Impact of Nonlinear Transformation on Signal Detection: A Minimum Error Probability Perspective

  • Feng ShenEmail author
  • Lizhen Chen
  • Guoru Ding
  • Qihui Wu
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 463)


This paper investigates the impact of nonlinear transformation on signal detection from a minimum error probability perspective. Firstly, we derive the probability density distributions of three transformed received signal over binary input additive white Gaussian noise (BIAWGN) channel, including square transformation, abs (absolute value) transformation and changing the sampling times. Then, we derive the three optimal decision thresholds respectively for the three transformations under the criteria of minimum error probability. Furthermore, we make simulations to compare the minimum error probability of the three transformed ones with the original signal, trying to find the nonlinear transformation with smaller minimum error probability.


Signal detection Nonlinear transformation Error probability 



This work is supported by the National Natural Science Foundation of China under Grants 61631020 and 61501510, and Natural Science Foundation of Jiangsu Province under Grant BK20150717.


  1. 1.
  2. 2.
    Cover, T., Thomas, J.: Elements of Information Theory. Wiley-Interscience, Hoboken (2006)Google Scholar
  3. 3.
    Ding, G., Wu, Q., Yao, Y.D., Wang, J., Chen, Y.: Kernel-based learning for statistical signal processing in cognitive radio networks: theoretical foundations, example applications, and future directions. IEEE Sig. Process. Mag. 30(4), 126–136 (2013)Google Scholar
  4. 4.
    Fan, C.: The Principle of Communications. National Defence of Industry Press, Beijing (2001)Google Scholar
  5. 5.
    Kay, S.M.: Fundamentals of Statistical Signal Processing: Practical Algorithm Development, vol. 3. Pearson Education, Upper Saddle River (2013)Google Scholar
  6. 6.
    Poor, H.V.: An Introduction to Signal Detection and Estimation. Springer, New York (2013)Google Scholar
  7. 7.
    Urkowitz, H.: Energy detection of unknown deterministic signals. Proc. IEEE 55(4), 523–531 (1967)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Nanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.PLA University of Science and TechnologyNanjingChina

Personalised recommendations