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Spectrum sensing exploiting the maximum value of power spectrum density in wireless sensor network

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Abstract

Spectrum sensing plays a foundational role in cognitive radio sensor networks. However, only the methods with low computational complexity can be utilized due to energy restriction of sensor node. To this end, a novel frequency-domain spectrum sensing method is presented to satisfy corresponding requirements of cognitive radio sensor networks. Only the maximum value of power spectrum density is utilized as test statistic to reduce the computational complexity. According to the dependence of 2L real parts and imaginary parts of the maximum value of power spectrum density, we model the maximum value of power spectrum density as the central Chi-square distribution for the \(H_0\) case and non-central Chi-square distribution for the \(H_1\) case. Exploiting resulting distributions, we derive the analytic expressions for the detection probability and the false-alarm probability. Additionally, the computational complexity of the proposed method is quantitatively analyzed. Finally, we certify the proposed test statistic and the probability distribution of the maximum value of power spectrum density and evaluate the impact of some parameters on the detection performance experimentally. The theoretical analysis and simulation results demonstrate that the proposed algorithm can offer high performance gains over the existing time-domain detection method.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (NSFC) (61671176). We would like to thank Linxiao Su for his suggestion, discussion and simulation code.

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Authors and Affiliations

  1. Communication Research Center, Harbin Institute of Technology, Harbin, 150080, Heilongjiang, China

    Yulong Gao

  2. School of Computer and Information Engineering, Harbin University of Commerce, Harbin, 150028, Heilongjiang, China

    Yanping Chen

Authors
  1. Yulong Gao
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  2. Yanping Chen
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Corresponding author

Correspondence to Yulong Gao.

Appendix

Appendix

To testify (19), we simulate cases of various FFT-point, as shown in Fig. 7. For simplification, we let

$$ Z=\frac{\sigma ^2}{{2MLU}}\sum \limits _{n = 0}^{M - 1}g^2(n) \cos \left(\frac{{2\pi }}{M}n2K\right) $$
(66)
Fig. 7
figure 7

The relation between Z and K for \(M=64, 128, 256\), 512-point FFT. \(K=0, 1, \ldots , M/2-1\)

Full size image

We can see from Fig. 7 that \(Z\approx 0\) when \(K \ge 3\). For IF signal, \(K=Mf_{max\_loca}/f_{s}\gg 3\). It should be noted that Z is symmetrical about M / 2. For simplicity, we only provide the result of \([0,M/2-1]\). Therefore, we can obtain that \(D[{X_R}(K,i)] \approx \frac{{{\sigma ^2}}}{{2L}}\). Similarly, the variance of the imaginary part \({X_I}(K,i)\) can be computed as

$$ \begin{aligned} D[{X_I}(K,i)]&= \frac{1}{{ML}}E[{w^2}(n + iM/2)]g^2(n)\sum \limits _{n = 0}^{M - 1}g^2(n) {{{\sin }^2}\left( \frac{{2\pi }}{M}Kn\right) } \\&= \frac{1}{{MLU}}\frac{{{\sigma ^2}}}{2}\sum \limits _{n = 0}^{M - 1} g^2(n){\left( 1 - \cos \left( 2\frac{{2\pi }}{M}Kn\right) \right) } \\&\approx \frac{{{\sigma ^2}}}{{2L}}\end{aligned} $$
(67)

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Gao, Y., Chen, Y. Spectrum sensing exploiting the maximum value of power spectrum density in wireless sensor network. Wireless Netw 25, 1949–1964 (2019). https://doi.org/10.1007/s11276-018-1789-x

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