On Oversampling-Based Signal Detection

A Pragmatic Approach
  • Andrea Mariani
  • Andrea GiorgettiEmail author
  • Marco Chiani


The availability of inexpensive devices allows nowadays to implement cognitive radio functionalities in large-scale networks such as the internet-of-things and future mobile cellular systems. In this paper, we focus on wideband spectrum sensing in the presence of oversampling, i.e., the sampling frequency of a digital receiver is larger than the signal bandwidth, where signal detection must take into account the front-end impairments of low-cost devices. Based on the noise model of a software-defined radio dongle, we address the problem of robust signal detection in the presence of noise power uncertainty and non-flat noise power spectral density (PSD). In particular, we analyze the receiver operating characteristic of several detectors in the presence of such front-end impairments, to assess the performance attainable in a real-world scenario. We propose new frequency-domain detectors, some of which are proven to outperform previously proposed spectrum sensing techniques such as, e.g., eigenvalue-based tests. The study shows that the best performance is provided by a noise-uncertainty immune energy detector (ED) and, for the colored noise case, by tests that match the PSD of the receiver noise.


Cognitive radio Colored noise Detection Internet-of-Things Noise uncertainty Oversampling Wideband spectrum sensing 



This work was supported in part by MIUR under the program “Dipartimenti di Eccellenza (2018–2022)—Precise-CPS,” and in part by the EU project eCircular (EIT Climate-KIC). The material in this paper was presented in part at the IEEE Int. Symp. on Personal, Indoor and Mobile Radio Comm. (PIMRC 2018), Bologna, Italy, Sep. 2018.


  1. 1.
    National Spectrum Consortium. [Online]. Available:
  2. 2.
    M. Chiani, A. Giorgetti, and E. Paolini, Sensor radar for object tracking, Proceedings of the IEEE, Vol. 106, No. 6, pp. 1022–1041, 2018.Google Scholar
  3. 3.
    S. Kandeepan and A. Giorgetti, Cognitive Radios and Enabling Techniques, Artech House Publishers, Boston, 2012.Google Scholar
  4. 4.
    A. Sharma, A. Mariani, A. Giorgetti, D. Mitra, and M. Chiani. Subspace-based spectrum guarding. In Proceedings of the IEEE International Conference on Communication Workshop (ICC 2015). London, UK (2015).Google Scholar
  5. 5.
    J. Mitola, Software radios: survey, critical evaluation and future directions, IEEE Aerospace and Electronic Systems Magazine, Vol. 8, No. 4, pp. 25–36, 1993.Google Scholar
  6. 6.
    E. Buracchini, The software radio concept, IEEE Communications Magazine, Vol. 38, No. 9, pp. 138–143, 2000.Google Scholar
  7. 7.
    F. K. Jondral, Software-defined radio: basics and evolution to cognitive radio, EURASIP Journal on Wireless Communications and Networking, Vol. 2005, No. 3, pp. 275–283, 2005.zbMATHGoogle Scholar
  8. 8.
    A. M. Wyglinski, D. P. Orofino, M. N. Ettus and T. W. Rondeau, Revolutionizing software defined radio: case studies in hardware, software, and education, IEEE Communications Magazine, Vol. 54, No. 1, pp. 68–75, 2016.Google Scholar
  9. 9.
    R. Bagheri, A. Mirzaei, M. E. Heidari, S. Chehrazi, M. Lee, M. Mikhemar, W. K. Tang and A. A. Abidi, Software-defined radio receiver: dream to reality, IEEE Communications Magazine, Vol. 44, No. 8, pp. 111–118, 2006.Google Scholar
  10. 10.
    A. A. Abidi, The path to the software-defined radio receiver, IEEE Journal of Solid-State Circuits, Vol. 42, No. 5, pp. 954–966, 2007.Google Scholar
  11. 11.
    R. W. Stewart, K. W. Barlee, D. S. W. Atkinson and L. H. Crockett, Software Defined Radio using MATLAB & Simulink and the RTL-SDR, vol. 1st, Wiley, Glasgow, 2015.Google Scholar
  12. 12.
    Ettus Research. Universal Software Radio Peripheral. [Online]. Available:
  13. 13.
    A. Mariani, S. Kandeepan and A. Giorgetti, Periodic spectrum sensing with non-continuous primary user transmissions, IEEE Transactions on Wireless Communications, Vol. 14, No. 3, pp. 1636–1649, 2015.Google Scholar
  14. 14.
    A. Mariani, A. Giorgetti and M. Chiani, Wideband spectrum sensing by model order selection, IEEE Transactions on Wireless Communications, Vol. 14, No. 12, pp. 6710–6721, 2015.Google Scholar
  15. 15.
    E. H. Gismalla and E. Alsusa, On the performance of energy detection using bartlett’s estimate for spectrum sensing in cognitive radio systems, IEEE Transactions on Signal Processing, Vol. 60, No. 7, pp. 3394–3404, 2012.MathSciNetzbMATHGoogle Scholar
  16. 16.
    J. Verlant-Chenet, J. Renard, J. M. Dricot, P. D. Doncker, and F. Horlin. Sensitivity of spectrum sensing techniques to RF impairments. In 2010 IEEE 71st Vehicular Technology Conference, pp. 1–5 (2010).Google Scholar
  17. 17.
    A. Zahedi-Ghasabeh, A. Tarighat, and B. Daneshrad. Cyclo-stationary sensing of OFDM waveforms in the presence of receiver RF impairments. In IEEE Wireless Communication and Networking Conference, pp. 1–6 (2010).Google Scholar
  18. 18.
    J. G. Proakis, Digital Communications, vol. 4th, McGraw-Hill, New York, 2001.zbMATHGoogle Scholar
  19. 19.
    A. Mariani, A. Giorgetti and M. Chiani, Effects of noise power estimation on energy detection for cognitive radio applications, IEEE Transactions on Communications, Vol. 59, No. 12, pp. 3410–3420, 2011.Google Scholar
  20. 20.
    L. Wei, O. Tirkkonen and Y.-C. Liang, Multi-source signal detection with arbitrary noise covariance, IEEE Transactions on Signal Processing, Vol. 62, No. 22, pp. 5907–5918, 2014.MathSciNetzbMATHGoogle Scholar
  21. 21.
    Y. Zeng and Y.-C. Liang, Eigenvalue-based spectrum sensing algorithms for cognitive radio, IEEE Transactions on Communications, Vol. 57, No. 6, pp. 1784–1793, 2009.Google Scholar
  22. 22.
    R. N. McDonough and A. Whalen, Detection of Signals in Noise, Academic Press, Boca Raton, 1995.Google Scholar
  23. 23.
    S. K. Sharma, S. Chatzinotas and B. Ottersten, Eigenvalue-based sensing and SNR estimation for cognitive radio in presence of noise correlation, IEEE Transactions on Vehicular Technology, Vol. 62, No. 8, pp. 3671–3684, 2013.Google Scholar
  24. 24.
    A. Sonnenschein and P. M. Fishman, Radiometric detection of spread-spectrum signals in noise of uncertain power, IEEE Transactions on Aerospace and Electronic Systems, Vol. 28, No. 3, pp. 654–660, 1992.Google Scholar
  25. 25.
    D. Torrieri. The radiometer and its practical implementation. In Proceedings of the IEEE Military Communications Conference (MILCOM 2010), pp. 304–310 (2010).Google Scholar
  26. 26.
    A. Mariani, A. Giorgetti, and M. Chiani, Test of independence for cooperative spectrum sensing with uncalibrated receivers. In Proceedings of the IEEE Global Communications Conference (GLOBECOM). Anaheim, CA, USA, 2012, pp. 1–6.Google Scholar
  27. 27.
    A. Mariani, A. Giorgetti and M. Chiani, Recent advances on wideband spectrum sensing for cognitive radio. In M. G. Di Benedetto and F. Bader, editors. Cognitive Communications and Cooperative HetNet Coexistence, Signals and Communication Technology, ch. 1, Springer Int Pub, Cham, 2014.Google Scholar
  28. 28.
    F. Penna, R. Garello, et al., Cooperative spectrum sensing based on the limiting eigenvalue ratio distribution in wishart matrices, IEEE Communications Letters, Vol. 13, No. 7, pp. 507–509, 2009.Google Scholar
  29. 29.
    A. Mariani, A. Giorgetti, and M. Chiani. Designing ITC selection algorithms for wireless sources enumeration. In IEEE International Conference on Communications (ICC 2015), pp. 4883–4888. London, UK (2015).Google Scholar
  30. 30.
    A. H. Gray Jr., and J. D. Markel, A spectral-flatness measure for studying the autocorrelation method of linear prediction of speech analysis, IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 22, No. 3, pp. 207–217, 1974.Google Scholar
  31. 31.
    A. Mariani, A. Giorgetti and M. Chiani, Model order selection based on information theoretic criteria: design of the penalty, IEEE Transactions on Signal Processing, Vol. 63, No. 11, pp. 2779–2789, 2015.MathSciNetzbMATHGoogle Scholar
  32. 32.
    H. Cao, and J. Peissig. Practical spectrum sensing with frequency-domain processing in cognitive radio. In Proceedings of the 20th European Signal Processing Conference (EUSIPCO 2012), pp. 435–439. Bucharest, Romania (2012).Google Scholar
  33. 33.
    G. B. Giannakis and C. Tepedelenlioglu, Basis expansion models and diversity techniques for blind identification and equalization of time-varying channels, Proceedings of the IEEE, Vol. 86, No. 10, pp. 1969–1986, 1998.Google Scholar
  34. 34.
    W. Han, C. Huang, J. Li, Z. Li and S. Cui, Correlation based spectrum sensing with over-sampling in cognitive radio, IEEE Journal on Selected Areas in Communications, Vol. 33, No. 5, pp. 788–802, 2015.Google Scholar
  35. 35.
    J. Lundén, S. A. Kassam and V. Koivunen, Robust nonparametric cyclic correlation-based spectrum sensing for cognitive radio, IEEE Transactions on Signal Processing, Vol. 58, No. 1, pp. 38–52, 2010.MathSciNetzbMATHGoogle Scholar
  36. 36.
    J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Algotithms, and Applications, vol. 3rd, Prentice Hall, New Jersey, 1996.Google Scholar
  37. 37.
    J. Mauchly, Significance test for sphericity of a normal n-variate distribution, The Annals of Mathematical Statistics, Vol. 11, No. 2, pp. 204–209, 1940.MathSciNetzbMATHGoogle Scholar
  38. 38.
    S. John, Some optimal multivariate tests, Biometrika, Vol. 58, No. 1, pp. 123–127, 1971.MathSciNetzbMATHGoogle Scholar
  39. 39.
    A. Leshem and A.-J. van der Veen, Multichannel detection of Gaussian signals with uncalibrated receivers, IEEE Signal Processing Letters, Vol. 8, No. 4, pp. 120–122, 2001.Google Scholar
  40. 40.
    Y. Zeng and Y.-C. Liang, Spectrum-sensing algorithms for cognitive radio based on statistical covariances, IEEE Transactions on Vehicular Technology, Vol. 58, No. 4, pp. 1804–1815, 2009.Google Scholar
  41. 41.
    M. Naraghi-Pour and T. Ikuma, Autocorrelation-based spectrum sensing for cognitive radios, IEEE Transactions on Vehicular Technology, Vol. 59, No. 2, pp. 718–733, 2010.Google Scholar
  42. 42.
    M. Jin, Y. Li and H.-G. Ryu, On the performance of covariance based spectrum sensing for cognitive radio, IEEE Transactions on Signal Processing, Vol. 60, No. 7, pp. 3670–3682, 2012.MathSciNetzbMATHGoogle Scholar
  43. 43.
    H. So, W. Ma and Y. Chan, Detection of random signals via spectrum matching, IEEE Transactions on Aerospace and Electronic Systems, Vol. 38, No. 1, pp. 301–307, 2002.Google Scholar
  44. 44.
    NooElec Inc. NESDR Mini SDR and DVB-T USB Stick (RTL2832U + R820T). [Online]. Available:
  45. 45.
    T. Hentschel, M. Henker and G. Fettweis, The digital front-end of software radio terminals, IEEE Personal Communications, Vol. 6, No. 4, pp. 40–46, 1999.Google Scholar
  46. 46.
    G. Sklivanitis, A. Gannon, S. N. Batalama and D. A. Pados, Addressing next-generation wireless challenges with commercial software-defined radio platforms, IEEE Communications Magazine, Vol. 54, No. 1, pp. 59–67, 2016.Google Scholar
  47. 47.
    Realtek, Taiwan. (2012, Dec.) Realtek rtl2832u. [Online]. Available:
  48. 48.
    O. Guillán-Lorenzo, and F. J. Díaz-Otero. Diseño de un receptor basado en rtl2832u para la medida del contenido electrónico de la ionosfera. In Proceedings of the XXVIII Simposium nacional del la unión científica internacional de radio (URSI 2013), Santiago de Compostela, Spain (2013).Google Scholar
  49. 49.
    R. K. Kodali, L. Boppana, and S. R. Kondapalli. DDC and DUC Filters in SDR platforms. In Proceedings of the IEEE International Conference on Advanced Computing Technologies (ICACT 2013), New Boyanapalli, Rajampet, India (2013).Google Scholar
  50. 50.
    D. Borio, E. Angiuli, R. Giuliani and G. Baldini, Robust spectrum sensing demonstration using a low-cost front-end receiver, International Journal of Antennas and Propagation, 2015. Scholar
  51. 51.
    B. Yazici and S. Yolacan, A comparison of various tests of normality, Journal of Statistical Computation and Simulation, Vol. 77, No. 2, pp. 175–183, 2007.MathSciNetzbMATHGoogle Scholar
  52. 52.
    M. A. Stephens, EDF statistics for goodness of fit and some comparisons, Journal of the American Statistical Association, Vol. 69, No. 347, pp. 730–737, 1974.Google Scholar
  53. 53.
    N. M. Razali and Y. B. Wah, Power comparisons of Shapiro–Wilk, Kolmogorov–Smirnov, Lilliefors and Anderson–Darling tests, Journal of Statistical Modeling and Analytics, Vol. 2, No. 1, pp. 21–33, 2011.Google Scholar
  54. 54.
    N. Henze and B. Zirkler, A class of invariant consistent tests for multivariate normality, Communications in Statistics-Theory and Methods, Vol. 19, No. 10, pp. 3595–3617, 1990.MathSciNetzbMATHGoogle Scholar
  55. 55.
    C. J. Mecklin and D. J. Mundfrom, On using asymptotic critical values in testing for multivariate normality, InterStat, Vol. 1, No. 1–12, p. 152, 2003.Google Scholar
  56. 56.
    S. A. Andersson and M. D. Perlman, Two testing problems relating the real and complex multivariate normal distributions, Journal of Multivariate Analysis, Vol. 15, No. 1, pp. 21–51, 1984.MathSciNetzbMATHGoogle Scholar
  57. 57.
    T. Adali, P. J. Schreier and L. L. Scharf, Complex-valued signal processing: the proper way to deal with impropriety, IEEE Transactions on Signal Processing, Vol. 59, No. 11, pp. 5101–5125, 2011.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Onit Group S.r.l.CesenaItaly
  2. 2.CNIT, IEIIT/CNR, Dept. of Electrical, Electronic, and Information Engineering “Guglielmo Marconi” (DEI)University of BolognaCesenaItaly

Personalised recommendations