# On Oversampling-Based Signal Detection

- 56 Downloads

## Abstract

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.

## Keywords

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

### Acknowledgements

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.

## References

- 1.National Spectrum Consortium. [Online]. Available: https://www.nationalspectrumconsortium.org.
- 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.S. Kandeepan and A. Giorgetti,
*Cognitive Radios and Enabling Techniques*, Artech House Publishers, Boston, 2012.Google Scholar - 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.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.E. Buracchini, The software radio concept,
*IEEE Communications Magazine*, Vol. 38, No. 9, pp. 138–143, 2000.Google Scholar - 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.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.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.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.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.Ettus Research. Universal Software Radio Peripheral. [Online]. Available: https://www.ettus.com/product.
- 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.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.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.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.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.J. G. Proakis,
*Digital Communications*, vol. 4th, McGraw-Hill, New York, 2001.zbMATHGoogle Scholar - 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.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.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.R. N. McDonough and A. Whalen,
*Detection of Signals in Noise*, Academic Press, Boca Raton, 1995.Google Scholar - 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.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.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.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.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.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.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.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.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.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.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.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.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.J. G. Proakis and D. G. Manolakis,
*Digital Signal Processing: Principles, Algotithms, and Applications*, vol. 3rd, Prentice Hall, New Jersey, 1996.Google Scholar - 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.S. John, Some optimal multivariate tests,
*Biometrika*, Vol. 58, No. 1, pp. 123–127, 1971.MathSciNetzbMATHGoogle Scholar - 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.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.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.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.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.NooElec Inc. NESDR Mini SDR and DVB-T USB Stick (RTL2832U + R820T). [Online]. Available: http://www.nooelec.com/store/sdr/sdr-receivers/nesdr-mini-rtl2832-r820t.html.
- 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.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.Realtek, Taiwan. (2012, Dec.) Realtek rtl2832u. [Online]. Available: http://www.realtek.com.tw/products/.
- 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.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.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. https://doi.org/10.1155/2015/464982.CrossRefGoogle Scholar - 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.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.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.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.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.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.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