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A novel gain distribution policy based on individual coefficient

Francisco Souza
Francisco Souza

This paper introduces a new gain distribution policy for proportionate normalized least-mean-square (PNLMS)-type algorithms. The proposed approach transfers gains from coefficients that have achieved convergence to other coefficients that have not. It uses a metric based on the variation rate of coefficient magnitude to assess individual coefficient convergence. The approach is applied to PNLMS, improved PNLMS (IPNLMS), and individual-activation-factor PNLMS (IAF-PNLMS), creating enhanced versions. Simulation results show the proposed approach performs well for different operating scenarios.

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Signal Processing 138 (2017) 294306 Contents lists available at ScienceDirect Signal Processing journal homepage: www.elsevier.com/locate/sigpro A novel gain distribution policy based on individual-coe鍖cient convergence for PNLMS-type algorithms F叩bio Luis Pereza , Eduardo Vinicius Kuhnb,c , Francisco das Chagas de Souzad , Rui Searab, a Department of Telecommunications and Electrical Engineering, University of Blumenau, 89030-080, Blumenau, SC, Brazil b LINSE: Circuits and Signal Processing Laboratory, Department of Electrical and Electronics Engineering, Federal University of Santa Catarina, 88040-900, Florian坦polis, SC, Brazil c Department of Electronics Engineering, Federal University of Technology - Paran叩, 85902-490, Toledo, PR, Brazil d LSAPS: Adaptive Systems and Signal Processing Laboratory, Department of Electrical Engineering, Federal University of Maranh達o, 65080-805, S達o Lu鱈s, MA, Brazil a r t i c l e i n f o Article history: Received 1 September 2016 Revised 24 February 2017 Accepted 1 March 2017 Available online 2 March 2017 Keywords: Adaptive 鍖ltering Coe鍖cient convergence Proportionate normalized least-mean-square (PNLMS)-type algorithms System identi鍖cation a b s t r a c t This paper introduces a new gain distribution policy for proportionate normalized least-mean-square (PNLMS)-type algorithms. In the proposed approach, gains assigned to the coe鍖cients that have achieved the vicinity of their optimal values are transferred to other coe鍖cients. To estimate such a vicinity, a metric based on the variation rate of the adaptive 鍖lter coe鍖cient magnitude is devised, which is used as a way for assessing the individual-coe鍖cient convergence. Then, the proposed approach is applied to the PNLMS, improved PNLMS (IPNLMS), and individual-activation-factor PNLMS (IAF-PNLMS), leading to enhanced versions of these algorithms. Simulation results show that the proposed approach (and the corresponding enhanced algorithms) performs well for different operating scenarios. 息 2017 Elsevier B.V. All rights reserved. 1. Introduction Least-mean-square (LMS) and normalized LMS (NLMS) are pop- ular algorithms in adaptive 鍖ltering applications due to their low computational complexity and very good stability characteristics [12]. However, such algorithms (which use the same adaptation step size for all 鍖lter coe鍖cients) exhibit poor convergence char- acteristics when the plant impulse response is sparse [36]. Then, aiming to improve the algorithm performance for sparse plants, which are commonly encountered in many real-world application areas (such as communications, acoustics, and chemical and seis- mic processes [711]), the proportionate NLMS (PNLMS) algorithm has been proposed [12]. This algorithm updates each 鍖lter coe鍖- cient proportionally to its magnitude, leading to a faster conver- gence speed as compared with the NLMS. Nevertheless, the fast initial convergence speed of the PNLMS algorithm is not preserved over the whole adaptation process [6,13]. Furthermore, the PNLMS presents a slower convergence speed when the plant impulse re- sponse exhibits medium and low sparseness [34]. Corresponding author. E-mail addresses: fabiotek@furb.br (F.L. Perez), kuhn@linse.ufsc.br, kuhn@utfpr.edu.br (E.V. Kuhn), francisco.souza@ufma.br (F.d.C. de Souza), seara@linse.ufsc.br (R. Seara). In order to circumvent the aforementioned drawbacks of the PNLMS, several versions of such an algorithm have been presented in the open literature [34,6,1420]. For instance, the PNLMS++ [3] and the improved PNLMS (IPNLMS) [4] algorithms consider a mixture of proportionate and non-proportionate adaptation gains, leading to better convergence characteristics than the PNLMS for a wide range of plant sparseness. In [19] and [20], the individual- activation-factor PNLMS (IAF-PNLMS) and the enhanced IAF-PNLMS (EIAF-PNLMS) algorithms are introduced, respectively. Such algo- rithms use individual activation factors for each adaptive 鍖lter co- e鍖cient to achieve fast convergence speed for plants with high sparseness degrees. Aiming to provide robustness with respect to sparseness variations of the plant, the sparseness controlled PNLMS (SC-PNLMS) [21] and sparseness controlled IPNLMS (SC- IPNLMS) [22] algorithms have been presented. In turn, looking for fast convergence speed during the whole adaptation process, the 亮-law PNLMS (MPNLMS) and adaptive MPNLMS (AMPNLMS) algo- rithms are obtained in [13] and [23], respectively. In [24], seek- ing to minimize the mean-square error with respect to the adap- tation gain, the water-鍖lling algorithm has been discussed. Such an algorithm uses an estimate of the mean-square weight devia- tion to determine its adaptation gain. Based on the water-鍖lling approach, some other algorithms have been derived [2427]. Other algorithms that use proportionate gain have also been presented in [11,2831]. http://dx.doi.org/10.1016/j.sigpro.2017.03.001 0165-1684/息 2017 Elsevier B.V. All rights reserved.

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A novel gain distribution policy based on individual coefficient

  • 1. Signal Processing 138 (2017) 294306 Contents lists available at ScienceDirect Signal Processing journal homepage: www.elsevier.com/locate/sigpro A novel gain distribution policy based on individual-coe鍖cient convergence for PNLMS-type algorithms F叩bio Luis Pereza , Eduardo Vinicius Kuhnb,c , Francisco das Chagas de Souzad , Rui Searab, a Department of Telecommunications and Electrical Engineering, University of Blumenau, 89030-080, Blumenau, SC, Brazil b LINSE: Circuits and Signal Processing Laboratory, Department of Electrical and Electronics Engineering, Federal University of Santa Catarina, 88040-900, Florian坦polis, SC, Brazil c Department of Electronics Engineering, Federal University of Technology - Paran叩, 85902-490, Toledo, PR, Brazil d LSAPS: Adaptive Systems and Signal Processing Laboratory, Department of Electrical Engineering, Federal University of Maranh達o, 65080-805, S達o Lu鱈s, MA, Brazil a r t i c l e i n f o Article history: Received 1 September 2016 Revised 24 February 2017 Accepted 1 March 2017 Available online 2 March 2017 Keywords: Adaptive 鍖ltering Coe鍖cient convergence Proportionate normalized least-mean-square (PNLMS)-type algorithms System identi鍖cation a b s t r a c t This paper introduces a new gain distribution policy for proportionate normalized least-mean-square (PNLMS)-type algorithms. In the proposed approach, gains assigned to the coe鍖cients that have achieved the vicinity of their optimal values are transferred to other coe鍖cients. To estimate such a vicinity, a metric based on the variation rate of the adaptive 鍖lter coe鍖cient magnitude is devised, which is used as a way for assessing the individual-coe鍖cient convergence. Then, the proposed approach is applied to the PNLMS, improved PNLMS (IPNLMS), and individual-activation-factor PNLMS (IAF-PNLMS), leading to enhanced versions of these algorithms. Simulation results show that the proposed approach (and the corresponding enhanced algorithms) performs well for different operating scenarios. 息 2017 Elsevier B.V. All rights reserved. 1. Introduction Least-mean-square (LMS) and normalized LMS (NLMS) are pop- ular algorithms in adaptive 鍖ltering applications due to their low computational complexity and very good stability characteristics [12]. However, such algorithms (which use the same adaptation step size for all 鍖lter coe鍖cients) exhibit poor convergence char- acteristics when the plant impulse response is sparse [36]. Then, aiming to improve the algorithm performance for sparse plants, which are commonly encountered in many real-world application areas (such as communications, acoustics, and chemical and seis- mic processes [711]), the proportionate NLMS (PNLMS) algorithm has been proposed [12]. This algorithm updates each 鍖lter coe鍖- cient proportionally to its magnitude, leading to a faster conver- gence speed as compared with the NLMS. Nevertheless, the fast initial convergence speed of the PNLMS algorithm is not preserved over the whole adaptation process [6,13]. Furthermore, the PNLMS presents a slower convergence speed when the plant impulse re- sponse exhibits medium and low sparseness [34]. Corresponding author. E-mail addresses: fabiotek@furb.br (F.L. Perez), kuhn@linse.ufsc.br, kuhn@utfpr.edu.br (E.V. Kuhn), francisco.souza@ufma.br (F.d.C. de Souza), seara@linse.ufsc.br (R. Seara). In order to circumvent the aforementioned drawbacks of the PNLMS, several versions of such an algorithm have been presented in the open literature [34,6,1420]. For instance, the PNLMS++ [3] and the improved PNLMS (IPNLMS) [4] algorithms consider a mixture of proportionate and non-proportionate adaptation gains, leading to better convergence characteristics than the PNLMS for a wide range of plant sparseness. In [19] and [20], the individual- activation-factor PNLMS (IAF-PNLMS) and the enhanced IAF-PNLMS (EIAF-PNLMS) algorithms are introduced, respectively. Such algo- rithms use individual activation factors for each adaptive 鍖lter co- e鍖cient to achieve fast convergence speed for plants with high sparseness degrees. Aiming to provide robustness with respect to sparseness variations of the plant, the sparseness controlled PNLMS (SC-PNLMS) [21] and sparseness controlled IPNLMS (SC- IPNLMS) [22] algorithms have been presented. In turn, looking for fast convergence speed during the whole adaptation process, the 亮-law PNLMS (MPNLMS) and adaptive MPNLMS (AMPNLMS) algo- rithms are obtained in [13] and [23], respectively. In [24], seek- ing to minimize the mean-square error with respect to the adap- tation gain, the water-鍖lling algorithm has been discussed. Such an algorithm uses an estimate of the mean-square weight devia- tion to determine its adaptation gain. Based on the water-鍖lling approach, some other algorithms have been derived [2427]. Other algorithms that use proportionate gain have also been presented in [11,2831]. http://dx.doi.org/10.1016/j.sigpro.2017.03.001 0165-1684/息 2017 Elsevier B.V. All rights reserved.