Key Lab of Mobile Communication Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

I. INTRODUCTION

The rapid development of mobile broadband services with continuously increasing traffic volumes in 5G communication system has posed requirements on the available frequency spectrum resource. However, traditional static spectrum allocation policy in cellular systems has resulted in the exhaustion of licensed spectrum, while on the other hand, a lot of allocated licensed spectrum is extremely under-utilized. To stress this problem, cognitive radio networks (CRNs) have been proposed which allow unlicensed users referred to as secondary users (SUs) to opportunistically utilize the licensed bands of licensed users,i.e., primary users (PUs) without affecting the normal communications of the PUs [1].

In CRNs, source and destination SU pairs may conduct information interaction with each other. In the case that the direct transmission link between one source SU and its destination SU is unavailable, relay technology can be applied through which one or multiple relay SUs are selected to help forwarding data packets for the SU pair, resulting in multi-hop CRNs.The optimal design of relay selection or route selection scheme for multi-hop CRNs is of particular importance for different transmission characteristics of relay SUs may result in various transmission performance of the SU pairs. Furthermore, the resource allocation issue of the source or relay SUs may also affect the transmission performance of the SU pairs significantly.

This paper considers a multi-hop CRN consisting of multiple PUs,SU transmission pairs and relay SUs.

1.1 Related works

In recent years, there are some research works focusing on the resource allocation problems in CRNs. Stressing the quality of service(QoS) guarantee issue in CRNs, the authors in [2] propose a framework for a twofold cognitive manager which is capable of managing spectrum availability on longer timescales and handling resource management on shorter timescales. Giving particular focus to the functionalities of the cognitive manager related to resource management, the authors present a few key scenarios and describe how QoS can be managed with the proposed approach without affecting the communications of serving users.

Channel assignment problems have been considered for CRNs in [3, 4]. Reference [3]presents a comprehensive survey on the stateof-the-art channel assignment algorithms in CRNs. In [4], the authors address the channel allocation problem for multi-channel cognitive vehicular networks and propose an optimal scheme with the objective of maximizing system-wide throughput. Since the formulated problem is an NP-hard non-linear integer programming problem, the authors develop a probabilistic polynomial- time-approximation algorithm and a deterministic constant factor approximation algorithm to obtain the suboptimal channel allocation strategy.

[5–7] stress the problems of power allocation in CRNs. In [5], the power allocation prob- lem in a CRN employing non-orthogonal multiple access (NOMA)technique is investigated. The authors propose an optimal power allocation algorithm, which aims to maximize the number of admitted SUs under the maximum power and interference constraints. Reference [6] studies energy-efficient power allocation schemes for SUs in sensing-based spectrum sharing CRNs. It is assumed that the SUs first perform channel sensing and then initiate data transmission with different power levels based on sensing decisions. The optimization problem is formulated to maximize energy efficiency subject to peak/average transmission power and interference constraints. The original problem is transformed into an equivalent parameterized concave problem, and an iterative power allocation algorithm is proposed to obtain the optimal power allocation strategy.

The authors in [7] investigate the energy-efficient power allocation for orthogonal frequency division multiplexing (OFDM)based relay-aided CRNs with imperfect spectrum sensing. The optimal power allo- cation problem is formulated as a fractional optimization problem which maximizes the energy efficiency of the users. To solve the formulated problem, the primal problem is transformed into a convex optimiza- tion problem using the fractional programming method, and the optimal and suboptimal algorithms are proposed to obtain the power allocation strategy.

Power allocation schemes are jointly designed with channel assignment or user scheduling schemes in [8, 9]. In [8], the authors present a framework for distributively optimizing the transmission strategies of SUs in an ad hoc CRN and design an optimal transmit power and channel access probability scheme which maximizes the number of SU transmissions per unit area. In [9], the uplink transmission in a CRN consisting of a single PU and a number of SUs is considered. The authors propose a dynamic scheduling and power allocation policy that provides the required average delay guarantees to all SUs and protects the PU from harmful interference. Joint channel and rate selection problem is studied for CRNs in [10]. Under the assumption that the SU transmitters are allowed to opportunistical-ly track and change the channel and rate pair during transmission, the authors formulate the problem of sequential channel and rate selection as an online optimization problem which aims at maximizing the throughput of the SUs.

For multi-hop CRNs, relay selection or route selection problems have received considerable atten- tions. The problem of prioritizing the routes for the packet transmission in CRNs is stressed in [11]. The authors analytically derive the optimal route priority rule to maximize the achievable capacity and propose a computational-efficient search algorithm to obtain the routing strategies. In [12], the authors s- tudy the routing problem in multihop CRNs and propose a spectrum-aware anypath routing scheme with consideration of both the salient spectrum uncertainty feature and the unreliable transmission character- istics of wireless medium. The authors in [13,14] study the routing protocols for cognitive radio ad-hoc networks (CRAHNs). In [13],the authors consider cluster-based underlay multi-hop CRNs and propose an ad-hoc routing protocol, namely, the highest transmit power relay selection (HTPRS) protocol and its improved version. The exact end-to-end outage probability of the networks when employing the two rout- ing protocols is derived by taking into account both peak-power and peak-interference constraints. The authors in[14] propose a spectrum aggregation-based cooperative routing protocol for CRAHNs.Aiming at achieving higher energy efficiency,improved throughput and reduced network delay, the authors de- sign different spectrum aggregation algorithms for SUs and propose routing protocols for achieving high energy efficiency and low end-to-end latency.

[15, 16] study routing protocols for cognitive radio sensor networks (CRSNs).To stress the problem of transmitting multimedia applications in CRSNs with energy and spectrum constraints, the authors in [15]propose a spectrum-aware cluster-based energy-efficient multimedia (SCEEM) routing protocol that overcomes the formidable limitations of energy and spectrum. In SCEEM routing scheme, the number of clusters is optimally determined to minimize the distortion of multimedia quality that oc- curs due to packet losses and latency. In [16], an opportunistic routing protocol is introduced for CRSNs. By taking into consideration the limited computational capabilities and energy resources of the wireless sensor nodes, multiple paths between the source and the destination are maintained and packets are al- lowed to follow any of those paths according to the dynamically changing network conditions, such as interference, channel and relay node availability.

While previous research works [3–16] focus on designing resource allocation or route selection strat- egy independently for users in CRNs, the joint optimal design of resource allocation and routing schemes for multi-hop CRNs may further enhance the transmission performance of users [17–21]. The authors in[17] study the robust relay selection and power allocation problem for OFDM-based cooperative CRN- s with channel uncertainties.By characterizing the channel uncertainties as ellipsoid set and interval set, a semi-infinite programming problem is formulated to maximize the capacity of the network, and the optimal joint relay selection and power allocation strategy can be obtained by solving the optimization problem. In [18, 19], the authors study joint routing and resource allocation problem of cognitive wireless mesh networks. The authors in [18] propose an economic framework for managing network resources with the goal of network profit maximization while the authors in [19] propose an optimal algorithm to minimize the aggregate end-to-end delay of all the network flows.

The authors in [20] propose a new multihop cognitive cellular network architecture to facilitate the ever exploding data transmissions in cellular networks. Under the proposed architecture, they investi- gate the minimum energy consumption problem by exploring joint frequency allocation, link scheduling,routing, and transmission power control. A maximum independent set-based energy consumption opti- mization problem is formulated and a column generation based approach is employed to circumvent the problem. To improve the transmission performance of SUs,cooperative routing using mutual-information accumulation is considered for CRNs in[21]. The authors formulate the joint routing and resource allo- cation problem as a transmission delay minimization problem which is then transformed into two sub- problems,i.e., the resource allocation sub-problem for a fixed route order and the optimal route order sub-problem with the minimal interference to the PU receiver. By solving the two sub-problems respec- tively, the optimal joint routing and resource allocation strategy can be obtained.

1.2 Main contributions

Previous research works mainly focus on maximizing the network capacity or minimizing transmission delay [17–19], which may result in large power consumption, thus is highly undesired especially for energy-sensitive user devices. While energy consumption is considered in [20], the authors mainly con- sider the problem of resource allocation strategy instead of jointly designing the resource allocation and route selection strategy.

In this paper, we consider a multi-hop CRN consisting of multiple PUs, a number of SU transmis- sion pairs and relay SUs, and jointly design resource allocation and route selection strategy for the SU pairs. To achieve joint routing and resource management of the SU pairs, we propose a centralized joint resource management architecture, based on which the information of users can be collected and joint resource allocation and route selection can be conducted in a centralized manner. Stressing the hops and the energy efficiency of the transmission routes between the source and destination SUs, we propose an energy efficient constrained shortest path first (CSPF)-based joint resource allocation and route se- lection algorithm, which consists of two sub-algorithms,i.e., CSPF-based route selection sub-algorithm and energy efficiency-based resource allocation sub-algorithm. Since the energy efficiency optimization problem formulated is a nonlinear fractional programming problem, which cannot be solved convenient- ly, we transform it into an equivalent optimization problem which can then be solved based on iterative algorithm and Lagrange dual method.

The major contributions of this paper are summarized as follows:

– We design a centralized resource management architecture based on which the proposed joint resource allocation and route selection algorithm can be conducted.

– Resource allocation and route selection problems in CRNs have been studied respectively in [2–10] and [11–16], in this paper, we consider the close coupling between resource allocation and route selection in multi-hop CRNs, and jointly design resource allocation and route selection strategy for the SU pairs.

– While the authors in [17–21] have considered joint optimal design of resource allocation and routing schemes for CRNs, they mainly focus on maximizing the network capacity or minimizing transmis- sion delay[17–19], which may result in large power consumption, thus is highly undesired especially for energy-sensitive user devices.While energy consumption is considered in[20], the authors mainly consider the problem of resource allocation strategy instead of jointly designing the resource allocation and route selection strategy. In this paper, to stress the tradeoff between transmission data rate and power consumption,and to jointly consider the transmission hop between the source and destination SU, we propose an energy efficient CSPF-based joint resource allocation and route selection algorith- m, which mainly consists of two sub-algorithms, i.e., CSPF-based route selection sub-algorithm and energy efficiency-based resource allocation sub-algorithm.Since the energy efficiency optimization problem formulated is a nonlinear fractional programming problem, which cannot be solved conve- niently, we transform it into an equivalent optimization problem which can then be solved based on iterative algorithm and Lagrange dual method.

The rest of this paper is organized as follows. The system model and the proposed resource man- agement architecture are discussed in Section 2. In Section 3, the proposed CSPF-based route selection sub-algorithm is presented. Energy efficiency optimization problem is formulated and solved in Section 4. Simulation results are given in Section 5.Finally, we conclude this paper in Section 6.

II. SYSTEM MODEL AND PROPOSED CENTRALIZED RESOURCE MANAGEMENT ARCHITECTURE

2.1 System model

In this paper, we consider a CRN in which PUs transmit their information to primary base station (PBS) on licensed spectrum, and a number of SU transmission pairs are allowed to transmit data packets in an ad-hoc mode. We assume that each PU is allocated one licensed channel for data transmission and each licensed channel is only assigned to one PU, hence, no spectrum competition and transmission interference exist between the PUs. For convenience, we assume that the number of PUs is equal to the number of licensed channels, denoted by K, and the kth PU is allocated the kth channel for data transmission, 1 ≤ k ≤ K.

Fig. 1 System model

To improve spectrum efficiency, SU pairs are allowed to share the spectrum resources with the PUs. More specifically, we assume that underlay spectrum sharing mode is applied between PUs and SUs, i.e., PUs and SUs may transmit simultaneously on the same licensed channel of the PUs provided that the transmission performance of both the PUs and the SUs can be guaranteed. In the case that the destination SU is out of the transmission range of the source SU, one or multiple relay SU(s)can be applied to forward the data packets for the SU pair. In this paper, it is assumed that decode-and-forward (DF) mode is employed in the relay SUs. Figure 1 shows the system model considered in this paper.

For a SU pair, in the case that multiple candidate routes are available, optimal route selection has to be conducted. In addition, for both the source SU and relay SUs, channel and transmit power allocation strategy should be designed in an optimal manner so that the transmission performance of the SU pair can be enhanced. In this paper, we study the resource allocation and route selection problem of SU pairs and design an optimal joint route selection, and channel and transmit power allocation strategy for the source SU and relay SUs.

2.2 Proposed centralized resource management architecture

In the multi-hop CRN described in figure 1,the available radio resources including the channels of the PUs, the transmit power of the PUs, source SUs and relay SUs, etc., need to be allocated in a coordinated way so that user transmission performance can be enhanced and the QoS requirements of both the PUs and the SUs can be guaranteed. To achieve these goals, a multi-layer centralized resource management architecture is proposed in this paper.

Figure 2 shows the proposed resource management architecture, in which various types of logically centralized resource management entities (RMEs) are applied to collect the dynamic information of PUs and SUs, and to conduct joint resource allocation and route selection algorithm for the SUs. According to the resource management functions and responsibilities, RMEs can be classified as user RMEs (URMEs), local RMEs (LRMEs) and global RME (GRME). The major functions and responsibilities of URME, LRME and GRME are summarized as follows.

URME:a functional entity embedded in the user equipment (UE) of both PUs and SUs, collecting and storing the channel state information (CSI) and QoS requirements of users. Through interacting with the associated LRME, a URME sends the collected information to the network and receives joint resource allocation and route selection strategy.

LRME:a functional entity deployed in certain network regions, collecting the CSI and QoS infor- mation from the associated URMEs, then forwarding to the GRME, and disseminating the joint resource allocation and route selection strategy received from the GRME to the URMEs.

GRME:a functional entity deployed in the multi-hop CRN, collecting the CSI and QoS informa- tion from the associated LRMEs,conducting joint resource allocation and route selection algorithm and sending the obtained optimal allocation strategy to the associated LRMEs.

III. CSPF-BASED ROUTE SELECTION SUB-ALGORITHM

For a pair of source SU and destination SU,a large number of transmission hops between the two users may result in long transmission delay and large resource overhead, which are highly undesired. Hence, the hops of the transmission routes should be considered in designing optimal resource allocation and route selection algorithm. Furthermore, as each SU pair may have certain QoS requirements,the selected routes may have to meet some transmission constraints. In this section, we jointly consider the number of hops and the constraints of the transmission routes, and propose a CSPF-based route selection sub-algorithm that selects the shortest candidate routes(SCRs) of SU pairs which meet the resource allocation and route selection constraints.

Fig. 2 Proposed centralized resource management architecture

3.1 Constraints on transmission routes

In this paper, user QoS requirement on transmission rate is stressed and the data rate of the transmission route is considered as the QoS metric of the SUs, i.e., each SU pair is assumed to have a minimum data rate requirement. It is apparent that the data rate requirement of the SU pair may pose constraints on transmission route. In this subsection, we analyze the data rate constraints on the transmission routes based on which the candidate transmission route set can be created.

For a given source and destination SU pair,we first determine all possible routes of the SU pair. Let Ψ0denote the set containing all the possible routes between the SU pair anddenote the ith possible route between the SU pair, 1≤i≤Ntot, where Ntotdenotes the total number of the possible routes. For simplicity,the ith possible route is also referred to as the ith route hereafter.

Denoting R(s,min)as the minimum data rate requirement of the SU pair, the ith route has to meet data rate constraint, i.e.,

where R(i)denotes the data rate of the ith route. We further denote the data rate of the lth hop of the ith route as, wheredenotes the number of hops of the ith route, we obtain

Combining (1) and (2), we obtain the following condition:

Jointly considering (3) and (4), we obtain

According to Shannon’s formula,can be calculated as

where Wkdenotes the bandwidth of the kth channel,anddenote the channel gain and the transmit power of the lth hop transmit SU of the ith route on the kth channel,denotes the transmit power of the kth PU,denotes the link gain from the kth PU to the lth hop receiving node of the ith route on the kth channel and σ2denotes the power of the channel noise.

We can then transform the data rate constraint in (5) equivalently into following transmit power constraint, i.e.,

As the parameters contained in the right side of (7) are assumed to be constants in this paper, (7) gives a fixed lower bound ofOn the other hand, for practical applications,user devices may have different maximum permissible transmit power. Denotingas the maximum transmit power of the lth hop transmit SU of the ith route, the maximum power constraint can be expressed as

Jointly considering (7) and (8), we can obtain

The above condition indicates that the lth hop of the ith route can be selected as the candidate route of the SU pair on the kth channel if only (9) holds. Collecting all the candidate routes of the SU pair into a candidate route set, denoted as Ψ1, we obtain

Collecting the candidate routes with the number of hops being Lmininto a set Ψ, we obtain a set of SCRs, i.e.,

3.2 Selecting the shortest candidate routes

The transmission hops between the source and destination SU may affect the transmission performance significantly, in particular, large transmission hops may result in long transmission delay and large transmission overhead,thus, in this paper, we apply the idea of CSPF on route selection and select the candidate routes with the smallest hops.

For all the candidate routes collected in Ψ1, the number of hops is examined and the candidate routes with the minimum number of hops are selected. Denote N1as the size of Ψ1, i.e., the total number of the candidate routes, and denoteas the ith candidate route in Ψ1, L(i)as the number of hops of the ith candidate route, the minimum hop of all the candidate routes can be calculated as

3.3 Energy efficiency optimizationbased route selection

In this paper, to stress the importance of both the transmission rate and power consumption of the SCRs and to achieve the tradeoff of the two parameters, the energy efficiency of the SCRs collected in Ψ is examined and optimized in terms of the transmit power and channel allocation strategy of the source and relay SUs, the detail optimization procedure will be discussed in Section 4.

Denote η(i)and η(i,*)as the energy efficiency and the corresponding optimal value of the ith SCR, denoteandas the optimal channel allocation variable and power allocation variable of the lth hop of the ith SCR when accessing the kth channel, we obtain

where N denotes the number of the SCRs. Examining η(i,*)for all the SCRs in Ψ , the route ψ(i,*)which achieves the maximum energy efficiency can then be selected as the optimal route, i.e.,

The optimal power and channel allocation strategy of ψ(i,*)can also be obtained through the energy efficiency optimization procedure discussed in Section 4.

IV. ENERGY EFFICIENCY-BASED RESOURCE ALLOCATION SUBALGORITHM

In this section, we propose an energy efficiency-based resource allocation sub-algorithm for the ith SCR, 1≤i≤N. In particular, we formulate the optimal power and channel allocation problem of the ith SCR as an energy efficiency optimization problem and solve the optimization problem by means of iterative method and Lagrange dual method.

4.1 Optimization problem formulation

In this section, we describe the formulation of the optimal power and channel allocation problem of the ith SCR, 1≤i≤N.

4.1.1 Energy efficiency modeling

The energy efficiency of the ith SCR can be defined as

where Pcirdenotes the circuit power consumption of the lth hop transmit SU of the ith SCR when transmitting on the kth channel. Without loss of generality, Pcir is assumed to be a constant for all the transmitters in this paper.

4.1.2 Optimization constraints

To achieve the maximum energy efficiency of the ith SCR, 1≤i≤N, the following optimization constraints have to be considered.

C1: The maximum transmit power constraint of the SUs

Due to the hardware limitation, the source and relay SUs of the lth hop of the ith SCR should meet the maximum transmit power constraint, 1≤l≤Lmin, i.e.,

C2: The minimum data rate constraint of the PUs

In CRN, due to the high priority of the PUs,the SUs can only access the licensed spectrum provided that the QoS requirements of the PUs can be guaranteed. Assuming each PU should meet a minimum data rate constraint, i.e.,

C3: The minimum data rate constraint of the SU pair

As the ith SCR should meet the minimum data rate constraint, i.e., R(i)R(s,min)≥, all the links of the route should also meet the data rate constraint, i.e.,:

C4: Binary constraint on channel allocation variables

In this paper, the channel allocation identifiers are defined as binary variables, i.e.,

C5: Channel allocation constraint

Due to hardware constraints, we assume that at most one channel can be allocated to the transmitter of the lth hop of the ith SCR,hence we obtain

4.1.3 Optimization problem formulation

Given the optimization constraints, we formulate the energy efficiency optimization problem of the ith SCR as follows

It is apparent that to maximize η(i)in (25)is equivalent to maximizing the energy efficiency among all the hops of the ith SCR. Furthermore, as the data transmission of various hops along the ith SCR occupies different time durations, no specific constraints need to be considered for channel allocation among various hops. Therefore, the resource allocation of different hops can be conducted independently, and the optimal energy efficiency of the ith SCR can then be calculated based on the optimal solution of each hop.

For the lth hop of the ith SCR, 1≤l≤Lmin,1≤i≤N, the optimization problem can be formulated as

4.2 Solution to the optimization problem

In this section, the optimization problem formulated in (26) is solved to obtain the optimal power and channel allocation strategy for the lth hop of the ith SCR, 1≤l≤Lmin, 1≤i≤N.As the optimization problem formulated in(26) involves the coupling of binary optimization and nonlinear fractional optimization,which cannot be solved conveniently using traditional optimization tools. Indeed, it can be shown that the power allocation for any given channel allocation strategy can be conducted independently, hence, the joint optimization problem can be equivalently transformed into power allocation subproblem and channel allocation subproblem. More specifically, by formulating and solving the power allocation subproblem, the optimal transmit power can be designed and the corresponding energy efficiency can be obtained for each channel allocation strategy, then the optimal channel which corresponds to the maximum energy efficiency can be selected through solving the channel allocation subproblem.

4.2.1 Iterative algorithm for energy efficiency maximization

In this subsection, we assume thati.e., the kth channel is allocated to the lth hop of the ith SCR, and formulate the power allocation subproblem as

The optimization problem formulated in(27) is a nonlinear fractional problem which can be transformed into a convex problem and solved using iterative algorithm. To solve the problem, we introduce variable q and denote q*as the maximum energy efficiency of the lth hop of the ith SCR when the kth channel is allocated, i.e.,

It can be proved that the maximum energy efficiency q_ is achieved if and only if [22]:

Hence, solving the optimization formulated in (27) is equivalent to solving the following optimization problem:

Applying iterative algorithm, the optimal energy efficiency q*and power allocation strategycan be obtained. The problem solving process can be summarized briefly:starting from an initial value of q, the locally optimal power allocation strategy can be obtained through applying traditional convex optimization tools, then the energy efficiency q can be updated based on the obtained power solution; given the updated q, the power allocation process can be reconducted, the process continues until the algorithm converges and the optimal energy efficiency and the power allocation strategy can be obtained [22]. The proposed iterative algorithm is summarized in Algorithm 1.

4.2.2 Lagrange dual method-based power allocation algorithm

For a given q, the power allocation subproblem can be formulated as

The optimization problem formulated in(31) is a constrained convex optimization problem which can be solved by applying Lagrangian dual method. The Lagrangian function can be formulated as

where λ,μ,ω are Lagrange multipliers, and

The optimization problem in (31) can then be transformed into Lagrange dual problem:

The optimization problem formulated in(34) consists of two subproblems, i.e., internal maximum subproblem and external minimum subproblem, which can be solved iteratively.For a set of fixed Lagrange multipliers, the internal maximum subproblem can be solved to obtain the locally optimal power allocation strategy, which can then be applied to solvethe external minimum subproblem to obtain the updated Lagrange multipliers.

Algorithm 1 Iterative algorithm for energy efficiency maximization

Algorithm 2 Lagrange dual method-based power allocation algorithm

The locally optimal power allocation strategy can be obtained by calculating the derivative of formulated Lagrange function with respect toand setting to zero, i.e.,

Table I Simulation Parameter

where [x]+ = maxfx;0g.

To solve the external minimum subproblem, we apply gradient descent algorithm to calculate the Lagrange multipliers, i.e.,

where t1denotes the iteration index,εk＞0,k=1,2,3, are defined as the iteration stepsize of λ, ω and μ, respectively. The iteration process over Lagrange multipliers repeats until it achieves convergence. The proposed Lagrange dual method-based power allocation algorithm is shown in Algorithm 2.

4.2.3 Channel allocation subproblem

After solving the power allocation subproblem for the lth hop of the ith SCR on the kth channel, we can obtain the local optimal power allocation strategy, i.e.,1≤l≤Lmin, 1≤k≤K, the optimal channel allocation subproblem can be formulated as follows.

The optimal channel allocation strategy for the lth hop of the ith SCR can be obtained by comparing the energy efficiency on various channels and selecting the one offering the maximum energy efficiency, i.e.,

V. SIMULATION RESULTS

In this section, the performance of the proposed joint resource allocation and route selection algorithm is evaluated via simulation.The simulation scenario considered is a square region of which the width is 500 meters. The number of PUs and the licensed channels are both set to be 4. The PUs, two pairs of source and destination SUs and multiple relay SUs are uniformly distributed in the simulation region and the number of relay SUs varies from 8 to 16. Other system parameters chosen in the simulation are summarized in Table 1.

Figure 3 shows the energy efficiency versus the number of iterations for different numbers of relay SUs. The maximum transmit poweris chosen as 0.2W in plotting the figure,and the number of relays is denoted as Nrs.It can be observed that the energy efficiency converges within a small number of iterations.

Figure 4 shows the energy efficiency versus the maximum transmit power for different numbers of the relays. For comparison, we plot the energy efficiency obtained from our proposed algorithm and the baseline algorithm, which is proposed in [17]. To examine the performance of the baseline algorithm,we first apply the CSPF algorithm to find the shortest routes, then choose the optimal route which maximizes the transmission rate of the SU pair. It can be seen from the figure that for small Pmax, the energy efficiency increases with the increase of Pmax, indicating a larger transmit power is desired for achieving the maximum energy efficiency. However, as Pmaxreaches to a certain value, the energy efficiency obtained from our proposed algorithm becomes a fixed value for the transmit power being less than Pmaxhas resulted in the optimal energy efficiency, which will no longer vary with Pmax, however, the energy efficiency obtained form the baseline algorithm begins to decrease after reaching the maximum value.This is because the baseline algorithm aims at maximizing the data rate, hence may require high transmit power, resulting in low energy efficiency. Comparing the results obtained from the two algorithms, we can see that the proposed algorithm outperforms the baseline algorithm.

Figure 5 shows the energy efficiency versus the maximum transmit power for different circuit power consumption obtained from both the proposed algorithm and the baseline algorithm. It can be seen from the figure that the energy efficiency obtained from both algorithms decreases with the increase of the circuit power consumption. Comparing the results obtained from the two algorithms, we can see that the proposed algorithm offers higher energy efficiency than that of the baseline algorithm.

Fig. 3 Energy efficiency versus the number of iterations iterations numbers of relay SUs)

Fig. 4 Energy efficiency versus Pmax (different numbers of relay SUs) numbers of relay SUs)

Fig. 5 Energy efficiency versus Pmax (different circuit power) circuit power (iterations numbers of relay SUs)

Fig. 6 Number of hops versus Pmax

Figure 6 shows the number of hops versus the maximum transmit power for different numbers of relays SUs. To verify the performance of algorithms, we plot the number of hops obtained from our proposed algorithm and the baseline algorithm. It can be observed from the figure that the number of hops obtained from both algorithms decreases at first and becomes a fixed value in the end with the increase of the maximum circuit power consumption. And the number of hops decreases with the increasing number of relays SUs.Comparing the results obtained from the two algorithms, we can see that the proposed algorithm requires smaller number of hops than that of the baseline algorithm, which is desired especially in terms of transmission cost and signal overhead.

VI. CONCLUSION

In this paper, an energy efficient CSPF-based joint resource allocation and route selection algorithm is proposed for multi-hop CRNs. The proposed algorithm consists of two sub-algorithms, i.e., CSPF-based route selection sub-algorithm and energy efficiency-based resource allocation sub-algorithm. Specifically, we first apply CSPF-based route selection to obtain the SCRs, then, for each SCR, we formulate the optimal resource allocation problem as energy efficiency maximization problem and solve the problem by applying iterative algorithm and Lagrange dual method. Finally, the energy efficiency of the SCR is examined and the globally optimal route selection and resource allocation strategy is obtained which offers the maximal energy efficiency of the transmission route. Simulation results demonstrate the effectiveness of the proposed algorithm.

ACKNOWLEDGEMENTS

This work is supported by the National Science and Technology Specific Project of China (2016ZX03001010-004), National Natural Science Foundation of China(6140105361571073), the Joint Scientific Research Fund Ministry of Education and China Mobile (MCM20160105), the special fund of Chongqing key laboratory (CSTC) and the project of Chongqing Municipal Education Commission (Kjzh11206).

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