Multiple-Phase Energy Detection and Effective Capacity Based Resource Allocation Against Primary User Emulation Attacks in Cognitive Radio Networks

Abstract

Cognitive radio (CR) is regarded as an effective approach to avoid the inefficient use of spectrum. However, CRNs have more special security problems compared with the traditional wireless communication systems due to its open and dynamic characteristics. Primary user emulation attack (PUEA) is a common method which can hinder secondary users (SUs) from accessing the spectrum by transmitting signals who has the similar characteristics of the primary users' (PUs) signals, and then the SUs' quality of service (QoS) cannot be guaranteed. To handle this issue, we first design a multiple-phase energy detection scheme based on the cooperation of multiple SUs to detect the PUEA more precisely. Second, a joint SUs scheduling and power allocation scheme is proposed to maximize the weighted effective capacity of multiple SUs with a constraint of the average interference to the PU. The simulation results show that the proposed method can effectively improve the effective capacity of the secondary users compared with the traditional overlay scheme which cannot be aware of the existence of PUEA. Also the good delay QoS guarantee for the secondary users is provided.

1. Introduction

With the rapid development of wireless communication technology, mobile devices and services become more diverse and the bandwidth demand for wireless networks increases dramatically. The traditional spectrum allocation policy assigns spectrum to the specific authorized users fixedly. The spectrum efficiency of such a static allocation is very low [1]. The survey data of Federal Communication Commission (FCC) show that many authorized bands are underutilized [2]. Cognitive radio is considered to be an efficient solution to overcome the problem of spectrum inefficiency and scarcity by the dynamic and flexible spectrum access. Actually, CR technology has been deemed as a promising approach to address the challenges and requirements on massive capacity of the fifth generation (5G) mobile networks [3], [4]. Spectrum sharing by dynamic spectrum access is the core idea of CR. In order to meet the much higher spectrum requirements of 5G, full spectrum sharing throughout all kinds of spectrum resources is expected, such as low and high frequency bands, licensed and unlicensed frequency bands, and continuous and discontinuous frequency bands [4]. Spectrum sensing and spectrum allocation are two key steps of spectrum sharing in cognitive radio networks (CRNs). The main purpose of spectrum sensing is to find the white spaces so that SUs can obtain more opportunities to access the authorized spectrum without causing harmful interference to PUs. Spectrum allocation aims to achieve the efficient utilization of licensed spectrum to guarantee the QoS requirements for SUs by distributing the spectrum white spaces to SUs optimally.

pectrum white spaces to SUs optimally. However, the openness of the wireless communication system makes the CRNs face more specific security issues. PUEA is a common problem. According to the attacking purpose, PUEA could be classified into two categories: a selfish SU and a malicious PUE attacker. A selfish SU would emulate the PU’s signal to access a primary channel as the PU does not use it, or broadcast fake information on the available channel in order to empty or pre-occupy a channel for its own transmission. A malicious PUE attacker would induce the denial of service (DoS) to the CRNs by sending the faked PU signal and then decrease the spectrum access opportunity of SUs. The existence of attack signal makes SUs unable to determine whether PUs or MUs occupy channel when channel is busy based on the traditional spectrum sensing methods. Meanwhile, the existing resource allocation schemes will not be suitable for such PUEA scenario either. The power allocation for SUs is also difficult to implement.

The correct detection of PUEA is of great significance for causing the low interference to PUs and maximizing the utilization of spectrum resource. Some works have studied the detection of PUEA. They can be generally divided into two categories namely location-aware methods [5],[6] and location-unaware methods [7]-[12]. Location-aware methods first locate the signal transmitter based on the measurements of received signal strength (RSS)[5] or time difference of arrival (TDOA)[6]. Then, the estimated location of the signal source is compared with the known position of the PU transmitter to determine whether the signal source is a PU or PUEA. However, location based detection schemes need a prior knowledge of the PUs’ locations. The location-unaware methods try to identify a PU and a PUEA mainly by using the signals’ some characteristics, such as the energy and the cyclic stationarity of signals. Moreover, cooperative spectrum sensing (CSS) technology based on the decisions or measured data fusion of multiple-SUs has been widely used in CRNs to obtain a high detection accuracy in deep fading environment. CSS could be also introduced to improve the PUEA detection performance. In [7], a two-phase PUEA detection algorithm based on multiple SUs cooperation was proposed toward a CRN with PUs communicating with OFDM signal. In the first phase, the cyclic stationary feature of non-zero autocorrelation property of OFDM signals is utilized to distinguish PUs from PUEAs which do not use OFDM signals. Then the energy based detection is executed in the second phase to further distinguish PUE attacks from the noise, if the first-phase detection reveals that the primary user is absent. However, this method would become invalid when the PUEA can emulate PUs to transmit OFDM signals. In fact, such a scenario would appear very likely for a selfish SU attack or a smart PUE attack. Moreover, hard decision fusion (HDF) detection schemes combining the binary decision of each SU with K-out-N rule at fusion center (FC) were studied to collaboratively detect PU and PUEA in [8],[9]. Concretely, the main parameters involved in cooperative spectrum sensing, such as the number of samples, the detection thresholds for the SU’s local decision and the parameter K in voting rule, were optimized to minimize the sensing error probability in the works of [8] and [9]. To retain more information of the local observations at each SU, soft decision fusion (SDF) schemes were studied also to realize the accurate PU detection in the presence of PUEA in [10], [11]. The local measured statistic of each SU rather than the binary decision result is sent to FC and a global decision is made by FU based on the original measurements of multiple SUs. The authors of [10] adopted a weighted combination of energy statistics from SUs at FC to make the global decision. Further, the weights were optimized to maximize the SU’s throughput. While, the work in [11] applied minimum Bayes cost criteria to determine the channel status in four cases. In addition, a selfish SU attack was discussed in [12]. In order to find the selfish SU who broadcasts faked available channel lists to its neighboring SUs for pre-occupying the channel, an attack detection method based on information exchanging and comparing among neighboring CR nodes was presented. However, the attack type in [12] is different from our work in this paper. We focus on the malicious PUE attack, where an attacker sends the faked PU signal rather than the false vacant channel lists to prevent legitimate SUs from accessing the available channel.

The purpose of accurate detection is to improve QoS of SUs as well as avoid any deleterious interference to the PU. Specifically, the real-time performance is one of important evaluation indexes of communication quality. Compared with conventional wireless networks, delay QoS guarantee is a more challenging issue for CRNs. Effective capacity [13] has been introduced as a powerful tool to describe the ability that a system provides real-time services. Thus, enhancing the effective capacity is a feasible way to ensure the delay QoS of SUs. Furthermore, different users may have different delay requirements. For example, the voice traffic may have stricter delay QoS constraint than the data traffic. Hence, it is meaningful to study on the discrepant delay QoS provision for different SUs. There exist some works considering the resource allocation for the PUEA scenarios. The authors of [14] proposed a power allocation to maximize the transmission rate of SUs for an OFDM CRNs with PUEA. Here, the secondary users only transmit signals when the primary channel is sensed to be idle. In order to improve the spectrum utilization, the scheme in [15] allowed the SUs to access the spectrum when it is idle or occupied by MUs. It also took the maximization of the SU’s rate as the design object. Furthermore, the works in [16], [17] investigated the energy efficiency (EE) maximization problem by SU selection, power allocation and sensing time assignment in the presence of PUEA. However, the above works did not consider the delay QoS requirement of the SU’s practical traffic. While, such a requirement is more difficult to be satisfied when the malicious attacker exists.

In order to provide better delay QoS for different secondary users, we first propose a multiple-phase energy detection scheme to detect the PUEA more accurately through fusing the energy statistics of multiple secondary users. Further, the weights in the fused statistic are determined and the decision thresholds are obtained based on the analyzed detection probabilities for three decision cases. Second, a joint SUs scheduling and power allocation scheme is proposed to maximize the weighted effective capacity of the SUs. Here, the secondary users will access the spectrum when it is sensed to be idle or occupied by the malicious users. Further, an iterative process, which includes an exhaustive search based user scheduling and a CVX based power allocation, is adopted to solve the joint optimization problem. The simulation results demonstrate that the proposed PUEA detector can recognize the primary users and malicious users efficiently. The delay QoS guarantee for SUs can be realized better by the proposed joint user scheduling and power allocation scheme.

The rest of the paper is organized as follows: In section 2, a system model with multiple SUs and several MUs is described and the transmission model is given. The multiple-phases energy detection scheme based on the cooperation of multiple SUs is presented in section 3. Section 4 introduces the joint user scheduling and power allocation method based on effective capacity in detail. Section 5 presents and analyzes the simulation results. Section 6 concludes the paper.

2. System Model

Consider a cognitive radio network shown in Fig. 1, which includes one primary channel, M secondary users and several malicious users. Assume the MUs occupy the primary channel with a certain probability when the PU is inactive. Multiple SUs can cooperatively sense the occupancy state of the primary channel and then access the channel legitimately based on the sensing result. The overlay mode is adopted. SUs will not access the channel when it is sensed to be occupied by PU in order to reduce interference to the PU as much as possible.

Fig. 1. System model of a CRN with PUEA

Assume the licensed spectrum bandwidth is B and the small-scale fading of wireless channel follows the independent and identically distributed (i.i.d.) Rayleigh block fading. The length of a frame is T seconds. The SUs perform spectrum sensing to detect the status of channel during the preceding T₀ seconds of a frame. Then, one SU is scheduled to transmit signal in the remaining T - T₀ seconds if the decision result is the PU being absent. The other main assumptions similar as the ones given in [18] are listed as followings:

1) The primary transmitter (PT) sends the signal with constant power and the SUs’ positions remain unchanged. While, MUs’ power and positions would change randomly.

2) The received signals from PT and MUs are both assumed to be independent and identically distributed (i.i.d.) random variables following cyclo-stationary complex Gaussian distribution with zero mean. The variances are \( \sigma_{Ps}^2\) and \(\sigma_{Ms}^2\) , respectively, where s = 1, 2,...,M is the index of SU.

3) The noise is the i.i.d. cyclo-stationary complex Gaussian distributed random variables with mean zero and the variance \(\sigma_{Ns}^2\).

There are three actual states for the primary channel. H₀ indicates idleness. H₁ and H₂ indicate that the channel is occupied by PU and MUs, respectively. Assume that MUs can sense the status of the primary channel correctly. MUs will not attack when the channel is used by the PU in order to prevent being detected by the conservation strategies of the PU. Moreover, MUs cannot occupy the idle channel continuously due to the power restriction. Then, the Priori probability of each status P(H_i) would be larger than 0.

In the system given above, the spectrum sensing problem could be modeled as a hypothesis testing problem with three actual states. Further, D₀, D₁ and D₂ are used to represent the three channel states sensed, namely being idle, being used by PU and being attacked by MUs. Then, the detection results have nine possible cases and the corresponding probabilities are denoted by {\({P_{ij}=P(H_i)\centerdot P(D_j/H_i),i,j\in{0,1,2}}\)}

3.1 Multiple Detection Statistics

Energy detection is a simple method for spectrum sensing in the traditional CRNs with two actual states, whose hypothesis testing problem for the s-th SU could be expressed as

\(Y_{s}=\frac{1}{N} \sum_{i=1}^{N}\left|y_{s}(i)\right|^{2} \gtrless_{H_{0}}^{H_{1}} \lambda\)       (1)

where we have

\(y_{s}(i)=\left\{\begin{array}{ll} n_{s}(i), & H_{0} \\ h_{s}(i) x_{\mathrm{p}}(i)+n_{s}(i), & H_{1} \end{array}\right.\)       (2)

Here, h_s is the primary channel coefficient and n_s is an additive noise. x_p is the signal sent by the PU’s transmitter. N is the number of samples for sensing. \(\lambda\) is the decision threshold to detect the presence of the signal x_p.The energy statistic Y_p in Eq. (1) follows the Chi-square distribution with a degree of freedom of N. However, according to the Central Limit Theorem (CLT), Y_s can be approximated by a Gaussian distribution with a long enough N. Actually, CLT has been usually applied to simplify the analysis and design in the spectrum sensing, such as in [9], [11] and [19]. Further, the authors of [9] and [11] considered that CLT could be used when N >10. This condition is commonly satisfied in a practical system.

However, the traditional binary hypothesis testing is unsuitable for the scenario with PUEA. As the primary channel is occupied by a MU, the received signal of the s-th SU is y_s(i)=g_s(i)x_M(i)+n_s(i) , where g_s is the channel coefficient from the MU to the s-th SU and x_M is the signal sent by the MU. Then, Y_s may still be larger than the threshold λ and the SU cannot distinguish whether the channel is occupied by PU or MUs. Therefore, combing the idea of multiple thresholds based scheme in [20] with the CSS methods in [10] and [11], we present a modified energy based PUEA detection method, called multiple-phase energy detection based on multiple users’ cooperation. Its main idea is to extract multiple detection statistics based on the energy statistics from M SUs to detect the presence of PU and MUs more accurately.

In this scheme, the key parameters of \(\sigma_{ps}^2\)and \(\sigma_{Ns}^2\)for each SU are assumed to be known by fusion center, but there is no information about \(\sigma_{Ms}^2\). The detection statistic used in the i-th phase is \(V_{i}=\mathbf{W}_{i}^{T} \mathbf{Y}=\sum_{s=1}^{M} w_{i_{-} s} Y_{s}\), where \(\mathbf{W}_{i}=\left[w_{i_{-} 1}, w_{i_{-} 2}, \ldots, w_{i_{-} M}\right]^{T}\) and \(\mathbf{Y}=\left[Y_{1}, Y_{2}, \ldots, Y_{M}\right]^{T}\). Furthermore, \(i \in\{1,2, \ldots, L\}\) and we take L M= in order to make full use of the energy statistics provided by all SUs. From observation, we can find that it is more difficult for MUs to emulate PU’s signals to make all of L detection statistics built by M SU’s measurements similar to the case of PU exiting, except that the location of MU is same as PU. For example, consider a simple case of two SUs, which corresponds to a two-phase energy detection. The two detection statistics can be simply built as V₁ = (Y₁+Y₂)/2 and V₁ = (Y_1-Y₂)/2 , respectively. Under the scenario assumption that PU’s signal has constant power and SUs’ positions are fixed, V₁ and V₂ would be stable around two certain values, denoted by ε₁ and ε₂ , when PU is present. Because the dynamic nature of PUEA’s behaviors, Y₁ and Y₂ would change randomly. Then, even though the PUEA could make V₁ near to ε₁ , it is still difficult to keep V₂ close to ε₂ simultaneously. From this point of view, we can think that the given multi-phase scheme has stronger robustness to PUEA.

3.2 Decision Procedure

The decision procedure of the proposed multiple phase energy detection for PUEA is presented in Fig. 2. There are 2L + 1 thresholds for L detection statistics. The first detection statistic V₁ is mainly used to distinguish whether the primary channel is idle or busy. All the other V_i are used to distinguish whether the channel is used by PU or by MUs. When V₁ is less than the threshold of λ₀ , the channel is deemed to be idle. Because the transmitting power of PU is constant, all of the detection statistics should keep stable under H₁ state. Therefore, only when all the V_i locate during the corresponding range of (λ_i1 , λ_i2 ), the detection result is D₁. In other situations, the channel would be deemed to be occupied by MUs based on the instability assumption of the MUs’ power and locations.

Fig. 2. Decision Procedure of Multiple-Phase Energy Detection

3.3 Determination of the Weights and Detection Thresholds

A. Determination of the weight vector W_i

Since V₁ is mainly used to decide whether the channel is occupied, the average received energy of all the SUs are taken as V₁ simply and then we have W_{1_s}=1/M,  ∀s ∈{1,...,M}.

In order to obtain the other weight vectors W_i, i = 2,..,L, an intuitive and heuristic method is given. We set \(\left|w_{i_{-} 1}\right|\left(\sigma_{\mathrm{N} 1}^{2}+\sigma_{\mathrm{P} 2}^{2}\right)=\left|w_{i_{-} 2}\right|\left(\sigma_{\mathrm{N2}}^{2}+\sigma_{\mathrm{P} 2}^{2}\right)=\ldots=\left|w_{i_{-} M}\right|\left(\sigma_{\mathrm{NM}}^{2}+\sigma_{\mathrm{PM}}^{2}\right)\) and then combine it with the constraints of \(0<\left|w_{i_{-} s}\right|<1\) and \(\sum_{s=1}^{M}\left|w_{i_{-} s}\right|=1\) to obtain

\(\left|w_{i_{-} s}\right|=\frac{\prod_{k=1, k \neq s}^{M}\left(\sigma_{\mathrm{Nk}}^{2}+\sigma_{\mathrm{Pk}}^{2}\right)}{\sum_{l=1}^{M} \prod_{k=1, k \neq l}^{M}\left(\sigma_{\mathrm{Nk}}^{2}+\sigma_{\mathrm{Pk}}^{2}\right)}\)       (3)

Because it is reasonable to deem that the SU with higher received power from the PU transmitter may not contribute more for detecting the MU, we set a smaller \(\left|w_{i_{-} s}\right|\) for a SU with larger (σ²_Ns + σ²_Ps).

As for the sign of w_i-s, some optimization criterion could be used. For example, \(D_{w}=\sum_{i=2}^{M} \sum_{j=i+1}^{M}\left\|\mathbf{W}_{i}-\mathbf{W}_{j}\right\|^{2}\) maximization which is adopted in this paper. In the simulation, a greedy search is used to find the signs of w_i-s.

B. Calculating Probability Density Function (PDF) of V_i

The probability density function of the detection statistics V_i under three Prior states could be easily obtained as

\(\left\{\begin{array}{l} H_{0}: V_{i} \sim \mathrm{N}\left(\sum_{s=1}^{M} w_{i_{-} s} \sigma_{\mathrm{Ns}}^{2}, 1 / N \sum_{s=1}^{M} w_{i_{-} s}^{2} \sigma_{\mathrm{Ns}}^{4}\right)=\mathrm{N}\left(\beta_{i 0}, \delta_{i 0}^{2}\right) \\ H_{1}: V_{i} \sim \mathrm{N}\left(\sum_{s=1}^{M} w_{i_{-} s}\left(\sigma_{\mathrm{Ns}}^{2}+\sigma_{\mathrm{P}_{s}}^{2}\right), 1 / N \sum_{s=1}^{M} w_{i_{-}s}^{2}\left(\sigma_{\mathrm{Ns}}^{2}+\sigma_{\mathrm{P}_{s}}^{2}\right)^{2}\right)=\mathrm{N}\left(\beta_{i \mathrm{P}}, \delta_{i \mathrm{P}}^{2}\right) \\ H_{2}: V_{i} \sim \mathrm{N}\left(\sum_{s=1}^{M} w_{i_{-} s}\left(\sigma_{\mathrm{Ns}}^{2}+\sigma_{\mathrm{Ms}}^{2}\right), 1 / N \sum_{s=1}^{M} w_{i_{-} s}^{2}\left(\sigma_{\mathrm{Ns}}^{2}+\sigma_{\mathrm{Ms}}^{2}\right)^{2}\right)=\mathrm{N}\left(\beta_{i \mathrm{M}}, \delta_{i \mathrm{M}}^{2}\right) \end{array}\right.\)       (4)

C. Setting the constraints for the probabilities of correction detection

Two constraints for the probabilities of correct detection under the cases of H₀ and H₁ are preset as P(D₀ / H₀) ≥ a and P(D₁ / H₁) ≥ b.

D. Calculating the threshold λ₀ for V₁

One threshold λ₀ is used to distinguish H₀ from the other two states and it can be derived by selecting the equality sign in P(D₀ / H₀) ≥ a. The detail is given by

\(\begin{array}{l} P\left(D_{0} / H_{0}\right)=P\left(\left.V_{1}\right|_{H_{0}} \leq \lambda_{0}\right)=1-Q\left(\left(\lambda_{0}-\beta_{10}\right) / \sqrt{\delta_{10}^{2}}\right)=a \\ \Rightarrow \lambda_{0}=Q^{-1}(1-a) \delta_{10}+\beta_{10} \end{array}\)       (5)

E. Calculating the rest thresholds λ_i1 and λ_i2

The rest thresholds λ_i1 and λ_i2 , ∀i ∈ {1,...,L} , are obtained by using the constraint P(D₁ / H₁) = b . In order to derive 2L thresholds from only one equalization determinately, we deem that V_i is independent with each other approximately, then it can be achieved that

\(P\left(D_{1} \mid H_{1}\right)=\prod_{i=1}^{L} P\left(D_{1} \mid H_{1}, V_{i}\right)=b, i=1, \ldots, L\)      (6)

Furthermore, we simply set

\(P\left(D_{1} \mid H_{1}, V_{i}\right)=P\left(D_{1} \mid H_{1}, V_{j}\right) \quad \forall i, j \in\{1, \ldots, L\}\)      (7)

Thus, we have

\(P\left(\lambda_{i 1} \leq\left. V_{i}\right|_{H_{1}} \leq \lambda_{i 2}\right)=Q\left(\left(\lambda_{i 1}-\beta_{i P}\right) / \sqrt{\delta_{i P}^{2}}\right)-Q\left(\left(\lambda_{i 2}-\beta_{i \mathrm{P}}\right) / \sqrt{\delta_{i P}^{2}}\right)=\sqrt[L]{\mathrm{b}}\)       (8)

Further, let λ_i1 and λ_i2 be symmetrical about β_iP and it can be easily obtained

\(\left\{\begin{array}{l} \lambda_{i 1}=\beta_{i \mathrm{P}}-Q^{-1}((1-\sqrt[L]{b}) / 2) \delta_{i \mathrm{P}} \\ \lambda_{i 2}=\beta_{i \mathrm{P}}+Q^{-1}((1-\sqrt[L]{b}) / 2) \delta_{i \mathrm{P}} \end{array}, \quad i=1,2, \ldots, \mathrm{L}\right.\)       ( 9)

It is worth noting that there is a special case for setting λ₀ and λ₁₁ . From Eq.(5) and Eq.(9), we can see that λ₁₁ may be smaller than λ₀ when σ_Pk² is small. For such a case, we will set them identical with the average value of them.

4. Effective Capacity Based Joint SUs Scheduling and Power Allocation under PUEA Scenario

Consider the case that multiple secondary users will share the primary channel after coordinate spectrum sensing. Furthermore, suppose that different SUs have different delay QoS requirements because different traffics usually have different delay constraints in practical communications. In order to address the resource allocation issue in the above scenario, an effective capacity based joint SUs scheduling and power allocation is proposed to guarantee the differential delay QoS requirements of multiple SUs who share one idle primary channel.

4.1 Effective Capacity of Secondary Users

Effective capacity can be used to describe the ability to provide real-time services. It is defined as the maximum constant arrival rate that a given service process can support under an appointed statistical QoS constraint [21],[22]. Effective capacity can be expressed as