IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v166y2023ics0960077922010669.html
   My bibliography  Save this article

Optimal added noise for minimizing distortion in quantizer-array linear estimation

Author

Listed:
  • Xie, Tianting
  • Ji, Yuandong
  • Yang, Zhongshan
  • Duan, Fabing
  • Abbott, Derek

Abstract

For linearly estimating the input signal, the optimization of suprathreshold stochastic resonance in an array of N parallel M-ary quantizers is theoretically investigated. We first prove that the mean square error (MSE) of the designed quantizer-array is a convex functional with respect to the cumulative probability function (CDF) of the added noise. Then, for an arbitrary input signal and the quantization interval being N times the decoding step size, we theoretically demonstrate that minimum MSE distortion can be obtained for optimal added uniform noise. Furthermore, for a uniform input signal, the optimality condition also holds if the system parameters and the boundary of the signal satisfy an inequality constraint condition. Moreover, under this condition, the optimal parameters of the quantizer-array can be also determined exactly. By applying both the optimal added noise and optimal parameters to the quantizer-array, the MSE can be further improved for larger array size N or quantization order M. Finally, the optimal added noise is also discussed for minimizing distortions of the quantizer-array linear estimation in the presence of the background noise.

Suggested Citation

  • Xie, Tianting & Ji, Yuandong & Yang, Zhongshan & Duan, Fabing & Abbott, Derek, 2023. "Optimal added noise for minimizing distortion in quantizer-array linear estimation," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922010669
    DOI: 10.1016/j.chaos.2022.112887
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922010669
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112887?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. D. Valenti & L. Schimansky-Geier & X. Sailer & B. Spagnolo, 2006. "Moment equations for a spatially extended system of two competing species," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 199-203, March.
    2. Yilmaz, Ergin & Uzuntarla, Muhammet & Ozer, Mahmut & Perc, Matjaž, 2013. "Stochastic resonance in hybrid scale-free neuronal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5735-5741.
    3. Yang, Ting & Tang, Mingchun & Wang, Pin & Zhang, Xinzheng, 2016. "Suitable or optimal noise benefits in signal detectionAuthor-Name: Liu, Shujun," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 84-97.
    4. Zhang, Wenyue & Shi, Peiming & Li, Mengdi & Han, Dongying, 2021. "A novel stochastic resonance model based on bistable stochastic pooling network and its application," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. Robert L. Badzey & Pritiraj Mohanty, 2005. "Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance," Nature, Nature, vol. 437(7061), pages 995-998, October.
    6. Cheng, Chaojun & Zhou, Bingchang & Gao, Xiao & McDonnell, Mark D., 2017. "M-ary suprathreshold stochastic resonance in multilevel threshold systems with signal-dependent noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 48-56.
    7. Mikhaylov, A.N. & Guseinov, D.V. & Belov, A.I. & Korolev, D.S. & Shishmakova, V.A. & Koryazhkina, M.N. & Filatov, D.O. & Gorshkov, O.N. & Maldonado, D. & Alonso, F.J. & Roldán, J.B. & Krichigin, A.V. , 2021. "Stochastic resonance in a metal-oxide memristive device," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    8. M. Perc, 2009. "Stochastic resonance on paced genetic regulatory small-world networks: effects of asymmetric potentials," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 69(1), pages 147-153, May.
    9. Wang, Jiang & Guo, Xinmeng & Yu, Haitao & Liu, Chen & Deng, Bin & Wei, Xile & Chen, Yingyuan, 2014. "Stochastic resonance in small-world neuronal networks with hybrid electrical–chemical synapses," Chaos, Solitons & Fractals, Elsevier, vol. 60(C), pages 40-48.
    10. Xu, Liyan & Duan, Fabing & Abbott, Derek & McDonnell, Mark D., 2016. "Optimal weighted suprathreshold stochastic resonance with multigroup saturating sensors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 348-355.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Dongjian & Ma, Qihua & Dong, Hailiang & Liao, He & Liu, Xiangyu & Zha, Yibin & Zhang, Xiaoxiao & Qian, Xiaomin & Liu, Jin & Gan, Xuehui, 2023. "Time-delayed feedback bistable stochastic resonance system and its application in the estimation of the Polyester Filament Yarn tension in the spinning process," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Ren, Yuhao & Pan, Yan & Duan, Fabing, 2022. "SNR gain enhancement in a generalized matched filter using artificial optimal noise," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Jin, Yanfei & Wang, Haotian & Xu, Pengfei, 2023. "Noise-induced enhancement of stability and resonance in a tri-stable system with time-delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    4. Dai, Shiqi & Lu, Lulu & Wei, Zhouchao & Zhu, Yuan & Yi, Ming, 2022. "Influence of temperature and noise on the propagation of subthreshold signal in feedforward neural network," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    5. Mi, Li-Na & Guo, Yong-Feng & Zhang, Meng & Zhuo, Xiao-Jing, 2023. "Stochastic resonance in gene transcriptional regulatory system driven by Gaussian noise and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    6. Guo, Yongfeng & Ding, Jiaxin & Mi, Lina, 2024. "Statistical complexity and stochastic resonance of an underdamped bistable periodic potential system excited by Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    7. Qiao, Zijian & Shu, Xuedao, 2021. "Coupled neurons with multi-objective optimization benefit incipient fault identification of machinery," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    8. Liu, Jian & Qiao, Zijian & Ding, Xiaojian & Hu, Bing & Zang, Chuanlai, 2021. "Stochastic resonance induced weak signal enhancement over controllable potential-well asymmetry," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    9. Kim, Tae-Hyeon & Kim, Sungjoon & Hong, Kyungho & Park, Jinwoo & Hwang, Yeongjin & Park, Byung-Gook & Kim, Hyungjin, 2021. "Multilevel switching memristor by compliance current adjustment for off-chip training of neuromorphic system," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    10. Choi, Woo Sik & Jang, Jun Tae & Kim, Donguk & Yang, Tae Jun & Kim, Changwook & Kim, Hyungjin & Kim, Dae Hwan, 2022. "Influence of Al2O3 layer on InGaZnO memristor crossbar array for neuromorphic applications," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    11. Zhdanov, Vladimir P., 2012. "Periodic perturbation of genetic oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 45(5), pages 577-587.
    12. Erkaymaz, Okan & Ozer, Mahmut, 2016. "Impact of small-world network topology on the conventional artificial neural network for the diagnosis of diabetes," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 178-185.
    13. Zhang, Wenyue & Shi, Peiming & Li, Mengdi & Han, Dongying, 2021. "A novel stochastic resonance model based on bistable stochastic pooling network and its application," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    14. Filatov, D.O. & Koryazhkina, M.N. & Novikov, A.S. & Shishmakova, V.A. & Shenina, M.E. & Antonov, I.N. & Gorshkov, O.N. & Agudov, N.V. & Carollo, A. & Valenti, D. & Spagnolo, B., 2022. "Effect of internal noise on the relaxation time of an yttria stabilized zirconia-based memristor," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    15. Zhdanov, Vladimir P., 2011. "Periodic perturbation of the bistable kinetics of gene expression," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(1), pages 57-64.
    16. Ai, Hao & Yang, GuiJiang & Liu, Wei & Wang, Qiubao, 2023. "A fast search method for optimal parameters of stochastic resonance based on stochastic bifurcation and its application in fault diagnosis of rolling bearings," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    17. Yu, Haitao & Guo, Xinmeng & Wang, Jiang & Deng, Bin & Wei, Xile, 2015. "Spike coherence and synchronization on Newman–Watts small-world neuronal networks modulated by spike-timing-dependent plasticity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 307-317.
    18. Hu, Yahong & Zhu, Quanyong, 2017. "New analytic solutions of two-dimensional nonlocal nonlinear media," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 53-61.
    19. Valenti, D. & Tranchina, L. & Brai, M. & Caruso, A. & Cosentino, C. & Spagnolo, B., 2008. "Environmental metal pollution considered as noise: Effects on the spatial distribution of benthic foraminifera in two coastal marine areas of Sicily (Southern Italy)," Ecological Modelling, Elsevier, vol. 213(3), pages 449-462.
    20. Koryazhkina, M.N. & Filatov, D.O. & Shishmakova, V.A. & Shenina, M.E. & Belov, A.I. & Antonov, I.N. & Kotomina, V.E. & Mikhaylov, A.N. & Gorshkov, O.N. & Agudov, N.V. & Guarcello, C. & Carollo, A. & S, 2022. "Resistive state relaxation time in ZrO2(Y)-based memristive devices under the influence of external noise," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922010669. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.