 Research
 Open Access
Energy efficiencybased joint spectrum handoff and resource allocation algorithm for heterogeneous CRNs
 Rong Chai†^{1}Email author,
 Qin Hu^{1},
 Qianbin Chen†^{1} and
 Zhiming Guo^{1}
https://doi.org/10.1186/s1363801607132
© The Author(s) 2016
 Received: 29 January 2016
 Accepted: 29 August 2016
 Published: 7 September 2016
Abstract
Cognitive radio networks (CRNs) are expected to improve spectrum utilization significantly by allowing secondary users (SUs) to opportunistically access the licensed spectrum of primary users (PUs). In an integrated network consisting of multiple heterogeneous CRNs, SUs with multiple interfaces may have to conduct intersystem or intrasystem spectrum handoff due to the arrival of PUs or performance degradation on serving spectrum. In this case, designing an optimal spectrum handoff scheme which offers quality of service (QoS) guarantee and performance enhancement of the SUs is of particular importance. On the other hand, resource allocation strategy on target channel also plays an important role in affecting the transmission performance of handoff SUs. In this paper, we jointly design spectrum handoff and resource allocation strategy for handoff SUs in heterogeneously integrated CRNs. To achieve joint resource management among various CRNs, we propose a joint radio resource management architecture, based on which the proposed spectrum handoff and resource allocation scheme can be conducted. Jointly considering the transmission performance of the handoff SUs, we formulate the total energy efficiency of the SUs and design an optimization problem which maximizes the energy efficiency subject to spectrum handoff, QoS, and power constraints of the SUs. An iterative algorithm is proposed to solve the formulated nonlinear fractional optimization problem. Within each iteration, the optimization problem is transformed equivalently into two subproblems, i.e., power allocation subproblem of each SUspectrum pair and spectrum handoff subproblem for all the SUs. The two subproblems are solved, respectively, through applying Lagrange dual method and the KuhnMunkres (KM) algorithm. Numerical results demonstrate the efficiency of the proposed algorithm.
Keywords
 Cognitive radio networks
 Spectrum handoff
 Resource allocation
 Energy efficiency
 KuhnMunkres algorithm
1 Introduction
Envisaged as a revolutionary technology to improve spectrum utilization, cognitive radio networks (CRNs) [1] have received considerable attentions from both academia and industry in recent years. In CRNs, secondary users (SUs) are allowed to share the spectrum of primary users (PUs) in an opportunistic manner without affecting the communication performance of the PUs. Multiple CRNs with heterogeneous access technologies may coexist in certain geographical regions resulting in heterogeneously integrated CRNs, in which, SUs with multiple interfaces may access various CRNs.
Due to the arrival of PUs or performance degradation on serving channel, SUs may have to interrupt their current transmission and conduct spectrum handoff, i.e., switching to another spectrum belonging to the same or different CRNs. For an interrupted SU, the design of optimal spectrum handoff scheme is of particular importance for it may affect user quality of service (QoS) significantly. In addition, resource allocation strategy, for instance, the transmit power of SUs on handoff target channel also plays an important role in affecting the transmission performance of handoff SUs. While most of previous research works study spectrum handoff problem or resource allocation problem independently, these two problems are indeed closely related especially under the scenario that multiple SUs may conduct spectrum handoff simultaneously.
In this paper, we jointly consider spectrum handoff and resource allocation problem for handoff SUs in heterogeneously integrated CRNs. To achieve joint resource management among various CRNs, we propose a centralized joint radio resource management architecture. Jointly considering the transmission performance of the handoff SUs, we formulate the total energy efficiency of the SUs and design an optimization problem which maximizes the energy efficiency subject to spectrum handoff, QoS, and power constraints of the SUs. An iterative algorithm is proposed to solve the formulated nonlinear fractional optimization problem.

We design a joint resource management architecture based on which the proposed joint spectrum handoff and resource allocation scheme can be conducted.

Spectrum handoff scheme has been designed for single SU [2–5]. In this paper, we study the spectrum handoff problem of both single SU and multiple SUs. In addition, instead of merely stressing the service time and waiting delay of handoff SUs, we jointly consider the waiting delay, switching time, and the transmission performance of the handoff SUs on the target spectrum and propose an efficient joint spectrum handoff and resource allocation scheme for the handoff SUs.

Spectrum handoff problem or resource allocation problem of SUs in CRNs has been studied independently in [2–16]. In this paper, we jointly consider spectrum handoff and resource allocation problem of SUs in heterogeneous CRNs and design a joint optimal strategy for all the SUs in terms of handoff target channel selection and transmit power allocation.

To characterize the joint performance of all the handoff SUs, we stress the tradeoff between transmission data rate and power consumption, examine the total energy efficiency of the SUs, and then formulate the joint spectrum handoff and resource allocation problem in heterogeneous CRNs as an energy efficiency maximization problem. Since the optimization problem formulated is a nonlinear fractional programming problem, which cannot be solved conveniently, we transform it to an equivalent optimization problem which can be solved based on iterative algorithm. Within each iteration, the optimization problem is transformed equivalently into two subproblems, i.e., power allocation subproblem of each SUspectrum pair and spectrum handoff subproblem for all the SUs. The two subproblems are then solved, respectively, through applying Lagrange dual method and the KuhnMunkres (KM) algorithm.
The rest of the paper is organized as follows. Section 2 presents an overview of related works. Section 3 describes system model and the proposed joint resource management architecture. In Section 4, a channel queuing model is proposed and the interruption time of the handoff SUs is examined. A candidate spectrum selection scheme is proposed in Section 5. A joint spectrum handoff and resource allocation scheme is proposed for single handoff SU in Section 6. In Section 7, we propose a joint spectrum handoff and resource allocation scheme for multiple handoff SUs. In Section 8, the optimization problem formulated in Section 7 is solved. Simulation results are presented in Section 9. Finally, we conclude this paper in Section 10.
2 Related works
In this section, we present an overview of related works, including spectrum handoff schemes and resource allocation schemes of CRNs.
2.1 Spectrum handoff schemes of CRNs
In recent years, various spectrum handoff schemes have been designed for SUs in CRNs. In [2], the authors propose a probabilistic approach to determining the initial and target channel for a handoff SU in a CRN. The average sojourn time and the extended service time of the SU are analyzed, and the optimal spectrum handoff strategy is obtained through solving the optimization problem of minimizing both time metrics. In [3], a contentionaware channel selection algorithm is proposed, in which the secondary network detects the available licensed channels of SUs by exploiting cooperative spectrum sensing scheme, estimates the probability of channel collision, and then selects a less competitive channel for the SUs. In [4], a review of periodic sensing and handoff schemes is presented and the tradeoff between the energy efficiency and the transmission reliability of SUs is examined. A switchstay model is then proposed to achieve the tradeoff in light of sensing accuracy, the probability of collision, throughput, and delay constraints. In [5], the authors study spectrum handoff problem for multimedia applications in CRNs and propose a learningbased quality of experience (QoE)driven spectrum handoff scheme which optimizes the quality of video transmissions in terms of handoff delay. The authors in [6] consider the stochastic characteristics of spatial and temporal spectrum availabilities in CRNs and develop a spectrum handoff scheme, which selects the handoff channel offering the maximum capacity.
Previous research studies [2–6] mainly focus on designing spectrum handoff scheme for single SU in CRNs; however, it is highly possible that multiple SUs may have to perform spectrum handoff at the same time. For instance, multiple SUs occupying the licensed channel of one PU may have to interrupt their transmission and switch to other channels due to the arrival of the PU. The spectrum handoff problem of multiple SUs has been studied in [7, 8]. The authors in [7] assume that the spectrum handoff of SUs should meet the constraint of handoff agility, i.e., SUs are only allowed to switch to their neighboring channels, and then formulate a continuoustime Markov model to analyze the forced termination and blocking probabilities of SUs. In [8], an analytical framework is presented to examine the impact of common control interface (CCI) on the performance of spectrum handoff. The potential benefits and disadvantages of employing CCI for spectrum handoff are analyzed in terms of handoff delay, energy consumption, and spectrum utilization. Although [7, 8] stress the problem of spectrum handoff of multiple SUs, they mainly study the performance evaluation of handoff scheme instead of optimal handoff scheme design.
2.2 Resource allocation schemes of CRNs
To achieve transmission performance optimization of handoff SUs, resource allocation problems, in particular, transmit power allocation issue should be considered. Indeed, resource allocation problems in CRNs have been studied extensively in recent years. In [9], a multiuser orthogonal frequencydivision multiple access (OFDMA) cognitive heterogeneous network (HetNet) is considered and the potential benefits of employing reconfigurable antennas (RA) are studied. The authors propose a game theoretical framework to jointly select the subcarriers as well as the RA state at each SU so that the overall capacity of the network can be maximized. The authors in [10] consider a CRN with imperfect spectrum sensing performance and propose an energyaware centralized resource allocation scheme which takes into account relay selection, channel access, and power allocation jointly. The CRN is formulated as a partially observable Markov decision process (POMDP), based on which, an optimal joint resource allocation policy is derived. In [11], the authors investigate joint uplink subchannel and power allocation problem in cognitive small cells. Jointly considering the effects of crosstier interference and imperfect channel state information (CSI), and the requirements on outage probability and transmission fairness, a cooperative Nash bargaining game model is formulated and a unified analytical framework is proposed to obtain the near optimal resource allocation strategy. The authors in [12] study joint power and channel allocation problem in CRNs offering heterogeneous services and propose an optimal resource allocation scheme which maximizes the capacity of all the SUs.
To meet the requirement on increasingly higher transmission rate, high transmit power is required, resulting in higher energy consumption at both user devices and base stations (BSs), which is highly undesired especially for energysensitive devices. To reduce power consumption and achieve highenergy efficiency of CRNs, energyefficient resource allocation schemes have recently received great attentions [13–15]. Jiang et al. [13] presents a brief overview of energyefficient schemes proposed for noncooperative CRNs, including spectrum sensing schemes, spectrum sharing schemes, and network deployment approaches. In [14], the authors study energyefficient opportunistic spectrum access strategies for an orthogonal frequency division multiplexing (OFDM)based CRN with multiple SUs. The worst energy efficiency and the average energy efficiency are, respectively, formulated and optimized for different application scenarios. In [15], approaches proposed for energyefficient spectrum sensing and spectrum handoff are investigated and the tradeoff between energy consumption and data transmission throughput is studied. In [16], an M/G/1 queuing model with preemptive resume priority is formulated for CRNs, the average waiting delay of SUs is analyzed, and the channel with the minimum service time is selected as the handoff channel.
Most of the previous works focus on either spectrum handoff scheme design or resource allocation scheme design for SUs in CRNs; indeed, it can be observed that resource allocation strategy on handoff target channel may affect the transmission performance of handoff SUs significantly; hence, it is highly desired to jointly design spectrum handoff and resource allocation strategy for SUs in CRNs. Indeed, in [6, 13–16], the authors also consider resource management policy when designing spectrum handoff schemes for SUs; however, instead of designing the optimal transmit power strategy, they simply assume that the SUs transmit with the maximum transmit power or a fixed power on handoff target channels, thus may result in undesired transmission performance, especially in terms of energy efficiency. In this paper, we jointly study the spectrum handoff and resource allocation problem in heterogeneously integrated CRNs and propose an energy efficiencybased joint spectrum handoff and resource allocation scheme for handoff SUs.
3 System model and proposed joint resource management architecture
3.1 System model
In this paper, we consider an integrated network scenario consisting of one PN, multiple heterogeneous CRNs, and a number of PUs and SUs. As the licensed users of the PN, PUs are allowed to transmit to primary base stations (PBSs) through licensed channels. We assume that different channels of the PN are allocated to various PUs; hence, no cochannel interference exists among PUs. To support spectrum sharing between PUs and SUs, the channels of PUs are further divided into multiple subchannels, and each subchannel can be allocated to one SU for information interaction with the cognitive base stations (CBS) of one CRN. We assume that the SUs are equipped with multiple interfaces and are capable of accessing various CRNs but can only access one subchannel of a CRN at a given time interval.
3.2 Proposed joint resource management architecture
In the integrated networks of PN and CRNs, available radio resources need to be allocated in a coordinated way to guarantee QoS requirements of both PUs and SUs and to achieve performance enhancement of the networks. To achieve joint resource management of the networks in the heterogeneously integrated network scenario, a joint radio resource management (JRRM) architecture is proposed in this paper.
URRM: functional module embedded in each PU and SU. URRMs collect and store CSI, device characteristics and service requirements, etc. Through interacting with the associated LRRMs, URRMs send their collected information to the network and receive spectrum handoff and resource allocation strategy.
LRRM: deployed in each PBS or CBS, being responsible for collecting and managing local resource status and resource management strategy through interacting with the associated URRMs and GRRM. More specifically, receiving network and service information from the associated URRMs and then forwarding to the GRRM, and receiving spectrum handoff and resource allocation strategy from GRRM and forwarding to URRMs.
GRRM: deployed over the PU and the CRNs. Through interacting with the associated LRRMs, the GRRM receives network and user state information and conducts the proposed joint spectrum handoff and resource allocation algorithm to obtain the optimal strategy and send back to the LRRMs.
It should be mentioned that the information interaction between GRRM, LRRMs, and URRMs can be performed over a common control channel [8]. Efficient random access control schemes and user scheduling schemes should be designed to guarantee the performance of information interaction between various functionality entities. In this paper, we assume that efficient information interaction between GRRM, LRRMs, and URRMs can be achieved and design joint spectrum handoff and resource allocation scheme based on the obtained information.
4 Channel queuing model and interruption time analysis
4.1 Channel queuing model
As PUs are of higher priority over SUs to access the licensed channels of PUs, once PUs reclaim their allocated channels, the SUs occupying the subchannels belonging to the PUs must interrupt their transmission. Without loss of generality, we assume that the service of SUs can tolerate certain interrupting delay; hence, when experiencing interruption, an SU may choose to stay at current subchannel or switch to other subchannel provided that the subchannel meets its interruption delay constraint. In the case that multiple SUs arrive at one subchannel, SUs may wait at the subchannel according to certain rules.

PUs and SUs may arrive at various channels/subchannels with different rates. In the case that the channels are busy, users will wait in their corresponding subqueues, i.e., PUs wait in the highpriority subqueues and SUs wait in the lowpriority subqueues till the channels/subchannels become available.

Users waiting in the same subqueue are allowed to access the channels/subchannels on the basis of first come first served (FCFS) scheduling scheme.

To reduce the possibility of call drop, higher priority is given to interrupted SUs over new SUs, i.e., SUs with initial service requirement; thus, interrupted SUs will be put before new SUs in the lowpriority subqueues.
4.2 Interruption time analysis
In the case that one PU reclaims its allocated channel, the SUs occupying the subchannels belonging to the channel should interrupt their transmission, stay at current subchannel, or switch to another subchannel. For both cases, the interrupted SUs cannot resume their data communications until the PU or previously interrupted SUs have completed their transmission, thus resulting in waiting delay. If the interrupted SUs choose to switch to another subchannel, additional switch delay may occur due to spectrum handoff procedure.
In the following subsections, the waiting delay and the switching delay of interrupted SUs will be calculated, respectively.
4.2.1 Waiting delay of interrupted SUs
In this subsection, the waiting delay of interrupted SUs is analyzed for both staying case and switching case.
4.2.1.1 Staying case:
where \(T_{k}^{\mathrm {(p)}}\) denotes the busy time of the kth channel due to the transmission of the kth PU and E[z] denotes the expectation value of z. \(\mathrm {E}\left [T_{k}^{\mathrm {(p)}}\right ]\) can be derived as follows.
4.2.1.2 Switching case:
4.2.2 Switching delay of interrupted SUs
In the case that an interrupted SU decides to switch from the n _{ m }th subchannel to the nth subchannel, intrasystem or intersystem handoff may occur as the n _{ m }th subchannel and the nth subchannel may belong to the same CRN or different CRNs. In addition, as one SU may perform spectrum switch and radio frequency (RF) reconfiguration before or after a PU reoccupies the channel, the corresponding spectrum handoff is referred to as proactive handoff and reactive handoff, respectively. Jointly considering these handoff scenarios, we obtain four types of spectrum handoff, i.e., proactive intrasystem handoff, proactive intersystem handoff, reactive intrasystem handoff, and reactive interSystem handoff; the corresponding switching delay is examined as follows.
4.2.2.1 Proactive intrasystem handoff
where \(t_{\text {syn}}^{\text {sen}}\) denotes the synchronization time for spectrum sensing, t _{sen} denotes the time period for sensing spectrum resource, t _{dec} denotes the time period for determining a target handoff spectrum, t _{switch} denotes the time period required for switching from current subchannel to target subchannel, and \(t_{\text {syn}}^{\text {tx}}\) denotes the time duration required for conducting synchronization with target subchannel.
4.2.2.2 Proactive intersystem handoff
4.2.2.3 Reactive intrasystem handoff
4.2.2.4 Reactive intersystem handoff
5 Candidate handoff spectrum selection scheme
Interrupted SUs with various user services may pose different QoS requirements on transmission subchannels. In this paper, we assume interrupted SUs may have different interruption delay and data rate requirements, which place constraints on handoff target subchannel. To reduce the computation complexity of the proposed spectrum handoff and resource allocation scheme, we present a candidate spectrum selection scheme which selects the qualified spectrum among all the available spectrum based on the QoS requirements of interrupted SUs; then, the proposed joint spectrum handoff and resource allocation scheme only applies to the candidate spectrum of the SUs.
In the following subsections, we first examine both interruption delay constraint and data rate constraint, based on which, we discuss the formation of candidate handoff spectrum set.
5.1 Interruption delay constraint
5.2 Data rate constraint
In the case that the candidate handoff spectrum set is empty, indicating that there is no subchannels meeting the transmission constraints of the interrupted SUs, thus, the SUs cannot conduct handoff successfully, resulting in transmission interruption.
5.3 Candidate handoff spectrum set
Among all the candidate handoff subchannels of the mth interrupted SU, i.e., \(\mathrm {C}_{n}\in \Phi _{m,n_{m}}\phantom {\dot {i}\!}\), the subchannel offering the optimal performance will be selected and the corresponding optimal transmit power of the SU will be designed, as discussed in the following two sections.
6 Proposed joint optimization scheme: single SU case
In this section, we consider the case that only one SU is interrupted and design an optimal joint spectrum handoff and power allocation scheme for the SU. While experiencing transmission interruption, the SU may tend to choose the subchannel corresponding to the optimal transmission performance. In this paper, to stress the importance of both the transmission rate and power consumption of the interrupted SUs, and to achieve the tradeoff between the two metrics, the energy efficiency of the interrupted SUs on the target subchannel is examined and optimized in terms of the transmit power of the SUs.
where P ^{cir} denotes the circuit consumption power of the interrupted SU, which is assumed to be a constant for all the SUs in this paper.
To achieve highenergy efficiency, the interrupted SU with current subchannel being n _{1} may choose the nth subchannel which offers the maximum energy efficiency among all the candidate subchannels as the handoff target subchannel. However, it can be seen from (23) that the energy efficiency, i.e., η _{ n }, varies with the transmit power P _{1,n } for given channel and device characteristics; thus, it is difficult to examine and compare the energy efficiency of various subchannels. To stress this problem, we propose a twostep algorithm which consists of both power allocation and spectrum handoff subalgorithms. More specifically, we first conduct optimal power allocation subalgorithm on the nth subchannel, i.e., optimizing η _{ n } in terms of P _{1,n } to obtain the maximum η _{ n }, denoted by \(\eta ^{*}_{n}\), for \(\mathrm {C}_{n}\in \Phi _{1,n_{1}}\phantom {\dot {i}\!}\), 1≤n≤N, and then apply optimal spectrum handoff subalgorithm, i.e., choosing the optimal subchannel corresponding to the maximum \(\eta ^{*}_{n}\).
For a given range of P _{1,n }, i.e., \(0<P_{1,n}\le P_{1}^{\max }\), the optimal energy efficiency of the interrupted SU on the nth subchannel, denoted by \(\eta ^{*}_{n}\), can be obtained through solving above problem via numerical method or optimization techniques [19].
7 Proposed joint optimization scheme: multiple SUs’ case
It can be seen from the previous section that in the case that the transmission of one SU is interrupted, the optimal spectrum handoff and power allocation problem can be solved through designing the optimal transmit power strategy and then selecting the optimal subchannel, which offers the maximal energy efficiency. In the case that multiple SUs may perform spectrum handoff simultaneously, allowing each interrupted SU to select its optimal subchannel may not be feasible for resource competition among handoff SUs exists. In this paper, we propose to jointly consider the performance of interrupted SUs and design an optimal spectrum handoff and power allocation strategy which achieves the performance optimization of all the SUs.
7.1 Total energy efficiency of interrupted SUs
7.2 Optimization problem formulation
8 Solution of the optimization problem
The optimization problem formulated in (33) is a nonconvex problem with the objective function being a nonlinear fractional function, which cannot be solved conveniently using traditional optimization tools. In this section, the optimization objective function is transformed into a convex function and the corresponding optimization problem is solved using iterative algorithm [22].
8.1 Iterative algorithmbased energy efficiency maximization
Examining the above optimization problem, we can observe that for a given energy efficiency q, the problem is still a joint spectrum handoff and power allocation problem with the objective function being a convex function, thus can be solved (as we will discuss in the following subsections) to obtain the locally optimal spectrum handoff and power allocation strategy, based on which the energy efficiency q can be updated. Repeating the process until the convergence condition meets, we can obtain the globally optimal energy efficiency and joint spectrum handoff and power allocation strategy.
The above iterative process can be implemented through an iterative algorithm, which proceeds as follows. Starting from an initial value of q, we can obtain the locally optimal x _{ m,n } and P _{ m,n } through solving the spectrum handoff and power allocation subproblem; then, q is updated based on (34). For the updated q, the spectrum and power allocation subproblem can be resolved to obtain updated x _{ m,n } and P _{ m,n }, the process continues until the convergence condition, i.e., R ^{tot}(x _{ m,n },P _{ m,n })−q P ^{tot}(x _{ m,n },P _{ m,n })≤ω _{1} meets, where ω _{1} denotes the maximum tolerance. The proposed algorithm is summarized in Algorithm 1 and the convergence of the algorithm can be guaranteed [20].
8.2 Locally optimal spectrum handoff and power allocation algorithm
It can be seen from (39) that if we assume the mth interrupted SU selects the nth subchannel as its handoff target subchannel, i.e., x _{ m,n }=1, for the given SUspectrum pair, maximizing (39) is equivalent to maximizing R _{ m,n }−q(P _{ m,n }+P ^{cir}) in terms of P _{ m,n }, which can be referred to as power allocation subproblem. From the constraints C1–C3 in (33), we can obtain that the power allocation for various SUspectrum pairs is independent, thus can be solved individually. Once we have obtained the optimal power allocation strategy for SUspectrum pairs, we can then solve spectrum handoff subproblem to obtain the optimal x _{ m,n }. Hence, the problem formulated in (37) can be transformed equivalently into two subproblems, i.e., power allocation subproblem of one SUspectrum pair and the spectrum handoff subproblem of all the SUs. In the following subsections, we solve the two subproblems, respectively.
8.2.1 Optimal power allocation subproblem
where ε _{1} and ε _{2} are stepsize. The proposed Lagrange dual methodbased power allocation algorithm is shown in Algorithm 2.
8.2.2 Spectrum handoff subproblem
Feasible vector labeling: A real valued function l such that for any x∈X and y∈Y, l(x)+l(y)≤w(x,y) holds. Equality subgraph: If l is a feasible labeling, let G _{ l } denotes a subgraph of G; if the condition l(x)+l(y)=w(x,y) is met, then G _{ l } is called the equality subgraph with respect to l. Theorem: If l is a feasible labeling of G, and H is an optimal matching of X to Y with H⊆G _{ l }, then H is an optimal assignment of X to Y. Thus, the problem of finding an optimal assignment is reduced to the problem of finding a feasible vertex labeling of which the equality subgraph contains an optimal matching from X to Y.
 1.
Find an initial feasible vertex labeling l(u)
 2.
For given l(u), determine \({G_{l}^{0}}\) from G ^{0} and select a maximum matching H.
 3.
If H is an optimal matching, then the optimization problem formulated in (48) is solved. Otherwise, a label having not being allocated by H is selected in \({G_{l}^{0}}\). Set S=V _{1}, and T=Ψ, which denotes the empty set.
 4.\(N_{{G_{l}^{0}}}(S)\) denotes the collection of points which connect with S in \({G_{l}^{0}}\). If \(N_{{G_{l}^{0}}}(S)\ne T\), go to step 3. Otherwise, \(N_{{G_{l}^{0}}}(S)=T\). Find$$ \Delta =\min_{u,v} (l(u)l(u)+l(v)w(u,v),u\in S,v\in V_{2}T) $$(51)and define$$l^{'}(u)= \left\{ \begin{array}{lr} l(u)\Delta,&u\in S\\[2pt] l(u)+\Delta,&u\in T\\[2pt] l(u),&\mathrm{others.} \end{array} \right. $$
 5.
Replace l(u) by l ^{′}(u), go back to step 2.
Through conducting above process iteratively, an optimal matching of G can be obtained corresponding to the optimal spectrum handoff strategy of interrupted SUs.
9 Simulation results and discussions
9.1 Simulation results
Parameters about the packet arrival rate and service rate of the PUs
PN  PU1  PU2  PU3  PU4  PU5  

Index of subchannel (n)  1–3  4–6  7–10  11–14  15–18  
Bandwidth of subchannel (MHz)  1  1  1  1.2  1.5  
Case 1  \(\lambda _{n}^{(\mathrm {p})}\)  5  10  10  10  5 
\(\mu _{n}^{(\mathrm {p})}\)  15  20  15  20  15  
Case 2  \(\lambda _{n}^{(\mathrm {p})}\)  5  10  10  10  5 
\(\mu _{n}^{(\mathrm {p})}\)  10  20  15  15  10  
Case 3  \(\lambda _{n}^{(\mathrm {p})}\)  8  15  10  12  5 
\(\mu _{n}^{(\mathrm {p})}\)  10  20  15  15  10 
Parameters about maximum tolerable delay of different SUs
Index of SU  1  2  3  4  5  6  7  8  9  10 

Maximum  0.55  0.65  0.45  0.65  0.65  0.55  0.65  0.65  0.65  0.45 
tolerable delay(s) 
Delay parameters
t _{prep}(s)  t _{recfg}(s)  t _{switch}(s)  \( t_{\text {syn}}^{\text {sen}}(s)\)  t _{sen}(s)  t _{dec}(s)  \(t_{\text {syn}}^{\text {tx}}(s)\)  

CRN1  0.1  0.3  0.002  0.025  0.05  0.025  0.025 
CRN2  0.1  0.3  0.002  0.025  0.025  0.025  0.025 
In Fig. 4, comparing the results obtained from the proposed scheme and the schemes proposed in [12, 16], we can see that for small \({P_{m}^{\max }}\), the energy efficiency increases with the increase of \({P_{m}^{\max }}\) for three algorithms, indicating a larger power threshold is desired for achieving the maximum energy efficiency. However, as \({P_{m}^{\max }}\) reaches to a certain value, the energy efficiency obtained from our proposed algorithm converges to a fixed value, which will not change with the increase of \({P_{m}^{\max }}\). The reason is that the optimal energy efficiency has achieved when the transmit power is less than \(P_{m}^{\max }\), further increasing \(P_{m}^{\max }\) will not change the optimal transmit power; thus, the resulted energy efficiency will not change. On the other hand, when \({P_{m}^{\max }}\) reaches to a certain value, the energy efficiency obtained from the other two schemes decreases with the increase of \({P_{m}^{\max }}\). This is because the schemes proposed in [12, 16] aim to achieve the maximum data rate and the minimum service time of the SUs, respectively, thus may require higher power consumption, resulting in undesired energy efficiency. Comparing the three curves in the figure, we can see that the proposed scheme outperforms the schemes proposed in [12, 16].
Figure 5 shows the energy efficiency versus the maximum transmit power of the interrupted SUs for different circuit power consumption. It can be seen from the figure that the energy efficiency decreases with the increase of circuit power consumption. Comparing the results obtained from the proposed algorithm and the algorithms proposed in [12, 16], we can see that the proposed scheme offers higher energy efficiency than the schemes proposed in [12, 16].
In Fig. 6, we examine the performance of various spectrum handoff schemes and compare the energy efficiency of the interrupted SUs obtained from the proposed joint optimization scheme and other two schemes, i.e., Schemes 1 and 2. For both Schemes 1 and 2, the optimal power allocation strategy is achieved through maximizing the energy efficiency of each SUspectrum pair; we then apply different spectrum handoff strategies. For Scheme 1, handoff subchannels are selected in order to achieve the minimum total transmission time of the SUs, while for Scheme 2, we apply random spectrum handoff scheme, i.e., the handoff subchannels of the interrupted SUs are randomly selected. It can be seen from the figure that the proposed algorithm offers better performance in comparison with the other two schemes, indicating that joint design of spectrum handoff and power allocation results in performance enhancement.
9.2 Discussion on channel model
The channel model considered in this paper is Friis freespace propagation model, where the channel gain of the links between SUs and their corresponding CBSs is constants, determined by the transmitterreceiver separation distance and carrier frequency; thus, for SUs located at different positions, applying different spectrum handoff and power allocation strategies may result in different transmission performance and energy efficiency in turn. In this paper, for given fixed channel characteristics, we jointly consider the transmission performance of a number of handoff SUs and design the optimal spectrum handoff and power allocation strategy for all the handoff SUs.
In wireless communication systems, wireless channel is usually timevarying, which is resulted from the movement of users and the fading effects during signal transmission. However, under the assumption that PUs and SUs move with relatively low speed, we can assume that at interested transmission time, channel characteristics will not change due to user movement. While fading effects may result in the variation of change gain, in the case that the variation of the channel gain is relatively slow, we can also assume that at interested transmission time, channel characteristics are static, i.e., the channel gain is a constant, and design the corresponding spectrum handoff and power allocation scheme.
It should be mentioned that smallscale fading effects caused by multipath propagation may affect link characteristics and transmission performance in turn; however, as smallscale fading effects describe the fluctuations in the received signal envelope relative to the local average of the path loss effects, in the case of week smallscale fading effects, i.e., the average power of the small fading effects, which are commonly modeled as Rayleigh random variables is relatively small, the impacts of smallscale fading on channel characteristics and transmission performance are relatively small compared to pass loss effects, thus can be ignored. In this case, the proposed algorithm in this paper can be applied under acceptable error threshold.
In the case of strong smallscale fading effects, the impacts of channel fading on transmission performance of users may not be ignored and Friis freespace propagation model cannot represent the channel effects accurately. However, as long as the channel characteristics can be obtained in advance, for instance, through applying channel training schemes and the variation of channel characteristics is slow compared to the transmission duration of user information, the basic idea of the proposed algorithm can still be applied to this type of channel scenario. As for given channel characteristics, the energy efficiency of all the SUs can be examined and optimized according to the method proposed in the paper. It should be noticed that in this case, the accuracy of channel estimation may affect the performance of spectrum handoff and power allocation. Although highly accurate channel estimation is desired, it may require large signaling cost and high power consumption; thus, a tradeoff between channel estimation and transmission performance should be stressed.
While it is commonly assumed that the channel fading varies relatively slow, thus follows slow fading, it is also possible that the channels between SUs and their corresponding CBSs may experience fast fading, in which case the assumption that the channel characteristics are constants during the transmission periods does not hold, we may not be able to apply the proposed algorithm in a straightforward manner. Instead, we may consider examining the average transmission performance of the channel and the average system performance by taking into account the statistical characteristics of the channels and managing to optimize the average performance of the system. In our future work, we will study the design of spectrum handoff and power allocation algorithms under fading channel scenarios.
10 Conclusions
In this paper, an optimal joint spectrum handoff and resource allocation scheme is proposed for interrupted SUs in heterogeneous CRNs. The interruption delay of the SUs is analyzed based on an M/G/1 model, and the subchannels which meet the interruption delay and data rate constraints are selected as handoff candidate subchannels. The optimization problem which maximizes the energy efficiency of the interrupted SUs under spectrum handoff, QoS requirement, and the maximum power constraints is formulated and solved through iterative algorithm, Lagrange dual method, and the KM algorithm. Numerical results demonstrate that compared to the previously proposed algorithms, our proposed energy efficiencybased joint spectrum handoff and resource allocation scheme offers better performance.
Declarations
Acknowledgements
The authors wish to thank the associate editor and the anonymous reviewers for their valuable suggestions, which helped significantly improve the quality of the paper. This work was supported by the 863 project (2014AA01A701), National Science and Technology Specific Project of China (2016ZX03001010004), the special fund of Chongqing key laboratory (CSTC), and the project of Chongqing Municipal Education Commission (Kjzh11206).
Authors’ contributions
The authors have equal contributions. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
 J Mitola, GQ Maguire, Cognitive radio: making software radios more personal. IEEE Pers. Commun. 6(4), 13–18 (1999). doi:10.1109/98.788210.View ArticleGoogle Scholar
 F Sheikholeslami, M NasiriKenari, F Ashtiani, Optimal probabilistic initial and target channel selection for spectrum handoff in cognitive radio networks. IEEE Trans. Wirel. Commun. 14(1), 570–584 (2015). doi:10.1109/TWC.2014.2354407.View ArticleGoogle Scholar
 A Mesodiakaki, F Adelantado, L Alonso, C Verikoukis, Performance analysis of a cognitive radio contentionaware channel selection algorithm. IEEE Trans. Veh. Technol. 64(5), 1958–1972 (2015). doi:10.1109/TVT.2014.2341115.View ArticleGoogle Scholar
 S Wang, F Tosato, J Coon, Reliable energyefficient spectrum management and optimization in cognitive radio networks: how often should we switch. IEEE Wirel. Commun. 20(6), 14–20 (2013). doi:10.1109/MWC.2013.6704469.View ArticleGoogle Scholar
 YQ Wu, FH Hu, S Kumar, YY Zhu, A Talari, N Rahnavard, JD Matyjas, A learningbased qoedriven spectrum handoff scheme for multimedia transmissions over cognitive radio networks. IEEE J. Sel. Areas Commun. 32(11), 2134–2148 (2014). doi:10.1109/JSAC.2014.141115.View ArticleGoogle Scholar
 WY Lee, IF Akyildiz, Spectrumaware mobility management in cognitive radio cellular networks. IEEE Trans. Mob. Comput. 11(4), 529–542 (2012). doi:10.1109/TMC.2011.69.View ArticleGoogle Scholar
 OM Norooz, B Hamdaoui, X Cheng, T Znati, M Guizani, Analyzing cognitive network access efficiency under limited spectrum handoff agility. IEEE Trans. Veh. Technol. 63(3), 1402–1407 (2014). doi:10.1109/TVT.2013.2283856.View ArticleGoogle Scholar
 BA Ozan, EB Pehlivanoglu, S Galmes, OB Akan, Dedicated radio utilization for spectrum handoff and efficiency in cognitive radio networks. IEEE Trans. Wirel. Commun. 14(9), 5251–5259 (2015). doi:10.1109/TW.2013.060413.121073.View ArticleGoogle Scholar
 MH Yllmaz, MM Abdallah, HM ElSallabi, J Chamberland, KA Qaraqe, H Arslan, Joint subcarrier and antenna state selection for cognitive heterogeneous networks with reconfigurable antennas. IEEE Trans. Commun. 63(11), 4015–4025 (2015). doi:10.1109/TCOMM.2015.2477088.View ArticleGoogle Scholar
 CQ Luo, G Min, FR Yu, Y Zhang, LT Yang, VCM Leung, Joint relay scheduling, channel access, and power allocation for green cognitive radio communications. IEEE J. Sel. Areas Commun. 33(5), 922–932 (2015). doi:10.1109/JSAC.2014.2361085.View ArticleGoogle Scholar
 HJ Zhang, CX Jiang, NC Beaulieu, XL Chu, XB Wang, TQS Quek, Resource allocation for cognitive small cell networks: a cooperative bargaining game theoretic approach. IEEE Trans. Wirel. Commun. 14(6), 3481–3493 (2015). doi:10.1109/TWC.2015.2407355.View ArticleGoogle Scholar
 R Xie, FR Yu, H Ji, Dynamic resource allocation for heterogeneous services in cognitive radio networks with imperfect channel sensing. IEEE Trans. Veh. Technol.61(2), 770–780 (2012). doi:10.1109/TVT.2011.2181966.View ArticleGoogle Scholar
 CX Jiang, HJ Zhang, Y Ren, HH Chen, Energyefficient noncooperative cognitive radio networks: micro, meso, and macro views. IEEE Commun. Mag. 52(7), 14–20 (2014). doi:10.1109/MCOM.2014.6852078.View ArticleGoogle Scholar
 C Xiong, L Lu, GY Li, Energyefficient spectrum access in cognitive radios. IEEE J. Sel. Areas Commun. 32(3), 550–562 (2014). doi:10.1109/JSAC.2014.1403005.View ArticleGoogle Scholar
 H ShokriGhadikolaei, I Glaropoulos, V Fodor, C Fischione, A Ephremides, Green sensing and access: energythroughput tradeoffs in cognitive networking. IEEE Commun. Mag. 53(11), 199–207 (2015). doi:10.1109/MCOM.2015.7321991.View ArticleGoogle Scholar
 LC Wang, CW Wang, CJ Chang, Modeling and analysis for spectrum handoffs in cognitive radio networks. IEEE Trans. Mob. Comput. 11(9), 1499–1513 (2012). doi:10.1109/TMC.2011.155.View ArticleGoogle Scholar
 TM Cover, JA Thomas, Elements of information theory (Wiley, New York, 2012).MATHGoogle Scholar
 TS Rappaport, Wireless communications: principles and practice, 2nd edn. (Prentice Hall Communications Engineering and Emerging Technologies Series, New York, 2001).MATHGoogle Scholar
 S Boyd, L Vandenberghe, Convex optimization (Cambridge Univ. Press, Cambridge, 2004).View ArticleMATHGoogle Scholar
 DWK Ng, ES Lo, R Schober, Energyefficient resource allocation in OFDMA systems with large numbers of base station antennas. IEEE Trans. Wirel. Commun. 11(9), 3292–3304 (2012). doi:10.1109/TWC.2012.072512.111850.View ArticleGoogle Scholar
 Q Xu, X Li, H Ji, X Du, Energyefficient resource allocation for heterogeneous services in OFDMA downlink networks: systematic perspective. IEEE Trans. Veh. Technol. 63(5), 2071–2082 (2014). doi:10.1109/TVT.2014.2312288.View ArticleGoogle Scholar
 W Dinkelbach, in Management Science, 13. On nonlinear fractional programming, (1967), pp. 492–498.Google Scholar
 L Lovász, MD Plummer, Matching theory (American Mathematical Soc, RI, 2009).View ArticleMATHGoogle Scholar