IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 29, NO. 4, APRIL Load-Balancing Spectrum Decision for Cognitive Radio Networks

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1 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 29, NO. 4, APRIL Load-Balancing Sectrum Decision for Cognitive Radio Networks Li-Chun Wang, Fellow, IEEE, Chung-Wei Wang, Student Member, IEEE, Fumiyuki Adachi, Fellow, IEEE Abstract In this aer, we resent an analytical framework to design system arameters for load-balancing multiuser sectrum decision schemes in cognitive radio (CR networks. Unlike the non-load-balancing methods that multile secondary users may contend for the same channel, the considered load-balancing schemes can distribute the traffic loads of secondary users to multile channels. Based on the reemtive resume riority (PRP M/G/ queueing theory, a sectrum decision analytical model is roosed to evaluate the effects of multile interrutions from the rimary user during each link connection, the sensing errors (i.e., missed detection false alarm of the secondary users, the heterogeneous channel caacity. With the objective of minimizing the overall system time of the secondary users, we derive the otimal number of cidate channels the otimal channel selection robability for the sensing-based the robability-based sectrum decision schemes, resectively. We find that the robability-based scheme can yield a shorter overall system time comared to the sensing-based scheme when the traffic loads of the secondary users is light, whereas the sensing-based scheme erforms better in the condition of heavy traffic loads. If the secondary users can intelligently adot the best sectrum decision scheme according to sensing time traffic conditions, the overall system time can be imroved by 50% comared to the existing methods. Index Terms Cognitive radio, sectrum decision, channel selection, overall system time, reemtion, queueing theory. I. INTRODUCTION COGNITIVE radio (CR techniques imrove sectrum efficiency by allowing the low-riority secondary users to temorarily utilize the unused licensed sectrum of the high-riority rimary users [] [6]. However, the secondary users need to vacate the occuied channel when the rimary users have data to transmit on this channel because the rimary users have the reemtive riority to access channel. In order to rovide reliable transmission for the secondary users, sectrum hoff rocedures are initiated to hel the secondary user return the channel to the rimary user resume the secondary user s unfinished transmission at other channel or at the same channel after the comletion of the rimary transmissions [7] [9]. Manuscrit received 3 December 2009; revised June 200. This work was suorted in art by the MoE ATU Plan (in Taiwan, by the National Science Council (NSC grants E MY3, E MY3, I (in Taiwan, by the Globe COE Program (in Jaan. Part of this work was resented at the IEEE Personal, Indoor Mobile Radio Communications Symosium (PIMRC, L.-C. Wang C.-W. Wang are with the Deartment of Electrical Engineering, National Chiao Tung University, Hsinchu, Taiwan ( lichun@cc.nctu.edu.tw hyer.cm9g@nctu.edu.tw. F. Adachi is with the Deartment of Electrical Communication Engineering at the Graduate School of Engineering, Tohoku University, Sendai, Jaan ( adachi@ecei.tohoku.ac.j. Digital Object Identifier 0.09/JSAC //$25.00 c 20 IEEE Sectrum decision is a crucial rocess in CR networks [0], which hels the secondary user select the best channel to transmit data from cidate channels. In order to distribute the traffic loads of the secondary users evenly to these cidate channels, an effective sectrum decision scheme should take the traffic statistics of the rimary users as well as the secondary users into account. In this aer, we introduce a erformance measure for evaluating various sectrum decision schemes the overall system time of the secondary connection, which is defined as the duration from the instant that data arrives at system until the instant of finishing the whole transmission. The overall system time of the secondary users connections is affected by the multile interrutions from the rimary users, the sensing errors like missed detection false alarm for the rimary users, the heterogeneous channel caacity. Within the transmission eriod of a secondary connection, it is likely to have multile sectrum hoffs due to the interrutions from the rimary users. Clearly, multile sectrum hoffs will increase the overall system time []. In the meanwhile, false alarm occurs when the detector mistakenly reorts the resence of a rimary user. In this situation, the overall system time of the secondary user s connections becomes longer because the secondary users cannot transmit data even with an idle channel. When the detection of a rimary user is missed, data collision of both the rimary user the secondary user occurs, resulting in retransmitting rolonging the overall system time of the secondary users connections. Furthermore, different channels may have various caacity data transmission rate, thereby resulting in different service time overall system time for the secondary users. Hence, it is crucial to incororate the effects of multile hoffs, sensing errors, heterogeneous channel caacity in sectrum decision methods for CR networks. In this aer, two kinds of sectrum decision schemes are considered: ( the sensing-based sectrum decision scheme; (2 the robability-based sectrum decision scheme. For the sensing-based sectrum decision method, a secondary user selects its oerating channel according to the instantaneous sensing results from scanning the wideb sectrum. For the robability-based sectrum decision method, the oerating channel is selected based on the redetermined robabilities which are determined according to traffic statistics from the long-term observation. Note that the goal of load-balancing sectrum decision can be achieved by considering the sensing outcomes when designing system arameters because these sensing outcomes in both the methods are related to the traffic statistics of both the rimary users the secondary users.

2 758 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 29, NO. 4, APRIL 20 The two considered sectrum decision schemes have different design issues. For the sensing-based sectrum decision scheme, the total number of cidate channels for channel selection significantly affects the overall system time because this scheme requires scanning all the cidate channels. Intuitively, a narrowb sensing (or a smaller number of cidate channels can reduce the total sensing time. However, it is difficult to find one idle channel from a small number of cidate channels. Hence, one challenge is to determine the otimal number of cidate channels to minimize the overall system time. On the other h, the robability-based sectrum decision scheme needs to revent the secondary users from selecting a busy channel. Hence, the most imortant issue is to determine the otimal channel selection robability to minimize the overall system time. In this aer, we investigate how to evaluate the overall system time for the sensing-based the robability-based sectrum decision schemes in the CR network when multile interrutions from the rimary user, sensing errors, channel caacity are taken into account. To this end, we design our multiuser sectrum decision schemes on to of the reemtive resume riority (PRP M/G/ queueing model. Based on the roosed analysis-based framework, we can design the suitable arameters to shorten the overall system time. Unlike the non-load-balancing methods that multile secondary users may contend for the same channel, the channel selection schemes based on the designed arameters of the roosed analytical model can evenly distribute the traffic loads of secondary users to multile channels, thereby reducing the average overall system time. The major contributions of this aer are summarized in the following: Derive the otimal selection robability for the robability-based channel selection method. Develo a method to determine the otimal number of cidate channels for the sensing-based channel selection method. Comare the sensing-based the robability-based channel selection methods suggest which sectrum decision scheme can result in shorter overall system time with various sensing error robabilities traffic arameters. Characterize the effects of sensing errors on the sectrum decision schemes of CR networks in terms of the overall system time of the rimary the secondary connections. The rest of this aer is organized as follows. Section II reviews the sectrum decision schemes in the literature. The system model the roblem formulations are resented in Sections III IV. Next, we investigate the effects of multile interrutions, sensing errors, channel caacity, sectrum sharing on the overall system time in Sections V VI. Numerical results are shown in Section VII. Finally, we give our concluding remarks in Section VIII. II. RELATED WORK Most of the sectrum decision schemes roosed in the literature can be classified into two categories: the non-loadbalancing the load-balancing schemes. The load-balancing sectrum decision schemes can be further categorized into two methods: the sensing-based sectrum decision the robability-based sectrum decision. Table I comares the existing load-balancing sectrum decision schemes, where indicate that the roosed method does does not consider the corresonding feature, resectively. In the following, we discuss the features of these sectrum decision methods in more details. A. Non-load-balancing Sectrum Decision For the non-load-balancing sectrum decision, the secondary user selects its oerating channel based on certain conditions, such as traffic load [26], [27], channel idle robability [28], the exected waiting time [29], [30], the exected remaining idle eriod [3], [32], or the exected throughut [33], [34]. Most of these methods ignored the necessity of sharing sectrum with other secondary users. When all the secondary users select the same channel, the channel contention issue arises. To solve this roblem, the loadbalancing sectrum decision methods, including sensing-based channel selection robability-based channel selection, are roosed to evenly distribute the traffic loads of the secondary users to multile channels. B. Probability-based Sectrum Decision In the literature, many robability-based sectrum decision schemes were roosed to balance the traffic loads of secondary users in multi-channel CR networks, which can be categorized into three tyes: ( acket-wise robabilistic (PP aroach [2] [6]; (2 game-theoretic (GT aroach [7] [9]; (3 learning automata (LA aroach [20]. Packet-wise robabilistic sectrum decision aroaches [2] [6] aim at maximizing the exected throughut of the secondary users at each slot by determining the robability of selecting each channel from the ool of cidate channel. Based on busy robability caacity of each channel, [2] suggested a method to determine the robability for selecting channels on to of -ersistent carrier sense multile access (CSMA medium access control (MAC rotocol in a decentralized manner. They claimed that their roosed sub-otimal channel robability assignment can achieve the Nash equilibrium as the number of secondary users tends to infinity. Furthermore, [3], [4] considered the effects of sensing errors in terms of false alarm missed detection on the throughut of the secondary users in a two-channel system, roosed a robabilistic channel selection aroach to maximize the throughut of the secondary users in each slot while maintaining the latency constraint of the rimary users. Moreover, [5] formulated an otimization roblem for channel selection robability to maximize the throughut of the secondary users in each slot while maintaining the interference constraint of the rimary users when the rimary secondary networks are asynchronous. Unlike [3] [5] considered only the case that one single secondary user can select the channel at each time instant, [6] further extended the robabilistic channel selection aroach of [3], [4] to the case that multile users can

3 WANG et al.: LOAD-BALANCING SPECTRUM DECISION FOR COGNITIVE RADIO NETWORKS 759 TABLE I COMPARISON OF VARIOUS LOAD-BALANCING SPECTRUM DECISION SCHEMES FOR COGNITIVE RADIO NETWORKS, WHERE PP, GT, AND LA STAND FOR THE PACKET-WISE PROBABILISTIC, GAME-THEORETIC, AND LEARNING AUTOMATA APPROACHES, RESPECTIVELY. Channel Occuancy Model Multile Sensing Heterogeneous of a Primary Network Interrutions Errors Channel Caacity Bernoulli Process [2] PP Probability- Bernoulli Process [3] [6] based Deterministic Process [7] GT Methods M/M/ [8] or M/G/ [9] LA General Distribution [20] Sensing- Deterministic Process [2] based Two-state Markov Chain [22] Methods Bernoulli Process [23] [25] Our Proosed Model M/G/ simultaneously select their oerating channels from the ool of cidate channels, analyzed the throughut of the secondary users based on the robabilistic channel selection aroach taking into account of the effects of channel contention as well as sensing errors. Note that the acket-wise robabilistic sectrum decision aroaches in [2] [6] were executed in a slot-by-slot manner, which may lead to many channel-switching behaviors during each secondary user s link connection. Moreover, it is assumed that the traffic loads of the secondary users are saturated. Further, the channel occuancy model of a rimary network is modeled as a Bernoulli rocess thus the length of busy idle eriods are exonentially distributed. Game-theoretic aroaches were roosed to solve the sectrum decision roblem in CR networks [7] [9]. Based on the game theory model, each layer (secondary user can decide the best strategy (channel selection robability to maximize its utility function. [7] roosed a game-theoretic load-balancing aroach to find a set of channel selection robabilities so that no secondary user has incentive to unilaterally change his/her action. To converge to such the Nash equilibrium, a best-rely algorithm was designed for each user to calculate each channel s selection robability as well as its transmission duration based on a utility function related to the loadbalancing channel selection. Beside the load-balancing issue, [8] suggested that the utility function in the gametheoretic sectrum decision should also incororate the channel bwidth its idle eriod as well as the cost of sectrum hoff because the sectrum decision rocedure must be executed many times due to multile interrutions. They emhasized that the channel selection game shall be reeated many times to cature the scenario when rimary users stochastically activate or deactivate at each eoch. Unlike the ervious work that considered the homogeneous secondary users, [9] assumed that the secondary users can have different riorities. They roosed a dynamic strategy learning algorithm to determine the channel selection strategies that can converge to the Nash equilibrium. Noteworthily, the Nash equilibrium solution of the game-theoretic aroach is not necessary the globally otimal solution from the viewoint of the overall network [35]. In [20], a learning automata (LA aroach was suggested to determine the channel selection robabilities by exloring the uncertainty of traffic atterns in CR networks. After a huge number of trials, the secondary users can estimate the otimal channel selection robability. However, the roblem for this method is its converging seed, esecially for a large number of users. C. Sensing-based Sectrum Decision As mentioned in Section I, the sensing-based sectrum decision scheme requires scanning all the cidate channels to determine the most suitable oerating channel. Thus, the total number of cidate channels significantly affects the overall system time in the sensing-based sectrum decision scheme. In [2] [23], the otimal number of cidate channels to maximize the sectrum accessibility the rocedures to determine the otimal set of cidate channels were investigated. Furthermore, the authors in [24], [25] formulated the sequential channel sensing roblem as an otimal stoing roblem with the objective of maximizing the throughut of the secondary users. They studied when the secondary users shall sto sensing start transmitting data. Nevertheless, the effects of multile interrutions from the rimary user the sensing errors for the rimary user s occurrence on the overall system time of the secondary users in the CR networks have not been addressed in these existing sensing-based sectrum decision methods. D. Objectives of This Paer The objective of this aer is to develo an analytical framework for the connection-based load-balancing sectrum decision schemes that can take into account of all the effects of ( the rimary users multile interrutions, (2 the secondary users sensing errors, (3 heterogeneous channel caacity. Furthermore, it is referred that the develoed analytical framework can be used in both the robability-based as well as the sensing-based sectrum decision schemes with general service time distributions of the rimary the secondary users. To the best of our knowledge, such an analytical framework has rarely been seen in the literature. We will detail the roosed modeling techniques for such general sectrum decision behaviors in the next section.

4 760 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 29, NO. 4, APRIL 20 Channel Selection Algorithm Channel with Channel 2 with Channel M with can balance the traffic loads of secondary users in multile channels. The distribution robability vector (denoted by = ( (, (2,, (M reresents the set of robabilities for selecting all the cidate channels, in which denotes the robability of a secondary connection selecting channel k for its oerating channel. Thus, the effective arrival rate of the secondary connection at channel k is λ s = λ s. Note that various channel selection algorithms yield different distribution robability vectors. Fig.. Sectrum decision behavior model. III. SYSTEM MODEL A. Assumtions We consider a time-slotted CR network where the slot structure was also adoted in [33], [36] [39]. In order to detect rotect the rimary users, the sectrum sensing rocedure must be executed by the secondary users at the beginning of each time slot. If the current oerating channel is idle, the secondary user can transmit data in this time slot. By contrary if the current oerating channel is busy, the secondary user must erform sectrum hoff rocedures to resume its unfinished transmission when the current channel becomes idle. This kind of listen-before-talk channel access scheme has been adoted in many wireless techniques, such as the clear channel assessment (CCA of the IEEE 802. stard [40] the quiet eriod of the IEEE stard [4]. B. Sectrum Decision Behavior Model Fig. illustrates the sectrum decision behavior model, which will be used to evaluate the overall system time of a secondary connection for different channel selection schemes. We assume that the arrival rocesses of the rimary the secondary connections are Poisson. Let λ (arrivals/slot λ s (arrivals/slot be the average arrival rates of the rimary connections at channel k the secondary connections of CR network, resectively. Also, denote L (bits/arrival L s (bits/arrival the sizes of the rimary connections of channel k the secondary connections, resectively; let f (l f s (l be robability mass functions (mf of L L s, resectively. It is assumed that λ, λ s, f (l, f s (l, which can be estimated by the existing methods [43], are known to all the secondary users. Furthermore, denote R (bits/slot R s (bits/slot as the data rate of the rimary the secondary connections at channel k, resectively. Hence, the service time of the rimary the secondary connections at channel k is X L /R (slots/arrival X s L s /R s (slots/arrival, resectively. As shown in Fig., each secondary connection can select one of M cidate channels for its oerating channel. Based on our roosed analytical framework, which will be discussed in more detail later, all the secondary users can dynamically select their oerating channels with suitable robability that When a secondary transmitter has data to send, how to establish a secondary connection to its intended receiver has been investigated in [42]. C. Sensing Errors The service time of the rimary secondary connections will be extended due to missed detection false alarm robabilities, resectively 2. When missed detections occur, the rimary user must retransmit these stained data frames in the next slots. Thus, the service time of a rimary connection will be extended from X (slots/arrival to (slots/arrival. Furthermore, a secondary user cannot transmit data even with an idle channel when a false alarm occurs. Hence, a secondary user needs to send more time to comlete its connection transmission. Then, the service time of a secondary connection will be extended to s (slots/arrival from X s (slots/arrival. In the remaining art of this aer, s are called the actual service time of the rimary secondary connections. s will be derived in Section VI. IV. PROBLEM FORMULATION A. Performance Metric: Overall System Time The overall system time (denoted by S is an imortant quality of service (QoS metric for the connection-based service of the secondary users. It consists of the waiting time (denoted by W the extended data delivery time (denoted by T as shown in Fig. 2. Hence, we have E[S] =E[W ]+E[T ], ( where E[ ] is the exectation function. Here, the waiting time is defined as the duration from the instant that a data transmission request arrives at the system until the instant of starting transmitting data. The duration of waiting time deends on the channel selection scheme that the secondary users adot. Furthermore, the extended data delivery time is defined as the duration from the beginning of transmitting the data in the first time slot until the comletion of the data in the last time slot. Clearly, multile hoff behaviors significantly affect the extended data delivery time. B. Overall System Time Minimization Problem for Probability-based Channel Selection Scheme For the robability-based channel selection method, each secondary user selects its oerating channel from all the M cidate channels based on a redetermined distribution robability vector b. In this case, an Overall System 2 The relationshi between the missed detection robability the false alarm robability can be characterized by the receiver oerating characteristic (ROC curve [44].

5 WANG et al.: LOAD-BALANCING SPECTRUM DECISION FOR COGNITIVE RADIO NETWORKS 76 S PRP M/G/ Queuing Model W SC A PCs SC A PCs SC A T Arrival of PC Arrival of SC A Sectrum Hoff Dearture of SC A t Probability -based Channel Selection Algorithm Low-riority Queue Low-riority Queue 2 Fig. 2. Examle of the overall system time of the secondary connection SC A. The white areas indicate that channel is occuied by SC A.Furthermore, the gray areas indicate that channel is occuied by the rimary connections (PCs its duration is the busy eriod resulting from transmissions of the rimary connections. Here, SC A exeriences two interrutions from the rimary connections during its transmission eriod. Time Minimization Problem for Probability-based Channel Selection Scheme can be formulated as follows. Given the set of cidate channels Ω={, 2,...,M}, we aim to find the otimal distribution robability vector (denoted by to minimize the average overall system time of the secondary connections (denoted by E[S b ]. Formally, subject to: =argmin b E[S b ( b ], (2 0 b k Ω b, k Ω, (3 = M k= b =, (4 ρ = ρ + ρ s <, (5 where ρ is the busy robability of channel k. Furthermore, ρ ρ s are the busy robabilities resulting from the rimary the secondary connections at channel k when sensing errors are considered, resectively. We can have ρ = λ E[ ] ρ s = λ s E[ s ]. C. Overall System Time Minimization Problem for Sensingbased Channel Selection Scheme For the sensing-based channel selection scheme, the secondary users erform wideb sensing to find an idle channel from all the cidate channels. If more than one idle channel is found, the secondary user romly selects one channel from the idle channels for its oerating channel. Furthermore, if all the cidate channels are busy, the secondary user still romly selects one channel from all the cidate channels wait for the available time slot of this selected channel. In order to decrease the total sensing time, the secondary users shall reduce the number of cidate channels by sensing only the best n channels among M channels. Without loss of generality, we assume that the channel reference of the secondary users follows the lexicograhic order. That is, channel i is not better than channel j if i > j. Note that the ordering issue for channel reference has been discussed in [45]. Let Ω be the set of cidate channels. Then, we Low-riority Queue Fig. 3. Performance model for the robability-based channel selection scheme where the channel usage behaviors are characterized by the PRP M/G/ queueing systems. can have Ω={, 2,...,n}, wheren = Ω M. Next,we formulate an Overall System Time Minimization Problem for Sensing-based Channel Selection Scheme as follows. Given the total number of channels M, we aim to find the otimal number of cidate channels (denoted by n to minimize the average overall system time of the secondary connections (denoted by E[S sb ]. Formally, n =argmine[s sb (n]. (6 n M D. Performance Model In order to calculate the overall system time of various sectrum decision schemes, we extend the general model in Fig. to characterize the robability- the sensing-based channel selection schemes. Fig. 3 shows the erformance model for the robability-based scheme. When the traffic of the secondary user (i.e., the secondary connection arrives at the system, it can be directly connected to the selected channel based on the redetermined distribution robability vector. On the other h, Fig. 4 shows the erformance model of the sensing-based scheme. When the traffic of a secondary user arrives at the system, the secondary user erforms sectrum sensing to find idle channels. The total sensing time can be modeled by a taed delay line S. In this case, S can be regarded as a server with constant service time, which equals to sensing time. If an idle channel can be found, the secondary connection can be served immediately. As shown in Figs. 3 4, the roosed channel selection model is integrated with the reemtive resume riority (PRP M/G/ queueing systems in order to characterize the effects of multile interrutions, sensing errors, channel caacity on the overall system time. Some imortant roerties for the PRP M/G/ queueing model are listed below [46]: Each server (channel has two tyes of customers (connections. The connections of the rimary secondary users are connected to the high-riority queue the low-riority queue, resectively. Note that the highriority queue has not been lotted in Figs. 3 4 due to sace limitations. M

6 762 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 29, NO. 4, APRIL 20 S Sensingbased Channel Selection Algorithm PRP M/G/ Queuing Model Low-riority Queue Low-riority Queue Low-riority Queue Fig. 4. Performance model for the sensing-based channel selection scheme where the channel usage behaviors are characterized by the PRP M/G/ queueing systems. The rimary users have the reemtive riority to interrut the transmission of the secondary user. The remaining transmission of the interruted secondary user will be ut into the head of the low-riority queue of the current oerating channel. Furthermore, the interruted secondary user can resume the unfinished transmission when the current channel becomes idle, instead of retransmitting the whole data. A secondary connection may exerience multile interrutions from the rimary connections during its transmission eriod. This model can characterize the effects of multile sectrum hoffs. Here, we assume that connections which have the same riority access channels with the first-come-first-served (FCFS scheduling disciline. Based on the roosed erformance models, we can analytically comare the overall system time resulting from both the sectrum decision schemes for various sensing time traffic arameters. Then, each secondary user can intelligently adot the best channel selection scheme to minimize its overall system time. Thus, the otimal overall system time (denoted by S can be exressed as follows: S =min(e[s b ], E[S sb ]. (7 In the next section, we will show how to derive E[S b ] E[S sb ]. V. ANALYSIS OF OVERALL SYSTEM TIME As discussed in Section IV-A, the overall system time consists of the waiting time the extended data delivery time. Let E[T b ] E[T sb ] be the average data delivery time for the robability- sensing-based sectrum decision methods, resectively. Furthermore, denote E[W b ] E[W sb ] as the average waiting time for the robability- sensing-based sectrum decision methods, resectively. Then, we can have E[S b ]=E[W b ]+E[T b ], (8 E[S sb ]=E[W sb ]+E[T sb ]. (9 In the following, we will investigate how to obtain the average extended data delivery time the average waiting time. 2 M A. Extended Data Delivery Time First, we investigate the effects of multile interrutions on the extended data delivery time. Within the transmission eriod of a secondary connection, it is likely to have multile sectrum hoffs due to the interrutions from the rimary users. The sectrum hoff rocedure hels the secondary users vacate the occuied channel then resume the unfinished transmission when this channel becomes idle. Clearly, multile sectrum hoffs will increase the extended data delivery time degrade the QoS for the latency-sensitive traffic of the secondary users. Based on the PRP M/G/ queueing model, we can derive the extended data delivery time of the secondary connections as follows. Let N be the total number of interrutions for a secondary connection at channel k. Furthermore, denote Y as the duration from the time instant that channel k is occuied by the rimary connections until the time instant that the highriority queue becomes emty. This duration is called the busy eriod resulting from transmissions of rimary connections at channel k. When a secondary connection is interruted by the rimary user, it must sto transmitting on the current oerating channel until all the rimary connections in the highriority queue have been served. In this case, this secondary connection of channel k must wait for the duration of E[Y ] on average after the interrution event occurs. Denote T as the extended data delivery time of the secondary connections at channel k. We can have E[T ]=E[ where E[N ]=λ E[ s ]+E[N ]E[Y ], (0 s ] E[Y ]= E[ e X ] λ E[ X e ] according to to [8]. Finally, the average extended data delivery time for the robability- sensing-based channel selection methods can be exressed as follows: E[T b ]= E[T sb ]= M k= n k= b E[T ], ( sb E[T ]. (2 For various channel selection algorithms, we use different methods to evaluate the corresonding distribution robability vectors. For the robability-based scheme, the distribution robability vector b can be designed by solving the Overall System Time Minimization Problem for Probability-based Channel Selection Scheme in (2. For the sensing-based scheme, the distribution robability vector sb is determined inherently based on the given traffic atterns. Intuitively, a channel with larger idle robability will be selected more frequently through sectrum sensing. How to derive sb from the given traffic arameters will be discussed in Aendix A. B. Waiting Time Probability-based Channel Selection Scheme: In this case, a secondary connection selects its oerating channel based on the redetermined robability. Then, it is directly

7 WANG et al.: LOAD-BALANCING SPECTRUM DECISION FOR COGNITIVE RADIO NETWORKS 763 connected to the low-riority queue of the selected channel. It cannot be served until all the rimary the secondary connections in the high-riority queue the resent lowriority queue of the selected channel have been served. Hence, the waiting time is the required duration from the time instant that a secondary connection arrives at the low-riority queue of the selected channel until the time instant that the selected channel becomes idle. That is, the waiting time is the duration sent in the waiting queue by a secondary connection. Hence, we have E[W b ]= M k= b E[W b ], (3 where W b is the waiting time of the secondary connections at channel k for the robability-based channel selection scheme. Alying the PRP M/G/ queueing theory [47], one can obtain E[W b ]= E[R ] ( ρ ( ρ ρ s, (4 where E[R ] is the average remaining time to comlete the service of the connection being served at channel k. Referring to [47], we have E[R ]= 2 λ 2 ]+ 2 b λ s s 2 ]. (5 Then, substituting (4 (5 into (3, we can obtain the closed-from exression for E[W b ]. Finally, substituting ( (3 into (8, we can obtain the relationshi between the average overall system time the distribution robability vector b for the robability-based channel selection scheme. Then, the otimal distribution robability vector can be determined by solving the Overall System Time Minimization Problem for Probability-based Channel Selection in (2. 2 Sensing-based Channel Selection Scheme: The waiting time W sb for the sensing-based channel selection method consists of the total sensing time the queueing time (denoted by W sb. Let τ be the sensing time for scanning one cidate channel. Hence, nτ is the total sensing time for scanning all the n cidate channels. After wideb sensing, the secondary user can decide channel availability then transmits data at one of the idle channels. Moreover, if the idle channel cannot be found, the secondary user cannot transmit immediately. In this case, the secondary connection will be ut into the low-riority queue of the romly selected channel. Hence, we can have E[W sb ]=nτ + Pr{E} 0+Pr{E c } E[W sb ], (6 where E is the event that at least one idle channel can be found after sensing, E c is the comliment of E. Next, the closed-form exressions for Pr{E} Pr{E c } can be derived by the following two observations. First, a channel is called actually idle if only if ( this channel is not occuied by the rimary connections (2 the lowriority queue of this channel is emty. Note that the second condition should be contained because the FCFS scheduling disciline is adoted. Secondly, an idle channel is assessed as idle through sectrum sensing if only if a false alarm does not occur. Hence, we can have Pr{E} = = n [Pr{E k channels are actually idle} k= Pr{k channels are actually idle}] n [ [ (PF k ] k= I Ω, I =k i I( ρ (i j Ω I ρ (j,(7 where ρ = ρ +ρ s P F is the false alarm robability. On the other h, E c is the comliment of E. Thatis, Pr{E c } = Pr{E}. (8 Moreover, when all channels are assessed as busy, each channel is selected by the secondary users with robability /n. Hence, in this case, one can derive the average queueing time based on the PRP M/G/ queueing theory as follows [47] : E[W sb] = n k= [ n E[R ] ( ρ ( ρ ρ s ]. (9 Finally, substituting (2 (6 into (9, we can obtain the relationshi between the average overall system time the number of cidate channels n for the sensing-based channel selection scheme. Determining the otimal number of cidate channels (denoted by n is the key issue for the sensing-based sectrum decision scheme. Intuitively, a small number of cidate channels can reduce the total sensing time nτ in (6. However, it is harder to find one idle channel from fewer cidate channels, resulting in a larger value of Pr{E c } in (6 thus increasing the overall system time. The otimal number of cidate channels n can be determined by solving the Overall System Time Minimization Problem for Sensingbased Channel Selection in (6. VI. EFFECTS OF SENSING ERRORS Sensing errors such as false alarm missed detection will degrade the erformance of the secondary users the rimary users. This section investigates the effects of false alarm missed detection on the actual service time of the secondary the rimary connections. Secifically, we will show how to derive the first the second moments of. s A. False Alarm First, we study the effect of false alarm on the actual service time of the secondary connections. When a false alarm occurs, the secondary user cannot transmit data even with an idle channel. Hence, the actual service time of a secondary connection will be extended to s (slots/arrival from X s

8 764 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 29, NO. 4, APRIL 20 (slots/arrival. The first the second moments of be exressed as follows: E[ s ]= E[ x= s 2 ]= x= s can s X s = x]pr{x s = x}, (20 s 2 X s = x]pr{x s = x}. (2 Note that because the false-alarm slot cannot be exloited by any secondary or rimary connections, it can be regarded as a busy slot. Hence, we can have ρ s = λ s E[ s ]. When a false alarm occurs, the data transmission is ostoned to the next slot. Hence, for a connection with x slots, its actual service time will be extended to x + i slots if only if false alarms occur in i slots out of the first x + i slots false alarm does not occur at the (x+i th slot. Thus, the conditional exectation of the actual service time follows the negative binomial distribution with arameter P F.Thatis, = = X E[ s s = x] ( x + i (x + i i i=0 i=0 s 2 X s = x] (x + i 2 ( x + i i ( P F x (P F i, ( P F x (P F i, (22 (23 where P F is the false alarm robability. Because Pr{X s = x} is given by f s (l, we can obtain E[ s ] s 2 ] by substituting (22 (23 into (20 (2, resectively. For examle, if f s (l is the geometric distribution, i.e., ( f s (l = x (, (24 E[L s ] E[L s ] we can have s 2 ]= E[ s E[X s where E[X s ]=E[L s ]/R s. ]= E[X s ] P F, (25 ](2E[X s ] +P F ( P F 2, (26 B. Missed Detection The data frame of the rimary connection will be stained by the secondary connection when a missed detection occurs. Thus, the rimary user will request to retransmit this stained data frame in the next slot. Hence, the actual service time of a rimary connection will be extended to (slots/arrival from X of E[ (slots/arrival. The first the second moments can be exressed as follows: ]= E[ x= 2 ]= x= X = x]pr{x = x}, (27 2 X = x]pr{x = x}. (28 Basically, there are two tyes of missed detections in CR networks [48], [49]. Firstly, when a rimary user transmits data, a newly arriving secondary connection may incorrectly determine that this secific channel is available in its first sensing hase. We call this situation the class-a missed detection. After a secondary user arrives at a CR network for a while, it may also fail to detect the resence of rimary users. In this case, the class-b missed detection occurs. It was found that the class-b missed detection is small because the sensing results at the first sensing hase can be emloyed to imrove the accuracy of the sensing results at the following sensing hases. Next, we exlain the effect of class-a missed detection on the actual service time of the rimary connection at channel k. We consider a transmission slot of this rimary connection. During this slot, more than one arrival of the secondary connection aears with robability e λ s Δ,whereΔ is the slot duration. For these arrivals of secondary connections, each of them will assess this busy slot as idle if only if ( a missed detection occurs (2 the low-riority queue of channel k is emty. Let Q s be the length of the low-riority queue at channel k. Hence, the first arrival at the considered slot will make an error channel assessment with robability P M Pr{Q s =0}, wherep M is the missed detection robability for sectrum sensing Pr{Q s =0} has been derived in [50]. However, for the remaining arrivals in the considered slot, we have Pr{Q s =0} =0because the first arrival has been ut into the low-riority queue of channel k. Thus, the remaining arrivals do not make the error channel assessment. From above observations, we can conclude that a rimary connection s transmission slot is stained by the arrivals of the secondary connections with robability =( e λδ s P M Pr{Q s =0}. (29 Similar to the case of false alarm, we find that the rom variables ( 2 follows the negative binomial distribution with arameter P I when X = x. Then, because Pr{X = x} can be determined by f (l, we can calculate the values of E[ ] 2 ] in (27 (28, resectively. For examle, if f (l is the geometric distribution, i.e., x ( f ( (l =, (30 E[L ] E[L ] P I we can have E[ E[X ]= ] P I, (3

9 WANG et al.: LOAD-BALANCING SPECTRUM DECISION FOR COGNITIVE RADIO NETWORKS 765 Otimal Distrubution Probability Vector ( * Channel Channel 2 Channel 3 Channel Average Arrival Rate of the Secondary Connections (λ s Channel Busy Probability Busy Probability of Channel Busy Probability of Channel 2 Busy Probability of Channel 3 Busy Probability of Channel Average Arrival Rate of the Secondary Connections (λ s Fig. 5. Otimal distribution robability vector for the robability-based sectrum decision with various arrival rates of the secondary connections, where P F =0., P M =0., E[X s]=0. Fig. 6. Channel busy robability for the robability-based sectrum decision with various arrival rates of the secondary connections, where P F =0., P M =0., E[X s]=0. where E[X 2 ]= E[X ]=E[L ](2E[X ] +P I, (32 ( P I 2 ]/R. VII. NUMERICAL RESULTS In this section, numerical results are resented to show how to design the system arameters for the load-balancing sectrum decision methods, including the robability-based the sensing-based sectrum decision schemes. We adot the system arameters in the IEEE stard in our simulation [5], where the time slot duration Δ is 0 msec, P M = 0., P F = 0.. Furthermore, we assume that R = R s = for any k. Hence, we have E[X ] = E[L ] E[X s ] = E[L s ] for any k. To ease the notation, let E[X s ] E[X s ] for any k. Moreover, because this aer focuses on the latency-sensitive traffic, we can assume that the connection length (or equivalently service time distributions of rimary secondary connections are geometrically distributed (see age 35 in [47]. Note that we only use the geometric distribution as an examle here. Indeed, the roosed analytical framework can be alied to any distributions. It only requires the knowledge of the first the second moments of the service time distributions for the rimary the secondary connections. A. Probability-based Sectrum Decision Scheme Figure 5 shows the effect of various arrival rates of the secondary connections on the otimal distribution robability vector, where the distribution robability vector is lotted in each bar the summation of all robabilities in each bar is. Inthefigure, we consider a four-channel system with the following traffic arameters: λ ( =0.0, λ (2 =0.0, λ (3 = 0.02, λ (4 = 0.02 as well as E[X ( ] = 20, E[X (2 ] = 30, E[X (3 ] = 20, E[X (4 ] = 25.When λ s =0.0, all the secondary users refer selecting channel to be their oerating channels because channel has the lightest traffic loads. Furthermore, as λ s increases, some secondary users tend to select other channels to transmit data in order to balance the traffic loads in each channel. For examle, when λ s = 0., the otimal distribution robability vector is (0.442, , 0.23, Inevitably, channel is still selected to be the oerating channel with the largest robability. Furthermore, Fig. 6 shows the channel busy robability under various arrival rates of the secondary connections. When λ s =0, channel has the lowest busy robability. However, when λ s 0.05, channel has the highest busy robability because most secondary users refer to select channel to transmit data. Although channel has the highest busy robability when λ s 0.05, one can find that the secondary users still favor channel from Fig. 5. Figure 7 shows that most secondary connections refer selecting a channel with the largest arrival rate the shortest service time of the rimary connections even though all the channels have the same busy robability of the rimary connections. Here, we consider the following traffic arameters: λ ( = 0.0, λ (2 = 0.02, λ (3 = 0.04, λ (4 = 0.08 as well as E[X ( ] = 40, E[X (2 ] = 20, E[X (3 ] = 0, E[X (4 ]=5. Hence, all channels have the same busy robability, which is equal to 0.4, whenλ s =0. According to (3 (4, we know that selecting channel 4 can result in shorter average waiting time (E[W b ] because channel 4 has the smallest value of E[R ]. Consequently, most of the secondary connections refer selecting channel 4 thus it has the highest busy robability when λ s > 0. Figure 8 shows the effects of false alarms on the otimal distribution robability vector. When P F =0.05, only three channels can be the cidate channels. However, all the four channels can be the cidate channels when P F 0.. This henomenon can be interreted as follows. When P F becomes higher, E[ s ] increases due to more false alarms. Hence, the actual traffic loads (ρ s = λ s E[ s ] of the secondary connections become heavy. Then, the secondary connections

10 766 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 29, NO. 4, APRIL Channel Busy Probability Busy Probability of Channel Busy Probability of Channel 2 Busy Probability of Channel 3 Busy Probability of Channel 4 Overall System Time (E[S sb ] E[X s ]=0 E[X s ]= Average Arrival Rate of the Secondary Connections (λ s Total Number of Cidate Channels (n Fig. 7. Channel busy robability for the robability-based sectrum decision with various arrival rates of the secondary connections, where P F = 0, P M =0,E[X s]=5. Fig. 9. Overall system time for the sensing-based sectrum decision with various numbers of cidate channels n, wherep F =0., P M =0., τ =2,E[X ]=20. Otimal Distrubution Probability Vector ( * Channel Channel 2 Channel 3 Channel False Alarm Probability (P F Overall System Time (E[S sb ] P F =0.5 P F = Total Number of Cidate Channels (n Fig. 8. Otimal distribution robability vector for the robability-based sectrum decision with various arrival rates of the secondary connections, where P M =0., λ s =0.03, E[X s]=5. Fig. 0. Overall system time for the sensing-based sectrum decision with various numbers of cidate channels n,wherep M =0., τ =2, E[X ]= 20, E[X s]=5. must distribute overall traffic loads to more channels in order to revent channel contention. B. Sensing-based Sectrum Decision Scheme Figures 9 0 show the effects of E[X s ] P F on the otimal number of cidate channels n, resectively. Here, we consider a four-channel system with the following traffic arameters: (λ (,λ (2,λ (3,λ (4 = (0.0, 0.05, 0.02, 0.025, λ s =0.02 τ =2. Moreover, E[X ]=20for any k. From Fig. 9, one can see that when P F =0., n = 2 for E[X s ]=5 0, resectively. In Fig. 0, we see that n = 2 for P F = when E[X s ]=5. It is observed that the otimal value of n monotonically increases as E[X s ] or P F increases. This is because a larger value of E[X s ] or P F can lead to a larger value of E[ s ] according to (25. From (9 one can exect that the queueing time will become longer for a larger value of E[ s ]. In this case, the secondary users shall sense more channels to increase the robability of finding idle channels Pr{E}, which will reduce the waiting time. C. Comarison between Different Sectrum Decision Schemes Figure shows the effects of λ s on the average overall system time for three different channel selection schemes: ( sensing-based method; (2 robability-based method; (3 non-load-balancing method. Consider a three-channel system with the following traffic arameters: (λ (,λ (2,λ (3 = (0.02, 0.02, 0.03, (E[X ( ], E[X (2 ], E[X (3 ] = (20, 25, 20, E[X s ]=0. The overall system time of the robabilitybased sensing-based channel selection schemes are calculated from (8 (9, resectively. For the non-load-balancing method, all the secondary connections will select channel to be their oerating channels because channel has the lowest busy robability. One can find that both the loadbalancing channel selection schemes can significantly reduce the average overall system time comared to the non-loadbalancing scheme, esecially for larger λ s.whenτ is small

11 WANG et al.: LOAD-BALANCING SPECTRUM DECISION FOR COGNITIVE RADIO NETWORKS 767 Overall System Time (E[S] Non load balancing Method Probability based Method Sensing based Method (τ = 7 Sensing based Method (τ = Average Arrival Rate of the Secondary Connections (λ s Fig.. Comarison of the overall system time for three considered sectrum decision schemes, where P F =0., P M =0., E[X s]=0. (e.g. 5 slots, the sensing-based sectrum decision scheme can result in the shortest overall system time. As τ increases, the imrovement of the sensing-based sectrum decision over other schemes decreases. In addition, we also observe that when τ =7 λ s < 0.026, the robability-based scheme has better overall system time erformance than the sensingbased scheme. This is because the robability-based sectrum decision scheme can select the channels with lower interruted robability. By contrast, if λ s > 0.026, the sensing-based scheme can result in shorter overall system time because the sensing-based scheme can significantly reduce waiting time through wideb sensing. Based on (7, each secondary user can intelligently adot the best channel selection scheme to minimize its overall system time. The two considered loadbalancing sectrum decision methods can reduce the overall system time by over 50% comared to the existing non-loadbalancing method when λ s =0.04. VIII. CONCLUSIONS In this aer, an analytical framework has been roosed to design the system arameters for the sensing- the robability-based sectrum decision schemes. The roosed model integrated with the PRP M/G/ queueing systems can evaluate the effects of multile interrutions, sensing errors, channel caacity on the overall system time of the secondary connections. Based on this analytical model, the otimal number of cidate channels for the sensing-based sectrum selection method the otimal channel selection robability for the robability-based sectrum selection method can be obtained analytically for various sensing time traffic arameters. We found that the robability-based scheme can reduce the overall system time comared to the sensing-based scheme when the traffic loads of the secondary users is light, whereas the sensing-based scheme erforms better in the condition of heavy traffic loads. This observation rovide an imortant insight into design a traffic-adative sectrum decision scheme in the resence of sensing errors. Some interesting research issues that can be extended from this aer include the following. First, it is worthwhile to determine the otimal distribution robability vector for the robability-based sectrum decision method when the secondary connections may have different oinions on the observed traffic statistics λ, λ s, f (l,f s (l. Secondly, it would be interesting to see how to analyze the overall system time for both considered load-balancing sectrum decision methods in the hoing mode, i.e., the oerating channel after the rimary user s interrution is different from the current channel. APPENDIX A DISTRIBUTION PROBABILITY VECTOR FOR THE SENSING-BASED CHANNEL SELECTION SCHEME The robability that a secondary user can select channel k for its oerating channel is determined inherently based on the traffic atterns for the sensing-based sectrum decision scheme. According to the sensing outcomes, this robability consists of three comonents. First, we consider the case that false alarm dose not occur at the idle channel k. When the channels in I Ω {k} are also actually idle false alarms do not occur at the channels in R I, channel k will be selected with robability + R. Secondly, we consider the case when a false alarm occurs at the idle channel k. If false alarms also occur at all the remaining idle channels, the secondary user will romly select one channel from all cidate channels to be its oerating channel. In this case, channel k is selected with robability / Ω. Thirdly, we consider the case when channel k is actually busy. With the similar argument in the revious case, the secondary user will romly select one channel if false alarms occur at all the idle channels. In this case, channel k will be selected with robability / Ω. On the other h, channel k cannot be selected when k/ Ω. From these observations, we can have (33. REFERENCES [] J.MitolaG.Q.Maguire, Cognitive Radio: Making Software Radios More Personal, IEEE Personal Commun., vol. 6,. 3 8, Aug [2] S. 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12 768 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 29, NO. 4, APRIL 20 sb = ( ρ ( P F ρ I Ω {k} i I( (i ρ (j + R ( P F R (P F I R + j Ω {k} I R I [ ( ρ P F + ρ ] i I( ρ (i ρ (j (P F I, k Ω Ω I Ω {k} j Ω {k} I 0, k/ Ω (33 [0] I. F. Akyildiz, W.-Y. Lee, M. C. Vuran, S. Mohanty, A Survey on Sectrum Management in Cognitive Radio Networks, IEEE Commun. Mag., vol. 46, no. 4, , Ar [] H.-J. Liu, Z.-X. Wang, S.-F. Li, M. Yi, Study on the Performance of Sectrum Mobility in Cognitive Wireless Network, IEEE Singaore International Conference on Communication Systems (ICCS, Jun [2] A. Banaei C. N. Georghiades, Throughut Analysis of a Romized Sensing Scheme in Cell-based Ad-hoc Cognitive Networks, IEEE International Conference on Communications (ICC, Jun [3] J. Gambini, O. Simeone, Y. Bar-Ness, U. Sagnolini, T. Yu, Packetwise Vertical Hover for Unlicensed Multi-stard Sectrum Access with Cognitive Radios, IEEE Trans. Wireless Commun., vol. 7, no. 2, , Dec [4] J. Gambini, O. Simeone, U. 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13 WANG et al.: LOAD-BALANCING SPECTRUM DECISION FOR COGNITIVE RADIO NETWORKS 769 [47] Chee-Hock Ng Boon-Hee Soong, Queueing Modelling Fundamentals with Alications in Communication Networks, 2nd. John Wiley & Sons Inc., [48] S. Tang B. L. Mark, Modeling Analysis of Oortunistic Sectrum Sharing with Unreliable Sectrum Sensing, IEEE Trans. Wireless Commun., vol. 8, , Ar [49] I. Suliman, J. Lehtomaki, T. Braysy, K. Umebayashi, Analysis of Cognitive Radio Networks with Imerfect Sensing, IEEE International Symosium on Personal, Indoor Mobile Radio Communications (PIMRC, Se [50] N. K. Jaiswal, Preemtive Resume Priority Queue, Oerations Research, vol. 9, no. 5, , Se./Oct. 96. [5] Draft Stard for Wireless Regional Area Networks Part 22: Cognitive Wireless RAN Medium Access Control (MAC Physical Layer (PHY Secifications, IEEE Working Grou. Li-Chun Wang (S 92-M 96-SM 06-F received the B.S. degree in electrical engineering from the National Chiao-Tung University, Hsinchu, Taiwan, in 986, the M.S. degree in electrical engineering from the National Taiwan University, Taiei, Taiwan, in 988, the M.Sc. Ph.D. degrees in electrical engineering from Georgia Institute of Technology, Atlanta, in , resectively. In 995, he was affiliated with Northern Telecom in Richardson, Texas. From 996 to 2000, he was with AT&T Laboratories, where he was a Senior Technical Staff Member in the Wireless Communications Research Deartment. Since August 2000, he has joined the Deartment of Communication Engineering of National Chiao- Tung University in Taiwan as an Associate Professor has been romoted to a full rofessor since August Dr. Wang was a coreciient of the Jack Neubauer Best Paer Award from the IEEE Vehicular Technology Society in 997. His current research interests are in the areas of cellular architectures, radio network resource management, cross-layer otimization for cooerative cognitive wireless networks. He is the holder of three U.S. atents with three more ending. Chung-Wei Wang (S 07 received the B.S. degree in electrical engineering from Tamkang University, Taiei, Taiwan, in 2003, the Minor M.S. Ph.D. degrees in alied mathematics communication engineering from the National Chiao-Tung University, Hsinchu, Taiwan, in , resectively. From 2009 to 200, he was also a visiting scholar in Tohoku University, Sendai, Jaan. He was awarded the student travel grant from IEEE ICC His current research interests include cross-layer otimization, MAC rotocols design, radio resource management in wireless sensor networks, ad hoc networks, cognitive radio networks. Fumiyuki Adachi (M 79-SM 90-F 00 received the B.S. Dr. Eng degrees in electrical engineering from Tohoku University, Sendai, Jaan, in , resectively. In Aril 973, he joined the Electrical Communications Laboratories of Nion Telegrah & Telehone Cororation (now NTT conducted various tyes of research related to digital cellular mobile communications. From July 992 to December 999, he was with NTT Mobile Communications Network, Inc. (now NTT DoCoMo, Inc., where he lead a research grou on wideb/broadb CDMA wireless access for IMT-2000 beyond. Since January 2000, he has been with Tohoku University, Sendai, Jaan, where he is a Professor of Electrical Communication Engineering at the Graduate School of Engineering. His research interests are in CDMA wireless access techniques, equalization, transmit/receive antenna diversity, MIMO, adative transmission, channel coding, with articular alication to broadb wireless communications systems.

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