Skip to main content
Erschienen in:

16.07.2024

A Novel Widely-Linear Complex-Valued Diffusion VSS-LMS Algorithm for Distributed Network and Its Performance Analysis

verfasst von: Xiaoqiang Long, Haiquan Zhao, Xinyan Hou, Wei Quan

Erschienen in: Circuits, Systems, and Signal Processing | Ausgabe 10/2024

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

To address the shortcomings of the widely-linear complex-valued distributed adaptive filtering algorithm that cannot combine convergence speed and steady-state performance when using a fixed step-size strategy. In this paper, by making the partial derivative of the square of the sum of a priori error and a posteriori error with respect to step-size equal to zero, we propose a novel variable step-size (VSS) strategy, which is formulated as a function of a priori error and a posteriori error. In addition, a corresponding adaptive filtering algorithm is proposed by using the VSS strategy. Then in the process of parameter update, the moving average method is used to avoid large perturbations in iteration of the algorithm. Secondly, the theoretically analysis of the transient and steady-state performance of the proposed algorithm is provided. Finally, in the numerical simulation experiments, the effect of each parameter on the algorithm is tested, the result of the comparison with the fixed-step algorithm illustrates that the proposed algorithm has more superiority, and the high degree of matching between theory and experiment also verifies the feasibility and accuracy of the theoretical analysis method.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

ATZelektronik

Die Fachzeitschrift ATZelektronik bietet für Entwickler und Entscheider in der Automobil- und Zulieferindustrie qualitativ hochwertige und fundierte Informationen aus dem gesamten Spektrum der Pkw- und Nutzfahrzeug-Elektronik. 

Lassen Sie sich jetzt unverbindlich 2 kostenlose Ausgabe zusenden.

ATZelectronics worldwide

ATZlectronics worldwide is up-to-speed on new trends and developments in automotive electronics on a scientific level with a high depth of information. 

Order your 30-days-trial for free and without any commitment.

Weitere Produktempfehlungen anzeigen
Literatur
1.
Zurück zum Zitat R. Arablouei, S. Werner, Y.-F. Huang, K. Doğançay, Distributed least mean-square estimation with partial diffusion. IEEE Trans. Signal Process. 62(2), 472–484 (2014)MathSciNet R. Arablouei, S. Werner, Y.-F. Huang, K. Doğançay, Distributed least mean-square estimation with partial diffusion. IEEE Trans. Signal Process. 62(2), 472–484 (2014)MathSciNet
2.
Zurück zum Zitat F.S. Cattivelli, A.H. Sayed, Diffusion LMS strategies for distributed estimation. IEEE Trans. Signal Process. 58(3), 1035–1048 (2010)MathSciNet F.S. Cattivelli, A.H. Sayed, Diffusion LMS strategies for distributed estimation. IEEE Trans. Signal Process. 58(3), 1035–1048 (2010)MathSciNet
3.
Zurück zum Zitat J. Chen, C. Richard, A.H. Sayed, Multitask diffusion adaptation over networks. IEEE Trans. Signal Process. 62(16), 4129–4144 (2014)MathSciNet J. Chen, C. Richard, A.H. Sayed, Multitask diffusion adaptation over networks. IEEE Trans. Signal Process. 62(16), 4129–4144 (2014)MathSciNet
4.
Zurück zum Zitat A.G. Dimakis, S. Kar, J.M.F. Moura, M.G. Rabbat, A. Scaglione, Gossip algorithms for distributed signal processing. Proc. IEEE 98(11), 1847–1864 (2010) A.G. Dimakis, S. Kar, J.M.F. Moura, M.G. Rabbat, A. Scaglione, Gossip algorithms for distributed signal processing. Proc. IEEE 98(11), 1847–1864 (2010)
5.
Zurück zum Zitat H.-C. Huang, J. Lee, A new variable step-size NLMS algorithm and its performance analysis. IEEE Trans. Signal Process. 60(4), 2055–2060 (2012)MathSciNet H.-C. Huang, J. Lee, A new variable step-size NLMS algorithm and its performance analysis. IEEE Trans. Signal Process. 60(4), 2055–2060 (2012)MathSciNet
6.
Zurück zum Zitat S.M. Jung, J.-H. Seo, P.G. Park, A variable step-size diffusion normalized least-mean-square algorithm with a combination method based on mean-square deviation. Circuits Syst. Signal Process. 34(10), 3291–3304 (2015) S.M. Jung, J.-H. Seo, P.G. Park, A variable step-size diffusion normalized least-mean-square algorithm with a combination method based on mean-square deviation. Circuits Syst. Signal Process. 34(10), 3291–3304 (2015)
7.
Zurück zum Zitat S.M. Jung, J.-H. Seo, P. Park, Efficient variable step-size diffusion normalised least-mean-square algorithm. Electron. Lett. 51(5), 395–397 (2015) S.M. Jung, J.-H. Seo, P. Park, Efficient variable step-size diffusion normalised least-mean-square algorithm. Electron. Lett. 51(5), 395–397 (2015)
8.
Zurück zum Zitat S. Kanna, D.P. Mandic, Steady-state behavior of General complex-valued diffusion LMS strategies. IEEE Signal Process. Lett. 23(5), 722–726 (2016) S. Kanna, D.P. Mandic, Steady-state behavior of General complex-valued diffusion LMS strategies. IEEE Signal Process. Lett. 23(5), 722–726 (2016)
9.
Zurück zum Zitat S. Kar, J.M.F. Moura, Distributed consensus algorithms in sensor networks with imperfect communication: link failures and channel noise. IEEE Trans. Signal Process. 57(1), 355–369 (2009)MathSciNet S. Kar, J.M.F. Moura, Distributed consensus algorithms in sensor networks with imperfect communication: link failures and channel noise. IEEE Trans. Signal Process. 57(1), 355–369 (2009)MathSciNet
10.
Zurück zum Zitat S.-E. Kim, J.-W. Lee, W.-J. Song, A theory on the convergence behavior of the affine projection algorithm. IEEE Trans. Signal Process. 59(12), 6233–6239 (2011)MathSciNet S.-E. Kim, J.-W. Lee, W.-J. Song, A theory on the convergence behavior of the affine projection algorithm. IEEE Trans. Signal Process. 59(12), 6233–6239 (2011)MathSciNet
11.
Zurück zum Zitat S. Koike, A class of adaptive step-size control algorithms for adaptive filters. IEEE Trans. Signal Process. 50(6), 1315–1326 (2002) S. Koike, A class of adaptive step-size control algorithms for adaptive filters. IEEE Trans. Signal Process. 50(6), 1315–1326 (2002)
12.
Zurück zum Zitat H.-S. Lee, S.-E. Kim, J.-W. Lee, W.-J. Song, A variable step-size diffusion LMS algorithm for distributed estimation. IEEE Trans. Signal Process. 63(7), 1808–1820 (2015)MathSciNet H.-S. Lee, S.-E. Kim, J.-W. Lee, W.-J. Song, A variable step-size diffusion LMS algorithm for distributed estimation. IEEE Trans. Signal Process. 63(7), 1808–1820 (2015)MathSciNet
13.
Zurück zum Zitat X.-L. Li, T. Adali, Complex-valued linear and widely linear filtering using MSE and gaussian entropy. IEEE Trans. Signal Process. 60(11), 5672–5684 (2012)MathSciNet X.-L. Li, T. Adali, Complex-valued linear and widely linear filtering using MSE and gaussian entropy. IEEE Trans. Signal Process. 60(11), 5672–5684 (2012)MathSciNet
14.
Zurück zum Zitat X. Long, H. Zhao, X. Hou, W. Quan, A variable regularization parameter widely linear complex-valued NLMS algorithm: performance analysis and wind prediction. Signal Process. 201, 108731 (2022) X. Long, H. Zhao, X. Hou, W. Quan, A variable regularization parameter widely linear complex-valued NLMS algorithm: performance analysis and wind prediction. Signal Process. 201, 108731 (2022)
15.
Zurück zum Zitat C.G. Lopes, A.H. Sayed, Diffusion least-mean squares over adaptive networks: formulation and performance analysis. IEEE Trans. Signal Process. 56(7), 3122–3136 (2008)MathSciNet C.G. Lopes, A.H. Sayed, Diffusion least-mean squares over adaptive networks: formulation and performance analysis. IEEE Trans. Signal Process. 56(7), 3122–3136 (2008)MathSciNet
16.
Zurück zum Zitat C.G. Lopes, A.H. Sayed, Incremental adaptive strategies over distributed networks. IEEE Trans. Signal Process. 55(8), 4064–4077 (2007)MathSciNet C.G. Lopes, A.H. Sayed, Incremental adaptive strategies over distributed networks. IEEE Trans. Signal Process. 55(8), 4064–4077 (2007)MathSciNet
17.
Zurück zum Zitat S. Lv, H. Zhao, W. Xu, Robust widely-linear affine projection m-estimate adaptive algorithm: performance analysis and application. IEEE Trans. Signal Process. 71, 3623–3636 (2023)MathSciNet S. Lv, H. Zhao, W. Xu, Robust widely-linear affine projection m-estimate adaptive algorithm: performance analysis and application. IEEE Trans. Signal Process. 71, 3623–3636 (2023)MathSciNet
18.
Zurück zum Zitat D. Morgan, Adaptive signal processing. IEEE Trans. Audio Speech Lang. Process. 34(4), 1017–1018 (1986) D. Morgan, Adaptive signal processing. IEEE Trans. Audio Speech Lang. Process. 34(4), 1017–1018 (1986)
19.
Zurück zum Zitat A. Nedic, A. Ozdaglar, Distributed subgradient methods for multi-agent optimization. IEEE Trans. Autom. Control 54(1), 48–61 (2009)MathSciNet A. Nedic, A. Ozdaglar, Distributed subgradient methods for multi-agent optimization. IEEE Trans. Autom. Control 54(1), 48–61 (2009)MathSciNet
20.
Zurück zum Zitat R.O. Saber, J.A. Fax, R.M. Murray, Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–233 (2007) R.O. Saber, J.A. Fax, R.M. Murray, Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–233 (2007)
21.
Zurück zum Zitat M.O.B. Saeed, A. Zerguine, An incremental variable step-size LMS algorithm for adaptive networks. IEEE Trans. Circuits Syst. II Exp. Briefs 67(10), 2264–2268 (2020) M.O.B. Saeed, A. Zerguine, An incremental variable step-size LMS algorithm for adaptive networks. IEEE Trans. Circuits Syst. II Exp. Briefs 67(10), 2264–2268 (2020)
22.
Zurück zum Zitat A.H. Sayed, Adaptive networks. Proc. IEEE 102(4), 460–497 (2014) A.H. Sayed, Adaptive networks. Proc. IEEE 102(4), 460–497 (2014)
23.
Zurück zum Zitat A.H. Sayed, Diffusion adaptation over networks. Acad. Press Lib. Signal Process. 3, 323–454 (2014) A.H. Sayed, Diffusion adaptation over networks. Acad. Press Lib. Signal Process. 3, 323–454 (2014)
24.
Zurück zum Zitat A.H. Sayed, S.-Y. Tu, J. Chen, X. Zhao, Z.J. Towfic, Diffusion strategies for adaptation and learning over networks: an examination of distributed strategies and network behavior. IEEE Signal Process. Mag. 30(3), 155–171 (2013) A.H. Sayed, S.-Y. Tu, J. Chen, X. Zhao, Z.J. Towfic, Diffusion strategies for adaptation and learning over networks: an examination of distributed strategies and network behavior. IEEE Signal Process. Mag. 30(3), 155–171 (2013)
25.
Zurück zum Zitat L. Shi, H. Zhao, Y. Zakharov, Performance analysis of shrinkage linear complex-valued LMS algorithm. IEEE Signal Process. Lett. 26(8), 1202–1206 (2019) L. Shi, H. Zhao, Y. Zakharov, Performance analysis of shrinkage linear complex-valued LMS algorithm. IEEE Signal Process. Lett. 26(8), 1202–1206 (2019)
26.
Zurück zum Zitat L. Shi, H. Zhao, Y. Zakharov, B. Chen, Y. Yang, Variable step-size widely linear complex-valued affine projection algorithm and performance analysis. IEEE Trans. Signal Process. 68, 5940–5953 (2020)MathSciNet L. Shi, H. Zhao, Y. Zakharov, B. Chen, Y. Yang, Variable step-size widely linear complex-valued affine projection algorithm and performance analysis. IEEE Trans. Signal Process. 68, 5940–5953 (2020)MathSciNet
27.
Zurück zum Zitat M.T.M. Silva, V.H. Nascimento, J. Arenas-García, A transient analysis for the convex combination of two adaptive filters with transfer of coefficients, in: 2010 IEEE International Conference on Acoustics Speech Signal Process (ICASSP). IEEE, pp. 3842–3845 (2010) M.T.M. Silva, V.H. Nascimento, J. Arenas-García, A transient analysis for the convex combination of two adaptive filters with transfer of coefficients, in: 2010 IEEE International Conference on Acoustics Speech Signal Process (ICASSP). IEEE, pp. 3842–3845 (2010)
28.
Zurück zum Zitat S.-Y. Tu, A.H. Sayed, Diffusion strategies outperform consensus strategies for distributed estimation over adaptive networks. IEEE Trans. Signal Process. 60(12), 6217–6234 (2012)MathSciNet S.-Y. Tu, A.H. Sayed, Diffusion strategies outperform consensus strategies for distributed estimation over adaptive networks. IEEE Trans. Signal Process. 60(12), 6217–6234 (2012)MathSciNet
29.
Zurück zum Zitat B.C. Ujang, C.C. Took, D.P. Mandic, Quaternion-valued nonlinear adaptive filtering. IEEE Trans. Neural Netw. 22(8), 1193–1206 (2011) B.C. Ujang, C.C. Took, D.P. Mandic, Quaternion-valued nonlinear adaptive filtering. IEEE Trans. Neural Netw. 22(8), 1193–1206 (2011)
30.
Zurück zum Zitat A. Uncini, Fundamentals of Adaptive Signal Processing (Springer, New York, 2015) A. Uncini, Fundamentals of Adaptive Signal Processing (Springer, New York, 2015)
31.
Zurück zum Zitat W. Wang, K. Dogancay, Convergence issues in sequential partial-update LMS for cyclostationary white Gaussian input signals. IEEE Signal Process. Lett. 28, 967–971 (2021) W. Wang, K. Dogancay, Convergence issues in sequential partial-update LMS for cyclostationary white Gaussian input signals. IEEE Signal Process. Lett. 28, 967–971 (2021)
32.
Zurück zum Zitat E.P. Wigner, Theory of traveling-wave optical laser. Phys. Rev. 134, A635–A646 (1965) E.P. Wigner, Theory of traveling-wave optical laser. Phys. Rev. 134, A635–A646 (1965)
33.
Zurück zum Zitat W. Xia, Y. Wang, A variable step-size diffusion LMS algorithm over networks with noisy links. Signal Process. 148, 205–213 (2018) W. Xia, Y. Wang, A variable step-size diffusion LMS algorithm over networks with noisy links. Signal Process. 148, 205–213 (2018)
34.
Zurück zum Zitat Y. Xia, D.P. Mandic, Augmented performance bounds on strictly linear and widely linear estimators with complex data. IEEE Trans. Signal Process. 66(2), 507–514 (2018)MathSciNet Y. Xia, D.P. Mandic, Augmented performance bounds on strictly linear and widely linear estimators with complex data. IEEE Trans. Signal Process. 66(2), 507–514 (2018)MathSciNet
35.
Zurück zum Zitat Y. Xia, D.P. Mandic, Complementary mean square analysis of augmented CLMS for second-order noncircular Gaussian signals. IEEE Signal Process. Lett. 24(9), 1413–1417 (2017) Y. Xia, D.P. Mandic, Complementary mean square analysis of augmented CLMS for second-order noncircular Gaussian signals. IEEE Signal Process. Lett. 24(9), 1413–1417 (2017)
36.
Zurück zum Zitat Y. Xia, D.P. Mandic, A.H. Sayed, An adaptive diffusion augmented CLMS algorithm for distributed filtering of noncircular complex signals. IEEE Signal Process. Lett. 18(11), 659–662 (2011) Y. Xia, D.P. Mandic, A.H. Sayed, An adaptive diffusion augmented CLMS algorithm for distributed filtering of noncircular complex signals. IEEE Signal Process. Lett. 18(11), 659–662 (2011)
37.
Zurück zum Zitat Y. Yu, H. Zhao, Robust incremental normalized least mean square algorithm with variable step sizes over distributed networks. Signal Process. 144, 1–6 (2018) Y. Yu, H. Zhao, Robust incremental normalized least mean square algorithm with variable step sizes over distributed networks. Signal Process. 144, 1–6 (2018)
38.
Zurück zum Zitat S. Zhang, W.X. Zheng, J. Zhang, A new combined-step-size normalized least mean square algorithm for cyclostationary inputs. Signal Process. 141, 261–272 (2017) S. Zhang, W.X. Zheng, J. Zhang, A new combined-step-size normalized least mean square algorithm for cyclostationary inputs. Signal Process. 141, 261–272 (2017)
39.
Zurück zum Zitat H. Zhao, Z. Cao, Robust generalized maximum Blake–Zisserman total correntropy adaptive filter for generalized Gaussian noise and noisy input. IEEE Trans. Syst. Man Cybern. Syst. 53(11), 6757–6765 (2023) H. Zhao, Z. Cao, Robust generalized maximum Blake–Zisserman total correntropy adaptive filter for generalized Gaussian noise and noisy input. IEEE Trans. Syst. Man Cybern. Syst. 53(11), 6757–6765 (2023)
40.
Zurück zum Zitat H. Zhao, Y. Liu, W. Luo, C. Wang, Augmented complex minimization of error entropy with fiducial points for power system frequency estimation. IEEE Trans. Circuits Syst. II Exp. Briefs 70(6), 2296–2300 (2023) H. Zhao, Y. Liu, W. Luo, C. Wang, Augmented complex minimization of error entropy with fiducial points for power system frequency estimation. IEEE Trans. Circuits Syst. II Exp. Briefs 70(6), 2296–2300 (2023)
41.
Zurück zum Zitat H. Zhao, G.L. Nefabas, Z. Wang, Augmented complex minimum error entropy for adaptive frequency estimation of power system. IEEE Trans. Circuits Syst. II Exp. Briefs 69(3), 1972–1976 (2022) H. Zhao, G.L. Nefabas, Z. Wang, Augmented complex minimum error entropy for adaptive frequency estimation of power system. IEEE Trans. Circuits Syst. II Exp. Briefs 69(3), 1972–1976 (2022)
42.
Zurück zum Zitat H. Zhao, G. Wang, F. Zhao, D. Liu, P. Song, Recursive general mixed norm algorithm for censored regression: performance analysis and channel equalization application. IEEE Trans. Syst. Man Cybern. Syst. 54(2), 752–763 (2024) H. Zhao, G. Wang, F. Zhao, D. Liu, P. Song, Recursive general mixed norm algorithm for censored regression: performance analysis and channel equalization application. IEEE Trans. Syst. Man Cybern. Syst. 54(2), 752–763 (2024)
43.
Zurück zum Zitat H. Zhao, Z. Wang, W. Xu, Augmented complex least lncosh algorithm for adaptive frequency estimation. IEEE Trans. Circuits Syst. II Exp. Briefs 70(7), 2685–2689 (2023) H. Zhao, Z. Wang, W. Xu, Augmented complex least lncosh algorithm for adaptive frequency estimation. IEEE Trans. Circuits Syst. II Exp. Briefs 70(7), 2685–2689 (2023)
Metadaten
Titel
A Novel Widely-Linear Complex-Valued Diffusion VSS-LMS Algorithm for Distributed Network and Its Performance Analysis
verfasst von
Xiaoqiang Long
Haiquan Zhao
Xinyan Hou
Wei Quan
Publikationsdatum
16.07.2024
Verlag
Springer US
Erschienen in
Circuits, Systems, and Signal Processing / Ausgabe 10/2024
Print ISSN: 0278-081X
Elektronische ISSN: 1531-5878
DOI
https://doi.org/10.1007/s00034-024-02769-0