Bhattacharyya distance criterion based multibit quantizer design for cooperative spectrum sensing in cognitive radio networks

  • Yuanhua FuEmail author
  • Zhiming He


Cooperative spectrum sensing (CSS) is crucial for dynamic spectrum access in cognitive radio networks. This paper considers a CSS scheme by using a multilevel quantizer in each sensing node (SN) to quantize the local energy detector’s observation. A log-likelihood ratio test detector by using quantized data received from each SN is proposed to determine the presence or absence of the primary user signal. The Bhattacharyya distance (BD) of the cooperative sensing system is derived. Then, a quantizer design scheme by maximizing the BD that as the criterion function in an optimization problem with respect to the quantization thresholds is proposed. As nonlinear and high-dimensional of the objective function, a particle swarm optimization algorithm is employed to solve operating parameters for the quantizer. Furthermore, we derive the upper bound performance on cooperative energy detection (CED) in CSS. To validate the effectiveness of the proposed approach, The quantizer is compared with other schemes in terms of detection performance. Simulation results show that 2- or 3-bit quantization of the proposed approach achieves comparable performance to upper bound of CED without quantization.


Multibit quantization Bhattacharyya distance Particle swarm optimization algorithm Cooperative spectrum sensing 



This work was supported by the Sichuan Province Science and Technology Program Research Project (No. 2019YJ0174). The authors would like to thank anonymous reviewers and editors for their constructive comments.


  1. 1.
    Axell, E., Leus, G., Larsson, E. G., & Poor, H. V. (2012). Spectrum sensing for cognitive radio: State-of-the-art and recent advances. IEEE Signal Process. Magazine, 29(3), 101–116.CrossRefGoogle Scholar
  2. 2.
    Liu, X., Jia, M., Na, Z., et al. (2018). Multi-modal cooperative spectrum sensing based on Dempster–Shafer fusion in 5G-based cognitive radio. IEEE Access, 6(99), 199–208.CrossRefGoogle Scholar
  3. 3.
    Akylidiz, I., Lo, B., & Balakrishan, R. (2011). Cooperative spectrum sensing in cognitive radio networks: A survey. Physical Communication, 4(1), 40–62.CrossRefGoogle Scholar
  4. 4.
    Sriharipriya, K. C., & Baskaran, K. (2018). Optimal number of cooperators in the cooperative spectrum sensing schemes. Circuits Systems & Signal Processing, 37(5), 1988–2000.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Zhu, S., Akofor, E., & Chen, B. (2013). Interactive distributed detection with conditionally independent observations. In Proceedings of IEEE wireless communications and networking conference (pp. 2531–2535). Shanghai.Google Scholar
  6. 6.
    Yang, X., Niu, R., Masazade, E., & Varshney, P. (2013). Channel-aware tracking in multi-hop wireless sensor networks with quantized measurements. IEEE Transactions on Aerospace and Electronic Systems, 49(4), 2353–2368.CrossRefGoogle Scholar
  7. 7.
    Gohain, P., & Chaudhari, S. (2017). Cooperative energy detection using Dempster–Shafer theory under noise uncertainties. In Proceedings of IEEE COMSNET (pp. 360–366). Bangalore.Google Scholar
  8. 8.
    Thanh, N., & Koo, I. (2009). An enhanced cooperative spectrum sensing scheme based on evidence theory and reliability source evaluation in cognitive radio context. IEEE Communications Letters, 13(7), 492–494.CrossRefGoogle Scholar
  9. 9.
    Boulogeorgos, A. A., Chatzidiamantis, N. D., & Karagiannidis, G. K. (2016). Spectrum sensing with multiple primary users over fading channels. IEEE Communications Letters, 20(7), 1457–1460.Google Scholar
  10. 10.
    Boulogeorgos, A. A., Salameh, H. A. B., & Karagiannidis, G. K. (2017). Spectrum sensing in full-duplex cognitive radio networks under hardware imperfections. IEEE Transactions on Vehicular Technology, 66(3), 2072–2084.CrossRefGoogle Scholar
  11. 11.
    Boulogeorgos, A. A. A., & Karagiannidis, G. K. (2018). Energy detection in full-duplex systems with residual RF impairments over fading channels. IEEE Wireless Communications Letters, 7(2), 246–249.CrossRefGoogle Scholar
  12. 12.
    Cacciapuoti, A., Caleffi, M., Izzo, D., & Paura, L. (2011). Cooperative spectrum sensing techniques with temporal dispersive reporting channels. IEEE Transactions on Wireless Communications, 10(10), 3392–3402.CrossRefGoogle Scholar
  13. 13.
    Cacciapuoti, A. S., Caleffi, M., & Paura, L. (2010). Widely linear cooperative spectrum sensing for cognitive radio networks. In IEEE global telecommunications conference (pp. 1–5). Florida.Google Scholar
  14. 14.
    Xin, L., Min, J., Xueyan, Z., & et al (2018). A novel multi-channel internet of things based on dynamic spectrum sharing in 5G communication. IEEE Internet of Things Journal, 14(8), 1–9.Google Scholar
  15. 15.
    Liu, X., Li, F., & Na, Z. (2017). Optimal resource allocation in simultaneous cooperative spectrum sensing and energy harvesting for multichannel cognitive radio. IEEE Access, 5, 3801–3812.CrossRefGoogle Scholar
  16. 16.
    Liu, X., Zhang, X., Jia, M., et al. (2018). 5G-based green broadband communication system design with simultaneous wireless information and power transfer. Physical Communication, 28, 130–137.CrossRefGoogle Scholar
  17. 17.
    Cacciapuoti, S. A., Caleffi, M., et al. (2013). Decision maker approaches for cooperative spectrum sensing: participate; or not participate in sensing? IEEE Transactions on Wireless Communications, 12(5), 2445–2457.CrossRefGoogle Scholar
  18. 18.
    Cacciapuoti, A. S., Akyildiz, I. F., & Paura, L. (2012). Correlation-aware user selection for cooperative spectrum sensing in cognitive radio ad hoc networks. IEEE Journal on Selected Areas in Communications, 30(2), 297–306.CrossRefGoogle Scholar
  19. 19.
    Liang, Y.-C., Zeng, Y., Peh, E. C., & Hoang, A. T. (2008). Sensing throughput tradeoff in cognitive radio networks. IEEE Transactions on Wireless Communications, 7(4), 1326–1337.CrossRefGoogle Scholar
  20. 20.
    Nguyen-Thanh, N., & Koo, I. (2011). Evidence-theory-based cooperative spectrum sensing with efficient quantization method in cognitive radio. IEEE Transactions on Vehicular Technology, 60(1), 185–195.CrossRefGoogle Scholar
  21. 21.
    Oh, D., Lee, H., & Lee, H. Y. (2010). Linear hard decision combining for cooperative spectrum sensing in cognitive radio systems. In Proceedings of 71nd IEEE vehicular technology conference (pp. 1–5). Taipei.Google Scholar
  22. 22.
    Althunibat, S., Palacios, R., & Granelli, F. (2012). Performance optimisation of soft and hard spectrum sensing schemes in cognitive radio. IEEE Communications Letters, 16(7), 998–1001.CrossRefGoogle Scholar
  23. 23.
    Althunibat, S., & Granelli, F. (2014). Energy efficiency analysis of soft and hard cooperative spectrum sensing schemes in cognitive radio networks. In Proceedings of 79th IEEE vehicular technology conference (pp. 18–21). Seoul.Google Scholar
  24. 24.
    Ma, J., Zhao, G., & Li, Y. G. (2008). Soft combination and detection for cooperative spectrum sensing in cognitive radio networks. IEEE Transactions on Wireless Communications, 7(11), 4502–4507.CrossRefGoogle Scholar
  25. 25.
    Nguyen-Thanh, N., Ciblat, P., Maleki, S., & Nguyen, V.-T. (2015). How many bits should be reported in quantized cooperative spectrum sensing? IEEE Wireless Communications Letters, 4(5), 465–468.CrossRefGoogle Scholar
  26. 26.
    Verma, P., & Singh, B. (2017). On the decision fusion for cooperative spectrum sensing in cognitive radio networks. Wireless Networks, 23(7), 2253–2262.CrossRefGoogle Scholar
  27. 27.
    Nhan, N.-T., & Insoo, K. (2011). Log-likelihood ratio optimal quantizer for cooperative spectrum sensing in cognitive radio. IEEE Communications Letters, 15(3), 317–319.CrossRefGoogle Scholar
  28. 28.
    Tarighati, A., & Jalden, J. (2016). Optimality of rate balancing in wireless sensor networks. IEEE Transactions on Signal Processing, 64(14), 3735–3794.MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Mhanna, M., Duhamel, P., & Piantanida, P. (2016). Quantization for distributed binary detection under secrecy constraints. In Proceedings of IEEE international conference on communications (pp. 1–6). Kuala Lumpur.Google Scholar
  30. 30.
    Tarighati, A., Gross, J., & Jalden, J. (2017). Decentralized hypothesis testing in energy harvesting wireless sensor networks. IEEE Transactions on Signal Processing, 65(18), 4862–4873.MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Shin, I., Lee, W., Kang, J., Kang, J., & Al-Araji, S. (2015). Quantization bit allocation for reporting-throughput tradeoff in cooperative cognitive radio networks. In Proceedings of IEEE MILCOM (pp. 233–237). Tampa.Google Scholar
  32. 32.
    Bastami, B. A., & Saberinia, E. (2013). A practical multibit data combining strategy for cooperative spectrum sensing. IEEE Transactions on Vehicular Technology, 62(1), 384–389.CrossRefGoogle Scholar
  33. 33.
    Ejaz, W., Hattab, G., Attia, T., Ibnkahla, M., Abdelkefi, F., & Siala, M. (2016). Joint quantization and confidence-based generalized combining scheme for cooperative spectrum sensing. IEEE Systems Journal, 12(2), 1–12.Google Scholar
  34. 34.
    Berisha, V., Wisler, A., Hero, A. O., & Spanias, A. (2016). Empirically estimable classification bounds based on a nonparametric divergence measure. IEEE Transactions on Signal Processing, 64(3), 580–591.MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Kailath, T. (1967). The divergence and Bhattacharyya distance measures in signal selection. IEEE Trans. Commun. Technol., 15(1), 52–60.CrossRefGoogle Scholar
  36. 36.
    Chernoff, H. (1952). A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. The Annals of Mathematical Statistics, 23(4), 493–507.MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Cover, T. M., & Thomas, J. A. (2012). Elements of information theory. Hoboken: Wiley.zbMATHGoogle Scholar
  38. 38.
    Hero, A. O., Ma, B., Michel, O., & Gorman, J. (2001). Alpha-divergence for classification, indexing and retrieval (online).
  39. 39.
    Jiang, M., Luo, Y. P., & Yang, S. Y. (2007). Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm. Information Processing Letter, 102(1), 8–16.MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Gao, F., Guo, L., Li, H., et al. (2014). Quantizer design for distributed GLRT detection of weak signal in wireless sensor networks. IEEE Transactions on Wireless Communications, 14(4), 2032–2042.CrossRefGoogle Scholar
  41. 41.
    Duarte, C., Barner, K. E., & Goossen, K. (2016). Design of IIR multi-notch filters based on polynomially-represented squared frequency response. IEEE Transactions on Signal Processing, 64(10), 2613–2623.MathSciNetCrossRefzbMATHGoogle Scholar

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

Authors and Affiliations

  1. 1.School of Information and Communication EngineeringUniversity of Electronic Science and Technology of ChinaChengduChina
  2. 2.Institute of Electronic and Information Engineering of University of Electronic Science and Technology of China in GuangdongDongguanChina

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