Power allocation policy and performance analysis of secure and reliable communication in cognitive radio networks
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Abstract
This paper investigates the problem of secure and reliable communications for cognitive radio networks. More specifically, we consider a single input multiple output cognitive model where the secondary user (SU) faces an eavesdropping attack while being subject to the normal interference constraint imposed by the primary user (PU). Thus, the SU must have a suitable power allocation policy which does not only satisfy the constraints of the PU but also the security constraints such that it obtains a reasonable performance for the SU, without exposing information to the eavesdropper. We derive four power allocation policies for different scenarios corresponding to whether or not the channel state information of the PU and the eavesdropper are available at the SU. Further, we introduce the concept secure and reliable communication probability (SRCP) as a performance metric to evaluate the considered system, as well as the efficiency of the four power allocation policies. Finally, we present numerical examples to illustrate the power allocation polices, and the impact of these policies on the SRCP of the SU.
Keywords
Secure and reliable communication Physical layer security Power allocation Cognitive radio networks Spectrum underlay networks Performance analysis1 Introduction
A cognitive radio network (CRN) is widely known as a promising solution to enhance spectrum utilization by means of dynamic spectrum access techniques [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. In a CRN, there are two types of users known as primary user (PU) and secondary user (SU), where the (SU) is allowed to access the spectrum licensed to the (PU) as long as it does not degrade the performance of the (PU). Due to this, the (SU) must be equipped with advanced sensing techniques to detect vacant spectrum (known as a spectrum hole) and the channel state information (CSI) of the PU [6, 11]. This, in turn, implies that the \(\hbox {PU}_{\mathrm{s}}\) and \(\hbox {SU}_{\mathrm{s}}\) may be exposed to internal or external attackers who pretend to be sensing devices [12, 13, 14]. Furthermore, malicious attackers can abuse the adaptive abilities of the (CRN) causing negative effects to the radio environment, e.g., by generating interference, which may degrade the performance, reveal the secrete communication information, or even cause malfunction to the operations of the legitimate users. Clearly, secure and reliable communication between \(\hbox {SU}_{\mathrm{s}}\) can be obtained only if neither the secrecy nor the reliable communication outage events happen. Therefore, solving the security problems from all aspects of the networking architecture becomes one of the most challenging problems with CRN [13, 15].
Recently, physical layer security has emerged as an effective approach to protect the communication of legitimate users from eavesdropping attacks, by e.g., using the characteristics of wireless channels such as multipath fading [16, 17, 18]. It has been proven that if the channel from the source to the destination is better than the one from the source to the eavesdropper, the communication of the legitimate users can be secure and reliable at a nonzero data rate [19]. To quantify the security performance more specifically, Wyner has introduced a secrecy capacity concept [16] which is defined as the difference between the capacity of the main channel and the illegitimate channel. Later on, the secrecy capacity concept was extended to include wireless channels, e.g., Gaussian and multipath fading [17, 20]. It revealed that the secrecy capacity may be reduced due to the effect of multipath fading in wireless channels.

Based on the CSI available at the STx, power allocation policies are derived for four scenarios as follows. Scenario 1 (\(S_1\)): The STx does not have the CSI of both the PTx\(\rightarrow \)PRx and the STx\(\rightarrow \)EAV links; Scenario 2 (\(S_2\)): The STx has the CSI of the STx\(\rightarrow \)EAV but not the PTx\(\rightarrow \)PRx link; Scenario 3 (\(S_3\)): The STx has the CSI of the PTx\(\rightarrow \)PRx but not the STx\(\rightarrow \)EAV links; Scenario 4 (\(S_4\)): The STx has the CSI of both the PTx\(\rightarrow \)PRx and the STx\(\rightarrow \)EAV links. Accordingly, a power allocation algorithm corresponding to the four scenarios is introduced.

Given the four power allocation policies, the the secure and reliable communication probability (SRCP) is introduced to analyse the performance of the considered CRN.

Our numerical results show that the SRCP of Scenario 1 and Scenario 2 (Scenario 3 and Scenario 4) are only different in the low signaltonoise ratio (SNR) regime of the PTx, but they are the same in the high SNR regime of the PTx.
The remainder of this paper is organized as follows. The related work is introduced in Sect. 2, whereas in Sect. 3 the system model, assumptions, constraints corresponding to four scenarios for the CSI at the STx together with problem statement for a SIMO CRN are introduced. In Sect. 4, power allocation policies corresponding to four scenarios are obtained. Further, a closedform expression for the SRCP is derived. In Sect. 5, the numerical results and discussions are provided. Finally, conclusions are given in Sect. 6.
2 Related work
3 System model
Let us consider a system model as shown in Fig. 1 in which there are three types of user in the same area, termed the SU, PU, and EAV. The PU allows the SU to reutilize its licensed spectrum provided that the SU does not cause harmful interference to the PU. On the other hand, the EAV wants to eavesdrop the information of the su’s communication over a wiretap channel. In fact, the EAV can overhear the information of both the STx and PTx, but in this system model the EAV wants to utilize the interference from the PTx to exploit the exchange of information from the SU. Here, we assume that the STx and PTx are equipped with a single antenna while the SRx, PRx, and EAV have \(N_s\), \(N_p\), and \(N_{e}\) antennas, respectively. This system model is considered as an instance of practical scenario where the PTx and STx may be mobile users while the PRx and SRx are base stations or access points. Note that the PU can transmit with an optional power level for its communication without caring about the existence of the SU. On the other hand, the SU should keep the interference inflicted onto the PU below a predefined threshold. Hence, the SU should have channel mean gain of the STx\(\rightarrow \)PRx link (not instantaneous channel gains) to adjust its transmit power. This is based on the fact that the SU and the PU can collaborate using a localization service where the channel mean gains of the PU and SU such as transmission distance, antenna gain, and so on, can be exchanged [40, 41]. Moreover, the STx and PTx are assumed to have full CSI of the STx\(\rightarrow \)SRx and PTx\(\rightarrow \)PRx links, respectively. This is reasonable due to the fact that both SU and PU are in the same systems and they should have dedicated feedback channels. In addition, the channel mean gain of the STx\(\rightarrow \)EAV can be selected offline following [42, 43, 44].
3.1 Performance Metric for the SU communication
3.2 Constraints for transmit power of the SU
 1)

Scenario 1 (\(S_1\)): STx does not have the CSI of neither PTx\(\rightarrow \)PRx nor theSTx\(\rightarrow \)EAV links
In this scenario, the STx transmits its confidential information without knowing the existence of the EAV. Also the STx does not have the CSI of the PTx\(\rightarrow \)PRx communication link. Accordingly, the STx only regulates its transmit power on the basis of the interference constraint given by the PU aswhere \(Q_{pk}\) is peak interference level that the PU can tolerate. This can be interpreted as that the STx is allowed to cause limited interference to the PRx, however, the probability of the interference caused by the STx should be kept below a predefined threshold \(\xi \) to not interrupt the PU communication. As a result, the constraints setting on the transmit power of the STx should satisfy two conditions as follows:$$\begin{aligned}&\mathcal {O}_{I}=\Pr \left\{ \max \limits _{m \in \{1,2,\ldots , N_p\}} \left\{ \frac{P^{}_{s}\varphi _m}{N_0}\right\} \ge Q_{pk} \right\} \le \xi , \end{aligned}$$(13)$$\begin{aligned}&\mathcal {O}_{I} \le \xi , \end{aligned}$$(14)where \(\xi \) and \(P^{max}_{s}\) are communication outage threshold given by the PU and the maximal transmit power of the STx, respectively.$$\begin{aligned}&0 \le P^{}_{s} \le P^{max}_{s}, \end{aligned}$$(15)  2)

Scenario 2 (\(S_2\)): STx has the CSI of the STx\(\rightarrow \)EAV but not PTx\(\rightarrow \)PRx
In this scenario, the STx knows the existence of the EAV in its coverage range and the CSI of the STx\(\rightarrow \)SRx link is available at the STx. However, the STx does not have the CSI of the PTx\(\rightarrow \)PRx link. Consequently, the transmit power of the STx should satisfy three constraints as follows:$$\begin{aligned}&\mathcal {O}_{I} \le \xi , \end{aligned}$$(16)$$\begin{aligned}&\mathcal {O}_{sec} \le \epsilon , \end{aligned}$$(17)where \(\epsilon \) is the secrecy outage constraint given by the SU and \(\mathcal {O}_{I}\) and \(\mathcal {O}_{sec}\) are defined in (10) and (13), respectively.$$\begin{aligned}&0 \le P^{}_{s} \le P^{max}_{s}, \end{aligned}$$(18)  3)

Scenario 3 (\(S_3\)): STx has the CSI of the PTx\(\rightarrow \)PRx but not STx\(\rightarrow \)EAV
In this scenario, the STx has the CSI of the PTx\(\rightarrow \)PRx communication link. However, it does not know the existence of the EAV. Accordingly, the constraints for the STx is as follows:$$\begin{aligned}&\mathcal {O}_{p} \le \theta , \end{aligned}$$(19)where \(\mathcal {O}_{p}\) is defined in (11), and \(\theta \) is the communication outage constraint of the PU. In other words, the transmit power of the STx should keep the outage probability of the PU below a given constraint.$$\begin{aligned}&0 \le P^{}_{s} \le P^{max}_{s}, \end{aligned}$$(20)  4)

Scenario 4 (\(S_4\)):STx has the CSI of both the PTx\(\rightarrow \)PRx and STx\(\rightarrow \)EAV
In this scenario, the STx adjust its transmit power to not reveal its confidential information to the EAV and to not cause harmful interference to the PRx. Thus, the transmit power of the STx is subject to three constraints as follows:$$\begin{aligned}&\mathcal {O}_{p} \le \theta , \end{aligned}$$(21)$$\begin{aligned}&\mathcal {O}_{sec} \le \epsilon , \end{aligned}$$(22)where \(\mathcal {O}_{p}\) and \(\mathcal {O}_{sec}\) are defined in (11) and (10).$$\begin{aligned}&0 \le P^{}_{s} \le P^{max}_{s}, \end{aligned}$$(23)
4 Performance analysis
In this section, we first derive the power allocation policy for the STx, and then use it to calculate the amount of fading, and outage performance of the STx. Let us commence by considering a property as follows.
property 1
Let a, b, and c be positive constants. Random variables \(X_i\) and \(Y_i\) are independent and exponentially distributed with mean values \(\Omega _X\) and \(\Omega _Y\), respectively. An RV U defined by
Proof
The proof is given in [48, Lemma 1]. \(\square \)
4.1 Transmission power allocation policies
To derive the power allocation policies for the STx, we need to calculate the secrecy outage probability of the SU given in (10), the outage probability of the PU given in (11), and the outage probability given in (13), respectively.
4.1.1 The transmit power of STx under the interference threshold of the PU
4.1.2 The transmit power of the STx under the secrecy outage constraint
4.1.3 The transmission power of the STx under the outage probability constraint of the PU
4.1.4 Power allocation policy for the considered scenarios
 Secondly, we obtain the power allocation policy for scenario S\(_2\) by combining (18), (29), with (33) as$$\begin{aligned} \mathcal {P}_{S_2}=\min&\left\{ \frac{Q_{pk}N_0}{\Omega _{\varphi }} \left( \log _e \frac{1}{1\root N_p \of {1\xi }}\right) ^{1} \right. \nonumber \\&\left. ,\frac{P^{}_{p} \Omega _{\rho }\gamma ^{e}_{th} }{\Omega _{\alpha }}\left( \frac{1}{\root N_e \of {1\epsilon }} 1\right) , P^{max}_{s} \right\} . \end{aligned}$$(39)
 Thirdly, the transmit power of the STx for scenario \(S_3\) is achieved by combining (20) with (36) aswhere \(\Xi \) is defined in (37) as$$\begin{aligned} \mathcal {P}_{S_3}=\min&\left\{ \frac{P^{}_{p}\Omega _{h} }{\gamma ^{p}_{th}\Omega _{\varphi }}\Xi , P^{max}_{s} \right\} , \end{aligned}$$(40)Note that this power allocation is exactly the one reported in [48, Eq. (9)].$$\begin{aligned} \Xi&= \max \left\{ 0, \frac{1}{1\root N_p \of {\theta }}\exp \left[  \frac{\gamma ^{p}_{th}N_0}{P^{}_{p}\Omega _{h}} \right] 1 \right\} . \end{aligned}$$(41)
 Finally, the transmit power policy of the STx for scenario \(S_4\) is established by combining (20), (36) with (33) as$$\begin{aligned} \mathcal {P}_{S_4}=\min&\left\{ \frac{P^{}_{p} \Omega _{\rho }\gamma ^{e}_{th} }{\Omega _{\alpha }}\left( \frac{1}{\root N_e \of {1\epsilon }} 1\right) \right. \nonumber \\&\left. ,\frac{P^{}_{p}\Omega _{h} }{\gamma ^{p}_{th}\Omega _{\varphi }}\Xi , P^{max}_{s} \right\} . \end{aligned}$$(42)
4.2 Secure and reliable communication probability
Finally, a closedform expression of the safe and secure communication probability is obtained by substituting (44) and (45) into (43), where \(\mathcal {P}_{}\)\(\in \)\(\left\{ \mathcal {P}_{S_1},\mathcal {P}_{S_2}, \mathcal {P}_{S_3},\mathcal {P}_{S_4}\right\} \) is the transmit power allocation policy of the STx.
5 Numerical results

System bandwidth: B= 5 MHz;

SU target rate: \(R_s\)=128 Kbps;

PU target rate: \(R_p\)=64 Kbps;

SU secrecy information rate: \(R_{e}\)=64 Kbps;

Pathloss exponent \(\nu =4\);

Outage probability constraints of the PU and SU: \(\theta =\xi =0.01\);

Outage probability constraint of the EAV: \(\epsilon =0.1\);

The maximal transmit SNR of the STx: \(\gamma ^{\max }_{s}=10\) (dB);

Peak interference level of the PU: \(Q_{pk}=5\) (dB)
Figure 2 shows the transmit SNR of the STx as a function of the PTx transmit SNR. Firstly, we observe the behavior of the transmit SNR of the STx in the scenarios \(S_1\) and \(S_2\), and can see that the transmit SNR of the STx in scenario \(S_1\) is constant for the entire range of the PTx SNR. This result matches (38) where the transmit SNR of the STx does not depend on the transmit SNR of the PTx. In contrast to scenario \(S_1\), the STx linearly increases with an increase of the STx transmit SNR in scenario \(S_2\),. However, when the transmit SNR of the PTx increases beyond 10 dB (\(A_1\)), the transmit SNR of the STx is saturated. This can be explained by the fact that the transmit SNR of the STx is allocated using Eq. (39). Thus, in the regime \([16,10]\) dB, the transmit SNR of the STx is controlled by the constraint of the EAV. However, if the transmit SNR of the PTx increases further, the transmit SNR of the STx is subject to the minimum value of the first term and third term in Eq. (39), i.e., in the high regime of the transmit SNR of PTx, the transmit SNR of the STx is similar to the one in Scenario 1. It is easy to understand that the transmit SNR of the STx in scenario \(S_1\) is always less than or equal to the one in scenario \(S_2\) since the transmit SNR STx in \(S_2\) is subject to a additional constraint, i.e., the outage constraint of the EAV. Secondly, we observe the behavior of the transmit SNR of the STx in scenarios \(S_3\) and \(S_4\). It can be seen that the transmit SNR of the STx in the scenario \(S_4\) is always less than the one of the scenario \(S_3\). However, in the high regime of the transmit SNR of the PTx, e.g. \(\bar{\gamma }_p \ge 16\) dB, they are equal and saturated at \(A_2\). This is because the transmit SNR of the STx in scenario \(S_4\) endures more constraints than the one of scenario \(S_3\), i.e., the constraint of the EAV. Finally, we can conclude that the appearance of the EAV leads to that the power allocation policy for the STx is more complicated and may degrade the performance of the SU.
Finally, we examine the impact of the number of antennas of the EAV on the SRCP of the SU as shown in Fig. 7. It can be seen that the SRCP for scenarios \(S_1\) and \(S_3\), where the secure constraint are not considered, are degraded rapidly. Alternatively, the SRCP in scenarios \(S_2\) and \(S_4\), where the secure constraint is integrated, degrade gradually. Clearly, the scenarios with the CSI of the EAV can make the information communication of the SU more secure and reliable.
6 Conclusions
In this paper, we have investigated how to obtain secure and reliable communication in a CRN in which the SU transmitter is subject to eavesdropping. Given the constraints of the PU, EAV, and SU, we derive four power allocation polices corresponding to four different scenarios depending on which type of CSI that is available. Accordingly, a performance measure in terms of secure and reliable communication probability is introduced to evaluate the considered system. Our results show that the security constraint only effects the SRCP of the SU in the low regime of the transmit SNR of the PTx. Further, the system performance degrades significantly when the security constraints are not considered and the number of antennas of the EAV increases. Finally, simulations validate our analytical results.
Notes
Acknowledgements
The research leading to these results has been performed in the research project of Ministry of Education and Training, Vietnam (No. B2017TNA50), and the SafeCOP project which is funded from the ECSEL Joint Undertaking under grant agreement n\(^{0}\) 692529, and from National funding.
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