A Novel Evolutionary-Based Cooperative Spectrum Sensing Mechanism for Cognitive Radio Networks

Abstract

Cognitive radio (CR) is considered as a feasible intelligent technology for 4G wireless networks or self-organization networks and envisioned as a promising paradigm of exploiting intelligence for enhancing efficiency of underutilized spectrum bands. In CR, one of the main concerns is to reliably sense the presence of primary users, to attain protection against harmful interference caused by the potential spectrum access of secondary users (SUs). In this paper, evolutionary algorithms, namely, genetic algorithm (GA) and particle swarm optimization (PSO) are investigated. An imperialistic competitive algorithm (ICA) is proposed to minimize error detection at the common soft data fusion (SDF) center for structurally centralized cognitive radio network (CRN). By using these techniques, evolutionary operations are invoked to optimize the weighting coefficients applied on the sensing measurement components received from multiple cooperative SUs. The proposed method is compared with other evolutionary algorithms, as well as other conventional deterministic, such as maximal ratio combining- (MRC-), modified deflection coefficient- (MDC-), normal deflection coefficient- (NDC-) based SDF schemes and OR-rule HDF based. MATLAB simulations confirm the superiority of the ICA-based scheme over the PSO-, GA-based and other conventional schemes in terms of detection performance. In addition, the ICA-based scheme also shows promising convergence and time running performance as compared to other iterative-based schemes. This makes ICA an adequate solution to meet real-time requirements.

Appendices

Appendix 1

$$\begin{aligned}&\displaystyle U_{i} \left[ {n|{\text {H}}_{0} } \right] = \sqrt{P_{{R,i}} } h_{i} W_{i} \left[ n \right] + N_{i} \left[ n \right] \end{aligned}$$

(9)

$$\begin{aligned}&\displaystyle U_{i} \left[ {n|{\text {H}}_{1} } \right] = \sqrt{P_{{R,i}} } h_{i} W_{i} \left[ n \right] + N_{i} \left[ n \right] \!+\! \sqrt{P_{{R,i}} } g_{i} h_{i} {\text {S}}\left[ {\text {n}} \right] \!=\! \sqrt{P_{{R,i}} } g_{i} h_{i} {\text {S}}\left[ {\text {n}} \right] \!+\! U_{i} \left[ {n|{\text {H}}_{0} } \right] \qquad \nonumber \\ \end{aligned}$$

(10)

This statistically shows i.e.

$$\begin{aligned} U_{i} \left[ {n|{\text {H}}_{0} } \right] \sim {\mathcal {N}}\left( {0,\sigma _{{1_{i} }}^{2} } \right) \sim {\mathcal {N}}\left( {0, P_{{R,i}} \left| {h_{i} } \right| ^{2} \sigma _{{W_{i} }}^{2} + {{\updelta }}_{{\text {i}}}^{2} } \right) \end{aligned}$$

and

$$\begin{aligned} U_{i} \left[ {n|{\text {H}}_{1} } \right] \sim {\mathcal {N}}\left( {0,\sigma _{{1_{i} }}^{2} } \right) \sim {\mathcal {N}}\left( {0, P_{{R,i}} \left| {g_{i} } \right| ^{2} \left| {h_{i} } \right| ^{2} \sigma _{S}^{2} + \sigma _{0}^{2} } \right) . \end{aligned}$$

In a Matrix form, the received signals at the FC through the control channel under ${\text {H}}_{0}$ and ${\text {H}}_{1}$, respectively, can be written as:

$$\begin{aligned} U_{i} \left[ {n|H_{0} } \right]&= \left[ \begin{array}{cccc} {\sqrt{P_{{R,1}} } h_{1} } &{}0&{}\cdots \cdots &{}0\\ 0&{}\sqrt{P_{{R,2}} } h_{2}&{} \cdots \cdots &{}0 \\ \vdots &{} \vdots &{}\ddots &{}\vdots \\ 0 &{} 0 &{}\cdots \cdots &{} {\sqrt{P_{{R,M}} } h_{M} } \end{array} \right] \nonumber \\&\times \left[ \begin{array}{c} {W_{1} \left[ n \right] } \\ \vdots \\ {W_{M} \left[ n \right] } \\ \end{array} \right] + \left[ \begin{array}{c} N_{1} \left[ n \right] \\ \vdots \\ N_{M} \left[ n \right] \\ \end{array}\right] \end{aligned}$$

(11)

$$\begin{aligned} U_{i} \left[ {n|H_{1} } \right]&= \left[ \begin{array}{cccc} \sqrt{P_{{R,1}} } g_{1} h_{1} &{} 0&{}\cdots \cdots &{}0\\ 0&{}\sqrt{P_{{R,2}} } g_{2} h_{2}&{}\cdots \cdots &{}0\\ \vdots &{} \vdots &{}\ddots &{}\vdots \\ 0&{}0 &{}\cdots \cdots &{} \sqrt{P_{{R,M}} } g_{M} h_{M} \end{array} \right] \nonumber \\&\times \left[ \begin{array}{c} S_{1} \left[ n \right] \\ \vdots \\ S_{M} \left[ n \right] \\ \end{array} \right] + \left[ \begin{array}{c} U_{1} \left[ {n|H_{0} } \right] \\ \vdots \\ U_{M} \left[ {n|H_{0} } \right] \end{array}\right] \end{aligned}$$

(12)

Appendix 2

$$\begin{aligned} E\left( {Z{\text {|}}H_{0} } \right)&= \sum \limits _{{i = 1}}^{M} \omega _{i} K\sigma _{{0,i}}^{2} \,\, = \,\sum \limits _{{i = 1}}^{M} \omega _{i} \mu _{{0,i}} \, = \,\vec {\omega }^{T} \overrightarrow{{\mu _{0} }}\end{aligned}$$

(13)

$$\begin{aligned} E\left( {Z{\text {|}}H_{1} } \right)&= \sum \limits _{{i = 1}}^{M} \omega _{i} K\sigma _{{1,i}}^{2} = \sum \limits _{{i = 1}}^{M} \omega _{i} \mu _{{1,i}} \, = \,\vec {\omega }^{T}\end{aligned}$$

(14)

$$\begin{aligned} var\left( {Z{\text {|}}H_{0} } \right)&= \sum \limits _{{i = 1}}^{M} 2\omega _{i} ^{2} K(\sigma _{{0,i}}^{2} + \delta _{i}^{2} )^{2} = ~\vec {\omega }^{T} \varPhi _{{H_{0} }} \vec {\omega }\end{aligned}$$

(15)

$$\begin{aligned} var\left( {Z{\text {|}}H_{1} } \right)&= \sum \limits _{{i = 1}}^{M} 2\omega _{i} ^{2} K(\sigma _{{1,i}}^{2} + \sigma _{{0,i}}^{2} )^{2} = ~\vec {\omega }^{T} \varPhi _{{H_{1} }} \vec {\omega } \end{aligned}$$

(16)

where ${\vec {\upomega }} = \left[ {{{\upomega }}_{1} ,{{\upomega }}_{2} , \ldots ,{{\upomega }}_{{\text {M}}} } \right] ^{{\text {T}}}$ marks the weighting vectors and the superscript $T$ denotes the transpose of the weighting coefficients vector. The covariance matrices under ${\text {H}}_{1}$ and ${\text {H}}_{0}$ are

$$\begin{aligned} \varPhi _{{H_{1} }} = diag\left( {2K\left( {P_{{R,i}} \left| {g_{i} } \right| ^{2} \left| {h_{i} } \right| ^{2} \sigma _{s}^{2} + \sigma _{{0,i}}^{2} } \right) ^{2} } \right) \end{aligned}$$

and $\varPhi _{{H_{0} }} = diag\left( {2K\sigma _{{0,i}}^{4} } \right)$, where square diagonal matrix is $diag(.)$ and given vector elements are diagonal elements.$\beta$ is assumed to be energy global threshold at FC then, $Z{ \gtrless }_{{~H_{0} }}^{{~H_{1} }} \beta$ presents the likelihood ratio.

$$\begin{aligned} P_{f} = P\left( {Z > \beta {\text {|}} H_{0} } \right)&= Q\left( {\frac{{\beta - E\left( {Z{\text {|}}H_{0} } \right) }}{{\sqrt{var\left( {Z{\text {|}}H_{0} } \right) } }}} \right) = Q\left( {\frac{{\beta - \vec {\omega }^{T} \overrightarrow{{\mu _{0} }} }}{{\sqrt{\vec {\omega }^{T} \varPhi _{{H_{0} }} \vec {\omega }} }}} \right) \end{aligned}$$

(17)

$$\begin{aligned} P_{d} = P\left( {Z > \beta {\text {|}} H_{1} } \right)&= Q\left( {\frac{{\beta - E\left( {Z{\text {|}}H_{1} } \right) }}{{\sqrt{var\left( {Z{\text {|}}H_{1} } \right) } }}} \right) = Q\left( {\frac{{\beta - \vec {\omega }^{T} \overrightarrow{{\mu _{1} }} }}{{\sqrt{\vec {\omega }^{T} \varPhi _{{H_{1} }} \vec {\omega }} }}} \right) \end{aligned}$$

(18)

Since $P_{f} = P_{m}$ or $P_{f} = (1 - P_{d} )$, by equating the expression in Eqs. (17) and (18), we would obtain:

$$\begin{aligned} Q\left( {\frac{{\beta - \vec {\omega }^{T} \overrightarrow{{\mu _{1} }} }}{{\sqrt{\vec {\omega }^{T} \varPhi _{{H_{1} }} \vec {\omega }} }}} \right)&= 1 - Q\left( {\frac{{\beta - \vec {\omega }^{T} \overrightarrow{{\mu _{0} }} }}{{\sqrt{\vec {\omega }^{T} \varPhi _{{H_{0} }} \vec {\omega }} }}} \right) \end{aligned}$$

(19)

$$\begin{aligned} Q\left( {\frac{{\beta - \vec {\omega }^{T} \overrightarrow{{\mu _{1} }} }}{{\sqrt{\vec {\omega }^{T} \varPhi _{{H_{1} }} \vec {\omega }} }}} \right)&= Q\left( {\frac{{\vec {\omega }^{T} \overrightarrow{{\mu _{0} }} - \beta }}{{\sqrt{\vec {\omega }^{T} \varPhi _{{H_{0} }} \vec {\omega }} }}} \right) \end{aligned}$$

(20)

After some simplifications, we can obtain the optimal threshold $\beta$ that will minimize the total probability of error

$$\begin{aligned} \beta = \left( {\frac{{\sqrt{\omega ^{T} \varPhi _{{H_{1} }} \omega } \mu _{0}^{T} \vec {\omega } + \sqrt{\omega ^{T} \varPhi _{{H_{1} }} \omega } \mu _{1}^{T} \omega }}{{\sqrt{\omega ^{T} \varPhi _{{H_{0} }} \omega } + \sqrt{\omega ^{T} \varPhi _{{H_{1} }} \omega } }}} \right) \end{aligned}$$

(21)