Circuits, Systems, and Signal Processing

, Volume 35, Issue 4, pp 1355–1375 | Cite as

Distinguishing CPFSK from QAM and PSK Modulations

  • Mohammad BariEmail author
  • Miloš Doroslovački


Digital modulation classification is important for many civilian as well as military applications. In this paper, we propose a simple and robust feature to distinguish continuous-phase FSK from QAM and PSK modulations. The feature is based on product of two consecutive signal values and on time averaging of imaginary part of the product. Conditional probability density functions of the feature given modulation type are determined. In order to overcome the complexity of calculating probability density functions, central limit theorem for strictly stationary m-dependent sequences is used to obtain Gaussian approximations. After calculating probability density functions, thresholds are determined based on minimization of total probability of misclassification. Since threshold-based results are valid for special cases requiring knowledge of some parameters, we resort to usage of support vector machines for classification, which require little training and no a priori information except for carrier frequency. Following that joint effects on the performance of carrier offset, fast fading, and non-synchronized sampling are studied in the presence of additive white Gaussian noise. For comparison purposes, rectangular pulse shape is used. To prove practical usefulness, not only the performance is analyzed for root-raised cosine pulses but also for quite less oversampling of symbols than what is found in other approaches. In the course of doing that, the performance is compared with wavelet-based feature that uses support vector machines for modulation separation.


Digital modulation classification Signal separation Root-raised-cosine pulses Wavelet Gaussian approximation Support vector machines 


  1. 1.
    M. Aslam, Z. Zhu, A. Nandi, Automatic modulation classification using combination of genetic programming and KNN. IEEE Trans. Wirel. Commun. 11(8), 2742–2750 (2012)Google Scholar
  2. 2.
    M. Bari, M. Doroslovački, Quickness of the instantaneous frequency based classifier distinguishing BFSK from QAM and PSK modulations. in Proceedings of 47th Annual Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA, 2013, pp. 836–840Google Scholar
  3. 3.
    M. Bari, H. Mustafa, M. Doroslovački, Performance of the instantaneous frequency based classifier distinguishing BFSK from QAM and PSK modulations for asynchronous sampling and slow and fast fading. in Proceedings of 47th Conference on Information Sciences and Systems (Johns Hopkins University, Baltimore, MD, 2013)Google Scholar
  4. 4.
    P. Brockwell, R. Davis, Time Series: Theory and Methods (Springer, New York, 1987)CrossRefzbMATHGoogle Scholar
  5. 5.
    C. Burges, A tutorial on support vector machines for pattern recognition. Data Min. Knowl. Discov. 2, 121–167 (1998)CrossRefGoogle Scholar
  6. 6.
    W. Cheney, D. Kincaid, Numerical Mathematics and Computing (Brooks/Cole, Pacific Grove, 1994)zbMATHGoogle Scholar
  7. 7.
    H. Deng, M. Doroslovački, H. Mustafa, X. Jinghao, K. Sunggy, Instantaneous feature based algorithm for HF digital modulation classification. in Proceedings of Conference on Information Sciences and Systems (Princeton University, NJ, 2003)Google Scholar
  8. 8.
    O. Dobre, A. Abdi, Y. Bar-Ness, W. Su, Survey of automatic modulation classification techniques: classical approaches and new trends. IET Commun. 1(2), 137–156 (2007)CrossRefGoogle Scholar
  9. 9.
    G. Feyh, M. Kuckenwaitz, J. Reichert, HF-signal surveillance: signal detection, classification and parameter estimation. in Proceedings of MILCOM, 1994, pp. 755–759Google Scholar
  10. 10.
    S. Haykin, Communication Systems (Wiley, New York, 1994)Google Scholar
  11. 11.
    K.C. Ho, W. Prokopiw, Y.T. Chan, Modulation identification of digital signals by the wavelet transform. IEE Proc. Radar Sonar Navig. 147(4), 169–176 (2000)CrossRefGoogle Scholar
  12. 12.
    S. Kay, A fast and accurate single frequency estimator. IEEE Trans. Acoust. Speech Signal Process. 37(12), 1987–1990 (1989)CrossRefGoogle Scholar
  13. 13.
    A. Leaon-Garcia, Probability and Random Processes for Electrical Engineering, 2nd edn. (Addison Wesley, Reading, 1994)Google Scholar
  14. 14.
    H. Li, O.A. Dobre, Y. Bar-Ness, W. Su, Nonlinear carrier frequency offsets estimation using antenna arrays. in Proceedings of IEEE MILCOM, vol. 1, Atlantic City, NJ, 2005, pp. 570–575Google Scholar
  15. 15.
    B.G. Mobasseri, Constellation shape as a robust signature for digital modulation recognition. in Proceedings of MILCOM, vol. 1, 1999, pp. 442–446Google Scholar
  16. 16.
    H. Mustafa, M. Doroslovački, Effects of symbol rate on the classification of digital modulation signals. in Proceedings of ICASSP, vol. 5, Philadelphia, 2005, pp. 437–440Google Scholar
  17. 17.
    H. Mustafa, M. Doroslovački, Expansion of maximum likelihood modulation classifier to nonlinear modulations. in Proceedings of Conference on Information Sciences and Systems (Johns Hopkins University, NJ, 2005)Google Scholar
  18. 18.
    H. Mustafa, M. Doroslovački, Effects of carrier offset on the classification of binary frequency shift keying based on the product of two consecutive signal values. in Proceedings of Conference on Information Sciences and Systems (The Princeton University, 2006)Google Scholar
  19. 19.
    C.L. Nikias, A.P. Petropulu, Higher-Order Spectra Analysis: A Nonlinear Signal Processing Framework (Prentice Hall, Upper Saddle River, 1993)zbMATHGoogle Scholar
  20. 20.
    P. Panagiotou, A. Anastasopoulos, A. Polydoros, Likelihood ratio tests for modulation classification. in Proceedings of MILCOM, vol. 2, Monterey, CA, 2000, pp. 670–674Google Scholar
  21. 21.
    A. Papoulis, S.U. Pillai, Probability, Random Variables and Stochastic Processes, 4th edn. (McGraw-Hill, New York, 2002)Google Scholar
  22. 22.
    S.U. Pawar, J.F. Doherty, Modulation recognition in continuous phase modulation using approximate entropy. IEEE Trans. Inf. Forensics Secur. 6(3), 843–852 (2011)CrossRefGoogle Scholar
  23. 23.
    Q. Shi, Y. Karasawa, Automatic modulation identification based on the probability density function of signal phase. IEEE Trans. Commun. 60(4), 1033–1044 (2012)CrossRefGoogle Scholar
  24. 24.
    A. Swami, B. Sadler, Modulation classification via hierarchical agglomerative cluster analysis. in Proceedings of Signal Processing Advances in Wireless Communications, 1997, pp. 141–144Google Scholar
  25. 25.
    A. Swami, B.M. Sadler, Hierarchical digital modulation classification using cumulants. IEEE Trans. Commun. 3, 416–429 (2000)CrossRefGoogle Scholar
  26. 26.
    H. Wang, O. Dobre, C. Li, R. Inkol, Joint classification and parameter estimation of M-FSK signals for cognitive radio. in Proceedings of IEEE ICC, Ottawa, Canada, 2012, pp. 1732–1736Google Scholar
  27. 27.
    W. Wei, J.M. Mendel, Maximum-likelihood classification for digital amplitude-phase modulations. IEEE Trans. Commun. 48(2), 189–193 (2000)CrossRefGoogle Scholar
  28. 28.
    J. Xu, W. Su, M. Zhou, Likelihood-ratio approaches to automatic modulation classification. IEEE Trans. Syst. Man Cybern. 41(2), 455–469 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.The George Washington UniversityWashingtonUSA
  2. 2.The George Washington UniversityWashingtonUSA

Personalised recommendations