Optimal Energy-Efficient Transmission for Hybrid Spectrum Sharing in Cooperative Cognitive Radio Networks

Linna Hu,Rui Shi＊,Minghe Mao,Zhiyu ChenHongxi ZhouWeiliang Li

1 Computer & Information College,Hohai University,Nanjing 210098,China

2 Nanjing University of Science & Technology Zijin College,Nanjing 210023,China

3 State Grid Information & Telecommunication Branch,State Grid Corporation of China,Beijing 100761,China

Abstract: In order to improve the energy eff iciency (EE) in cognitive radio (CR),this paper investigates the joint design of cooperative spectrum sensing time and the power control optimization problem for the secondary user systems to achieve the maximum energy eff iciency in a cognitive network based on hybrid spectrum sharing,meanwhile considering the maximum transmit power,user quality of service (QoS) requirements,interference limitations,and primary user protection.The optimization of energy efficient sensing time and power allocation is formulated as a non-convex optimization problem.The Dinkelbach's method is adopted to solve this problem and to transform the non-convex optimization problem in fractional form into an equivalent optimization problem in the form of subtraction.Then,an iterative power allocation algorithm is proposed to solve the optimization problem.The simulation results show the effectiveness of the proposed algorithms for energy-efficient resource allocation in the cognitive network.

Keywords: cognitive radio networks; cooperative spectrum sensing; energy-efficiency; hybrid spectrum sharing; power control; sensing time optimization

I.INTRODUCTION

With the rapid development of the next generation mobile communication technology (5G)and the new wireless communication service,the scarce wireless spectrum resources have been difficult to meet the needs of the development of the communication industry [1-3].Despite this fact,the report released by the Federal Communication Commission showed that a large portion of the radio spectrum is not fully utilized most of the time [4].With the ever-increasing growth of data generated from mobile devices,some spectrum bands are getting congested while other spectrum bands such as the TV bands are still underutilized[5].

With the situation mentioned above,cognitive radio (CR) technology has been put forward to solve the shortage of spectrum resources by allowing unlicensed secondary users (SUs) to opportunistically access the spectrum bands unoccupied by licensed primary users (PUs).Generally,CR devices are designed based on software-defined radios to allow SUs to have the capabilities to sense,learn and adapt to wireless environments and then coexist with PUs in such a way that SUs'transmissions will not interfere with Pus [6-7].However,the shadow effect and multipath effect significantly reduce the sensing performance of cognitive users.In order to reduce these effects,scholars have proposed a cooperative spectrum sensing scheme [8-9].Cooperative spectrum sensing refers to the sensing of multiple cognitive users,and the sensing information is sent to the fusion center for the fusion decision to get the final sensing results.

At present,most of the existing cognitive radio research work focuses on maximizing the throughput of communication systems by optimizing cooperative sensing and transmission parameters.The authors in [10]consider the threshold optimization problem of cooperative spectrum sensing for cognitive radio(CR) and investigate the threshold optimization algorithm for both single - channel and multichannel cooperative spectrum sensing.The issues on performance analysis of cooperative spectrum sensing under guaranteed throughput constraints for cognitive radio networks were studied in [11-12].Cooperative spectrum sensing can indeed improve sensing performance,but multi user collaborative sensing necessarily means consuming more energy.For wireless devices with limited energy,such as devices powered by batteries,it is necessary to consider how to improve the system efficiency under the premise of ensuring sensing performance.

In cognitive radio systems,secondary users use their sense functions to detect whether PUs are idle or busy,then decide how to transmit their data without affecting the primary users,thereby improving the spectrum utilization.The coexistence of PUs and SUs,such as in recent work [13],is determined by dynamic spectrum sharing techniques (i.e.underlay,overlay,hybrid) [14].In the overlay technique,the SU can transmit its data only with the absence of PU's transmission whereas in the underlay technique,the SU can transmit simultaneously with the PU as long as caused interference to the primary receiver is below an acceptable threshold.In the hybrid technique,where secondary user senses the channel status and optimizes the power allocation based on the spectrum sensing result.Most of the previous works in the literature are focused on underlay and overlay technique,they focused on optimizing either cooperative sensing or resource allocation to maximize the throughput of the whole CR system [15-18].However,there is not much literature to study hybrid spectrum sharing.In this paper we take into account the hybrid spectrum sharing techniques to improve the performance of the secondary system.

In recent years,the emergence of new applications,growing demand for high data rates and increased number of users,lead to a large amount of energy consumption.Moreover,due to the limited battery capacity of mobile terminal and the slow progress of battery technology,the high energy consumption and exponential growth in wireless communication networks face serious challenges.With the spread of green communication ideas,the new green evaluation of the energy efficiency(EE) of communication systems has gradually attracted the attention of researchers [19-21].The energy efficiency of communication will have a significant impact on the endurance of these terminals.People no longer only pay attention to the system throughput,but hope to save the energy loss as much as possible before the quality of the system is guaranteed[22-23].Therefore,energy efficient design has become a vital consideration in cognitive radio with cooperative spectrum sensing from the perspective of green communication.

In this paper,we studied the joint design of cooperative spectrum sensing time and power control for the secondary system energy efficiency based on hybrid spectrum sharing.

Spectrum sensing for the EE maximization in a cognitive system has been investigated in[24-28].In particular,[24]studies the spectrum sensing and obtains the optimal spectrum sensing duration.[25]maximizes energy eff iciency assumed that secondary users perform channel sensing possibly with errors and then initiate data transmission with different power levels based on sensing decisions.[26]studies the impact of imperfect spectrum sensing and formulate the average EE maximization problem in fading channels.In [27]authors propose a new metric,namely the average sensing EE,and develop a valid algorithm to improve it at each cognitive transmitter (CT).[28]optimizes the decision threshold of an energy detector,spectrum sensing duration,and the number of cooperative CTs.Note that the cooperative spectrum sensing and the impacts of sensing energy consumption on EE are neglected in [24-28].

In addition,the spectrum sharing strategies for the EE maximization in a cognitive system have been investigated in [29-35].Some significant works for the use of energy efficiency can be found in [29-30]for the underlying scenario,in [31-33]for the case of overlay cognitive radio networks (CRNs) and in [33]cooperative perception is considered simultaneously.To further increase the transmission opportunities of the secondary users,hybrid spectrum sharing was proposed [34-35]which allows the secondary users to transmit under both idle and busy sensing decisions while adapting the transmission power according to the sensing results.However,[34]investigated the throughput-efficient power allocation strategies rather than energy efficiency strategies,and [35]discussed energy efficient in cognitive small cell scenario.

Besides,among those existing works,the problem of both sensing time optimization and power control in the cognitive network has not been well investigated.Although some works have been performed to optimize sensing time and power allocation in cognitive networks,most of these work focused on throughput maximization rather than energy efficiency.

Moreover,most existing work does not consider cooperative spectrum sensing and hybrid spectrum sharing simultaneously for secondary system energy efficient maximization in the cognitive network.In this paper,we investigate the joint design of cooperative spectrum sensing time and power control for the secondary system energy efficiency based on hybrid spectrum sharing by considering QoS requirement,interference limitation and the maximum transmit power.The main contributions of this paper are summarized below:

1) Design a novel energy efficient optimization framework of cooperative spectrum sensing considering energy efficiency maximization,interference mitigation,hybrid spectrum sharing,and user QoS requirements.

2) Study the impact of imperfect spectrum sensing and formulate the average energy-efficient maximization problem as a joint optimization problem of the cooperative spectrum sensing duration and the secondary user transmit power.

3) Since the maximization problem of the energy efficiency is the non-convex optimization problem,it is computationally hard to obtain the optimal solution directly.Instead,we decompose the energy efficient maximization problem into two sub-problems with the cooperative spectrum sensing duration and the transmit power as variables,respectively.Then we use the Dinkelbach's method to find the optimal power allocation schemes.

The rest of this paper is organized as follows.The system model is introduced in Section II and an energy-efficient optimization problem is formulated in Section III.Then,in Section IV,a joint optimal algorithm of the spectrum sensing duration and the transmit power schemes are derived.Simulation results and conclusions are finally presented in Section V and VI,respectively.

II.SYSTEM MODEL

We consider an OFDMA cognitive radio network which concludes the primary user (PU)system and secondary user (SU) system.The secondary user system includes K secondary cognitive users.In cognitive radio networks,primary users have the priority of channel access.Secondary cognitive users detect the occupation status of the sub-channel through periodic cooperative spectrum sensing,then adjust their transmission power according to the sensing results to access authorized sub-channel.The OFDMA system has a bandwidth of B,which is divided into N sub-channels.

The channel model for each channel includes small - scale fading,the shadow fading and path-loss.In order to simplify the problem,we usehnssto denote the channel coefficients between secondary cognitive users,and usehnpsto denote the channel coefficients between the secondary cognitive user and the primary user,respectively.The channel fading coefficients are assumed the same within a sub-channel,but may vary across different sub-channels.We assume that the primary user signal is a complex-valued phase shift keying(PSK) signal,and the noise is addition Gaussian white noise (AWGN) with mean zero and variance σ2.

The frame structure of the primary and cognitive network is shown in figure 1.As we can be seen from figure 1,one cognitive frame consists of three phases,i.e.,the spectrum sensing phase,the cooperative sensing fusion phase and the data transmission phase.Denote the time slot period asT.In the spectrum sensing stage,some secondary cognitive users are chosen to perform the cooperative sensing to determine the occupation status of the sub-channels in the duration τ.Assume that all secondary cognitive users have the same timing synchronization system to ensure the synchronization of spectrum sensing.In the phase of cooperative sensing fusion,each secondary cognitive user transfers the sensing results to the fusion center with the durationμ,then the fusion center summarizes the primary information according to the OR criterion and makes a comprehensive decision on the status of the primary user.The cooperative sensing fusion duration ofKsecondary cognitive users isKμ.To further increase the transmission opportunities of the secondary users,hybrid spectrum sharing based cooperative sensing was proposed in the stage of data transmission,which allows the secondary users to transmit under both idle and busy sensing decisions while adapting the transmission power according to the sensing results.The energy detector is used by the secondary users to sense the primary channel status.It is simple and easy to be realized,and the relevant information of authorized users must not be known in the process of sensing.TheH1is the hypothesis that the primary users occupy the channel.TheĤ1represents the spectrum sensing result that primary users occupy the channel.TheH0is the hypothesis that primary users do not occupy the channel.TheĤ0represents the spectrum sensing result that primary users do not occupy the sub-channel.

The false alarm probabilities indicate that the channel is vacant but the spectrum sensing decision is occupied .The probabilities of the detection and false alarm on sub-channelnareQndandQnf,respectively.Then,the channel detection probability and false alarm probability are respectively given by

and

whereQ(x)is the complementary Gaussian function,εnis a chosen threshold of energy detector on sub-channeln;τis the spectrum sensing time;γnis the received signal to-noise ratio (SNR) of the primary user measured at the secondary user on sub-channeln;fis the sampling frequency.

In the stage of cooperative sensing and fusion,OR rule is adopted in data fusion.In the process of cooperative sensing,if any secondary cognitive user detects the sub-channel is occupied,then the final decision is occupied.

Fig.1.Frame structure.

By using the OR rule,the detection probability of the cognitive system will be improved with the increase of the number of cognitive users,effectively avoiding the interference to the primary user and improving the sensing performance of system.Therefore,the channel joint detection probability and joint false alarm probability are respectively given by

wherekn(1≤kn≤K)represents the number of secondary users participating in cooperative sensing on the sub-channeln.

In this paper,an improved hybrid spectrum sharing method is adopted to increase secondary user access to channels.Hybrid spectrum sharing method combines the way of underlay spectrum sharing access and the way of overlay opportunistic spectrum access.The secondary cognitive users can not only access the channel when the spectrum is idle but also access the channel when the spectrum is busy,which increases the access opportunity of the secondary users.Under the hybrid spectrum sharing model,the secondary users sense the status of the primary user respectively,and finally determine whether the primary user is idle through the cooperative fusion center,and then adjust transmission power according to the status of the primary user.If the primary user is idle,the secondary user adjusts the maximum transmission power to access the channel in the way of the overlay.If the primary user is busy,the secondary user will access the channel through the way of underlay at lower transmission power.

III.OPTIMIZATION PROBLEM FORMULATION

Denote the case that the primary channel is idle byH0with the probabilityQH0and the case that the primary channel is busy byH1with the probabilityQH1,respectively.If the sub-channelndetected to be idle,the secondary cognitive user can transmit powerpns0; if the sub-channelndetected to be occupied,the secondary cognitive user could transmit powerpns1without interfering with the primary user.Due to imperfect spectrum sensing,there are four different cases as follows.

Case 1:In this case,sub-channelnis vacant,and the cooperative spectrum sensing decision made by cooperative fusion center is vacant.Then,the idle channel is correctly detected with the probabilityBased on Shannon's capacity formula,we can calculate the achievable capacities on sub-channelnin secondary user for this case as

Case 2:In this case,sub-channelnis vacant,but the cooperative spectrum sensing decision made by cooperative fusion center is occupied.It is a false alarm and happens with the probabilityAccordingly,the achievable capacities on sub-channelnare given by

Case 3:In this case,sub-channelnis occupied,but the cooperative spectrum sensing decision made by cooperative fusion center is vacant.It is a misdetection and happens with the probabilityThen,the achievable capacities on sub-channelncan be de fined by

Case 4:In this case,sub-channelnis occupied,and the cooperative spectrum sensing decision made by cooperative fusion center is occupied.Then,the busy channel is correctly detected with the probabilityThus the achievable capacities on sub-channelnare given by

In this paper,we only analyze the performance of the cognitive secondary user system.The power consumption of secondary user system includes sensing power consumption,data transmission power and static circuit consumption.The sensing power consumption is consumed by local sensing power consumption and cooperative sensing power consumption.Incase 1andcase 3,the fusion center determines is idle,so the secondary user transmits data with a higher transmission powerpns0.

The power consumption is defined as

Incase 2andcase 4,the primary user occupies the authorized channel,and the secondary user transmits data at a lower transmit powerpns1without interfering with primary user.The power consumption is defined by

WherePcis the constant circuit power consumption which includes a low-pass filter,a mixer for modulation,frequency synthesizer,and a digital-to-analog converter,andPcis assumed to be independent of the transmitted power.Psis the sensing power consumption andPfis the cooperative sensing power consumption.Kis the number of secondary users involved in cooperative sensing.

In addition,we suppose that the length of the time slot used by each cooperative SU to deliver local sensing data to the fusion center isμ.Then the data transmission duration isT-τ-kμ.Therefore,the throughput and average power consumption of secondary user on sub-channelnis given as

and

Consequently,the objective function of the average energy efficiency of the cognitive system on sub-channelncan be defined as a tradeoff between the throughput and the entire power consumed in a time slot.

In this paper,we aim to maximize the cognitive secondary user energy efficiency while protecting the QoS of the primary users.We assume that the cross-tier interference power limit is sent by a primary periodically.Due to the range ofkis a set of finite integers,it can be optimized by exhaustive method.So we discuss the problem of optimization under fixedkvalues.Assuming that the detection threshold of each sub channel is the same when using energy detection,the detection threshold can be obtained for a given sensing time and detection probability.In this case,the sensing time optimization and power control of primary users are not part of our optimization.Thus,the optimization problem of maximizing energy efficiency of secondary users system can be expressed as follows:

where C1 represents the constraint of sensing time in each frame; C2 set the range ofn; C3 expresses the non-negative power constraint of the transmit power on each sub-channel; C4 denotes the minimum transmission data rate constraint of each sub-channel to guarantee the QoS requirement; C5 represents the maximum allowed average interference power at the primary receiver; C6 limits the maximum average transmission power of the secondary transmitter.

However,the optimal problem under the proposed constraint is non-convex optimization problem.In order to solve this problem,a double layer optimization algorithm is used to decompose the optimization problem into two sub-layer optimization problems,in which the lower layer optimization problem is to optimize the transmit power given the sensing timeτ,while the upper optimization problem is to optimize the sensing time.

IV.JOINT OPTIMIZATION OF SENSING TIME AND POWER ON ENERGY EFFICIENCY

The optimization problem in (13) under the constraints of (C1-C6) is a non-convex problem with respect towhich is a mixed integer nonlinear programming problem, known to be NP-hard.We fi rst investigate the problem of energy eff i cient power control given the sensing timeτ.Notice that the optimization problem is a fractional optimization problem that the feasible domain is a continuous compact convex set,andare continuous positive functions in the feasible domain.The optimization problem can be solved by Dinkelbach optimization algorithm.The Dinkelbach algorithm transforms the initial fractional optimization problem into an equivalent parameter optimization problem.The formula (13) is transformed into an optimization problem with positive parameterηas

Theorem 1: Ifη*is the sum of average energy efficiency under the constraints C1-C6,if and only ifF(η*)=0.

Whereαn,βnandχare the Lagrangian multipliers vectors for the constraints C4,C5 and C6,respectively.For any given sensing timeτˆ,the near optimal power allocation ofandon sub-channelncan be obtained by using Lagrangian function and the Karush-Kuhn Tucker (KKT) conditions.The sub-gradient method is introduced to search the optimal power allocation scheme.The main idea of the sub-gradient method is designing a step sequence to update the dual variables,the corresponding update can be written as follows:

Where δ1l,δ2land δ3ldenote the step size of iterationl(l∈{1,2,...,Lmax}) forα,βandχrespectively,andLmaxis the maximum number of iterations.Moreover,the sub-gradient method can ensure thatα,βandχconverge to the optimal point when δ1l,δ2land δ3lis sufficiently small.

The optimal power allocation problem can be rapidly solved by an iterative procedure which is described as Algorithm 1.The near optimal sensing time can be found by one-dimensional exhaustive search.We have obtained the optimal power through Algorithm 1.

V.NUMERICAL RESULTS AND DISCUSSIONS

In this section,numerical results are presented to illustrate the performance of the proposed strategy.We use MATLAB to solve the system model and to run simulations.In the following simulations,the channel gains are modeled as independent,exponentially distributed with a mean of 0.1.

We consider the CR system consists ofK=10SUs andN = 32subcarriers.The sampling frequency of the received signal is as-sumed to be5MHz,noise (AWGN) varianceσ2= 2 × 10-5.The duration of the OFDM symbolT=0.15sec,the time used by each cooperative SU to deliver local sensing data to the fusion center is1ms.The transmission power of PU on sub-channel n is set as20mW.Both the sensing and circuit power are set as1mW.Both the idle and busy probabilities of the channels are0.5.

TableI.Proposed Energy-Efficient allocation algorithm.

Fig.2 displays the average energy efficiency of the whole CR system versus sensing timeτwith the number of cooperative sensing users which is set as4,6,8,10.As can be seen,the energy efficiency performance of the system is the worst whenkis equal to4.With the increase of the number of secondary users participating in cooperative sensing,the performance of the average energy efficiency is improved.The system has the best energy efficiency performance atk=8.However,as the number of users increases,the overall energy efficiency of the system decreases when the10secondary users are all involved in cooperative sensing.This is because that with the increase of the number of users participating in the sensing,the system false alarm probability is also decreas-ing,which means that the performance of the system is increasing and the energy efficiency of the cognitive radio system is increased.Therefore,the optimal performance simulation curves show an upward trend at the beginning.However,as the number of cooperative sensing users increases,the impact of the sensing performance is gradually weakened.When the number of users increases to a certain extent,the resulting decrease in transmission time is gradually dominated,leading to the final decline in the optimal performance curve.

Fig.2.Average energy efficiency versus sensing time with different cooperative sensing users.

Fig.3.Average energy efficiency versus sensing time with the different interference threshold.

Figure 3 and figure 4 show the relationship between sensing time and average energy efficiency of each sub-channel in cognitive network under different interference threshold and different maximum transmit power.It can be observed from the figure 3 and figure 4 that the system energy efficiency is less at the beginning.This is because the sensing time and the detection probability are small at the beginning results in the data transmitted by the cognitive users are often disturbed by the primary users,which leads to the invalid data transmission.Thus the system energy efficiency is less.As the increasing of sensing time,the system energy efficiency raises.This is because the detection probability becomes larger with the increasing of the sensing time.In other words,the probability of the data received by the cognitive users is larger,the system throughput is increasing and the system energy efficiency increases.However,the system energy efficiency begins to decline as the sensing time increased.This is because with the increase of sensing time,the improvement of sensing performance is limited,and as the time of sensing growing,the transmission time becomes shorter and the throughput of the system becomes smaller,which leads to the decline of the energy efficiency of the system.

As can be seen from figure 3,the average energy efficiency first increases and then drops as the sensing time is increased.LargerInthvalue results in higher average energy.

efficiency since a larger of value ofInthleads to a larger optimization variable region.As shown in Fig4,the average energy efficiency of each sub-channel first increases and then drops as the sensing time is increased from0sec to0.15sec with the maximum transmission power set as10,13,15dBm.It is also observed that energy efficiency increases with increasing transmit power constraints because a larger value ofPmaxenlarges the feasible re-gion of the variables in the original optimization problem .

Fig.5 provides the energy efficiency performance of different algorithms with different maximum transmission power.The influence of the maximum transmission power of the user on the energy efficiency of the system is compared under the fixed sensing time scheme,without cooperative sensing scheme and the joint allocation mechanism proposed in this paper.As shown in figure 5,when the maximum transmission power of the user changes from 5 to 25,energy efficiency of the system increases with the three schemes.Under the condition of the same maximum transmission power,the system energy efficiency of the proposed mechanism is obviously better than the other two resource allocation schemes.Fixed sensing time scheme has the worst performance.Figure 2 Average energy efficiency versus sensing time with different cooperative sensing users.

VI.CONCLUSION

In this paper,we studied the joint design of cooperative spectrum sensing time and power control for the secondary system energy efficiency based on hybrid spectrum sharing.Meanwhile,we consider the transmission power,interference limitation,the minimum transmission rate and imperfect spectrum sensing.However,the energy efficient sensing time optimization and power allocation were modeled as a non-convex optimization problem.Instead,we developed the Dinkelbach's algorithm to solve the problem.The simulation results showed the effectiveness of the proposed algorithms for energy efficient resource allocation in cognitive radio network.In the future,we will study energy efficiency in multi-users heterogeneous networks.

ACKNOWLEDGMENT

This work was supported in part by the National Natural Science Foundation of China for Young Scholars under Grant No.61701167,and Young Elite Backbone Teachers in Blue and Blue Project of Jiangsu Province,China.

Fig.4.Average energy efficiency versus sensing time with different Pmax values.

Fig.5.Average energy efficiency versus maximum transmission power Pmax with different resource allocation schemes.