Discrimination of primary user emulation attack on cognitive radio networks using machine learning based spectrum sensing scheme

Abstract

The identification of the presence of primary user enhances the spectrum efficiency in cognitive radio (CR). The studies suggested that the existence of malicious user adversely affects the system performances; especially the primary user emulation attack (PUEA) has a greater influence in spectrum sensing on the CR network. Moreover, the detection of PUEA is a challenging and complex task and involves constructive design with sensing algorithm. In this study, a support vector machine (SVM) along with energy vectors is designed to improve the spectrum sensing mechanism. The presented approach integrates the SVM with the Bayesian optimization algorithm (BOA) in which SVM aims to detect the malicious user by randomly selecting the primary and secondary users. The BOA aims to optimize the hyperparameters of the SVM, thereby improving the detection performances and maximizes the algorithms convergence speed. The experimental analysis illustrate that the presented approach predicts the PUEA with 98% accuracy and reduces the average node power is 9.7. Moreover, the results demonstrated that the system performance does not vary on implementing it with the large-scale CR network. Finally, the system performances are compared and evaluated with existing techniques in terms of accuracy, and average noise power.

Appendix

Derivation for mean and variance of Yj.

In this section, the derivation of mean and variance of Yj is presented

$$E\left[{Y}_{j}|{H}_{0}\right]= \frac{1}{\eta }{\sum }_{n=1}^{w}E\left[{\left|{y}_{j}(n)\right|}^{2}\right]$$

$$E\left[{Y}_{j}|{H}_{0}\right]= \frac{1}{\eta }{\sum }_{n=1}^{w}E\left[{\left|{\beta }_{j}q\left(n\right)+{v}_{j}(n)\right|}^{2}\right]$$

(17)

Assuming that the malicious user’s signal samples and noise samples are independent of each other.

$$E\left[{Y}_{j}|{H}_{0}\right]- \frac{1}{\eta }{\sum }_{n=1}^{w}E\left[{\beta }_{j}^{2}{\left|q\left(n\right)\right|}^{2}\right]+ \frac{1}{\eta }{\sum }_{n=1}^{w}E\left[{\left|{v}_{j}\left(n\right)\right|}^{2}\right]$$

$$E\left[{Y}_{j}|{H}_{0}\right]+ \frac{1}{\eta }T\gamma MU{\left|{\beta }_{j}\right|}^{2}+\frac{1}{\eta } {\sum }_{n=1}^{w}n$$

$$E\left[{y}_{j}|{H}_{0}\right]={\gamma }_{MU}{\left|{\beta }_{j}\right|}^{2} | W ; {H}_{0}$$

The mean under hypothesis ${H}_{1}$ is obtained as

$$E\left[ {Y_{j} |H_{1} } \right] = \frac{1}{\eta }\mathop \sum \limits_{n = 1}^{w} \left| {\alpha_{j} p\left( n \right) + \beta_{j} q\left( n \right) + {}_{j}^{\upsilon } \left( n \right)} \right|^{2}$$

$$E\left[{Y}_{j}|{H}_{1}\right]= \frac{1}{\eta } {\sum }_{n=1}^{w}\left\{{\alpha }_{j}^{2}{p}^{2}\left(n\right)+{\beta }_{j}^{2}{p}^{2}\left(n\right)+{v}_{j}{(n)}^{2}+2{\alpha }_{j}{\beta }_{j}p\left(n\right)q\left(n\right)+2{\alpha }_{j}p\left(n\right){v}_{j}(n)+2{\beta }_{j}q\left(n\right){v}_{j}(n)\right\}$$

$$E\left[{Y}_{j}|{H}_{1}\right]= \frac{1}{\eta }T{\rho }_{pu}{\alpha }_{j}^{2}+{\gamma }_{mu}{\beta }_{j}^{2}+w$$

$$E\left[{Y}_{j}|{H}_{1}\right]= \frac{{\alpha }_{j}^{2}}{\eta }W+\frac{{\beta }_{j}^{2}}{\eta }W+w$$

The variance in ${H}_{0}$ is.

$$var\left({H}_{0}\right)= \frac{1}{{\eta }^{2}} {\sum }_{n=1}^{W}E{\left[\left[{y}_{j}^{2}\left(n\right) E\left[{y}_{j}^{2}(n)\right]\right] |{H}_{0}\right]}^{2}$$

(18)

The term $E\left[{y}_{j}^{2}(n)\right]$ in (18) is

$$E\left[{y}_{j}^{2}(n)\right]=E{\left[{\beta }_{j}q\left(n\right)+{v}_{j}(n)\right]}^{2}=E\left[{\beta }_{j}^{2}{q}^{2}(n)\right]+\eta ={\beta }_{j}^{2}+\eta$$

Substituting the above result in (18), gives

$$var\left({H}_{0}\right)= \frac{1}{{\eta }^{2}} {\sum }_{n=1}^{W}E{\{{y}_{j}^{2}\left(n\right)-({\beta }_{j}^{2}+\eta )\}}^{2}$$

$$var\left({H}_{0}\right)= \frac{1}{{\eta }^{2}} {\sum }_{n=1}^{W}E\left\{{y}_{j}^{4}\left(n\right)+{\beta }_{j}^{4}+{\eta }^{2}+2{\beta }_{j}^{2}\eta -2{y}_{j}^{2}\left(n\right){\beta }_{j}^{2}-2{y}_{j}^{2}\left(n\right)\eta \right\}$$

$$var\left({H}_{0}\right)= \frac{w}{{\eta }^{2}} \left[2{\beta }_{j}^{4}+2{\eta }^{2}+4\eta {\beta }_{j}^{2}\right]$$

The variance in ${H}_{1}$ is

$$var\left({H}_{1}\right)= \frac{1}{{\eta }^{2}} {\sum }_{n=1}^{W}E{\left[\left[{y}_{j}^{2}\left(n\right) E\left[{y}_{j}^{2}(n)\right]\right] |{H}_{1}\right]}^{2}$$

The term $E\left[{y}_{j}^{2}(n)\right]$ in (19) is

$$E\left[{y}_{j}^{2}\left(n\right){H}_{1}=E\left\{{\left[{\beta }_{j}q\left(n\right)+{\alpha }_{j}p\left(n\right)+{v}_{j}(n)\right]}^{2}\right\}\right]-{\beta }_{j}^{2}+{\alpha }_{j}^{2}+\eta$$

Substituting in 19, gives

$$var\left({H}_{1}\right)= \frac{1}{{\eta }^{2}} {\sum }_{n=1}^{W}E\left\{{y}_{j}^{4}\left(n\right)+{\beta }_{j}^{4}+{\alpha }_{j}^{4}+{\eta }^{2}+2{\alpha }_{j}^{2}{\beta }_{j}^{2}+2{\alpha }_{j}^{2}\eta +2{\beta }_{j}^{2}\eta -2{y}_{j}^{2}\left(n\right)\left[{\beta }_{j}^{2}+{\alpha }_{j}^{2}+\eta \right]\right\}$$

$$= \frac{1}{{\eta }^{2}} {\sum }_{n=1}^{W}3{({\beta }_{j}^{4}+{\alpha }_{j}^{4}+\eta )}^{2}+{\beta }_{j}^{4}+{\alpha }_{j}^{4}+{\eta }^{2}+2{\alpha }_{j}^{2}{\beta }_{j}^{2}+2{\alpha }_{j}^{2}\eta +2{\beta }_{j}^{2}\eta -E\left[2{y}_{j}^{2}\left(n\right){\beta }_{j}^{2}\right]-E\left[2{\alpha }_{j}^{2}\eta {y}_{j}^{2}\left(n\right)\right]-2\eta E\left[{y}_{j}^{2}\left(n\right)\right]$$

$$= \frac{1}{{\eta }^{2}} {\sum }_{n=1}^{W}\left[{\beta }_{j}^{4}+{\alpha }_{j}^{4}+{\eta }^{2}+2{\beta }_{j}^{2}{\alpha }_{j}^{2}+2{\alpha }_{j}^{2}\eta +2{\beta }_{j}^{2}\eta \right]+{\beta }_{j}^{4}+{\alpha }_{j}^{4}+{\eta }^{2}+2{\alpha }_{j}^{2}{\beta }_{j}^{2}+2{\alpha }_{j}^{2}\eta +2{\beta }_{j}^{2}\eta +2{\beta }_{j}^{2}\left[{\beta }_{j}^{4}+{\alpha }_{j}^{4}+\eta \right]-2{\alpha }_{j}^{2}\left[{\beta }_{j}^{4}+{\alpha }_{j}^{4}+\eta \right]$$

After Reducing, we get

$$var\left({H}_{0}\right)= \frac{w}{{\eta }^{2}} \left(2{\beta }_{j}^{4}+2{\alpha }_{j}^{4}+2{\eta }^{2}+4{\alpha }_{j}^{2}{\beta }_{j}^{2}+4{\alpha }_{j}^{2}\eta +{\beta }_{j}^{2}\eta \right)$$