Journal of Professor & SPaC member

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Last Updated : 03/2016
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  • Second-order reciprocally convex approach to stability of systems with interval time-varying delays

    WI Lee, PG Park

    Applied Mathematics and Computation 229, 245-253

    Abstract Recently, some triple integral terms in the Lyapunov–Krasovskii functional have been introduced in the literature to reduce conservatism in the stability analysis of systems with interval time-varying delays. When we apply the Jensen inequality to partitioned double integral terms in the derivation of LMI conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters emerges. This paper proposes an efficient method to manipulate such a combination by extending the lower bound lemma. Some numerical examples are given to demonstrate the improvement of the proposed method.
  • Variable matrix-type step-size affine projection algorithm with orthogonalized input vectors

    PG Park, JH Seo, NW Kong

    Signal Processing 98, 135-142

    Abstract In this paper, we propose a variable matrix-type step-size affine projection algorithm (APA) with orthogonalized input vectors. We generate orthogonalized input vectors using the Gram–Schmidt process to implement the weight update equation of the APA using the sum of normalized least mean squares (NLMS)-like updating equations. This method allows us to use individual step sizes corresponding to each NLMS-like equation, which is equivalent to adopting the step size in the form of a diagonal matrix in the APA. We adopt a variable step-size scheme, in which the individual step sizes are determined to minimize the mean square deviation of the APA in order to achieve the fastest convergence on every iteration. Furthermore, because of the weight vector updated successively only along each innovative one among the reused inputs and effect of the regularization absorbed into the derived step size, the algorithm works well even for badly excited input signals. Experimental results show that our proposed algorithm has almost optimal performance in terms of convergence rate and steady-state estimation error, and these results are remarkable especially for badly excited input signals.
  • Variable Step-Size Affine Projection Sign Algorithm

    JW Yoo, JW Shin, PG Park

    IEEE

    Abstract In this paper, we propose a variable matrix-type step-size affine projection algorithm (APA) with orthogonalized input vectors. We generate orthogonalized input vectors using the Gram–Schmidt process to implement the weight update equation of the APA using the sum of normalized least mean squares (NLMS)-like updating equations. This method allows us to use individual step sizes corresponding to each NLMS-like equation, which is equivalent to adopting the step size in the form of a diagonal matrix in the APA. We adopt a variable step-size scheme, in which the individual step sizes are determined to minimize the mean square deviation of the APA in order to achieve the fastest convergence on every iteration. Furthermore, because of the weight vector updated successively only along each innovative one among the reused inputs and effect of the regularization absorbed into the derived step size, the algorithm works well even for badly excited input signals. Experimental results show that our proposed algorithm has almost optimal performance in terms of convergence rate and steady-state estimation error, and these results are remarkable especially for badly excited input signals.
  • A variable step-size affine projection algorithm with a step-size scaler against impulsive measurement noise

    I Song, PG Park

    Signal Processing 96, 321-324

    Abstract This letter proposes a variable step-size (VSS) affine projection algorithm (APA) associated with a step-size scaler to improve the APA’s robustness against impulsive measurement noise. In the proposed VSS APA, the step-size scaler is applied to the equations for updating the step size, which are developed by interpreting the behavior of the mean square deviation (MSD) of the conventional APA. To reduce the computational complexity, we also propose a simplified version of the step-size scaler, which is suitable for application in the APA. Simulations show that the proposed algorithm leads to an excellent transient and steady-state behavior with colored inputs in impulsive-noise environments.
  • Variable Step-Size Affine Projection Sign Algorithm

    JW Yoo, JW Shin, PG Park

    Signal Processing 104, 407-411

    Abstract This letter proposes a band-dependent variable step-size sign subband adaptive filter using the concept of mean-square deviation (MSD) minimization. Since it is difficult to obtain the value of the MSD accurately, the proposed step size is derived by minimizing the upper bound of the conditional MSD with given input. By assigning the different step size in each band, the filter performance can be improved. Moreover, we suggest the estimation method of the measurement-noise variance in an impulsive-noise environment, because the proposed algorithm needs the measurement-noise variance to calculate the step size. The reset algorithm is also applied for maintaining the filter performance when a system change occurs suddenly. Simulation results demonstrate that the proposed algorithm performs better than the existing algorithms in aspects of the convergence rate and the steady-state estimation error.
  • Variable individual step-size subband adaptive filtering algorithm

    JH Seo, PG Park

    Electronics Letters 50 (3), 177-178

    Abstract A subband adaptive filtering algorithm is proposed which improves its performance by adjusting step sizes. The proposed algorithm derives the individual step sizes for each subband instead of using a common step size for multiple subbands. The derivation of the step sizes is based on the mean-square deviation minimisation in order to achieve the fastest convergence at the instant. Furthermore, the individual step sizes contain the squared norm of the input vector, hence it leads to the regularisation effect that helps the algorithm work well in the case of badly excited input signals. The simulation results show that the proposed algorithm achieves a faster convergence rate and a smaller steady-state estimation error than the existing algorithms.
  • Non-periodic-partial-update affine projection algorithm with data-selective updating

    NW Kong, JW Shin, SY Lee, J Song, H Choi, P Park

    Signal Processing Letters, IEEE 20 (2), 173-176

    Abstract This paper presents a new variable step-size diffusion affine projection algorithm (VSS-DAPA) to advance the filter performance of the diffusion affine projection algorithm (DAPA). The proposed VSS strategy is developed for the DAPA, which can solve the distributed estimation problem over diffusion networks well. To obtain the optimal step size reasonably, we seek the update recursion of mean-square deviation (MSD) that is suitable for the DAPA. The step size is optimally given through the minimization for the MSD of the DAPA at each iteration. The derived step size through the MSD minimization improves the filter performance with respect to the convergence and the estimation error in steady state. The results based on simulations demonstrate that the proposed VSS-DAPA performs better than the existing algorithms with a system-identification scenario in diffusion network. Copyright © 2015 John Wiley & Sons, Ltd.
  • An Affine Projection Algorithm with Evolving Order Using Variable Step-Size.

    JW Yoo, JW Shin, HT Choi, PG Park

    International Journal of Computer & Electrical Engineering 5 (1)

    Abstract This paper proposes an affine projection algorithm (APA) with evolving order using variable step-size. The proposed algorithm has not only a variable projection order with an evolutionary method but also changeable step-size in a certain condition. The step-size varies only when the projection order is not changed by the evolutionary method. The experimental results show that the proposed algorithm achieves faster convergence rate and smaller steady-state estimation errors than the existing algorithms.
  • Variable step-size sign subband adaptive filter

    JW Shin, JW Yoo, PG Park

    Signal Processing Letters, IEEE 20 (2), 173-176

    Abstract This letter proposes a variable step-size sign subband adaptive filter (SSAF) based on the minimization of mean-square deviation (MSD). In the process of minimizing the MSD, because it is not feasible to know the exact value of the MSD, the step size is derived by minimizing the upper bound of the MSD in each iteration. The proposed algorithm uses this step size in the SSAF update equation so as to improve the filter performance in terms of the convergence rate and the steady-state estimation error. The proposed algorithm is tested in a system-identification scenario that includes impulsive noise. Simulation results show that the proposed algorithm performs better than the previous algorithms.
  • An evolving update interval algorithm for the optimal step-size affine projection algorithm

    J Song, SY Lee, HT Choi, PG Park

    Intelligent Signal Processing and Communications Systems (ISPACS), 2013

    Abstract This paper introduces an evolving update interval algorithm for the optimal step-size affine projection algorithm. The optimal step-size affine projection algorithm is one of numerous approaches to get better performance for the affine projection algorithm. It is suggested by analyzing the mean square deviation of fixed step-size affine projection algorithm. With the optimal step-size affine projection algorithm, in this paper, by evolving the update interval, it is able to show much better performance. From the MSD analysis, the learning curve is dived into two stage: the transient stage and the steady-state. By finding the cross point of affine projection algorithm’s learning curve, the update interval is modified. By updating the weight vector for updated interval, the proposed algorithm reduces the computational complexity. With the proposed algorithm from simulations, it shows higher convergence rate and lower steady-state error.