Target Channel Visiting Order Design Using Particle Swarm Optimization for Spectrum Handoff in Cognitive Radio Networks

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1 Algorthms 204, 7, ; do:0.3390/a Artcle OPEN ACCESS algorthms ISSN Target Channel Vstng Order Desgn Usng Partcle Swarm Optmzaton for Spectrum Handoff n Cognte Rado Networs Shlan Zheng,2, *, Zhjn Zhao 3, Changln Luo 4 and Xaonu Yang, Scence and Technology on Communcaton Informaton Securty Control Laboratory, Jaxng 34033, Chna; E-Mal: xaonyang@26.com School of Telecommuncatons Engneerng, Xdan Unersty, X an 7007, Chna School of Telecommuncatons Engneerng, Hangzhou Danz Unersty, Hangzhou 3008, Chna; E-Mal: zhaozj03@hdu.edu.cn Nanhu School, Jaxng Unersty, Jaxng 3400, Chna; E-Mal: luochangln@gmal.com * Author to whom correspondence should be addressed; E-Mal: lanshzheng@26.com; Tel.: Receed: 29 March 204; n resed form: 29 July 204 / Accepted: 8 August 204 / Publshed: 8 August 204 Abstract: In a dynamc spectrum access networ, when a prmary user (lcensed user) reappears on the current channel, cognte rados (CRs) need to acate the channel and reestablsh a communcatons ln on some other channel to aod nterference to prmary users, resultng n spectrum handoff. Ths paper studes the problem of desgnng target channel stng order for spectrum handoff to mnmze expected spectrum handoff delay. A partcle swarm optmzaton (PSO) based algorthm s proposed to sole the problem. Smulaton results show that the proposed algorthm performs far better than random target channel stng scheme. The solutons obtaned by PSO are ery close to the optmal soluton whch further aldates the effecteness of the proposed method. Keywords: partcle swarm optmzaton; cognte rado; spectrum handoff; target channel. Introducton Spectrum s generally regulated by goernments a a command and control approach. Howeer, ths approach has led to underutlzaton of a spectrum n ast temporal and geographc dmensons as

2 Algorthms 204, 7 49 shown n the surey made by the Federal Communcatons Commsson (FCC) []. Motated by ths obseraton, cognte rado (CR) has been proposed to mproe spectrum utlzaton by dynamcally accessng spectrum whte spaces (.e., spectrum holes) wthout causng harmful nterference to prmary users [2]. In ths dynamc spectrum access framewor, CRs are consdered as secondary users (SUs) of the spectrum. When a prmary user (lcensed user) reappears on the current channel, the CRs need to acate the channel and reestablsh a communcatons ln on some other channel to aod nterference to prmary users. Ths process s referred to as spectrum handoff [3]. Target channels play an mportant role n spectrum handoff desgn because target channels are the hopes that SUs can resume ther unfnshed transmssons. Based on the decson tmng for selectng target channels for spectrum handoff, the target channel selecton approaches can be categorzed nto two nds: on-demand channel selecton for reacte-decson spectrum handoff and predetermned channel selecton for proacte-decson spectrum handoff [4]. On-demand channel selecton searches target channels after spectrum handoff [5 7]. Ths may result n long spectrum handoff delay because an aalable channel needs to be searched n a wde frequency range. Predetermned channel selecton determnes target channels before spectrum handoff based on the long-term hstory nformaton on channel status. It can sae spectrum sensng tme. Ths paper focuses on predetermned channel selecton. Most pror wor on predetermned channel selecton selected a sngle target channel based on some objecte, for nstance, maxmum spectrum lfetme [8], maxmum resdual dle tme [9], maxmum dle probablty [0], and mnmum watng tme []. Howeer, n a dynamc spectrum enronment, as the pre-selected channel may no longer be aalable, relyng on a sngle target channel may result n low probablty of ln mantenance. A better mechansm s to select multple target channels and try each target channel sequentally. The stng order of these target channels s crucal to spectrum handoff. In our pror wor [2], we desgned a target channel stng order whch can realze the mnmum probablty of spectrum handoff falure. In ths paper, we consder spectrum handoff delay as the objecte for target channel stng order desgn. We propose to use partcle swarm optmzaton (PSO) to sole ths combnatoral problem. PSO s an ntellgent bo-nspred optmzaton algorthm that has shown ts effecteness for spectrum sensng, spectrum allocaton and ln adaptaton n cognte rado n our pror wor [3 5]. To the best of our nowledge, ths paper apples PSO for target channel stng order desgn for spectrum handoff for the frst tme. Smulatons are conducted to aldate the effecteness of the proposed PSO based algorthm n determnng the target channel stng order n ths paper. The rest of the paper s organzed as follows. In Secton 2, we formulate the target channel stng order desgn problem for spectrum handoff as a combnatoral optmzaton problem whch ams to mnmze spectrum handoff delay. In Secton 3, we propose PSO for solng the problem. In Secton 4, smulaton results are proded and fnally n Secton 5, conclusons are made. 2. Problem Formulaton We consder a smlar system model as we formulated n [2]. Specfcally, we consder two cognte rados n a cognte rado networ communcatng wth each other. They operate on the same frequency range whch conssts of N channels. Durng communcatons, the two rados exchange the channel state nformaton so common acant channels are nown to both rados. We

3 Algorthms 204, denote M current acant channels (except the current operatng channel) as c,2,..., }} M N =, M N. If a prmary user appears on the current channel, the two cognte rados would ntate spectrum handoff and swtch to another acant channel for data transmsson. A proacte-sensng spectrum handoff s assumed where the target channels for spectrum handoff are ready before ntatng the spectrum handoff process [6]. In ths paper, c,2,..., }} M N = are used as target channels for spectrum handoff. Before spectrum handoff, the stng order of these target channels needs to be determned to optmze some objecte. Denote the ector correspondng to the stng order as = [, 2,..., M ], then the process of spectrum handoff can be llustrated as n Fgure. When handshae on a partcular channel s successful, spectrum handoff s completed successfully and a new ln s mantaned on ths channel. Howeer, n a dynamc spectrum enronment, as prmary users may reoccupy the stng target channel durng spectrum handoff, handshae may stll fal. When CRs try out all the channels and all handshaes fal, then spectrum handoff s faled. Fgure. Handshae process for spectrum handoff. CR A T Handshae on 2 Handshae on 3 T CR B T h... Handshae on Handshae Denote ρ as the probablty that the handshae on s successful, then the probablty of spectrum handoff falure s P fal M ( ρ ) () = = An mportant metrc for ealuatng spectrum handoff s spectrum handoff delay. If spectrum handoff s successful, then the handoff delay s Tl, where l s the number of handshaes tll success. If spectrum handoff s faled, then some other rendezous scheme needs to be performed to mantan communcatons. We assume the rendezous tme s τ. So the handoff delay when spectrum handoff s faled s MT + τ. The expected handoff delay s M ( τ) ( ) ( τ) ( ) E[] t = LT Pr l = L} + MT + P = Tp + Tp p + MT + p (2) fal L= = 2 = = Denote the set of ectors correspondng to all permutatons of all elements n c } M = as Ω, then n order to mnmze spectrum handoff delay, the problem of target channel stng order desgn for spectrum handoff can be represented as * M = arg mn Et [ ] Ω M (3)

4 Algorthms 204, 7 42 Note that ρ depends on the specfc dstrbuton of channel remanng acant. In ths paper, we consder fe dstrbutons: Unform, Exponental [7], Generalzed Pareto [8], Raylegh [9], and Webull [9]. As n [7], we do not consder the case where the channel state changes twce or more because the probablty s too low wthn the relately short duraton. The probablty densty functons (PDFs) and the correspondng expressons of ρ are shown n Table. For unform dstrbuton, the probablty that the handshae on s faled equals to the probablty that the state of channel changes to occuped before the end of ths handshae, whch s + ( ) T + Th / bdx=, ( ) T+ T< b b ( ) T Th 0 ρ = +, ( ) T T b (4) Equaton (4) can be further smplfed as ( ) T + T h ρ = mn, b Other expressons of ρ can be obtaned smlarly. (5) Table. Dstrbutons of the tme duraton durng whch a channel remans acant. Dstrbuton PDF ρ / b, 0< x< b ( ) T + T h Unform ( b > 0 ) f( x) = mn, 0, else. b x λ, 0 Exponental ( λ > 0 ) f( x) e λ x > = exp ( λ (( ) T + T )) h 0, else. Generalzed Pareto ( σ > 0, 0 ) Raylegh ( σ > 0 ) Webull ( λ > 0, α > 0 ) / x / +, x> 0 f( x) σ σ ( ) T + T h = + σ 0, else 2 2 x x /2σ, 0 2 e x > 2 (( ) T + T ) f( x) = σ h exp 2 2σ 0, else, 0 ( ) x e α α λ x αλ x > f x = 0, else ( λ T + T α h ) exp (( ) ) 3. Proposed Target Channel Vstng Order Desgn Algorthm The optmal soluton for combnatoral optmzaton problem (3) s hard to deduct. In ths paper, we propose to use PSO for solng ths problem.

5 Algorthms 204, Introducton of PSO PSO s a bo-nspred optmzaton method whch s nspred by obserng the brd floc [20]. In PSO, each soluton s a brd n the swarm and s referred to as a partcle. In order to sole optmzaton problems n a dscrete number space, Kennedy and Eberhart [2] deeloped a dscrete bnary erson of PSO, whch s the focus of ths paper. To begn wth the teraton, a swarm wth S partcles s ntalzed. Let x [, 2,..., = x x xd] denote the poston of partcle ( S ) at teraton, where D s the number of dmensons to represent a partcle. x d taes bnary alues from 0,}. The elocty of partcle at teraton s denoted as [, 2,..., y = y y yd], y d R. Each partcle n the swarm s assgned a ftness alue ndcatng how good t s for an optmzaton objecte. We use p [, 2,... = p p pd] and p [, 2,..., g = pg pg pgd] to denote the best soluton that partcle and the whole swarm hae obtaned untl teraton, respectely. At each teraton, each partcle adjusts ts elocty accordng to ts last elocty, ts dstance to the best soluton t has obtaned and ts dstance to the best soluton of the swarm. The elocty of the partcle s updated as follows: yd = y d + ξ r( p d x d ) + ξ2r2( p gd x d ) (6) where ξ and ξ 2 are two poste constants, r and r 2 are random numbers unformly chosen from the range [0,]. Furthermore, the elocty s transformed to a alue n the range [0,] by usng the followng sgmod functon: sg( yd ) = (7) + exp( y ) d where sg( y ) denotes the probablty of d x tang. Accordng to sg( y ), d d x d can be updated as: x t d, f r < sg( yd ) = (8) 0, else where r s a random number unformly dstrbuted n [0,]. In the dscrete PSO, a maxmum elocty V max s used to aod sg( y ) approachng 0 or,.e., y [ Vmax, + Vmax ]. d 3.2. Proposed PSO Based Algorthm for Target Channel Vstng Order Desgn The frst step to use PSO for solng problem (3) s to map the partcle to a possble soluton. As the poston of a partcle contans bnary bts whle the stng order taes decmal alues, we need to conert these bnary bts to decmal ntegers or the way around. Fgure 2a shows the mappng process. We need B = log 2 M bts to represent a alue n [, M ], where a denotes the closest nteger whch s greater than a. In consequence, the number of bts n a partcle poston s MB= M log 2 M. Consecute B bts n the poston represent a channel ndex. For nstance, 000 represents channel c, 00 represents channel c 2, and so on. Fgure 2b llustrates an example. d

6 Algorthms 204, Fgure 2. Mappng the poston to the soluton. (a) General representaton. (b) An example where M = 6 and B= log2 M = 3. x L x B x ( B+ ) L x (2 B ) L x ( D B+ ) = [ ],,..., M (a) 2 L x D c4 c c5 c3 c2 c6 = [ c, c, c, c, c, c ] (b) The ntal swarm s generated randomly to mantan a unform dstrbuton of these partcles on the search space. Mappng a randomly generated poston to a specfc may result n a soluton whch contans repeated channels. As a same target channel wll not be sted twce or more n spectrum handoff, we propose the followng procedure to ensure that a soluton s ald. For poston x [, 2,..., = x x xd], we conert t to decmal ntegers and denote the resultng ector as z [, 2,..., = z z zm]. Update z by computng z [ mod, 2mod,..., = z M z M zm mod M], where amod M computes the remnder obtaned after a s dded by M. Store all dstnct alues n z on a set Ω. Denote = [0,,2,..., M ]. If the number of elements n Ω s smaller than M, we repeat the followng two steps to mae z ald: (a) For any two elements n z whch are dentcal, randomly choose one of them and replace t wth a alue (denoted by λ ) randomly chosen from the set Θ= Ω; (b) update Ω by addng λ nto the set. The aboe procedure s repeated when all elements n z are dstnct. After the aboe procedure, [, 2,..., = x x xd] z s conerted bac to bnary strng and x s replaced by ths strng. For smplcty, we refer to ths procedure as poston correcton n the rest of the paper. Fg.3 shows an example of poston correcton. Fgure 3. An example of poston correcton where M =

7 Algorthms 204, After ntalzaton, the ftness of each partcle s ealuated. We use the opposte of handoff delay (2) for ftness functon. After ftness ealuaton, the elocty and the poston are updated by (6) and (8) and a new swarm of partcle s obtaned. Note that we also need to use the procedure of poston correcton dscussed preously to mae all postons ald. The teraton contnues untl the maxmum number of teratons s reached. The proposed algorthm s shown n Table 2. Table 2. Proposed algorthm for target channel stng order. Steps Procedures Swarm ntalzaton. Set = 0, and randomly generate x d and y d, where xd 0,}, y [ V, + V ], and S. Apply poston correcton procedure to all partcles n the d max max swarm. 2 Ftness ealuaton. Compute the ftness alue of each partcle accordng to (2). Set p [, 2,... = p p pd] and p [, 2,..., g = pg pg pgd], where g s the ndex of the partcle whch has the hghest ftness alue. 3 Velocty updatng. Set = +, and update the elocty of the partcle accordng to (6). If yd > Vmax, set yd = Vmax ; f yd < Vmax, set yd = Vmax. 4 Poston updatng. Update the poston of the partcle accordng to (7). Apply poston correcton procedure to all partcles n the swarm. 5 Ftness ealuaton. Compute the ftness alue of each partcle accordng to (2). For partcle, f t s ftness alue s greater than the ftness alue of p, then set p = x ; f t s ftness alue s greater than the ftness alue of p, then set p = x. g 6 Stop crtera ealuaton. If equals to the predefned maxmum teraton, the algorthm s termnated; otherwse, go to step Smulaton Results In the smulatons, we assume T = 40 ms, T h = 4 ms and T r = 400 ms. Eght target channels are consdered wth the mean acant tme duratons of 0 ms, 60 ms, 25 ms, 70 ms, 83 ms, 5 ms, 54 ms, and 55 ms, respectely. The parameters for PSO are as follows. Thrty habtats n a swarm are used. ξ = ξ =. V max = 4. Fgure 4 llustrates the conergence property of the algorthm. It can be obsered 2 2 that as the number of teratons ncreases, better solutons are obtaned. Note that we only plot results when tme duraton durng whch a channel remans acant follows Unform and Exponental dstrbutons. Smlar trends hae been obsered wth the other three dstrbutons. For smplcty, we omtted these results. Tables 3 and 4 show the performance of the proposed algorthm compared wth the other two target channel stng methods: the random target channel stng and the optmal target channel stng. Two cases are consdered respectely: (Case A) Nne target channels wth the mean acant tme duratons of 70 ms, 30 ms, 20 ms, 300 ms, 52 ms, 5 ms, 30 ms, 59 ms, ms, respectely, and (Case B) Eght target channels wth the mean acant tme duratons of 0 ms, 60 ms, 25 ms, 70 ms, 83 ms, 5 ms, 54 ms, and 55 ms, respectely. The optmal target channel stng order s obtaned by exhauste search. It can be seen that the proposed method performs far better than the random channel stng scheme. The solutons obtaned by the proposed algorthm are ery close to the optmal solutons. The small standard deaton alues also ndcate that the proposed scheme s qute stable. g

8 Algorthms 204, Fgure 4. Conergence property of the algorthm aeraged oer 00 ndependent experments. (a) Performance of the best partcle of the swarm (tme duraton durng whch a channel remans acant follows Unform dstrbuton). (b) Aerage performance of the whole swarm (tme duraton durng whch a channel remans acant follows Unform dstrbuton). (c) Performance of the best partcle of the swarm (tme duraton durng whch a channel remans acant follows Exponental dstrbuton). (d) Aerage performance of the whole swarm (tme duraton durng whch a channel remans acant follows Exponental dstrbuton). Mean delay (ms) Iteratons Mean delay (ms) Iteratons Mean delay (ms) Mean delay (ms) Iteratons Iteratons Table 3. Performance comparson (Case A). Note that Proposed0 and Proposed50 stands for Proposed algorthm wth 0 teratons and Proposed algorthm wth 50 teratons, respectely. Dstrbuton Unform Exponental Pareto Raylegh Webull Random Mean Optmal Proposed Proposed Standard Deaton Random Proposed Proposed

9 Algorthms 204, Table 4. Performance comparson (Case B). Note that Proposed0 and Proposed50 stands for Proposed algorthm wth 0 teratons and Proposed algorthm wth 50 teratons, respectely. Dstrbuton Unform Exponental Pareto Raylegh Webull Random Mean Optmal Proposed Proposed Standard Deaton Random Proposed Proposed Tables 3 and 4 show the performance of the proposed algorthm compared wth the other two target channel stng methods: the random target channel stng and the optmal target channel stng. Two cases are consdered respectely: (Case A) Nne target channels wth the mean acant tme duratons of 70 ms, 30 ms, 20 ms, 300 ms, 52 ms, 5 ms, 30 ms, 59 ms, ms, respectely, and (Case B) Eght target channels wth the mean acant tme duratons of 0 ms, 60 ms, 25 ms, 70 ms, 83 ms, 5 ms, 54 ms, and 55 ms, respectely. The optmal target channel stng order s obtaned by exhauste search. It can be seen that the proposed method performs far better than the random channel stng scheme. The solutons obtaned by the proposed algorthm are ery close to the optmal solutons. The small standard deaton alues also ndcate that the proposed scheme s qute stable. 5. Conclusons In ths paper, we hae nestgated the problem of desgnng target channel stng order for spectrum handoff to mnmze the expected spectrum handoff delay. We proposed dscrete PSO for solng ths combnatoral problem. Our results show that the proposed algorthm performs far better than random target channel stng scheme n terms of the obtaned mean handoff delay and the standard deaton of obtaned solutons. Another attracte result s that the solutons obtaned by our PSO based algorthm are ery close to the optmal solutons whch are obtaned by exhauste search. An nterestng future wor s to use some other bo-nspred optmzaton method such as cucoo search [22] and bat algorthm [23] to sole the problem. Acnowledgments The authors than the anonymous reewers for ther nsghtful comments. Author Contrbutons Xaonu Yang ntated the dea of ths research. Shlan Zheng formulated the optmzaton problem, proposed the procedure of the algorthm, and wrote the ntal manuscrpt, whch s crtcally reewed by Zhjn Zhao and Xaonu Yang. Zhjn Zhao also helped wth the PSO desgn. Changln Luo helped wth the Matlab codng and dd the smulatons.

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