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

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  • 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
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    1. 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.
    2. 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.
    3. 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.
    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. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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).
    Full references (including those not matched with items on IDEAS)

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