# A Robust Cooperative Spectrum Sensing-Assisted Multiuser Resource Allocation Scheme

Authors: Jun Du; Daoxing Guo; Bangning Zhang; Yunxia Su
Journal: Mathematical Problems in Engineering
 (2015)

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## Abstract

Cognitive radio (CR), which is proposed as a solution for spectrum scarcity, imposes some threats to the network. One severe attack to cognitive radio network is the primary user emulation attack (PUEA), in which an attacker may transmit its signal with high power or mimic specific features of the primary user’s signal to prevent secondary users from accessing the licensed spectrum. In this paper, we study a subcarrier and power allocation problem for orthogonal frequency division multiple access-(OFDMA-) based CR systems in the presence of PUEA. To maximize the system throughput while keeping the interference introduced to the primary user (PU) below given thresholds with a certain probability, a joint design of a robust cooperative spectrum sensing and a resource allocation scheme is proposed. In the proposed scheme, the inaccurate classification of PU signals and PUEA signals provided by robust cooperative spectrum sensing is utilized by resource scheduling module. To further exploit the underutilized spectrum bands, we also evaluate the performance of the proposed scheme in the hybrid overlay/underlay spectrum access mechanism. Numerical results demonstrate the effectiveness of the proposed scheme compared to conventional scheme regardless of the number of SUs or the kind of spectrum access mechanism being used.


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## Body

## 1. Introduction

Cognitive radio networks (CRNs) are expected to bring a revolution to the spectrum scarcity problem through intelligent use of the underutilized or the free spectrum bands [1]. In CRNs, a secondary (unlicensed) user (SU) can access the licensed bands under the condition that the induced interference to the primary (licensed) users (PUs) does not reach an unacceptable level. In general, to exploit unused and underutilized spectrum bands, an SU has three spectrum sharing approaches for a dynamic spectrum access mechanism [2], namely, the underlay spectrum access mechanism (USAM), the overlay spectrum access mechanism (OSAM), and hybrid overlay/underlay spectrum access mechanism (HOUSAM) [3]. According to the OSAM, SUs access the spectral bands only when they are not being used by the PUs; in the USAM, the PUs and SUs can coexist in the same spectral band which means the SUs can utilize the underutilized frequency bands of the PUs. In HOUSAM, the SU can transmit in both the unused and underutilized spectrum bands. It improves the throughput of the secondary network while maintaining a harmless interference to the PU.Orthogonal frequency division multiplexing (OFDM) is a promising candidate for CRNs [4]. With OFDM, the SU has the ability to flexibly fill the spectral gaps left by PUs and/or utilize the underutilized frequency bands of the PUs, by disabling or decreasing the power allocated to a set of subcarriers. In a conventional OFDM system, to maximize the efficiency of the spectral resources utilization, a power-allocation algorithm is proposed in [5]. In an orthogonal-frequency-division multiple-access- (OFDMA-) based system, to exploit the time-varying nature of fading gains across users in a given subcarrier, a subcarrier allocation algorithm is proposed in [6]. For conventional OFDMA wireless systems, resource allocation algorithms have been studied extensively [7]. Using these resource allocation algorithms directly into CRNs may result in higher mutual interference in the PUs’ band, since they coexist in side-by-side bands and the nonorthogonality of transmitting signals. Recently, resource allocations in OFDM-based CRNs have received a great deal of attention.Finding unused and underutilized spectrum bands in CRNs is based on the information gathered from SUs’ spectrum sensing reports. However, in the hostile network environment, an attacker can mount primary user emulation attack (PUEA) to affect SUs’ reports. In such scenario, an attacker transmits signals whose characteristics resemble that of the PU transmitter, misleading the SUs to believe that the spectrum bands are occupied by the PU. Robust spectrum sensing [8] and resource allocation are two key enabling technologies for cognitive radio (CR). The former mainly concerns how to reliably recognize the existence of the unused spectrum bands and the latter concerns how to maximize the utilization of the recognized unused spectrum bands. For instance, in [9] a hybrid PUEA defense strategy based on a combination of energy detection and variance detection is proposed. The authors in [10] proposed a robust cooperative spectrum sensing that considers an always present PUEA. For a smart PUEA, who is able to perform spectrum sensing and send its signal in a planned way, the authors in [11] proposed a new spectrum sensing scheme. In [12], the authors study resource allocation problem for OFDMA-based cognitive radio systems. A subcarrier and power allocation schemes for a hybrid overlay and underlay spectrum access mechanism are proposed in [13]. In [14], a distributed power allocation algorithm for underlay CRNs is proposed, where channel gains between SUs and PU base stations are uncertain.In most of existing designs for CRNs, robust spectrum sensing and resource allocation are implemented separately. That is, in the first step, robust spectrum sensing makes a relatively reliable decision on whether the primary signal is present or not. Then this decision is transferred to the next step. Based on the information got from the first step, a resource scheduling module could accomplish the power allocation and/or spectrum band assignment task. In this paper, we study the joint design of robust spectrum sensing and resource allocation in OFDMA-based cognitive radio systems. The feasibility of this idea is as follows.Firstly, robust spectrum sensing has the ability to make a relatively reliable classification of PU signals and PUEA signals not just distinguish vacant bands from occupied bands. Secondly, conventional resource allocation assumes a secure environment and did not utilize the information of imperfect classification of PU signals and PUEA signals got from robust spectrum sensing. Recently, a valuable work [15] has revealed that robust resource allocation, which takes into account possible spectrum sensing errors occurring due to the presence of PUEA signals in the environment, is more efficient than conventional resource allocation. The scenario that the authors in [15] considered is composed of a primary and a secondary transceiver. This scenario is simple and the proposed resource allocation scheme is based on OSAM, which does not utilize the underused spectral regions.Due to the uncertainty present in the secondary base station- (SBS-) to-SU channel, underlay SU subcarriers may experience relatively better channel qualities, whereas the channel quality between the SBS and an overlay SU subcarrier can be poor. Therefore, to increase the overall spectrum utilization, the SUs may need to utilize not only the unused frequency bands but also underutilized frequency bands in a given geographical location and in a particular time. In this paper, considering the factor of the not fully reliable spectrum sensing results due to the PUEA, we propose a robust cooperative spectrum sensing-assisted multiuser resource allocation scheme (Rope-Alone) for OFDM-based CRNs. We showed that joint design of a robust cooperative spectrum sensing and a resource allocation outperforms the separated design. The proposed Rope-Alone can be used not only with an OSAM but also with a HOUSAM.The rest of the paper is organized as follows. In Section2, the system model is introduced and the problem discussed in this paper is formulated as an optimization problem. Section 3 presents the details of the solution for our proposed Rope-Alone. The results of numerical tests are presented in Section 4, followed by conclusions in Section 5.


## 2. System Model

### 2.1. Overall Description

In this paper, as shown in Figure1, we consider a downlink transmission scenario consisting of a centralized primary user network (PN) and a centralized cognitive radio network. An attacker attempts to fool the SUs in the CRN by transmitting PUEA signals, whereas the CRN endeavors to distinguish PU signals from PUEA signals and arrive at an optimal resource allocation scheme. As shown in Figure 2, the total available bandwidth licensed to the PU is equal to W which is divided into N subcarriers of equal width Δf. N={1,…,N} is the set of subcarriers. The CRN which employs an OFDM scheme includes a secondary base station (SBS) and K SUs and operates on a frame-by-frame basis. K={1,…,K} is the set of SUs. At the beginning of each frame, each SUii∈N carries out robust spectrum sensing to determine the vacant subcarriers and distinguish PU signals from PUEA signals in the occupied subcarriers. Then, each SUi sends its sensing results through the uplink reporting link to the SBS. Based on the reports collected from the SUs, we assume the SBS canperfectly differentiate vacant subcarriers from occupied subcarriers. Also, we assume that the SBS can distinguish between the PU and the PUEA signals in occupied subcarriersimperfectly. With the imperfect knowledge of the PU activity in occupied subcarriers, the SBS performs resource allocation, that is, channel or spectrum band assignment and power allocation, and feeds back the decisions to all SUs through the downlink broadcast link.Figure 1
System model.Figure 2
Example of the total available bandwidth.In this paper, perfect synchronization is assumed between FC and SU. This is because the IEEE 802.22 standard has defined Quiet Periods (QPs) where spectrum sensing is performed and SUs are not allowed to transmit. CRNs can synchronize their QPs through an offset synchronization technique using beacons [16]. In a centralized CRN, the FC distributes synchronization information through the control channel [17]. It is reasonable to assume that SUs are able to synchronize with the FC.In downlink transmission scenario shown in Figure1, there are four interference links: (1) between the primary user’s transmitter (PT) and the secondary user’s receiver (SR), let hk,nPS denote the channel fading gain between the PT and the kth SR in the nth subcarrier; (2) between the attacker’s transmitter (AT) and the primary user’s receiver (PR), let hlEP denote the channel fading gain between the AT and the PR in the lth subcarrier; (3) between the AT and the SR, let hk,nES denote the channel fading gain between the AT and the kth SR in the nth subcarrier; (4) between the SBS and the PR, let hlSP denote the channel fading gain between the SBS and the PR in the lth subcarrier. Furthermore, the link between the SBS and SR is the downlink broadcast link; let hk,nSS denote the channel fading gain between the SBS and the kth SR in the nth subcarrier. These instantaneous channel fading gains are assumed to follow a Rayleigh distribution and we assume these instantaneous fading gains are known at the SBS. Specifically, we assume that the SU can estimate instantaneous fading gains and report to the SBS through the uplink reporting link [18].


### 2.2. Modeling of the Imperfect Robust Cooperative Spectrum Sensing

Robust spectrum sensing can not only distinguish vacant subcarriers from occupied subcarriers, but also make a relatively reliable decision on the classification of PU signals and PUEA signals. In order to exploit this extra information, we will quantify the accuracy of classification and provide this to the subsequent resource allocation module to improve the spectrum utilization efficiency.Each SU senses the subcarriers periodically and makes a local decision about the presence of the PU signals and PUEA signals based on its own observations. The local decisions are to be sent to the SBS in consecutive time slots based on a time division multiple access (TDMA) scheme through the uplink reporting link. The reported local decisions are combined at the SBS, as shown in Figure2; all of these subcarriers S={1,…,N} will be divided into three parts [15]: the set of vacant subcarriers V, the set of subcarriers OP occupied by the PU, and the set of subcarriers OA occupied by the PUEA. Note that intersymbol interference (ISI) and intercarrier interference (ICI) are two factors of degrading the OFDM system performance. The shorter time of SU occupancy of the estimated free carriers may result in ISI.Furthermore, mobility of the SUs generates Doppler frequency spread, which may destroy the orthogonality between subcarriers. The loss of orthogonality (of the carriers) at the SUs results in ICI [19]. Many methods have been proposed to combat ICI. Among these methods, adaptive subcarrier bandwidth is one of the representatives. The authors in [20] reveal that increasing the subcarrier bandwidth (i.e., decreasing N) can reduce ICI. However, as the subcarrier bandwidth increases, the ISI also increases. Therefore, the subcarrier bandwidth selection is a tradeoff between decreasing the subcarrier bandwidth to eliminate the ISI and increasing the subcarrier bandwidth to reduce the ICI.We can write(1)S=V∪OP∪OA,OP∩OA=⌀.Due to the imperfect robust spectrum sensing, there would be errors in classification ofOP and OA. Let pl denote the real state in which the PU is sending signals over subcarrier l  (l∈OP∪OA), and let p^l denote the estimate of pl by robust spectrum sensing. Similarly, we denote el to indicate the real state in which the attacker is sending PUEA signals over subcarrier l  (l∈OP∪OA), and let e^l denote the estimate of el by robust spectrum sensing.So when the signal is from the PU, the probability that the SBS falsely classifies it as from the attacker ispfE=Pr⁡(e^l∣pl). When the signal is from the attacker, the probability that the SBS falsely classifies it as from the PU is pfP=Pr⁡(p^l∣el). Note that the probability of detection of PU signals and PUEA signals can be written as pdP=Pr⁡(p^l∣pl)=1-pfE and pdE=Pr⁡(e^l∣el)=1-pfP, respectively.Here, let us definePr⁡(pl∣p^l) as the probability that the SBS classifies the signals to be from the PU when it is indeed from the PU, and Pr⁡(el∣e^l) as the probability that the SBS classifies the signals to be from the PUEA when it is indeed from the PUEA. Hence, we use αlP and αlA to evaluate the accuracy of classification for the PU signals and the PUEA signals. Formally, these two probabilities which will be used in the subsequent resource allocation are defined as(2)αlP=Pr⁡pl∣p^l=pdPPr⁡⁡plPr⁡⁡p^l,(3)αlA=Pr⁡el∣e^l=pdEPr⁡elPr⁡e^l,respectively. The probability of Pr⁡(p^l) in (2) and the probability of Pr⁡(e^l) in (3) can be rewritten as Pr⁡(p^l)=pdPPr⁡(pl)+pfPPr⁡(el) and Pr⁡(e^l)=pdEPr⁡(el)+pfEPr⁡(pl), respectively, where Pr⁡(pl) denotes the probability of presence of the PU which is signal in the subcarrier l, Pr⁡(el) denotes the probabilities of presence of the PUEA signal in the subcarrier l.


### 2.3. Modeling of the Resource Allocation Problem in the Presence of an Attacker

In this paper, the goal of resource allocation is to maximize the total transmission rate ofK SUs while keeping total interference introduced to the PU subcarriers below a certain threshold and total power below a constraint.The capacity for thenth subcarriers used by the kth SU is calculated via the Shannon formula as [21] (4)rk,n=Δflog21+pk,nhk,nSS2σ2+ik,n+jk,n,where pk,n is the transmission power of the kth SU for the nth subcarrier, σ2 denotes the additive white Gaussian noise (AWGN) variance, ik,n denotes the interference introduced to the nth subcarriers of the kth SU due to the transmission of all PUs, and jk,n denotes the interference introduced to the nth subcarriers of the kth SU due to the transmission of PUEA signals.The sum capacity of thekth SU is (5)rk,n=Δf∑n=1NCk,nlog21+pk,nhk,nSS2σ2+ik,n+jk,n,where Ck,n can have only value of either 1 or 0, indicating whether the nth subcarrier is used by the kth SU or not, as only one SU can occupy a particular subcarrier.Mathematically, the objective is to find the optimal exclusive subcarrier assignment policyCk,n and power allocation policy pk,n jointly such that the CRN system throughput is maximized, while satisfying the interference temperature constraint required by the PU on each channel and the power budget of the SBS simultaneously; that is,(6)max⁡Ck,n,pk,nΔf∑k=1K∑n=1NCk,nlog21+pk,nhk,nSS2σ2+ik,n+jk,ns.t.iiiiiiiiC1:Pr⁡Il≤Ithl≥a,l∈OP∪OAiiiiiiiiiiC2:Ck,n=0,1,∀k∈K,∀n∈NiiiiiiiiiiC3:∑k=1KCk,n=1,∀n∈NiiiiiiiiiiC4:pk,n≥0,∀k∈K,∀n∈NiiiiiiiiiiC5:∑k=1K∑n=1NCk,npk,n≤PT,where PT denotes the total power budget, I(l) denotes the interference introduced to the lth subcarriers of the PU due to the transmission of all SUs, and Ith(l) denotes the interference threshold for the lth PU subcarriers. C1 are the interference constraints for all PUs subcarriers; it can be guaranteed that the interference introduced to the lth PU subcarriers remains below a specified interference threshold Ith(l) with specified probability a [12]. C2 and C3 indicate each subcarrier can be allocated to only one SU. C4 and C5 are the transmitter power constraints.In the subsequent section, this optimization problem will be deduced in detail; an optimal subcarrier-and-power allocation can be obtained.


## 2.1. Overall Description

In this paper, as shown in Figure1, we consider a downlink transmission scenario consisting of a centralized primary user network (PN) and a centralized cognitive radio network. An attacker attempts to fool the SUs in the CRN by transmitting PUEA signals, whereas the CRN endeavors to distinguish PU signals from PUEA signals and arrive at an optimal resource allocation scheme. As shown in Figure 2, the total available bandwidth licensed to the PU is equal to W which is divided into N subcarriers of equal width Δf. N={1,…,N} is the set of subcarriers. The CRN which employs an OFDM scheme includes a secondary base station (SBS) and K SUs and operates on a frame-by-frame basis. K={1,…,K} is the set of SUs. At the beginning of each frame, each SUii∈N carries out robust spectrum sensing to determine the vacant subcarriers and distinguish PU signals from PUEA signals in the occupied subcarriers. Then, each SUi sends its sensing results through the uplink reporting link to the SBS. Based on the reports collected from the SUs, we assume the SBS canperfectly differentiate vacant subcarriers from occupied subcarriers. Also, we assume that the SBS can distinguish between the PU and the PUEA signals in occupied subcarriersimperfectly. With the imperfect knowledge of the PU activity in occupied subcarriers, the SBS performs resource allocation, that is, channel or spectrum band assignment and power allocation, and feeds back the decisions to all SUs through the downlink broadcast link.Figure 1
System model.Figure 2
Example of the total available bandwidth.In this paper, perfect synchronization is assumed between FC and SU. This is because the IEEE 802.22 standard has defined Quiet Periods (QPs) where spectrum sensing is performed and SUs are not allowed to transmit. CRNs can synchronize their QPs through an offset synchronization technique using beacons [16]. In a centralized CRN, the FC distributes synchronization information through the control channel [17]. It is reasonable to assume that SUs are able to synchronize with the FC.In downlink transmission scenario shown in Figure1, there are four interference links: (1) between the primary user’s transmitter (PT) and the secondary user’s receiver (SR), let hk,nPS denote the channel fading gain between the PT and the kth SR in the nth subcarrier; (2) between the attacker’s transmitter (AT) and the primary user’s receiver (PR), let hlEP denote the channel fading gain between the AT and the PR in the lth subcarrier; (3) between the AT and the SR, let hk,nES denote the channel fading gain between the AT and the kth SR in the nth subcarrier; (4) between the SBS and the PR, let hlSP denote the channel fading gain between the SBS and the PR in the lth subcarrier. Furthermore, the link between the SBS and SR is the downlink broadcast link; let hk,nSS denote the channel fading gain between the SBS and the kth SR in the nth subcarrier. These instantaneous channel fading gains are assumed to follow a Rayleigh distribution and we assume these instantaneous fading gains are known at the SBS. Specifically, we assume that the SU can estimate instantaneous fading gains and report to the SBS through the uplink reporting link [18].


## 2.2. Modeling of the Imperfect Robust Cooperative Spectrum Sensing

Robust spectrum sensing can not only distinguish vacant subcarriers from occupied subcarriers, but also make a relatively reliable decision on the classification of PU signals and PUEA signals. In order to exploit this extra information, we will quantify the accuracy of classification and provide this to the subsequent resource allocation module to improve the spectrum utilization efficiency.Each SU senses the subcarriers periodically and makes a local decision about the presence of the PU signals and PUEA signals based on its own observations. The local decisions are to be sent to the SBS in consecutive time slots based on a time division multiple access (TDMA) scheme through the uplink reporting link. The reported local decisions are combined at the SBS, as shown in Figure2; all of these subcarriers S={1,…,N} will be divided into three parts [15]: the set of vacant subcarriers V, the set of subcarriers OP occupied by the PU, and the set of subcarriers OA occupied by the PUEA. Note that intersymbol interference (ISI) and intercarrier interference (ICI) are two factors of degrading the OFDM system performance. The shorter time of SU occupancy of the estimated free carriers may result in ISI.Furthermore, mobility of the SUs generates Doppler frequency spread, which may destroy the orthogonality between subcarriers. The loss of orthogonality (of the carriers) at the SUs results in ICI [19]. Many methods have been proposed to combat ICI. Among these methods, adaptive subcarrier bandwidth is one of the representatives. The authors in [20] reveal that increasing the subcarrier bandwidth (i.e., decreasing N) can reduce ICI. However, as the subcarrier bandwidth increases, the ISI also increases. Therefore, the subcarrier bandwidth selection is a tradeoff between decreasing the subcarrier bandwidth to eliminate the ISI and increasing the subcarrier bandwidth to reduce the ICI.We can write(1)S=V∪OP∪OA,OP∩OA=⌀.Due to the imperfect robust spectrum sensing, there would be errors in classification ofOP and OA. Let pl denote the real state in which the PU is sending signals over subcarrier l  (l∈OP∪OA), and let p^l denote the estimate of pl by robust spectrum sensing. Similarly, we denote el to indicate the real state in which the attacker is sending PUEA signals over subcarrier l  (l∈OP∪OA), and let e^l denote the estimate of el by robust spectrum sensing.So when the signal is from the PU, the probability that the SBS falsely classifies it as from the attacker ispfE=Pr⁡(e^l∣pl). When the signal is from the attacker, the probability that the SBS falsely classifies it as from the PU is pfP=Pr⁡(p^l∣el). Note that the probability of detection of PU signals and PUEA signals can be written as pdP=Pr⁡(p^l∣pl)=1-pfE and pdE=Pr⁡(e^l∣el)=1-pfP, respectively.Here, let us definePr⁡(pl∣p^l) as the probability that the SBS classifies the signals to be from the PU when it is indeed from the PU, and Pr⁡(el∣e^l) as the probability that the SBS classifies the signals to be from the PUEA when it is indeed from the PUEA. Hence, we use αlP and αlA to evaluate the accuracy of classification for the PU signals and the PUEA signals. Formally, these two probabilities which will be used in the subsequent resource allocation are defined as(2)αlP=Pr⁡pl∣p^l=pdPPr⁡⁡plPr⁡⁡p^l,(3)αlA=Pr⁡el∣e^l=pdEPr⁡elPr⁡e^l,respectively. The probability of Pr⁡(p^l) in (2) and the probability of Pr⁡(e^l) in (3) can be rewritten as Pr⁡(p^l)=pdPPr⁡(pl)+pfPPr⁡(el) and Pr⁡(e^l)=pdEPr⁡(el)+pfEPr⁡(pl), respectively, where Pr⁡(pl) denotes the probability of presence of the PU which is signal in the subcarrier l, Pr⁡(el) denotes the probabilities of presence of the PUEA signal in the subcarrier l.


## 2.3. Modeling of the Resource Allocation Problem in the Presence of an Attacker

In this paper, the goal of resource allocation is to maximize the total transmission rate ofK SUs while keeping total interference introduced to the PU subcarriers below a certain threshold and total power below a constraint.The capacity for thenth subcarriers used by the kth SU is calculated via the Shannon formula as [21] (4)rk,n=Δflog21+pk,nhk,nSS2σ2+ik,n+jk,n,where pk,n is the transmission power of the kth SU for the nth subcarrier, σ2 denotes the additive white Gaussian noise (AWGN) variance, ik,n denotes the interference introduced to the nth subcarriers of the kth SU due to the transmission of all PUs, and jk,n denotes the interference introduced to the nth subcarriers of the kth SU due to the transmission of PUEA signals.The sum capacity of thekth SU is (5)rk,n=Δf∑n=1NCk,nlog21+pk,nhk,nSS2σ2+ik,n+jk,n,where Ck,n can have only value of either 1 or 0, indicating whether the nth subcarrier is used by the kth SU or not, as only one SU can occupy a particular subcarrier.Mathematically, the objective is to find the optimal exclusive subcarrier assignment policyCk,n and power allocation policy pk,n jointly such that the CRN system throughput is maximized, while satisfying the interference temperature constraint required by the PU on each channel and the power budget of the SBS simultaneously; that is,(6)max⁡Ck,n,pk,nΔf∑k=1K∑n=1NCk,nlog21+pk,nhk,nSS2σ2+ik,n+jk,ns.t.iiiiiiiiC1:Pr⁡Il≤Ithl≥a,l∈OP∪OAiiiiiiiiiiC2:Ck,n=0,1,∀k∈K,∀n∈NiiiiiiiiiiC3:∑k=1KCk,n=1,∀n∈NiiiiiiiiiiC4:pk,n≥0,∀k∈K,∀n∈NiiiiiiiiiiC5:∑k=1K∑n=1NCk,npk,n≤PT,where PT denotes the total power budget, I(l) denotes the interference introduced to the lth subcarriers of the PU due to the transmission of all SUs, and Ith(l) denotes the interference threshold for the lth PU subcarriers. C1 are the interference constraints for all PUs subcarriers; it can be guaranteed that the interference introduced to the lth PU subcarriers remains below a specified interference threshold Ith(l) with specified probability a [12]. C2 and C3 indicate each subcarrier can be allocated to only one SU. C4 and C5 are the transmitter power constraints.In the subsequent section, this optimization problem will be deduced in detail; an optimal subcarrier-and-power allocation can be obtained.


## 3. Robust Cooperative Spectrum Sensing-Assisted Multiuser Resource Allocation

The optimization problem considered here is similar to the conventional resource allocation problem, except for the added interference to the CRN due to the presence of the attacker and the modified interference constraints C1 got from robust cooperative spectrum sensing algorithm. In the following, we derive three kinds of interferences. Then, we formulate the objective function with the constraints in (6) and propose the Rope-Alone.


### 3.1. PU-SU Interference

This is the PN interference on the SU subcarrier. Since the waveform of the PU activity is unknown, an elliptically filtered white noise process is assumed as PU signal [22]. We assume that ΦlPU(ω) is the power spectrum density of the PU signal at subcarrier l; then the interference introduced by the lth PU subcarrier to the SU k that is using subcarrier n can be calculated as follows [22]: (7)ik,nPUl=hk,nPS2∫dn,l-Δf/2dn,l+Δf/2ΦlPUωdω,where dn,l is the frequency distance between subcarrier n and subcarrier l.The interference introduced by the PU subcarriers that are correctly detected in the setOP, imposed to the SU k that is using subcarrier n, can be written as(8)ik,nP=∑l∈OPαlPik,nPUl.The interference introduced by the PU subcarriers that are incorrectly detected as PUEA signals in the setOA, imposed to the SU k that is using subcarrier n, can be written as(9)ik,nA=∑l∈OA1-αlAik,nPUl.Thus, the interference introduced by the PU signal to the SUk that is using subcarrier n can be written as(10)ik,n=ik,nP+ik,nA.


### 3.2. PUEA-SU Interference

This is the PUEA signal interference on the SU subcarrier. As an attacker attempts to fool SUs via mimicking the characteristics of the PU signal, the interference introduced by thelth PUEA subcarrier to the SU k that is using subcarrier n can be calculated as follows:(11)ik,nEAl=hk,nES2∫dn,l-Δf/2dn,l+Δf/2ΦAejωdω,where ΦA(ejω) is the power spectrum density of the PUEA signal.Then the interference introduced by the PUEA subcarriers that are incorrectly detected as PU signals in the setOP, imposed to the SU k that is using subcarrier n, can be written as(12)jk,nP=∑l∈Op1-αlPik,nEAl.Similarly, the interference introduced by the PUEA subcarriers that are correctly detected as PUEA signals in the set OA, imposed to the SU k that is using subcarrier n, can be written as(13)jk,nA=∑l∈OAαlAik,nEAl.Thus, the interference introduced by the PUEA signal to the SU k that is using subcarrier n can be written as(14)jk,n=jk,nP+jk,nA.


### 3.3. SU-PU Interference

This is the CRN interference on the PN. Since SBS-SU is an OFDM signal, we assume an ideal Nyquist pulse shaping; the power density spectrum of thenth subcarrier in the SU subcarrier can be written as [22] (15)ΦnSUf=pnTssinπfTsπfTs2,where pn is the power loaded in the nth subcarrier and Ts is the symbol duration.The interference, introduced by the SUk that is using subcarrier n, to the lth PU subcarrier (l∈OP∪OA) can be written as follows:(16)ik,nSUl=Ck,nhlSP2∫dn,l-Δf/2dn,l+Δf/2ΦnSUfdf=Ck,npnhlSP2Ts∫dn,l-Δf/2dn,l+Δf/2sinπfTsπfTs2df=Ck,npnhlSP2fdn,l,where (17)fdn,l=Ts∫dn,l-Δf/2dn,l+Δf/2sinπfTsπfTs2df.Using similar methods discussed in Section 3.1, the interference introduced by the SUs’ signal to the lth PU subcarrier (l∈OP∪OA) can be written as(18)Il=∑k=1K∑n=1NαlPik,nSUl,l∈OP,(19)Il=∑k=1K∑n=1N1-αlAik,nSUl,l∈OA,respectively.Hence, the C1 constraint in (6) can be written as(20)Pr⁡hlSP2∑k=1K∑n=1NCk,nαlPpnfdn,l≤Ithl≥a,l∈OP,(21)Pr⁡hlSP2∑k=1K∑n=1NCk,n1-αlApnfdn,l≤Ithl≥a,UUUUUUUUUUUuUUUUUUUUUUUUUIl∈OA.Since the amplitude fading gain |hlSP| is Rayleigh distributed with known parameter λl, the distribution of |hlSP|2 is an exponential distribution. Hence, (20) can be written as(22)1-exp⁡-Ithl2λl∑k=1K∑n=1NCk,nαlPCk,npnfdn,l≥a,iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiil∈OP.Equation (22) can be rewritten as(23)∑k=1K∑n=1NCk,nαlPCk,npnfdn,l≤Ithl2λl-ln⁡1-a,l∈OP.Similarly, (21) can be written as(24)∑k=1K∑n=1NCk,n1-αlACk,npnfdn,l≤Ith(l)2λl-ln⁡1-a,UUUUUUUUUUUUUUUUUUUUUUUUUUIl∈OA.


### 3.4. Subcarrier Allocation

The optimization problem defined by (6) is a mixed binary integer programming problem which is generally hard to solve. We decouple the optimization problem into two separate problems: a subcarrier allocation problem and a power allocation problem. In order to maximize the CRN system throughput, we allocate a particular subcarrier to a CR user that has the highest channel gain to interference and noise ratio (CINR).Taking the background noise and interference from PU signal and PUEA signal into consideration, the CINR at SUk that is using subcarrier n can be expressed as(25)γk,n=hk,nSS2σ2+ik,n+jk,n.Theorem 1.
Using the subcarrier allocation in (26), the optimization problem in (6) is decoupled into two separate problems, and the decoupling is optimal(26)Ck,n=1,k=k*0,k≠k*(27)k*=argmax⁡kγk,n.Proof.
The proof is shown in AppendixA.


### 3.5. Power Allocation

After the subcarrier allocation, the optimization problem defined in (6) is turned into (28)max⁡pk,nΔf∑k=1K∑n=Ωklog21+pk,nhk,nSSσ2+ik,n+jk,nis.t.iiiiC1:∑k=1K∑n=ΩkαlPCk,npnfdn,liiiiiii≤Ithl2λl-ln⁡1-a,l∈OPiiiiiiiC2:∑k=1K∑n=ΩkCk,n1-αlACk,npnfdn,liiiiiii≤Ithl2λl-ln⁡1-a,l∈OAiiiiiiiC3:pk,n≥0,∀k∈K,∀n∈NiiiiiiiC4:∑k=1K∑n=Ωkpk,n≤PT,where Ωk denotes the set of subcarriers allocated to the kth SU according to (26).Theorem 2.
The optimal power allocated tonth subcarrier that the kth SU is using can be written as(29)pk,n*=1×ln⁡2θ+∑l∈OPβlαlPfdn,l∑l∈OPβliiiiiiiiiiiiiiiiiiiiiiiiii+∑l∈OAρl1-αlAfdn,l-1iiiiiiiiiii-σ2+ik,n+jk,nhk,nSS+∀k∈K,n∈Ωk,where [x]+=max⁡(0,x), θ, βl (l∈OP), and ρl (l∈OA) are Lagrange constants.The proof of Theorem2 and the method of calculating the optimal power allocation pk,n* and the Lagrange multipliers are given in Appendix B.


### 3.6. Proposed Rope-Alone

The whole process of the proposed Rope-Alone can be summarized in Algorithm1.Algorithm 1:Robust cooperative spectrum sensing-assisted multiuser resource allocation scheme.
The ProposedRope-Alone
Step  1. Each SU performs local robust spectrum sensing on each subcarrier,
then sends the sensing results and the channel state information to the SBS
through the uplink reporting link.
Step  2. The SBS performs subcarrier allocation according to (26) and set
appropriate initial values to the dual variablesθ, β and ρ for ∀k, n∈Ωk.
Step  3. calculate the value of popt={pk,n*≥0;∀k,n∈Ωk} from (29).
Step  4. Substitute popt and the dual variable into (B.6)/(B.7)/(B.8), update the dual variables.
Step 4. If the conditions of
|
θ
n
+
1
(
P
T
-
∑
k
=
1
K
∑
n
=
Ω
k
p
k
,
n
*
)
|
≤
ε,
|
β
l
n
+
1
(
I
th
(
l
)
2
λ
l
[
-
ln
⁡
(
1
-
a
)
]
-
∑
k
=
1
K
∑
n
=
Ω
k
α
l
P
p
k
,
n
*
f
(
d
n
,
l
)
)
|
≤
ε, l∈OP
and|ρln+1(Ith(l)2λl[-ln⁡(1-a)]-∑k=1K∑n=Ωk(1-αlA)pk,n*f(dn,l))|≤ε, l∈OA
are satisfied simultaneously, then terminate the algorithm. Otherwise, jump to Step  3


## 3.1. PU-SU Interference

This is the PN interference on the SU subcarrier. Since the waveform of the PU activity is unknown, an elliptically filtered white noise process is assumed as PU signal [22]. We assume that ΦlPU(ω) is the power spectrum density of the PU signal at subcarrier l; then the interference introduced by the lth PU subcarrier to the SU k that is using subcarrier n can be calculated as follows [22]: (7)ik,nPUl=hk,nPS2∫dn,l-Δf/2dn,l+Δf/2ΦlPUωdω,where dn,l is the frequency distance between subcarrier n and subcarrier l.The interference introduced by the PU subcarriers that are correctly detected in the setOP, imposed to the SU k that is using subcarrier n, can be written as(8)ik,nP=∑l∈OPαlPik,nPUl.The interference introduced by the PU subcarriers that are incorrectly detected as PUEA signals in the setOA, imposed to the SU k that is using subcarrier n, can be written as(9)ik,nA=∑l∈OA1-αlAik,nPUl.Thus, the interference introduced by the PU signal to the SUk that is using subcarrier n can be written as(10)ik,n=ik,nP+ik,nA.


## 3.2. PUEA-SU Interference

This is the PUEA signal interference on the SU subcarrier. As an attacker attempts to fool SUs via mimicking the characteristics of the PU signal, the interference introduced by thelth PUEA subcarrier to the SU k that is using subcarrier n can be calculated as follows:(11)ik,nEAl=hk,nES2∫dn,l-Δf/2dn,l+Δf/2ΦAejωdω,where ΦA(ejω) is the power spectrum density of the PUEA signal.Then the interference introduced by the PUEA subcarriers that are incorrectly detected as PU signals in the setOP, imposed to the SU k that is using subcarrier n, can be written as(12)jk,nP=∑l∈Op1-αlPik,nEAl.Similarly, the interference introduced by the PUEA subcarriers that are correctly detected as PUEA signals in the set OA, imposed to the SU k that is using subcarrier n, can be written as(13)jk,nA=∑l∈OAαlAik,nEAl.Thus, the interference introduced by the PUEA signal to the SU k that is using subcarrier n can be written as(14)jk,n=jk,nP+jk,nA.


## 3.3. SU-PU Interference

This is the CRN interference on the PN. Since SBS-SU is an OFDM signal, we assume an ideal Nyquist pulse shaping; the power density spectrum of thenth subcarrier in the SU subcarrier can be written as [22] (15)ΦnSUf=pnTssinπfTsπfTs2,where pn is the power loaded in the nth subcarrier and Ts is the symbol duration.The interference, introduced by the SUk that is using subcarrier n, to the lth PU subcarrier (l∈OP∪OA) can be written as follows:(16)ik,nSUl=Ck,nhlSP2∫dn,l-Δf/2dn,l+Δf/2ΦnSUfdf=Ck,npnhlSP2Ts∫dn,l-Δf/2dn,l+Δf/2sinπfTsπfTs2df=Ck,npnhlSP2fdn,l,where (17)fdn,l=Ts∫dn,l-Δf/2dn,l+Δf/2sinπfTsπfTs2df.Using similar methods discussed in Section 3.1, the interference introduced by the SUs’ signal to the lth PU subcarrier (l∈OP∪OA) can be written as(18)Il=∑k=1K∑n=1NαlPik,nSUl,l∈OP,(19)Il=∑k=1K∑n=1N1-αlAik,nSUl,l∈OA,respectively.Hence, the C1 constraint in (6) can be written as(20)Pr⁡hlSP2∑k=1K∑n=1NCk,nαlPpnfdn,l≤Ithl≥a,l∈OP,(21)Pr⁡hlSP2∑k=1K∑n=1NCk,n1-αlApnfdn,l≤Ithl≥a,UUUUUUUUUUUuUUUUUUUUUUUUUIl∈OA.Since the amplitude fading gain |hlSP| is Rayleigh distributed with known parameter λl, the distribution of |hlSP|2 is an exponential distribution. Hence, (20) can be written as(22)1-exp⁡-Ithl2λl∑k=1K∑n=1NCk,nαlPCk,npnfdn,l≥a,iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiil∈OP.Equation (22) can be rewritten as(23)∑k=1K∑n=1NCk,nαlPCk,npnfdn,l≤Ithl2λl-ln⁡1-a,l∈OP.Similarly, (21) can be written as(24)∑k=1K∑n=1NCk,n1-αlACk,npnfdn,l≤Ith(l)2λl-ln⁡1-a,UUUUUUUUUUUUUUUUUUUUUUUUUUIl∈OA.


## 3.4. Subcarrier Allocation

The optimization problem defined by (6) is a mixed binary integer programming problem which is generally hard to solve. We decouple the optimization problem into two separate problems: a subcarrier allocation problem and a power allocation problem. In order to maximize the CRN system throughput, we allocate a particular subcarrier to a CR user that has the highest channel gain to interference and noise ratio (CINR).Taking the background noise and interference from PU signal and PUEA signal into consideration, the CINR at SUk that is using subcarrier n can be expressed as(25)γk,n=hk,nSS2σ2+ik,n+jk,n.Theorem 1.
Using the subcarrier allocation in (26), the optimization problem in (6) is decoupled into two separate problems, and the decoupling is optimal(26)Ck,n=1,k=k*0,k≠k*(27)k*=argmax⁡kγk,n.Proof.
The proof is shown in AppendixA.


## 3.5. Power Allocation

After the subcarrier allocation, the optimization problem defined in (6) is turned into (28)max⁡pk,nΔf∑k=1K∑n=Ωklog21+pk,nhk,nSSσ2+ik,n+jk,nis.t.iiiiC1:∑k=1K∑n=ΩkαlPCk,npnfdn,liiiiiii≤Ithl2λl-ln⁡1-a,l∈OPiiiiiiiC2:∑k=1K∑n=ΩkCk,n1-αlACk,npnfdn,liiiiiii≤Ithl2λl-ln⁡1-a,l∈OAiiiiiiiC3:pk,n≥0,∀k∈K,∀n∈NiiiiiiiC4:∑k=1K∑n=Ωkpk,n≤PT,where Ωk denotes the set of subcarriers allocated to the kth SU according to (26).Theorem 2.
The optimal power allocated tonth subcarrier that the kth SU is using can be written as(29)pk,n*=1×ln⁡2θ+∑l∈OPβlαlPfdn,l∑l∈OPβliiiiiiiiiiiiiiiiiiiiiiiiii+∑l∈OAρl1-αlAfdn,l-1iiiiiiiiiii-σ2+ik,n+jk,nhk,nSS+∀k∈K,n∈Ωk,where [x]+=max⁡(0,x), θ, βl (l∈OP), and ρl (l∈OA) are Lagrange constants.The proof of Theorem2 and the method of calculating the optimal power allocation pk,n* and the Lagrange multipliers are given in Appendix B.


## 3.6. Proposed Rope-Alone

The whole process of the proposed Rope-Alone can be summarized in Algorithm1.Algorithm 1:Robust cooperative spectrum sensing-assisted multiuser resource allocation scheme.
The ProposedRope-Alone
Step  1. Each SU performs local robust spectrum sensing on each subcarrier,
then sends the sensing results and the channel state information to the SBS
through the uplink reporting link.
Step  2. The SBS performs subcarrier allocation according to (26) and set
appropriate initial values to the dual variablesθ, β and ρ for ∀k, n∈Ωk.
Step  3. calculate the value of popt={pk,n*≥0;∀k,n∈Ωk} from (29).
Step  4. Substitute popt and the dual variable into (B.6)/(B.7)/(B.8), update the dual variables.
Step 4. If the conditions of
|
θ
n
+
1
(
P
T
-
∑
k
=
1
K
∑
n
=
Ω
k
p
k
,
n
*
)
|
≤
ε,
|
β
l
n
+
1
(
I
th
(
l
)
2
λ
l
[
-
ln
⁡
(
1
-
a
)
]
-
∑
k
=
1
K
∑
n
=
Ω
k
α
l
P
p
k
,
n
*
f
(
d
n
,
l
)
)
|
≤
ε, l∈OP
and|ρln+1(Ith(l)2λl[-ln⁡(1-a)]-∑k=1K∑n=Ωk(1-αlA)pk,n*f(dn,l))|≤ε, l∈OA
are satisfied simultaneously, then terminate the algorithm. Otherwise, jump to Step  3


## 4. Simulations and Discussions

### 4.1. Simulation Settings

We give simulation results to evaluate the performance of the proposed algorithm in this section. The total available bandwidth (W), which is equally divided into 16 OFDM subcarriers, is assumed to be equal to 8 MHz. So the bandwidth Δf is 0.5 MHz for each subcarrier. The values of Ts and σ2 have been taken to be 4 μs and 10-7 Watt, respectively. We assumed that there are K=4 SUs. The channel fading gains hlSP, hk,nSS, and hk,nPS are assumed to be Rayleigh distributed with mean values of −46dB, −40dB, and −54dB, respectively. In addition, the channel fading gain hlEP is assumed to be Rayleigh distributed with mean values of −46dB. The transmit power of the PU is assumed to be 0.1 W. The probability a, with which the interference introduced to the PU lth subcarrier remains below the threshold Ithl, is equal to 0.95.We also assume that, after the robust spectrum sensing, all of these subcarriers will be divided into three parts:V = [1,2,6,7,8,12,13,16], OP = [3,4,5,9,10], and OA = [11,14,15]. To analyze the performance of the proposed Rope-Alone, we give the detection performance of the robust spectrum sensing being used. Given PfP= 0.06, the PdP is equal to [0.99, 0.98, 0.97, 0.98, 0.96] over subcarriers in the set OP. In addition, the PdA is equal to [0.97, 0.98, 0.96] over subcarriers in the set OA. The probability of PU activity in each subcarrier follows normal distribution with mean 0.7 and variance 0.01.


### 4.2. Impact of Power Budget

For a given value of interference thresholdIthl=5×10-9 Watt for PU subcarrier l, l∈OP∪OA, we study the performance of the proposed Rope-Alone and conventional scheme [12] in subcarrier-and-power allocation in Figure 3. The conventional scheme in subcarrier-and-power allocation makes no distinction between the subcarriers in set OP and the subcarriers in set OA and extends the same protection to all subcarrier l, l∈OP∪OA. In Figure 3, we have plotted the maximum system throughput of the CRN versus the total power budget for Rope-Alone and conventional scheme with the HOUSAM. In this figure, we have also plotted the maximum system throughput of the CRN for Rope-Alone and conventional scheme with the OSAM. It can be observed that both schemes with the HOUSAM achieve higher transmission rate compared with OSAM. Furthermore, regardless of the spectrum access mechanism (OSAM or HOUSAM) being used, the achievable maximum system throughput for the Rope-Alone is greater than that of the conventional scheme.Figure 3
System throughput versus total power budget for various schemes.In Figure3, we also observed that, for the conventional scheme when the power budget exceeds 180 mW, the maximum system throughout becomes roughly constant, while for Rope-Alone this power budget threshold is approximately 370 mW. This is due to the fact that, when the power budget exceeds a certain threshold, these schemes will operate in the interference-limited scenario; that is, interference constraints C1 in (28) become the boundary constraint, and the total power loaded on all subcarriers became a constant and does not change with power budget increases. To gain a clearer vision of how much power can be loaded into different subcarriers under diffident power budget, Figures 4 and 5 provide the power loading profile for Rope-Alone and conventional scheme under various spectrum access mechanisms with the power budget of 160 mW and 300 mW, respectively. In Figures 4 and 5, we also have fixed the values of Ithl = 5 × 10−9. From Figure 5, it can be observed that the power loaded in some subcarriers with Rope-Alone is much higher than that with conventional scheme as expected. We find that, owning to the assist of robust cooperative spectrum sensing, the proposed Rope-Alone could exploit spectrum opportunity more effectively; that is, making full use of the sensing information to some extent means better system performance.Figure 4
Power profile for various schemes (power budget = 160 mW).Figure 5
Power profile for various schemes (power budget = 300 mW).


### 4.3. Impact on Energy Efficiency

We define an energy efficiency metric,ψ, as the ratio between the system throughput and the total achievable transmission power. To see the performance of energy efficiency of the Rope-Alone and the conventional scheme allocation schemes, we further plotted the energy efficiency ψ versus the total power budget for both schemes with HOUSAM and OSAM. In Figure 6, we have fixed the values of Ithl=5×10-9 for all l. From Figure 6, we notice that the energy efficiency of Rope-Alone is higher than that of conventional scheme, regardless of the spectrum access mechanism (OSAM or HOUSAM) being used. We also find when the power budget is over 220 mW, the energy efficiency of the HOUSAM based scheme is smaller than that of the OSAM based scheme. However, in Figure 3, we find that the achievable system throughput with the HOUSAM based scheme is higher than that of the OSAM based scheme when the power budget is over 220 mW. This fact demonstrates that the performance improvement of the HOUSAM based scheme comes at the expense of energy efficiency.Figure 6
Energy efficiencyψ versus total power budget.


### 4.4. Impact of Interference Threshold

Figure7 shows the impact of interference threshold Ithl on the system throughput in different schemes. For this plotting, we have used power budget PT = 100 mW. We can see that, for all schemes, the system throughput increases almost linearly as the interference threshold Ithl increases up to a certain value of interference threshold and then it becomes roughly constant. The reason behind this is that, for the given power budget, with the interference threshold increasing, the interference constraint is no longer a boundary constraint, but the power budget becomes the boundary constraint which restricts the improvement of the system throughput. Moreover, we can see that Rope-Alone outperforms the conventional scheme under all spectrum access mechanisms.Figure 7
System throughput versus interference threshold for various schemes.


### 4.5. Impact of Secondary Users

The system throughput versus number of secondary users for various schemes is shown in Figure8. In this figure, we have fixed the values of Ithl = 5 × 10−9 and the total power budget PT to be 250 mW. It is shown that the system throughput increases with the number of SUs. This is mainly because the more the number of SUs in CRN, the more likely for the CRN to have high quality channel. In addition, the Rope-Alone performs better than the conventional scheme regardless of the number of SUs.Figure 8
System throughput versus number of secondary users for various schemes.


### 4.6. Impact of the Accuracy of Detecting the PUEA Signal

We evaluate the impact on the system throughput when varying the accuracy of detecting the PUEA signal for the robust cooperative spectrum sensing. In Figure9, we have fixed the values of Ithl to be 5 × 10−9 Watt and total power budget to 100 mW. We have plotted αlA (the accuracy of detecting the PUEA signal) versus system throughput for various schemes under consideration. The value αlA is determined by the performance of robust cooperative spectrum sensing to differentiate PUEA signal from PU signal. Higher αlA means less ambiguity between PUEA signals from PU signals. As can be observed from Figure 9, the system throughput increases as αlA increases as expected. When αlA is close to 1, the improvement in system throughput with HOUSAM is much higher than that with OSAM.Figure 9
System throughput versus the accuracy of detecting the PUEA signal.


## 4.1. Simulation Settings

We give simulation results to evaluate the performance of the proposed algorithm in this section. The total available bandwidth (W), which is equally divided into 16 OFDM subcarriers, is assumed to be equal to 8 MHz. So the bandwidth Δf is 0.5 MHz for each subcarrier. The values of Ts and σ2 have been taken to be 4 μs and 10-7 Watt, respectively. We assumed that there are K=4 SUs. The channel fading gains hlSP, hk,nSS, and hk,nPS are assumed to be Rayleigh distributed with mean values of −46dB, −40dB, and −54dB, respectively. In addition, the channel fading gain hlEP is assumed to be Rayleigh distributed with mean values of −46dB. The transmit power of the PU is assumed to be 0.1 W. The probability a, with which the interference introduced to the PU lth subcarrier remains below the threshold Ithl, is equal to 0.95.We also assume that, after the robust spectrum sensing, all of these subcarriers will be divided into three parts:V = [1,2,6,7,8,12,13,16], OP = [3,4,5,9,10], and OA = [11,14,15]. To analyze the performance of the proposed Rope-Alone, we give the detection performance of the robust spectrum sensing being used. Given PfP= 0.06, the PdP is equal to [0.99, 0.98, 0.97, 0.98, 0.96] over subcarriers in the set OP. In addition, the PdA is equal to [0.97, 0.98, 0.96] over subcarriers in the set OA. The probability of PU activity in each subcarrier follows normal distribution with mean 0.7 and variance 0.01.


## 4.2. Impact of Power Budget

For a given value of interference thresholdIthl=5×10-9 Watt for PU subcarrier l, l∈OP∪OA, we study the performance of the proposed Rope-Alone and conventional scheme [12] in subcarrier-and-power allocation in Figure 3. The conventional scheme in subcarrier-and-power allocation makes no distinction between the subcarriers in set OP and the subcarriers in set OA and extends the same protection to all subcarrier l, l∈OP∪OA. In Figure 3, we have plotted the maximum system throughput of the CRN versus the total power budget for Rope-Alone and conventional scheme with the HOUSAM. In this figure, we have also plotted the maximum system throughput of the CRN for Rope-Alone and conventional scheme with the OSAM. It can be observed that both schemes with the HOUSAM achieve higher transmission rate compared with OSAM. Furthermore, regardless of the spectrum access mechanism (OSAM or HOUSAM) being used, the achievable maximum system throughput for the Rope-Alone is greater than that of the conventional scheme.Figure 3
System throughput versus total power budget for various schemes.In Figure3, we also observed that, for the conventional scheme when the power budget exceeds 180 mW, the maximum system throughout becomes roughly constant, while for Rope-Alone this power budget threshold is approximately 370 mW. This is due to the fact that, when the power budget exceeds a certain threshold, these schemes will operate in the interference-limited scenario; that is, interference constraints C1 in (28) become the boundary constraint, and the total power loaded on all subcarriers became a constant and does not change with power budget increases. To gain a clearer vision of how much power can be loaded into different subcarriers under diffident power budget, Figures 4 and 5 provide the power loading profile for Rope-Alone and conventional scheme under various spectrum access mechanisms with the power budget of 160 mW and 300 mW, respectively. In Figures 4 and 5, we also have fixed the values of Ithl = 5 × 10−9. From Figure 5, it can be observed that the power loaded in some subcarriers with Rope-Alone is much higher than that with conventional scheme as expected. We find that, owning to the assist of robust cooperative spectrum sensing, the proposed Rope-Alone could exploit spectrum opportunity more effectively; that is, making full use of the sensing information to some extent means better system performance.Figure 4
Power profile for various schemes (power budget = 160 mW).Figure 5
Power profile for various schemes (power budget = 300 mW).


## 4.3. Impact on Energy Efficiency

We define an energy efficiency metric,ψ, as the ratio between the system throughput and the total achievable transmission power. To see the performance of energy efficiency of the Rope-Alone and the conventional scheme allocation schemes, we further plotted the energy efficiency ψ versus the total power budget for both schemes with HOUSAM and OSAM. In Figure 6, we have fixed the values of Ithl=5×10-9 for all l. From Figure 6, we notice that the energy efficiency of Rope-Alone is higher than that of conventional scheme, regardless of the spectrum access mechanism (OSAM or HOUSAM) being used. We also find when the power budget is over 220 mW, the energy efficiency of the HOUSAM based scheme is smaller than that of the OSAM based scheme. However, in Figure 3, we find that the achievable system throughput with the HOUSAM based scheme is higher than that of the OSAM based scheme when the power budget is over 220 mW. This fact demonstrates that the performance improvement of the HOUSAM based scheme comes at the expense of energy efficiency.Figure 6
Energy efficiencyψ versus total power budget.


## 4.4. Impact of Interference Threshold

Figure7 shows the impact of interference threshold Ithl on the system throughput in different schemes. For this plotting, we have used power budget PT = 100 mW. We can see that, for all schemes, the system throughput increases almost linearly as the interference threshold Ithl increases up to a certain value of interference threshold and then it becomes roughly constant. The reason behind this is that, for the given power budget, with the interference threshold increasing, the interference constraint is no longer a boundary constraint, but the power budget becomes the boundary constraint which restricts the improvement of the system throughput. Moreover, we can see that Rope-Alone outperforms the conventional scheme under all spectrum access mechanisms.Figure 7
System throughput versus interference threshold for various schemes.


## 4.5. Impact of Secondary Users

The system throughput versus number of secondary users for various schemes is shown in Figure8. In this figure, we have fixed the values of Ithl = 5 × 10−9 and the total power budget PT to be 250 mW. It is shown that the system throughput increases with the number of SUs. This is mainly because the more the number of SUs in CRN, the more likely for the CRN to have high quality channel. In addition, the Rope-Alone performs better than the conventional scheme regardless of the number of SUs.Figure 8
System throughput versus number of secondary users for various schemes.


## 4.6. Impact of the Accuracy of Detecting the PUEA Signal

We evaluate the impact on the system throughput when varying the accuracy of detecting the PUEA signal for the robust cooperative spectrum sensing. In Figure9, we have fixed the values of Ithl to be 5 × 10−9 Watt and total power budget to 100 mW. We have plotted αlA (the accuracy of detecting the PUEA signal) versus system throughput for various schemes under consideration. The value αlA is determined by the performance of robust cooperative spectrum sensing to differentiate PUEA signal from PU signal. Higher αlA means less ambiguity between PUEA signals from PU signals. As can be observed from Figure 9, the system throughput increases as αlA increases as expected. When αlA is close to 1, the improvement in system throughput with HOUSAM is much higher than that with OSAM.Figure 9
System throughput versus the accuracy of detecting the PUEA signal.


## 5. Conclusion

How to maximize the system throughput of OFDMA-based CRN while keeping the interference introduced to the PU below certain thresholds in the present of a PUEA is a challenging issue. To address this problem, we studied the joint design of robust spectrum sensing and resource allocation in OFDMA-based CRN and formulated a joint design scheme as a convex optimization problem. The Lagrange duality theory has been introduced to solve this problem. To further exploit the underutilized spectrum bands, we also have evaluated the performance of the proposed scheme in the hybrid overlay/underlay spectrum access mechanism. Simulation results have confirmed the superiority of our proposed Rope-Alone compared to conventional resource allocation scheme under various spectrum access mechanisms. These results also have shown that the Rope-Alone achieves higher energy efficiency than conventional scheme. The proposed Rope-Alone is mainly for stationary SUs and may be applicable to low speeds; an interesting challenge ahead is to design a robust resource allocation scheme applicable to OFDMA-based medium/high speed mobile CRN. Since the high mobility of the SU leads to Doppler frequency spread, which will give rise to intercarrier interference. Such intercarrier interference severely affects the performance of OFDMA-based CRN.



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*Source: 839698-2015-03-19.xml*