Adaptive filtering algorithms designed using control Liapunov functions

Diene, Oumar; Bhaya, Amit

doi:10.1109/lsp.2005.863659

Cited by 26 publications

(27 citation statements)

References 6 publications

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“…Equation (1) can be rewritten as (4) and represented as a system of equations with respect to the unknown vector (5) Instead of solving the original problem (1), one can find a solution of the auxiliary system of equations (6) where (7) and obtain an approximate solution of the original system (1) as (8) It is seen from (7) that this approach requires the residual vector for the solution to the original system (1) to be known at each time instant . After some algebra, we obtain that the residual vector for the solution to the auxiliary system (1) is also equal to , i.e.,…”

Section: Problem Statement and Recursive Solution Of The Rls Normmentioning

confidence: 99%

“…At other iterations, , the direction is updated to guarantee -conjugacy of the direction vectors. Due to its fast convergence, the CG method has already been used for adaptive filtering for a long time (e.g., see [5], [7], [18], [8] and references therein).…”

Section: A Conjugate Gradient Algorithmmentioning

confidence: 99%

“…Such an approach is used in the direction set (or line search) based adaptive algorithms. These techniques have either a good RLS-like performance but a high complexity of , e.g., the conjugate gradient [5]- [8] or Euclidean direction search (EDS) [9] adaptive algorithms, or a low complexity of but a low performance, e.g., the fast EDS algorithm [9]- [11] or the stochastic line search algorithm [12].…”

Section: Introductionmentioning

confidence: 99%

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Low-Complexity RLS Algorithms Using Dichotomous Coordinate Descent Iterations

Zakharov

White

Liu

2008

IEEE Trans. Signal Process.

211

143

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In this paper, we derive low-complexity recursive least squares (RLS) adaptive filtering algorithms. We express the RLS problem in terms of auxiliary normal equations with respect to increments of the filter weights and apply this approach to the exponentially weighted and sliding window cases to derive new RLS techniques. For solving the auxiliary equations, line search methods are used. We first consider conjugate gradient iterations with a complexity of ( 2 ) operations per sample; being the number of the filter weights. To reduce the complexity and make the algorithms more suitable for finite precision implementation, we propose a new dichotomous coordinate descent (DCD) algorithm and apply it to the auxiliary equations. This results in a transversal RLS adaptive filter with complexity as low as 3 multiplications per sample, which is only slightly higher than the complexity of the least mean squares (LMS) algorithm (2 multiplications). Simulations are used to compare the performance of the proposed algorithms against the classical RLS and known advanced adaptive algorithms. Fixed-point FPGA implementation of the proposed DCD-based RLS algorithm is also discussed and results of such implementation are presented.

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Section: Problem Statement and Recursive Solution Of The Rls Normmentioning

confidence: 99%

Section: A Conjugate Gradient Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Low-Complexity RLS Algorithms Using Dichotomous Coordinate Descent Iterations

Zakharov

White

Liu

2008

IEEE Trans. Signal Process.

211

143

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“…For the conlputation of the step-size a(k), the multiplicative parameter 11 in [3] was made equal to .-\ for its proved optimality, as shown in [4] (with correction in [5]). The result is as follows:…”

Section: The Generalized Data Windowing Conjugate Gradient (Gdwcg) Almentioning

confidence: 99%

The constrained generalized data windowing conjugate gradient algorithm

Apolinario

Campos

2008

2008 IEEE 9th Workshop on Signal Processing Advances in Wireless Communications

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where F is as given above and P is the projection matrix, which can also be written as P == B (BTB) -1 BT. This paper introduces a constrained version of the GDWCG algorithm, namely the CGDWCG algorithm, and is organized as follows: After Section 2 presents the equations of the GDWCG algorithm, Section 3 presents a step-by-step derivation of the new algorithm, and Section 4 presents the simulation results. Finally, Section 5 concludes this work. algorithm from [3] was introduced in [8]. The constrained version was equivalent, in infinite precision environment, to the MCG algorithm used within the so-called Generalized Sidelobe Canceler (GSC) structure [9,10]. This structure is well-known to be able to transform the linearly constrained minimization problem into an unconstrained minimization problem.In order to nlinimize the Mean Squared-Error (MSE) with respect to w, subject to CTw == f, the GSC structure decomposes the coefficient vector using a transformation matrix that can be represented by [C -B], where C is the constraint matrix, w is the coefficient vector, f is the gain vector, and B is the blocking matrix which spans the null space of the constraint matrix C, i.e., B T C == o. The transformed coefficient vector is intrinsically partitioned yielding and overall filter w(k) == F -BWGsc(k), where F == C(C T C)-lf and w GSC is the reduced-dimension coefficient vector that operates on the input-signal vector modified by the blocking matrix B.Given a projection matrix P == I -C(C T C)-IC T , then any constrained adaptive filter w (k) can be decomposed in two parts: A projection onto the subspace orthogonal to the space spanned by the constraint matrix C, i.e., w(k) premultiplied by the projection matrix P, and a translation that brings the projected vector back to the hyperplane C T w == f, i.e., ABSTRACT This paper introduces a constrained version of a recently proposed generalized data windowing scheme applied to the Conjugate Gradient algorithm. This scheme combines two types of data windowing, the finite-data sliding window and the exponentially weighted data window, in an attempt to attain the best of both methods in a linearly constrained scenario. The proposed algorithm was tested in a simple adaptive beamforming application, where the expected better performance was demonstrated.

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“…However, the computing complexity possesses a high computing complexity of O(N 2 ) operations per sample (N is the filter length) in the conventional recursive least squares (RLS) adaptive algorithm [25] with a fixed forgetting factor in the DFE receiver. A lot of researches about reducing the computing complexity of the RLS algorithm are carried on [26][27][28][29][30][31][32][33]. However, these algorithms can reduce the computing complexity at the cost of performance degradation.…”

Section: Introductionmentioning

confidence: 99%

Single‐carrier underwater acoustic communication combined with channel shortening and dichotomous coordinate descent recursive least squares with variable forgetting factor

Zhang

Sun

et al. 2015

IET Communications

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In this study, the authors propose a novel decision feedback equaliser (DFE)-based receiver, which combines channel shortening methods and dichotomous coordinate descent (DCD) recursive least squares (RLS) adaptive algorithm with variable forgetting factor (VFF). The proposed receiver can obtain its performance gain via two aspects: (i) reducing the computing complexity by channel shortening method, such as passive time reversal (pTR) filter or minimised mean-square error (MMSE) filter and (ii) improving the performance of the receiver, such as a lower bit error rate and mean-square error. Underwater acoustic (UWA) channel has the features of long multi-path spread and time-varying property. When the multi-path spread is very long, pTR or MMSE filter is used as a channel shortening pre-processing method to reduce the computing complexity in the DFE receiver. When the channel is time varying, VFF is incorporated into DCD-RLS adaptive algorithm to improve the tracking capability of the DFE receiver. The proposed receiver is appealing for practical implementations. Numerical examples and lake experimental results show that, the proposed DFE receiver can achieve a better performance in the UWA communication system.

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Adaptive filtering algorithms designed using control Liapunov functions

Cited by 26 publications

References 6 publications

Low-Complexity RLS Algorithms Using Dichotomous Coordinate Descent Iterations

Low-Complexity RLS Algorithms Using Dichotomous Coordinate Descent Iterations

The constrained generalized data windowing conjugate gradient algorithm

Single‐carrier underwater acoustic communication combined with channel shortening and dichotomous coordinate descent recursive least squares with variable forgetting factor

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