters have attracted attention as a simple solution to improve filter performance, including tracking properties. In this paper, we consider combinations of LMS and RLS filters, and study their performance for tracking time-varying solutions. We show that a combination of two filters from the same family (i.e., two LMS or two RLS filters) cannot improve the performance over that of a single filter of the same type with optimal selection of the step size (or forgetting factor). However, combining LMS and RLS filters it is possible to simultaneously outperform the optimum LMS and RLS filters. In other words, combination schemes can achieve smaller errors than optimally adjusted individual filters. Experimental work in a plant identification setup corroborates the validity of our results.
Acoustics Speech and Signal Processing (ICASSP), 2010 IEEE International Conference on; 04/2010 · 4.63 Impact Factor
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ABSTRACT: This paper proposes an improved model for the transient of convex combinations of adaptive filters. A previous model, based on a first-order Taylor series approximation of the nonlinear functions that appear in convex combinations, tended to overestimate the variance of the auxiliary variable used to estimate the mixing parameter. In this paper, we apply a second-order Taylor approximation that improves these estimates, and obtains better agreement with simulations. In addition, we also extend the model to include a simple mechanism for the transfer of coefficients between the constituent filters, a procedure that greatly improves the convergence of the overall filter, and provide an expression to select the free parameter used in such a scheme.
Acoustics Speech and Signal Processing (ICASSP), 2010 IEEE International Conference on; 04/2010 · 4.63 Impact Factor
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ABSTRACT: We extend the analysis presented in for the affine combination of two least mean-square (LMS) filters to allow for colored inputs and nonstationary environments. Our theoretical model deals, in a unified way, with any combinations based on the following algorithms: LMS, normalized LMS (NLMS), and recursive-least squares (RLS). Through the analysis, we observe that the affine combination of two algorithms of the same family with close adaptation parameters (step-sizes or forgetting factors) provides a 3 dB gain in relation to its best component filter. We study this behavior in stationary and nonstationary environments. Good agreement between analytical and simulation results is always observed. Furthermore, a simple geometrical interpretation of the affine combination is investigated. A model for the transient and steady-state behavior of two possible algorithms for estimation of the mixing parameter is proposed. The model explains situations in which adaptive combination algorithms may achieve good performance.
Signals, Systems and Computers, 2008 42nd Asilomar Conference on; 11/2008
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ABSTRACT: We derive an easy-to-compute approximate bound for the range of step-sizes for which the constant-modulus algorithm (CMA) will remain stable if initialized close to a minimum of the CM cost function. Our model highlights the influence of the signal constellation used in the transmission system: for smaller variation in the modulus of the transmitted symbols, the algorithm will be more robust, and the steady-state misadjustment will be smaller. The theoretical results are validated through several simulations, for long and short filters and channels.
IEEE Transactions on Signal Processing 11/2008; · 2.63 Impact Factor
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ABSTRACT: As is well known, Hessian-based adaptive filters (such as the recursive-least squares algorithm (RLS) for supervised adaptive filtering, or the Shalvi-Weinstein algorithm (SWA) for blind equalization) converge much faster than gradient-based algorithms [such as the least-mean-squares algorithm (LMS) or the constant-modulus algorithm (CMA)]. However, when the problem is tracking a time-variant filter, the issue is not so clear-cut: there are environments for which each family presents better performance. Given this, we propose the use of a convex combination of algorithms of different families to obtain an algorithm with superior tracking capability. We show the potential of this combination and provide a unified theoretical model for the steady-state excess mean-square error for convex combinations of gradient- and Hessian-based algorithms, assuming a random-walk model for the parameter variations. The proposed model is valid for algorithms of the same or different families, and for supervised (LMS and RLS) or blind (CMA and SWA) algorithms.
IEEE Transactions on Signal Processing 08/2008; · 2.63 Impact Factor
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ABSTRACT: One of the most popular algorithms for blind equalization is the constant modulus algorithm (CMA), due to its simplicity and low computational cost. However, if the step-size is not properly chosen or if the initialization is distant from the optimal solution, CMA can diverge or converge to undesirable local minima. In order to avoid divergence, we propose a dual-mode algorithm, which works as CMA with a time-variant step-size, but rejects non-consistent estimates of the transmitted signal. We present a deterministic analysis of the stability of the new algorithm for scalar filters. In the vector case, the good performance of the new algorithm is confirmed through numerical simulations.
Acoustics, Speech and Signal Processing, 2008. ICASSP 2008. IEEE International Conference on; 05/2008 · 4.63 Impact Factor
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ABSTRACT: Recently, we proposed a model for the steady-state estimation error of real-valued constant-modulus-based algorithms as a function of the a priori error and of a term that measures the variability in the modulus of the transmitted signal. In this paper, we extend this model to complex-valued data and use it in conjunction with the feedback analysis method to obtain an analytical expression for the steady-state excess mean-square error (EMSE) of the Constant Modulus Algorithm (CMA). Such expression is more accurate for larger step-sizes than the previous ones in the literature, as confirmed by the good agreement between analytical and simulation results. Furthermore, from the EMSE expression, we obtain an estimate for the CMA step-size interval to ensure its convergence and stability, when it is initialized sufficiently close to the zero-forcing solution.
Acoustics, Speech and Signal Processing, 2008. ICASSP 2008. IEEE International Conference on; 05/2008 · 4.63 Impact Factor
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ABSTRACT: Recently, an adaptive convex combination of two LMS (least mean-square) filters was proposed and its tracking performance analyzed. Motivated by the performance of such scheme and by the differences between the tracking capabilities of the RLS (recursive least-squares) and LMS algorithms, we propose a convex combination of one LMS and one RLS filter. The resulting combination should profit of the best tracking behavior of each component filter. A steady-state analysis via energy conservation relation is also presented for stationary and non-stationary environments.
Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on; 05/2007 · 4.63 Impact Factor
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ABSTRACT: In blind equalization, the constant modulus algorithm (CMA) and Shalvi-Weinstein algorithm (SWA) present an unfavorable tradeoff between convergence rate and computational cost. Inspired in supervised order-recursive algorithms, we propose a lattice SWA, which has the number of operations per iteration of the equalizer order and maintains the SWA convergence rate. It presents a more robust behavior than that of SWA, avoiding numerical divergence when implemented in finite precision
Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on; 05/2007 · 4.63 Impact Factor
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ABSTRACT: We propose a convex combination of two blind equalizers adapted respectively by CMA (constant modulus algorithm) and SWA (Shalvi-Weinstein algorithm). The performance of the proposed scheme is, in the worst case, as good as that of the best of its components. This behavior provides a good tracking capability, since both CMA or SWA may have a better tracking performance, depending on the kind of nonstationary environment. A steady-state analysis (using energy conservation) is also presented, considering both the proposed scheme, and the convex combination of two CMAs
Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on; 05/2007 · 4.63 Impact Factor
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ABSTRACT: We address the problem of signal separation using space-time blind decision feedback equalizer. Assuming correct decisions and absence of noise, the perfect equalization conditions are obtained. We present an extension of the blind algorithm which avoids degenerated solutions in the single-input single output case. The proposed algorithm jointly adapts the feedforward and feedback filters of DFE, avoids degenerated solutions, and has capability of simultaneously recovering all sources.
Telecommunications Symposium, 2006 International; 10/2006
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Electronics Letters 09/2005; 41(16):63- 64. · 0.96 Impact Factor
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ABSTRACT: Although space-time blind equalization algorithms have been widely studied in the last decade, their convergence and tracking behavior are not yet completely characterized. In this paper, we address the tracking analysis of space-time blind quasi-Newton algorithms, using the energy conservation relation. We obtain an expression to adjust the algorithms to reach the same steady-state mean-square error. Assuming a low degree of nonstationarity and high signal-to-noise ratio, close agreement between analytical and simulation results is observed
Statistical Signal Processing, 2005 IEEE/SP 13th Workshop on; 08/2005
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ABSTRACT: Due to the growing demand for mobile communications, blind adaptive algorithms have an important role in improving data transmission efficiency. In this context, the convergence and tracking analysis of such algorithms is a problem of interest. Recently, a tracking analysis of the Constant Modulus Algorithm was presented based on an energy conservation relation. In this letter we extend that analysis to blind quasi-Newton algorithms that minimize the Constant Modulus cost function. Under certain conditions, the considered algorithms can reach the same steady-state mean-square error. Close agreement between analytical and simulation results is shown.
IEEE Signal Processing Letters 10/2004; · 1.39 Impact Factor
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ABSTRACT: The efficient separation of signals is a frequent problem in multiuser communication systems. Among many algorithms for blind deconvolution of a multiple-input multiple-output (MIMO) system, the one that utilizes higher-order cumulants has advantages in regards to convergence rate. Inspired by this algorithm, and on a stochastic gradient approach, we propose an algorithm with the capacity of recovering simultaneously all sources, denoted as MU-SWA (multiuser Shalvi-Weinstein algorithm). Based on the steady-state analysis, recently presented by Luo and Chambers for the multiuser constant modulus algorithm, we derive the expression for the mean-square error of MU-SWA. Simulation results show that MU-SWA presents a more robust behavior with respect to convergence rate and tracking capability when compared to others known algorithms for blind multiuser equalization.
Acoustics, Speech, and Signal Processing, 2004. Proceedings. (ICASSP '04). IEEE International Conference on; 06/2004 · 4.63 Impact Factor
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58(8):4064-4078.
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Simpósio Brasileiro de Telecomunicações (SBrT'09);
