Estimation of Probability Density Function of Digital Substrate Noise in Mixed Signal System

  • Manisha Sharma
  • Pawan Kumar Singh
  • Tejbir Singh
  • Sanjay Sharma
Conference paper
Part of the Lecture Notes on Data Engineering and Communications Technologies book series (LNDECT, volume 18)


The substrate noise generated in the mixed signal-integrated circuits, which encapsulates the analog, the RF, and the memory parts, is assumed to possess the non-Gaussian cyclostationary nature. This noise creates interference among the various parts of mixed signal circuits and even within the memory circuits itself. To estimate the PDF parameters of non-Gaussian noise, which is modeled by Cauchy’s distribution function (kind of non-Gaussian), the non-Gaussian noise is modeled by the non-Gaussian mixture density. The PDF parameters are estimated using the maximum log likelihood function, and the priori and post priori updates are used for updating the PDF parameters. The substrate noise in a CMOS inverter and in a chain of five CMOS inverters is estimated first, and then this has been considered as an example of non-Gaussian cyclostationary noise for PDF estimation. The probability density function (PDF) of non-Gaussian cyclostationary noise is analytically estimated in this paper.


Substrate noise Probability density function Gaussian distribution Non-Gaussian distribution Cyclostationary process Cauchy’s distribution 


  1. 1.
    A. Mukherjee, A. Sengupta, Estimating the probability density function of a nonstationary non-Gaussian noise. IEEE Trans. Ind. Electron. 57(4), 1429–1435 (2010)CrossRefGoogle Scholar
  2. 2.
    R.A. Redner, H.F. Walker, Mixture densities maximum likelihood and the EM algorithms. SIAM Rev. 26(2), 195–239 (1984)MathSciNetCrossRefGoogle Scholar
  3. 3.
    N. Jung Hsu, F. Jay Breidt, Exact maximum likelihood estimation for non-Gaussian moving averages. Stat. Sin. 19, 545–560 (2009)MathSciNetzbMATHGoogle Scholar
  4. 4.
    W. Liu, P.P. Pokharel, J.C. Principe, Correntropy: Properties and applications in non-Gaussian signal processing. IEEE Trans. Signal Process. 55(11), 5286–5298 (2007)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Y. Zhao, X. Zhuang, S.J. Ting, Gaussian mixture density modeling of non-Gaussian source for autoregressive process. IEEE Trans. Signal Process. 43(4), 894–903 (1995)CrossRefGoogle Scholar
  6. 6.
    D. Sengupta, S.M. Kay, Efficient estimation of parameters non-Gaussian autoregressive processes. IEEE Trans. Acoust. Speech Signal Process 37(6), 785–794 (1989)CrossRefGoogle Scholar
  7. 7.
    F. Gini, A radar application of a modified Cram’er-Rao bound: Parameter estimation in non-Gaussian clutter. IEEE Trans. Signal Process 46(7), 1945–1953 (1998)CrossRefGoogle Scholar
  8. 8.
    H.S. Ahn, K.H. Ko, Simple pedestrian localization algorithms based on distributed wireless sensor network. IEEE Trans. Ind. Electron 56(10), 4296–4302 (2009)CrossRefGoogle Scholar
  9. 9.
    W.H. Zhu, T. Lamarche, Velocity estimation by using position and acceleration sensors. IEEE Trans. Ind. Electron 54(5), 2706–2715 (2007)CrossRefGoogle Scholar
  10. 10.
    W. Panusittikorn, M.C. Lee, P.I. Ro, Modeling and sliding mode control of friction-based object transport using two-mode ultrasonic excitation. IEEE Trans. Ind. Electron 51(4), 917–926 (2004)CrossRefGoogle Scholar
  11. 11.
    P.K. Singh, S. Sharma, Analysis of substrate coupling in design mixed signal VLSI circuit for 0.18 μm technology using resistive macromodel method. Appl. Math. Inf. Sci. Int. J 9(6), 3003–3008 (2015)Google Scholar
  12. 12.
    P.K. Singh, S. Sharma, Substrate coupling of RF CMOS on lightly doped substrate for nanoscale mixed-signal design. J. Comput. Theor. Nanosci. 11(4), 1184–1188 (Apr. 2014)CrossRefGoogle Scholar
  13. 13.
    P.K. Singh, S. Sharma, Analytical parametric modeling of nanoscale surrounding gate MOSFET based on the Poisson’s equation. J. Comput. Theor. Nanosci. 10, 557–560 (2013)CrossRefGoogle Scholar
  14. 14.
    P.K. Singh, S. Sharma, Substrate noise analysis of full adder circuit using nanometer Technology for High-Ohmic Substrate. J. Comput. Theor. Nanosci 9, 2245–2249 (2012)CrossRefGoogle Scholar
  15. 15.
    P.K. Singh, S. Sharma, Low power narrow band inductively source degenerated LNA in presence of substrate noise. Int. J. Appl. Sci. Eng. Technol., Maxwell Scientific Publisher 5(16), 4190–4194 (2013)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Manisha Sharma
    • 1
  • Pawan Kumar Singh
    • 1
  • Tejbir Singh
    • 1
  • Sanjay Sharma
    • 2
  1. 1.ECED, SRM University Delhi-NCRSonepatIndia
  2. 2.ECED, Thapar UniversityPatialaIndia

Personalised recommendations