Recognition and elimination of SSDF attackers in cognitive radio networks

Abstract

The nature of cognitive radio (CR) technology creates a lot of opportunities for attackers. When an attack occurs, the function of the primary network is affected and thus the overall system performance will be reduced. In the present paper, we introduce and simulate a novel method for identifying spectral sensing data falsification (SSDF) attack and recognizing the malicious users (MU), which we refer to as “Recognition and Elimination of SSDF Attackers”. Our proposed scheme uses the generalized likelihood ratio test (GLRT) approach for solving the MUs detection problem. In this method, we do not need previous information about the network and number of the MUs and secondary users (SUs). In addition to detecting the occurrence of an attack, our method can recognize attackers. By recognizing the MUs, their negative effect will be eliminated and the cognitive radio network (CRN) performance will return to normal condition. Consequently, our scheme can save resources by identifying the strategy of the known attackers. Simulation results reveal that our detection and recognition scheme is better than some of methods available.

Appendices

Appendix A

By giving ${\hat{X}}$, the pdf of observation signals under $H_1^{1}$ can be written as follows:

$$\begin{aligned} f\left( {Y;{\hat{X}},\varDelta _i,H_1^1}\right) = \left( {\frac{1}{{\sqrt{2\pi } \sigma }}}\right) ^N\exp \left( {-\frac{{\left\| {Y-G{\hat{X}} -\varDelta _i e_i } \right\| ^2}}{{2\sigma ^2}}}\right) \end{aligned}$$

(37)

By replacing ${\hat{X}}$ from Eq. (19) into Eq. (37) and simplifying, we have

$$\begin{aligned} f\left( {Y;{\hat{X}},\varDelta _i,H_1^1} \right) = \left( {\frac{1}{{\sqrt{2\pi } \sigma }}} \right) ^N \exp \left( { - \frac{{ \left\| {P_G^ \bot \left( {Y - \varDelta _i e_i } \right) } \right\| ^2 }}{{2\sigma ^2 }}} \right) \end{aligned}$$

(38)

Where $P_G^ \bot$ is defined as follows:

$$\begin{aligned} P_G^ \bot = I - G\left( {G^T G^{ - 1} } \right) G^T \end{aligned}$$

(39)

We can derive the MLE of $\varDelta _i$ by solving Eq. (40)

$$\begin{aligned} \frac{\partial f\left( {Y;{\hat{X}},\varDelta _i,H_1^1} \right) }{\partial \varDelta _i}=0 \end{aligned}$$

(40)

Equation (38) can be replaced into Eq. (40) and simplified as follows:

$$\begin{aligned} \frac{\partial }{\partial \varDelta _i}&\left\| {P_G^ \bot \left( {Y - \varDelta _i e_i } \right) } \right\| ^2 =0 \end{aligned}$$

(41)

Equation (41) can be solved as follows:

$$\begin{aligned}&\frac{\partial }{\partial \varDelta _i}\left\| {P_G^ \bot \left( {Y - \varDelta _i e_i } \right) } \right\| ^2 =\frac{\partial }{\partial \varDelta _i} \left[ \left( Y- \varDelta _i e_i \right) ^T P_G^\bot \left( Y-\varDelta _i e_i\right) \right] \nonumber \\&\quad =2e_i^T P_G^ \bot \left( Y-\varDelta _i e_i\right) +\left( Y-\varDelta _i e_i\right) ^T P_G^ \bot e_i \end{aligned}$$

(42)

By replacing Eq. (42) into Eq. (41) and simplifying, The $\hat{\varDelta }_i$ can be obtained as:

$$\begin{aligned} \hat{\varDelta }_i = \frac{{e_i^T P_G^ \bot Y}}{{\left\| {e_i } \right\| ^2 }} = e_i^T P_G^ \bot Y \end{aligned}$$

(43)

Appendix B

By giving $\hat{\varDelta }_i$, the pdf of observation signals under $H_1^{1}$, can be written as follows:

$$\begin{aligned} f\left( {Y;{\hat{X}},\hat{\varDelta }_i,H_1^1} \right) = \left( {\frac{1}{{\sqrt{2\pi } \sigma }}} \right) ^N \exp \left( { - \frac{{ \left\| {P_G^ \bot \left( {Y - \hat{\varDelta }_i e_i } \right) } \right\| ^2 }}{{2\sigma ^2 }}} \right) \end{aligned}$$

(44)

Equation (44) can be simplified as follows:

$$\begin{aligned} f&\left( {Y;{\hat{X}},\hat{\varDelta }_i,H_1^1} \right) \nonumber \\&=\left( {\frac{1}{{\sqrt{2\pi } \sigma }}} \right) ^N \exp \left( { - \frac{{\left( {Y - \hat{\varDelta }_i e_i} \right) ^T P_G^ \bot \left( {Y - \hat{\varDelta }_i e_i}\right) }}{{2\sigma ^2 }}} \right) \nonumber \\&=\left( {\frac{1}{{\sqrt{2\pi } \sigma }}} \right) ^N \exp \left( { - \frac{{ Y^T P_G^ \bot Y - \hat{\varDelta }_i Y^T P_G^ \bot e_i - \hat{\varDelta }_i e_i^T P_G Y + {\hat{\varDelta }_i}^2 }}{{2\sigma ^2 }}} \right) \end{aligned}$$

(45)

By replacing Eq. (43) into Eq. (45) and simplifying, the pdf of observation signals under $H_1^{1}$ can be written as follows:

$$\begin{aligned} f\left( {Y;{\hat{X}},\hat{\varDelta }_i,H_1^1} \right) =\left( {\frac{1}{{\sqrt{2\pi } \sigma }}} \right) ^N \exp \left( { - \frac{{ Y^T P_G^\bot Y-{\hat{\varDelta }_i}^2 }}{{2\sigma ^2 }}} \right) \end{aligned}$$

(46)

The pdf of observation signals under $H_0^{1}$ can be written as follows:

$$\begin{aligned} f\left( {Y;{\hat{X}},H_0^1} \right) = \left( {\frac{1}{{\sqrt{2\pi } \sigma }}} \right) ^N \exp \left( { - \frac{{ \left\| {P_G^ \bot {Y } } \right\| ^2}}{{2\sigma ^2 }}} \right) \end{aligned}$$

(47)

Similarly the pdf of observation signals under $H_1^{1}$, Eq. (47) can be simplified as follows:

$$\begin{aligned} f\left( {Y;{\hat{X}},H_0^1} \right) =\left( {\frac{1}{{\sqrt{2\pi } \sigma }}} \right) ^N \exp \left( { - \frac{{ Y^T P_G^\bot Y }}{{2\sigma ^2 }}} \right) \end{aligned}$$

(48)