# Optimal Energy-Efficient Sensing and Power Allocation in Cognitive Radio Networks

Authors: Xia Wu; Jin-Ling Xu; Ming Chen; Junbo Wang
Journal: Mathematical Problems in Engineering
 (2014)

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## Abstract

We consider a joint optimization of sensing parameter and power allocation for an energy-efficient cognitive radio network (CRN) in which the primary user (PU) is protected. The optimization problem to maximize the energy efficiency of CRN is formulated as a function of two variables, which are sensing time and transmit power, subject to the average interference power to the PU and the target detection probability. During the optimizing process, the quality of service parameter (the minimum rate acceptable to secondary users (SUs)) has also been taken into consideration. The optimal solutions are analyzed and an algorithm combined with fractional programming that maximizes the energy efficiency for CRN is presented. Numerical results show that the performance improvement is achieved by the joint optimization of sensing time and power allocation.


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## Body

## 1. Introduction

The traditional approach of fixed spectrum allocation leads to spectrum underutilization with the fast development of wireless communications. It is reported that there are vast temporal and spatial variations in the usage of allocated spectrum, which can be as low as 15% in recent studies by the FCC [1, 2]. This motivates the concept of CRN that allows SUs to opportunistically exploit the underutilized spectrum. In other words, CRN enables SUs to share the spectrum bands opportunistically with PUs.In a practical CRN which is powered by batteries, the concept of energy-efficient design is essential. Both the sensing time and the transmission power affect the energy efficiency of a CRN. For example, if the sensing time is too short, it may reduce the energy consumption in sensing phase and increase the transmission time, but data loss probability and interference to the PU are also introduced due to false detection. If the sensing time swells, detection accuracy is improved. However, it consumes more energy without ameliorating data transmission. Similarly, transmission power is also salient from the viewpoint of energy efficiency. The larger the transmission power is, the more throughput can be obtained. However, it consumes more energy.Some recent works dealing with the issues of CRN’s energy efficiency have been presented in [3–7]. In [3], the authors discuss the CRN’s energy-efficient transmission with variable transmission duration and interference to the PU when the sensing duration is fixed. In [4], a joint design of energy-efficient sensing and transmission durations for a CRN is considered. In [5], a joint optimization problem of the fusion rule threshold and detector’s threshold to maximize the energy efficiency of the CRN is studied. In [6], the authors identify the sensing-access strategies and the sensing order that achieve the maximum energy efficiency. In [7], the authors propose a low complexity solution to the problem of finding the power allocation that maximizes the energy efficiency, while limiting the interference to the PU and meeting the SUs’ minimum rate requirements.In this paper, we will focus on the joint optimization between the spectrum sensing time and power allocation to maximize energy efficiency, which is defined as the number of transmitted data bits per Joule of energy, with limited interference power to the PU. During the optimizing process, the target detection probability and the quality of service parameter (such as the minimum rate acceptable to SU) have also been taken into consideration. We consider the scenario that multiple SUs jointly sense one licensed spectrum band which can be divided into multiple subbands, and each SU operates exclusively in one of the subbands when the PU is detected to be absent. An optimization algorithm combined with fractional programming to solve the optimization problem is proposed. We compare the proposed scheme that jointly optimizes sensing time and power allocation with the schemes that only optimize either sensing time or power allocation, and numerical results demonstrate that the performance improvement is achieved by the joint optimization of sensing time and power allocation.The rest of this paper is organized as follows. In Section2, we present the system model. In Section 3, we address an optimization problem for an energy-efficient CRN. In Section 4, the optimization problem is analyzed and an algorithm combined with fractional programming is given to achieve the optimum value. Then we present numerical results in Section 5. Finally, we conclude our paper in Section 6.


## 2. System Model

### 2.1. System Model

In this paper we consider a CRN where multiple SUs are allowed to access one licensed spectrum band. The entire licensed band is divided intoM subbands, and each SU operates exclusively in one of the subbands when the PU is detected to be absent. Such assumption is widely used in [7, 8].The system is assumed to be perfectly synchronized, and time is divided into slots, each with a fixed lengthT. Each slot includes three phases [9]: (1) the sensing phase, (2) the reporting phase, and (3) the transmission phase. We assume that the PU is either absent or present during each slot. During the sensing time, the SUs need to sense the PU’s activity. Since the PU will operate in all the subbands once becoming active, the SUs can jointly sense the PU’s presence and send the spectrum results to the fusion center via a common control channel [5] in the reporting phase. Finally, based on the spectrum sensing results of the SUs, the fusion center determines the absent or active status of PU. With the cooperative spectrum sensing, each SU can spend less time detecting while enjoying a low false alarm probability. In addition, to keep the duration of the reporting phase at an acceptable level, the number of SUs that are involved should be limited. It can be seen that the reporting phase adds a fixed time overhead [10]. Without loss of generality, the duration of the reporting phase is assumed to be zero. The transmission phase is used for data transmission of SUs when the PU is detected to be absent. The structure of the time slot is shown in Figure 1, where τs denotes the sensing time, τr represents the reporting time of single SU, and Tt is the transmission time.Figure 1
Structure of the time slot.


### 2.2. Cooperative Spectrum Sensing

The spectrum sensing is considered as a binary hypothesis testing problem: hypothesisH0 when the PU is absent and hypothesis H1 when the PU is active. For the energy detection scheme, the test statistic for the energy detector of the ith SU is compared with a detection threshold ɛ, to decide the absent or active status of PU. Denote γi is the received average SNR of PU’s signal measured at the ith secondary detector under hypothesis H1. Under AWGN fading channel assumption, the probabilities of detection and false alarm of the ith SU are given, respectively, by [11]
(1)Pd(τs,ɛ)=Q(ɛ-τsfs-γi2τsfs+4γi),(2)Pf(τs,ɛ)=Q(ɛ-τsfs2τsfs),
where τs represents the sensing time, fs denotes the sampling frequency, and finally the Q(·) is the complementary distribution function of standard Gaussian.The “most rule” is used to make the final decision by the fusion center, where at least half of SUs’ decisions say that the PU is active; then the final decision declares that the PU is active [11]. Note that our model can be readily extended to different cooperative spectrum sensing schemes. Similar to [12], we assume that the size of the CRN is small compared with its distance from the primary system. Therefore, the received signal at each SU experiences almost identical path loss. Hence each SU has the same Pd and Pf. For a given time slot, M SUs perform spectrum sensing; the final probabilities of false alarm and detection based on the most rule are given, respectively, by [12]
(3)QF(τs,ɛ)=∑m=⌈M/2⌉MCMmPf(τs,ɛ)m(1-Pf(τs,ɛ))M-m,QD(τs,ɛ)=∑m=⌈M/2⌉MCMmPd(τs,ɛ)m(1-Pd(τs,ɛ))M-m,
where CMm=M!/m!(M-m)!.


## 2.1. System Model

In this paper we consider a CRN where multiple SUs are allowed to access one licensed spectrum band. The entire licensed band is divided intoM subbands, and each SU operates exclusively in one of the subbands when the PU is detected to be absent. Such assumption is widely used in [7, 8].The system is assumed to be perfectly synchronized, and time is divided into slots, each with a fixed lengthT. Each slot includes three phases [9]: (1) the sensing phase, (2) the reporting phase, and (3) the transmission phase. We assume that the PU is either absent or present during each slot. During the sensing time, the SUs need to sense the PU’s activity. Since the PU will operate in all the subbands once becoming active, the SUs can jointly sense the PU’s presence and send the spectrum results to the fusion center via a common control channel [5] in the reporting phase. Finally, based on the spectrum sensing results of the SUs, the fusion center determines the absent or active status of PU. With the cooperative spectrum sensing, each SU can spend less time detecting while enjoying a low false alarm probability. In addition, to keep the duration of the reporting phase at an acceptable level, the number of SUs that are involved should be limited. It can be seen that the reporting phase adds a fixed time overhead [10]. Without loss of generality, the duration of the reporting phase is assumed to be zero. The transmission phase is used for data transmission of SUs when the PU is detected to be absent. The structure of the time slot is shown in Figure 1, where τs denotes the sensing time, τr represents the reporting time of single SU, and Tt is the transmission time.Figure 1
Structure of the time slot.


## 2.2. Cooperative Spectrum Sensing

The spectrum sensing is considered as a binary hypothesis testing problem: hypothesisH0 when the PU is absent and hypothesis H1 when the PU is active. For the energy detection scheme, the test statistic for the energy detector of the ith SU is compared with a detection threshold ɛ, to decide the absent or active status of PU. Denote γi is the received average SNR of PU’s signal measured at the ith secondary detector under hypothesis H1. Under AWGN fading channel assumption, the probabilities of detection and false alarm of the ith SU are given, respectively, by [11]
(1)Pd(τs,ɛ)=Q(ɛ-τsfs-γi2τsfs+4γi),(2)Pf(τs,ɛ)=Q(ɛ-τsfs2τsfs),
where τs represents the sensing time, fs denotes the sampling frequency, and finally the Q(·) is the complementary distribution function of standard Gaussian.The “most rule” is used to make the final decision by the fusion center, where at least half of SUs’ decisions say that the PU is active; then the final decision declares that the PU is active [11]. Note that our model can be readily extended to different cooperative spectrum sensing schemes. Similar to [12], we assume that the size of the CRN is small compared with its distance from the primary system. Therefore, the received signal at each SU experiences almost identical path loss. Hence each SU has the same Pd and Pf. For a given time slot, M SUs perform spectrum sensing; the final probabilities of false alarm and detection based on the most rule are given, respectively, by [12]
(3)QF(τs,ɛ)=∑m=⌈M/2⌉MCMmPf(τs,ɛ)m(1-Pf(τs,ɛ))M-m,QD(τs,ɛ)=∑m=⌈M/2⌉MCMmPd(τs,ɛ)m(1-Pd(τs,ɛ))M-m,
where CMm=M!/m!(M-m)!.


## 3. Problem Formulation

### 3.1. Average Throughput of CRN

The spectrum band’s availability for SUs’ transmission is based on the outcome of the spectrum sensing. If the PU is detected to be absent while the PU is actually active, the PU’s signal is an interference to SUs’ transmission, and we assume the transmission will not succeed. Hence, when the PU is absent and no false alarm is generated, the SUs can successfully transmit the data.DenoteCi as the achievable data rate when the ith SU transmits under no interference from the PU over the subband labeled i, and the value of Ci is assumed to be [11]
(4)Ci=log⁡2(1+gipiN0),
where pi represents the transmission power of the ith SU, gi denotes the gain on subband i, and N0 is the background noise power per Hz.The average throughput in a time slotT on subband i can be expressed as
(5)Ri(τs,pi,ɛ)=(T-τs)P0(1-QF(τs,ɛ))Ci,
where P0 denotes the absent probability of the PU.Therefore, the average throughput of the CRN in a time slotT is
(6)R(τs,p,ɛ)=∑i=1MRi(τs,pi,ɛ).Ifri is the minimum rate acceptable to the ith SU, then we have
(7)log⁡2(1+gipiN0)≥ri,fori=1,…,M.If we let(2ri-1)N0/gi=P¯i, we can rewrite (7) as
(8)pi≥P¯i,fori=1,…,M.It is easy to observe that the SUs will cause interference to the PU when PU is active. Therefore, the average interference power constraint can be written as [13]
(9)∑i=1MP1(1-QD(τs,ɛ))gipi≤Ith,
where Ith represents an acceptable average interference threshold of PU and P1=1-P0 denotes the active probability of the PU.


### 3.2. Average Energy Consumption of CRN

In our model, the energy consumption of theith SU consists of three parts: circuit consumption power Pc, spectrum sensing power Ps, and data transmit power pi.In the CRN, there are four different scenarios between the activities of the PU and the SUs.(S1)
In this scenario, the SUs successfully detect the PU’s absent status with probabilityP0(1-QF(τs,ɛ)), and the energy consumed is given by
(10)C1(τs,p)=M(Ps+Pc)τs+(T-τs)(∑i=1Mpi+MPc).(S2)
For this scenario, the SUs falsely detect the PU’s absent status with probabilityP0QF(τs,ɛ), and the energy used is given by
(11)C2(τs,p)=M(Ps+Pc)τs.(S3)
In this case, the SUs falsely detect the PU’s active status with probabilityP1(1-QD(τs,ɛ)), and the energy used is given by
(12)C3(τs,p)=C1(τs,p).(S4)
Under this scenario, the SUs successfully detect the PU’s active status with probabilityP1QD(τs,ɛ), and the energy consumed is given by
(13)C4(τs,p)=C2(τs,p)The average energy consumption in a time slotT can be expressed by
(14)ψ(τs,p,ɛ)=MPsτs+MPcτs+(T-τs)·(1-P0QF(τs,ɛ)-P1QD(τs,ɛ))·(MPc+∑i=1Mpi).


### 3.3. Energy Efficiency

Our objective is to maximize the energy efficiency of the CRN subject to the target detection probability constraint while keeping the average interference introduced to the PU below a certain threshold, which can be expressed as(15a)max⁡τs,p,ɛmmmmη(τs,p,ɛ)=R(τs,pi,ɛ)ψ(τs,pi,ɛ)(15b)subject to0<τs<T(15c)mmmhmmmQD(τs,ɛ)=α(15d)mmmhmmmQF(τs,ɛ)≤β(15e)mmhmmmmpi≥P¯i(15f)mmmhmmm∑i=1MP1(1-QD(τs,ɛ))gipi≤Ith,where α is the target detection probability.Notably, the above problem is not convex, and directly obtaining the optimal solution is difficult. Hence, in the next section, fractional programming [14] is utilized to solve it.


## 3.1. Average Throughput of CRN

The spectrum band’s availability for SUs’ transmission is based on the outcome of the spectrum sensing. If the PU is detected to be absent while the PU is actually active, the PU’s signal is an interference to SUs’ transmission, and we assume the transmission will not succeed. Hence, when the PU is absent and no false alarm is generated, the SUs can successfully transmit the data.DenoteCi as the achievable data rate when the ith SU transmits under no interference from the PU over the subband labeled i, and the value of Ci is assumed to be [11]
(4)Ci=log⁡2(1+gipiN0),
where pi represents the transmission power of the ith SU, gi denotes the gain on subband i, and N0 is the background noise power per Hz.The average throughput in a time slotT on subband i can be expressed as
(5)Ri(τs,pi,ɛ)=(T-τs)P0(1-QF(τs,ɛ))Ci,
where P0 denotes the absent probability of the PU.Therefore, the average throughput of the CRN in a time slotT is
(6)R(τs,p,ɛ)=∑i=1MRi(τs,pi,ɛ).Ifri is the minimum rate acceptable to the ith SU, then we have
(7)log⁡2(1+gipiN0)≥ri,fori=1,…,M.If we let(2ri-1)N0/gi=P¯i, we can rewrite (7) as
(8)pi≥P¯i,fori=1,…,M.It is easy to observe that the SUs will cause interference to the PU when PU is active. Therefore, the average interference power constraint can be written as [13]
(9)∑i=1MP1(1-QD(τs,ɛ))gipi≤Ith,
where Ith represents an acceptable average interference threshold of PU and P1=1-P0 denotes the active probability of the PU.


## 3.2. Average Energy Consumption of CRN

In our model, the energy consumption of theith SU consists of three parts: circuit consumption power Pc, spectrum sensing power Ps, and data transmit power pi.In the CRN, there are four different scenarios between the activities of the PU and the SUs.(S1)
In this scenario, the SUs successfully detect the PU’s absent status with probabilityP0(1-QF(τs,ɛ)), and the energy consumed is given by
(10)C1(τs,p)=M(Ps+Pc)τs+(T-τs)(∑i=1Mpi+MPc).(S2)
For this scenario, the SUs falsely detect the PU’s absent status with probabilityP0QF(τs,ɛ), and the energy used is given by
(11)C2(τs,p)=M(Ps+Pc)τs.(S3)
In this case, the SUs falsely detect the PU’s active status with probabilityP1(1-QD(τs,ɛ)), and the energy used is given by
(12)C3(τs,p)=C1(τs,p).(S4)
Under this scenario, the SUs successfully detect the PU’s active status with probabilityP1QD(τs,ɛ), and the energy consumed is given by
(13)C4(τs,p)=C2(τs,p)The average energy consumption in a time slotT can be expressed by
(14)ψ(τs,p,ɛ)=MPsτs+MPcτs+(T-τs)·(1-P0QF(τs,ɛ)-P1QD(τs,ɛ))·(MPc+∑i=1Mpi).


## 3.3. Energy Efficiency

Our objective is to maximize the energy efficiency of the CRN subject to the target detection probability constraint while keeping the average interference introduced to the PU below a certain threshold, which can be expressed as(15a)max⁡τs,p,ɛmmmmη(τs,p,ɛ)=R(τs,pi,ɛ)ψ(τs,pi,ɛ)(15b)subject to0<τs<T(15c)mmmhmmmQD(τs,ɛ)=α(15d)mmmhmmmQF(τs,ɛ)≤β(15e)mmhmmmmpi≥P¯i(15f)mmmhmmm∑i=1MP1(1-QD(τs,ɛ))gipi≤Ith,where α is the target detection probability.Notably, the above problem is not convex, and directly obtaining the optimal solution is difficult. Hence, in the next section, fractional programming [14] is utilized to solve it.


## 4. Solution of Formulation

In this section, we will apply optimization algorithm combined with fractional programming to solve problem (15a)–(15f).When the constraint (15c) is considered only, for any given τs, we can determine a threshold from (1) that is able to satisfy constraint (15c), which is given by
(16)ɛ(τs)=2τsfs+4γiQ-1(P¯d)+τsfs+γi,
where P¯d is the single SU detection probability satisfying QD(τs,ɛ)=α.Similarly, when the constraint (15d) is considered only, the optimal solution occurs only when constraint (15d) is at equality. The proof is similar to [12]. When constraint (15d) is at equality, for any given τs, we can determine a threshold from (2) that is able to satisfy constraint (15d), which is given by
(17)ɛ(τs)=2τsfsQ-1(P¯f)+τsfs,
where P¯f is the single SU detection probability satisfying QF(τs,ɛ)=β.In order to satisfy both constraints (15c) and (15d), ɛ(τs) should choose the max value between (16) and (17):
(18)ɛ(τs)=max⁡{2τsfs+4γiQ-1(P¯d)+τsfsmmm+γi,2τsfsQ-1(P¯f)+τsfs}.Since constraints (15c) and (15d) can be satisfied by (18) for any given τs, the optimization (15a)–(15f) is reduced to(19a)max⁡τs,pmmmmη(τs,p)=R(τs,pi,ɛ(τs))ψ(τs,pi,ɛ(τs))(19b)subject to0<τs<T(19c)mmmhmmmpi≥P¯i(19d)mmmhmmm∑i=1MP1qmgipi≤Ith,where qm=1-α.Sinceτs lies within the limited interval (0,T), similar to [15], we can exhaustively search for the optimal sensing time over (0,T). Hence, for a given τs, problem (19a)–(19d) can be simplified as follows:(20a)max⁡pmmmmη(p)=c1∑i=1Mlog2(1+gipi/N0)c2+c3∑i=1Mpi(20b)subject topi≥P¯i(20c)mmmhmmm∑i=1MP1qmgipi≤Ith,where c1=(T-τs)P0(1-QF(τs,ɛ)), c3=(T-τs)(1-P0QF(τs,ɛ)-P1α), and c2=MPsτs+MPcτs+c3MPc.The fractional programming [14] can be used to solve problem (20a)–(20c). First, a new objective function is defined as
(21)h(p,λ)=c1∑i=1Mlog2(1+gipiN0)-λ(c2+c3∑i=1Mpi),
where λ is a positive parameter.Hence, another problem is formulated as(22a)max⁡pmmmmh(p,λ)(22b)subject topi≥P¯i(22c)mmmhmmm∑i=1MP1qmgipi≤Ith.Define the optimal value and solution of problem (22a)–(22c) as F(λ)=max⁡p{h(p,λ)} and p^(λ)=argmax⁡p{h(p,λ)}, respectively. The following lemma introduced by Dinkelbach [14] can relate problem (20a)–(20c) and (22a)–(22c), and detailed proof can be found in [14].Lemma 1.
The optimal solutionp* achieves the optimal value λ* of problem (20a)–(20c); that is, λ*=max⁡p{η(p)}=η(p*) according to (20a), if and only if
(23)F(λ*)=0,p^(λ)=p*.This lemma indicates that at the optimal parameterλ*, the optimal solution to problem (22a)–(22c) is also the optimal solution to problem (20a)–(20c). Hence, solving problem (20a)–(20c) can be realized by finding the optimal power allocation of problem (22a)–(22c) for a given λ and then update λ until (23) is established.For a givenλ, the optimal power allocation can be obtained using convex theory [16] because of the characteristic of problem (22a)–(22c). First, the constraint (22b) is not considered; then the Lagrange function of problem (22a)–(22c) is
(24)L=c1∑i=1Mlog2(1+gipiN0)-λ(c2+c3∑i=1Mpi)-μ(∑i=1MP1qmgipi-Ith),
where μ is the Lagrange multiplier for constraint (22c). Using the Karush-Kuhn-Tucker (KKT) condition, the optimal solution for problem (22a)–(22c) without constraint (22b) is
(25)pi=max⁡{c1ln⁡2(λc3+μP1qmgi)-N0gi,0}
and the value of μ can be found by subgradient method [16].The optimal value of problem (22a)–(22c) without constraint (22b) can be obtained by Algorithm 1.Algorithm 1:Fractional programming to solve problem (20a)–(20c) without the constraint (20b).
Initialization: λ0 satisfying F(λ0)>0, tolerance ρ, n=0
While  F(λn)>ρ
Givenλ=λn, solve optimal p^n(λ) through (23).
λn+1=η(p^(λ))
n←n+1
end
Output: optimal λ*=λn and p*=p^n(λ).In the following, we classify the optimal value obtained by Algorithm1 into two cases considering the constraint (22b); we start with Case 1, where S represents the set of all SUs in the CRN.Case 1.
Whenpi≥P¯i for all SUs, the maximum energy efficiency of problem (20a)–(20c) is η(p)=λ*.Case 2.
p
i
≥
P
¯
i for i∈S1, and pi<P¯i for i∈S2. Note that for those i∈S2 the only way to satisfy the condition (22b) is to set
(26)pi=P¯i,fori∈S2.After assigning these powers to SUs who fall inS2, we can reformulate the problem (20a)–(20c) with optimization variables pi for i∈S1 and fixed pi=P¯i for i∈S2 and resolve it through the above method.Hence, the optimal solution for problem (15a)–(15f) is given in Algorithm 2.Algorithm 2:Optimal sensing time and power allocation for energy-efficient CRN.
Initialization: n=0
For  τ-=0:T
Givenτn=τ-, solve optimal pn to problem (18) and obtain
maximum energy efficiencyηn.
n←n+1
end
n*=arg⁡max⁡{ηn}
Output: optimal τs=τn*, p=pn* and ηmax⁡=ηn*.


## 5. Numerical Results

The default parameters are set as follows: the number of SUsM=8, the fixed time slot T=20ms, and the sampling frequency of the received signal is assumed to be 6 MHz. The SNR of the PU’s signal received at the SUs is set to be -20 dB. The background noise power is N0=10-2 W/Hz. The active probability of the channel is set to be P1=0.3. The threshold of the detection probability on all channel is assumed to be α=0.9. The threshold of the false alarm probability on all channel is β=0.2. The sensing and circuit power are set as 0.02W and 0.01W, respectively. The minimum rate requirement is 2bit/s/Hz; we consider a Rayleigh fading environment with average channel power gain, that is, E{gi} equal to 0.1.In Figure2, the energy efficiency versus the sensing time is compared among different SNR when power allocation is optimized with the fixed average interference power Ith=-20dBW. It can be observed that when sensing time initially increases, the energy efficiency increases. This means that the improvement in sensing performance is able to outweigh the loss in shorter transmission time and larger energy used for sensing. However, when sensing time is increased further, the energy efficiency decreases as it is no longer worth to improve the sensing performance. Furthermore, when the SNR is high, the optimal sensing time is shorter and the energy efficiency is larger.Figure 2
Energy efficiency versus sensing time.In Figure3, the energy efficiency versus the average interference power threshold is compared between different schemes. In the proposed scheme, the sensing time and power allocation are jointly optimized. In scheme I, the sensing time is optimized while all SUs share the same transmit power which satisfies the constraint (15f). And in scheme II, the power allocation is optimized with a fixed sensing time τs=5ms. It can be observed that the proposed scheme outperforms scheme I and scheme II. Energy efficiency in all schemes increases when the average interference power threshold initially increases. However, when the average interference power threshold is increased further, the energy efficiency does not increase any more as the constraint of the average interference power is loose.Figure 3
Energy efficiency versus average interference power threshold.


## 6. Conclusion

In this paper, we consider the scenario that multiple SUs jointly sense one licensed spectrum band which can be divided into multiple subbands and each SU operates exclusively in one of the subbands when the PU is detected to be absent. We focus on the joint optimization between the spectrum sensing time and power allocation to maximize energy efficiency of the CRN, with limited interference to the PU. During the optimizing process, the target detection probability and the quality of service parameter have also been taken into consideration. An optimization algorithm combined with fractional programming to solve the optimization problem is proposed. Numerical results show that the performance improvement is achieved by joint optimization of sensing time and power allocation.



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*Source: 694254-2014-08-05.xml*