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Multiband Spectrum Sensing Using Modified Daniell Windowing Technique in Full-Duplex Cognitive Radio Networks: A Performance Study

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Abstract

Full-duplex cognitive radio (CR) is a promising technology for upcoming 5G wireless communication systems. This paper presents a robust fast Fourier transform (FFT) based multiband spectrum sensing using two-dimensional averaging algorithms in orthogonal frequency division multiplexing systems in full-duplex CR networks with residual self interference under Rayleigh flat fading scenario. In the proposed algorithm, we have used modified Daniell windowing technique both in time and frequency dimensions to smoothen the FFT spectrum under full-duplex scenario. The analytical expressions for the performance metrics are derived for the aforementioned algorithm. The simulated and analytical results, obtained for the proposed algorithm using modified Daniell windowing technique are found in good agreement. Finally, the comparison studies between the proposed scheme using modified Daniel windowing technique and the conventional rectangular windowing scheme clearly depict that the proposed scheme gives optimal performance even at low SNR using fewer filter lengths in time and frequency dimensions as the modified Daniell windowing algorithm is less influenced due to spectral leakage.

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References

  1. Yucek, T., & Arslan, H. (2009). A survey of spectrum sensing algorithms for cognitive radio applications. IEEE Communications Surveys and Tutorials, 11(1), 116–130.

    Article  Google Scholar 

  2. Ding, G., Jiao, Y., Wang, J., Zou, Y., Wu, Q., Yao, Y., et al. (2018). Spectrum inference in cognitive radio networks: Algorithms and applications. IEEE Communications Surveys and Tutorials, 20(1), 150–182.

    Article  Google Scholar 

  3. Badoi, C. I., Prasad, N., Croitoru, V., & Prasad, R. (2011). 5G based on cognitive radio. Wireless Personal Communications, 57(3), 441–464.

    Article  Google Scholar 

  4. Umar, R., Sheikh, A. U. H., & Deriche, M. (2014). Unveiling the hidden assumptions of energy detector based spectrum sensing for cognitive radios. IEEE Communications Surveys and Tutorials, 16(2), 713–728.

    Article  Google Scholar 

  5. Axell, E., Leus, G., & Larsson, E. G. (2012). Spectrum sensing for cognitive radio: State-of- the-art recent advances. IEEE Signal Processing Magazine, 29(3), 101–1316.

    Article  Google Scholar 

  6. Nguyen, D., Tran, L., Pirinen, P., & Latva-aho, M. (2014). On the spectral efficiency of full-duplex small cell wireless systems. IEEE Transactions on Wireless Communications, 13(9), 4896–4910.

    Article  Google Scholar 

  7. Shen, Y., Zhou, J., & Tang, Y. (2015). Digital self-interference cancellation in wireless co-time and co-frequency full-duplex system. Wireless Personal Communications, 82(4), 2557–2565.

    Article  Google Scholar 

  8. Tripta, Kumar, A., & Saha, S. (2017). Performance evaluation of NP and ML based spectrum sensing in FDCRNs under small scale fading scenario. In TENCON IEEE region 10 conference (pp. 2051–2055), Penang, Malaysia.

  9. Badawy, A., Khattab, T., Elfouly, T., Chiasserini, C., & Trinchero, D. (2016). On the performance of spectrum sensing based on GLR for full-duplex cognitive radio networks. In IEEE wireless communications and networking conference (pp. 1–6), Doha, Qatar.

  10. Riihonen, T., & Wichman, R. (2014). Energy detection in full-duplex cognitive radios under residual self-interference. In 9th international conference on cognitive radio oriented wireless networks and communications (CROWNCOM) (pp. 57–60), Oulu, Finland.

  11. Tandra, R., & Sahai, A. (2005). Fundamental limits on detection in low SNR under noise uncertainty. In Proceedings of international conference on wireless networks, communications and mobile computing (pp. 464–469).

  12. Vilar, G. V., Valcarce, R. L., & Sala, J. (2011). Multiantenna spectrum sensing exploiting spectral a priori information. IEEE Transactions on Wireless Communications, 10(12), 4345–4355.

    Article  Google Scholar 

  13. Srinivasan, S., Dikmese, S., & Renfors, M. (2012). Spectrum sensing and spectrum utilization model for OFDM and FBMC based cognitive radios. In Proceedings of SPAWC (pp. 139–143), Cesme, Turkey.

  14. Dikmese, S., Sofotasios, P. C., Ihalainnen, T., & Renfors, M. (2015). Efficient energy detection methods for spectrum sensing under non-flat spectral characteristics. IEEE Journal on Selected Areas in Communications, 33(5), 755–770.

    Article  Google Scholar 

  15. Boroujeny, B. F., & Kempter, R. (2008). Multicarrier communication techniques for spectrum sensing and communication in cognitive radios. IEEE Communication Magazine, 48(4), 80–85.

    Article  Google Scholar 

  16. Tang, H. (2005). Some physical layer issues of wide-band cognitive radio systems. In Proceedings of 1st IEEE international symposium on new frontiers in dynamic spectrum access networks (DySPAN) (pp. 151–159), Baltimore, USA.

  17. Quan, Z., Cui, S., Sayed, A. H., & Poor, H. V. (2008). Wideband spectrum sensing in Cognitive Radio Networks. Proceedings of IEEE international conference (ICC) (pp. 901–906), Beijing, China.

  18. Dikmese, S., Renfors, M., & Dincer, H. (2011). FFT and filter bank based spectrum sensing for WLAN signals. In Proceedings of ECCTD (pp. 781–784), Linkoping, Sweden.

  19. Dikmese, S., Srinivasan, S., & Renfors, M. (2012). FFT and filter bank based spectrum sensing and spectrum utilization for cogntive radios. In 5th international symposium on communications, control and signal processing (pp. 1–5), Rome, Italy.

  20. Bloomfield, P. (2000). Fourier analysis of time series: An introduction. New York: Wiley.

    Book  Google Scholar 

  21. Guo, H., Jiang, W., & Luo, W. (2017). Linear soft combination for cooperative spectrum sensing in cognitive radio networks. IEEE Communications Letters, 21(7), 1573–1576.

    Article  Google Scholar 

  22. Rodriguez-Parera, S., Ramon, V., Bourdoux, A., Horlin, F. & Lauwereins, R. (2008). Spectrum sensing over SIMO multi-path fading channels based on energy detection. In IEEE global telecommunications conference (GLOBECOM) (pp. 1–6), New Orleans, LO, USA.

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Authors and Affiliations

  1. Electronics and Communication Engineering Department, National Institute of Technology Patna, Patna, India

    Tripta & Seemanti Saha

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  1. Tripta
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  2. Seemanti Saha
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Appendix

Appendix

The mean of the text statistic T(Y[n, k]) normalized with respect to \(\sigma _{H_0}^2\) under \(H_0\) is calculated as:

$$\begin{aligned} E\left[ \frac{T(Y[n,k])}{\sigma _{H_0}^2}\right]= & {} \sum _{k=k_0,N_f}\frac{1}{2(N_f-1)}\left[ \sum _{n=n_0,N_t}\frac{1}{2(N_t-1)}E\left[ \frac{\vert Y(n,k)\vert ^2/H_0}{\sigma _{H_0^2}}\right] \right. \\&+\,\left. \sum _{n=n_0+1}^{N_t-1}\frac{1}{N_t-1}E\left[ \frac{\vert Y(n,k)\vert ^2/H_0}{\sigma _{H_1^2}}\right] \right. \\&+\,\sum _{k=k_0+1}^{N_f-1}\frac{1}{(N_f-1)}\left[ \sum _{n=n_0,N_t}\frac{1}{2(N_t-1)}E\left[ \frac{\vert Y(n,k)\vert ^2/H_0}{\sigma _{H_0^2}}\right] \right. \\&+\,\left. \sum _{n=n_0+1}^{N_t-1}\frac{1}{N_t-1}E\left[ \frac{\vert Y(n,k)\vert ^2/H_0}{\sigma _{H_0^2}}\right] \right. . \end{aligned}$$
(31)

Considering Eq. (7), the above equation is simplified as:

$$\begin{aligned} E\left[ \frac{T(Y[n,k])}{\sigma _{H_1}^2}\right]= & {} \sum _{k=k_0,N_f}\frac{1}{2(N_f-1)}\left[ \frac{1}{2(N_t-1)}(1+1)+\frac{1}{N_t-1}(1+1+\cdots N_t-2)\right] \\&\quad +\,\sum _{k=k_0+1}^{N_f-1}\frac{1}{(N_f-1)}\left[ \frac{1}{2(N_t-1)}(1+1)+\frac{1}{N_t-1}(1+1+\cdots N_t-2)\right] =1. \end{aligned}$$
(32)

Similarly, the mean of the text statistic T(Y[n, k]) normalized with respect to \(\sigma _{H_1}^2\) under \(H_1\) is calculated as:

$$\begin{aligned} E\left[ \frac{T(Y[n,k])}{\sigma _{H_1}^2}\right]= & {} \sum _{k=k_0,N_f}\frac{1}{2(N_f-1)}\left[ \sum _{n=n_0,N_t}\frac{1}{2(N_t-1)}E\left[ \frac{\vert Y(n,k)\vert ^2/H_1}{\sigma _{H_1^2}}\right] \right. \\&+\,\left. \sum _{n=n_0+1}^{N_t-1}\frac{1}{N_t-1}E\left[ \frac{\vert Y(n,k)\vert ^2/H_1}{\sigma _{H_1^2}}\right] \right. \\&+\,\sum _{k=k_0+1}^{N_f-1}\frac{1}{(N_f-1)}\left[ \sum _{n=n_0,N_t}\frac{1}{2(N_t-1)}E\left[ \frac{\vert Y(n,k)\vert ^2/H_1}{\sigma _{H_1^2}}\right] \right. \\&+\,\left. \sum _{n=n_0+1}^{N_t-1}\frac{1}{N_t-1}E\left[ \frac{\vert Y(n,k)\vert ^2/H_1}{\sigma _{H_1^2}}\right] \right. . \end{aligned}$$
(33)

Using Eq. (11), the above equation is written as:

$$\begin{aligned} E\left[ \frac{T(Y[n,k])}{\sigma _{H_1}^2}\right]= & {} \sum _{k=k_0,N_f}\frac{1}{2(N_f-1)}\left[ \frac{1}{2(N_t-1)}(1+1)+\frac{1}{N_t-1}(1+1+\cdots N_t-2)\right] \\&+\,\sum _{k=k_0+1}^{N_f-1}\frac{1}{(N_f-1)}\left[ \frac{1}{2(N_t-1)}(1+1)+\frac{1}{N_t-1}(1+1+\cdots N_t-2)\right] =1. \end{aligned}$$
(34)

Further, under \(H_0\), the variance of the text statistic T(Y[n, k]) normalized with respect to \(\sigma _{H_0}^2\) is calculated as:

$$\begin{aligned} var\left[ \frac{T(Y[n,k])}{\sigma _{H_0}^2}\right]= & {} \frac{1}{4(N_f-1)^2}\frac{1}{4(N_t-1)^2}\sum _{k=k_0,N_f}\sum _{n=n_0,N_t}\left[ \frac{1}{\sigma _{H_0^4}}var(\vert Y(n,k)\vert ^2/H_0)\right] \\&+\,\frac{1}{4(N_f-1)^2}\frac{1}{(N_t-1)^2}\sum _{k=k_0,N_f}\sum _{n=n_0+1}^{N_t-1}\left[ \frac{1}{\sigma _{H_0^4}}var(\vert Y(n,k)\vert ^2/H_0)\right] \\&+\,\frac{1}{(N_f-1)^2}\frac{1}{4(N_t-1)^2}\sum _{k=k_0+1}^{N_f-1}\sum _{n=n_0,N_t}\left[ \frac{1}{\sigma _{H_0^4}}var(\vert Y(n,k)\vert ^2/H_0)\right] \\&+\,\frac{1}{(N_f-1)^2}\frac{1}{(N_t-1)^2}\sum _{k=k_0+1}^{N_f-1}\sum _{n=n_0+1}^{N_t-1}\left[ \frac{1}{\sigma _{H_0^4}}var(\vert Y(n,k)\vert ^2/H_0)\right] , \end{aligned}$$
(35)

where, \(var[\vert Y[n,k]\vert ^2/H_0]=var[\vert Z[n,k]+W[n,k]\vert ^2]=2\sigma _{z,k}^4+2\sigma _{w,k}^4.\) Thus, Eq. (35) is further simplified as:

$$\begin{aligned}&var\left[ \frac{T(Y[n,k])}{\sigma _{H_0}^2}\right] =\frac{8}{16(N_f-1)^2(N_t-1)^2}+\frac{4N_t-8)}{4(N_f-1)^2(N_t-1)^2} \\&\quad +\,\frac{4N_f-8}{4(N_f-1)^2(N_t-1)^2}+\frac{2(N_t-2)(N_f-2)}{(N_f-1)^2(N_t-1)^2}=\frac{4N_tN_f-6N_t-6N_f+9}{2(N_f-1)^2(N_t-1)^2}. \end{aligned}$$
(36)

Similarly, the calculation of varT(Y[n, k]) under the hypothesis \(H_1\) is summarized as:

$$\begin{aligned} var\left[ \frac{T(Y[n,k])}{\sigma _{H_1}^2}\right]= & {} \frac{1}{4(N_f-1)^2}\frac{1}{4(N_t-1)^2}\sum _{k=k_0,N_f}\sum _{n=n_0,N_t}\left[ \frac{1}{\sigma _{H_1^4}}var(\vert Y(n,k)\vert ^2/H_1)\right] \\&+\,\frac{1}{4(N_f-1)^2}\frac{1}{(N_t-1)^2}\sum _{k=k_0,N_f}\sum _{n=n_0+1}^{N_t-1}\left[ \frac{1}{\sigma _{H_1^4}}var(\vert Y(n,k)\vert ^2/H_1)\right] \\&+\,\frac{1}{(N_f-1)^2}\frac{1}{4(N_t-1)^2}\sum _{k=k_0+1}^{N_f-1}\sum _{n=n_0,N_t}\left[ \frac{1}{\sigma _{H_1^4}}var(\vert Y(n,k)\vert ^2/H_1)\right] \\&+\,\frac{1}{(N_f-1)^2}\frac{1}{(N_t-1)^2}\sum _{k=k_0+1}^{N_f-1}\sum _{n=n_0+1}^{N_t-1}\left[ \frac{1}{\sigma _{H_1^4}}var(\vert Y(n,k)\vert ^2/H_1)\right] \\= & {} \frac{4N_tN_f-6N_t-6N_f+9}{2(N_f-1)^2(N_t-1)^2}. \end{aligned}$$
(37)

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Tripta, Saha, S. Multiband Spectrum Sensing Using Modified Daniell Windowing Technique in Full-Duplex Cognitive Radio Networks: A Performance Study. Wireless Pers Commun 117, 293–309 (2021). https://doi.org/10.1007/s11277-020-07869-z

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