Enhancing the Reliability of Cognitive Radio Networks via Channel Assignment: Risk Analysis and Redundancy Allocation

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1 Enhancng the Relablty of Cogntve Rado Networks va Channel Assgnment: Rsk Analyss Redundancy Allocaton Husheng L Ljun Qan Abstract-A key challenge n cogntve rado networks s the unrelablty of cogntve rado lnks due to the nterruptons from prmary users. To enable relable data transmsson over cogntve rado networks the large avalable bwdth obtaned from cogntve rado can be used to mprove the system redundancy n order to guarantee the system relablty. Usng the termnology n the theory of optmal relablty desgn n ndustral engneerng a sngle path data flow can be consdered as a parallel-seres system n whch each cut set represents a secondary user contans several assgned channels. A heurstc algorthm s proposed to assgn the channels n the lcensed spectrum b to dfferent cut sets n the parallel-seres system to mnmze the overall rsk. By adoptng the concept of cut set hazard the algorthm s appled n both sngle path multple path stuatons. t s also extended to the decentralzed scenaro. Channel reuse whch ncurs the correlaton of falures n the system s also consdered for the channel assgnment. Smulaton shows that the proposed algorthms can sgnfcantly mprove the relablty of cogntve rado networks.. NTRODUCTON n the prevous decade cogntve rado [11] has caused a paradgm shft n the area of wreless communcatons. t mproves the effcency of spectrum utlzaton provdes much more bwdth for developng wreless communcaton systems. Meanwhle t also brng a severe challenge.e. the nterruptons] from prmary users who have lcense to the spectrum snce secondary users who have no lcense must yeld to prmary users once prmary users begn to transmt over the lcensed spectrum. Such nterruptons are tolerable n elastc data traffc among secondary users snce the secondary users can wat untl the prmary users leave or look for new avalable channels. However for realtme data traffcs lke vdeo streamng or delay-senstve sensor reports such nterruptons may cause sgnfcant delay or jtter thus makng cogntve rado unsutable for a wde range of applcatons. Many current studes on cogntve rado are focused on how to detect the emergence of prmary users.e. spectrum sensng [12] [16]. Other studes deal wth the resource allocaton after the spectrum holes have been located [6] [8] [14]. Although some researches dscussed the mpact of the nterruptons from prmary users e.g. the queung analyss for secondary H. L s wth the Department of Electrcal Engneerng Computer Scence the Unversty of Tennessee Knoxvlle TN (emal: husheng@eecs.utk.edu). L. Qan s the wth the Department of Electrcal Engneerng Prare Vew A&M Unversty Houston TX (emal: lqan@pvamu.edu). Ths work was supported by the Natonal Scence Foundaton under grants CCF ECCS 'The termnology 'ntetl!pton' s from the queung theory /1U/$26.0(J 2010 EEE Node A Node B Node C Fg. 1: An llustraton of the parallel-seral structure for redundancy allocaton. users subject to the rom arrval of prmary users [13] algorthms combatng the prmary users e.g. the protocol to reorganze the network after the current data traffc s dsrupted by emergng prmary users [10] no study has been done from the vewpont of explctly enhancng the relablty of data traffcs n cogntve rado networks to the authors' best knowledge. n ths paper we study the relablty of cogntve rado networks from the vewpont ofrelablty engneerng [2J [7J whch has been extensvely studed n ndustral engneerng. We can consder each secondary user as a stage n a ppelne of a manufacturng system each channel n the spectrum as a redundant component the arrval of prmary users as the falures of channels whch the prmary users use. Then the technques developed n relablty engneerng can be leveraged to enhance the relablty of cogntve rado networks. t s well known that an effectve way to mprove the relablty ofa complex system s to allocate more redundancy for each stage ofthe system e.g. assgnng more than one parallel computers to compute for the control of an arcraft. Therefore we can allocate redundances.e. multple channels to dfferent secondary users for ncreasng the relablty of each secondary user. The avalablty of suffcent channels s justfed by the large bwdth brought by cogntve rado. An example s shown n Fg. 1 n whch the data flow passes through three secondary users A B C. Suppose that there are totally 9 channels. Each secondary user can sense three channels but can transmt over only one channel-. Then we assgn three channels to each secondary user such that each secondary user s able to transmt f one or more channel assgned to t s not nterrupted by prmary users. Then the path of the data flow forms a parallel-seres system ts relablty s sgnfcantly mproved. For example f the probablty that each channel s not nterrupted by prmary 2Ths assumpton s reasonable snce sensng s easer than transmttng.

2 2 users s 0.9 the nterruptons for dfferent channels are ndependent t s easy to verfy that the probablty that the data flow s blocked by prmary users s 0.3% whle t s 27% f each secondary user s equpped wth only one channel. Then the major problem studed n ths paper s how to allocate dfferent channels to dfferent secondary users to obtan a hgh relablty of cogntve rado networks how to analyze the correspondng rsks of traffc dsrupton. A straghtforward copy paste of the technques developed n tradtonal relablty engneerng does not work due to a challenge unque for wreless networks.e Channel Reuse: When two secondary users are far away from each other the same channel can be reused by both secondary users. Ths s mpossble n tradtonal relablty engneerng snce the same part cannot be used at two dfferent locatons smultaneously. Other challenges whch are dffcult to address although not unque to cogntve rado networks nclude Locaton dependency: the falure rate of a channel may be dfferent at dfferent secondary users snce the spectrum actvtes may be dfferent at dfferent locatons. Multple data flows: when there are multple data flows the system s no longer a smple parallel-seres one. Note that the problem of channel assgnment n ths paper s dfferent from other studes on the channel assgnment for cogntve rado networks [3] [9] [15]. n those studes the number of channels assgned to each secondary user s no more than the number of channels t can use for transmsson. Therefore the goal of channel assgnment n those studes s to mprove the effcency nstead of mprovng the relablty. The remander of ths paper s organzed as follows. The system model problem formulaton are gven n Secton. The redundancy allocaton for a sngle path wthout channel reuse s studed n Secton. Then the proposed algorthm s extended to Secton V. The numercal results conclusons are gven n Sectons V V respectvely.. SYSTEM MODEL We consder N secondary users wthn a cogntve rado network. There are M channels wthn the lcensed b. Each secondary user can sense Q channels smultaneously (1 < Q «M) but can transmt over only one channel". The avalabltes of dfferent channels are determned by the actvtes of prmary users. f a channel s occuped by prmary users the correspondng secondary user cannot transmt over t. For smplcty we assume that the occupances at dfferent channels are mutually ndependent. n practcal systems the channel occupances could be correlated. As wll be seen later the channel occupancy correlaton can ncrease the relablty. We denote by rkn the probablty that channel k s not occuped at secondary user n. We assume that each secondary user s assgned a set of channels. The set s denoted by nn for secondary user n. Obvously nn ~ Q.e the number of assgned channels should be no larger than the number of channels that a secondary user can sense smultaneously. For smplcty we 3t s easy to extend to the generc case that each secondary user can transmt over two or more channels assume that the channel avalablty probabltes are perfectly known to all secondary users. Ths knowledge can be obtaned from a long-term learnng of the envronment. Due to the nterference among secondary users two secondary users may not be able to transmt smultaneously f they are close to each other. Such a constrant s denoted by a conflct matrx C n whch C j == 1 f secondary users j cannot share the same channel C j == 0 otherwse.. REDUNDANCY ALLOCATON FOR SNGLE PATH n ths secton we assume that all the N secondary users are on the path of a sngle data flow. Moreover we assume that the secondary users are all close to each other such that the channel cannot be reused. We frst analyze the rsk of the data flow.e. the probablty that the path s blocked by emergng prmary users. Then we study the channel assgnment for redundancy allocaton. For smplcty we assume that NQ ~ M.e each secondary user can be assgned Q channels. Therefore we should assgn Q channels to each secondary user whch mples nnl == Q \n == 1... N. We can further assume that NQ == M snce we can choose the N Q most relable channels for the redundancy allocaton. A. Rsk Analyss Obvously when the channel assgnment s gven by nn}n=looon' the correspondng rsk s gven by R ({On}n=l... N) = 1 ~ f (1 - (1 - rkn )). (1) n=l keo n Next we rewrte (1) for facltatng the analyss. n the parallel-seres structure as llustrated n Fg. 1 there are totally N Q locatons. The set of locaton ndces belongng to secondary user n whch can also be consdered as a cut set n the graph s denoted by Cn. We denote by X n m the assgnment of channel m to locaton n m == 1... M n == 1... N Q. When channel m s assgned to locaton n X m n == 1; otherwse X m n == O. Then the channel assgnment can be represented by a vector x whch s gven by where x == (X...XM X21... X2M... XN... XNM). (2) (1) can be rewrtten as N R (x) == 1 - (1 - e- Z n ) n=l M Zn == L L SmXm EC n m=l Sm == -log (1 - r n m ) n lteratures of relablty desgn [7] Zn s called the cut set hazard of cut set Cn. (3) (4) (5)

3 3 B. Channel Assgnment: Centralzed Case The optmal channel assgnment should mnmze the rsk n (3) subject to the followng constrants: M LXj == 1 j=l NQ LXj == 1 =l == 1...NQ j == 1... M where (6) means that each locaton s assgned one channel whle (7) means that each channel can be assgned once due to the assumpton of on channel reuse. For the general case the problem of mnmzng the rsk s an NP-complete problem [7]. Under the assumpton that the probabltes {rnm} are ndependent of the locatons wthn a cut set en the channel assgnment has been studed n [1] [4] [5]. A heurstc approach called top-down heurstc (TDH) has been proposed n [1]. The optmal assgnment s found for the case of Q == 2.e. each cut set has only two locatons n [4]. n [5] t has been shown that f the cut set hazards Zl... ZN are all the same n an allocaton then the allocaton mnmzes the rsk of the parallel-seres system. The concluson n [5] provdes us an nsght.e. the homogenety of the cut set hazards can mprove the relablty of the system. Motvated by the concluson n [5] we propose a heurstc algorthm wth a mnmax flavor to decrease the rsk. The key prncple s to assgn the channels n a sequental way let the secondary user havng the hghest cut set hazard have the hghest prorty to get a new channel. The detal of the algorthm s gven n Procedure 1. Note that the procedure s centralzed whch requres a control center. Procedure 1 Centralzed Procedure of Channel Assgnment for Sngle-path Data Flow wthout Channel Reuse 1: ntalze the channel sets On n == 1... N to be empty. 2: ntalze the resdual channel set S == {... M. 3: for Secondary users n n == 1... N do 4: Choose the channel m havng the hghest r n rn n the resdual 5: Assgn channel m to secondary user n.e. add m to On. 6: Remove m from the resdual 7: end for 8: Compute the cut set hazards for all secondary users. 9: for The resdual channel set S s nonempty do 10: Choose the secondary user n havng the hghest cut set hazards On < Q. 11: Choose the channel m havng the hghest r n.rr n the resdual 12: Assgn channel m to secondary user n.e. add m to On. 13: Remove m from the resdual 14: Update the cut set hazard for secondary user n. 15: end for (6) (7) t s easy to extend the centralzed algorthm n Procedure 1 to decentralzed case. The key procedure s: every secondary user broadcasts ts current cut set hazard; the most unrelable secondary user chooses a channel then broadcast the channel [D. The detaled procedure s gven n Procedure 2. Procedure 2 Decentralzed Procedure of Channel Assgnment for Sngle-path Data Flow wthout Channel Reuse 1: ntalze the channel sets On n == 1... N to be empty. 2: ntalze the resdual channel set S == {... M. 3: for Secondary users n n == 1... N do 4: Choose the channel m havng the hghest r n.rr n the resdual 5: Broadcast the D of channel m add m to On. 6: Every secondary user removes m from the resdual channel set S upon the recept of the broadcast. 7: end for 8: Each secondary user computes ts cut set hazard. 9: for The resdual channel set S s nonempty do 10: Every secondary user broadcasts ts current cut set hazard f ts channel set On s not full. 11: The most unrelable secondary user say n chooses the channel m havng the hghest r n.rr n the resdual channel set S. 12: Broadcast the D of channel m add m to On. 13: Update the cut set hazard for secondary user n. 14: end for V. REDUNDANCY ALLOCATON FOR MULTPLE PATHS n ths secton we study the redundancy allocaton for multple data traffc paths. Agan we assume that there s no channel reuse. Each channel can be used only once. For smplcty we assume that there are two paths A B. The analyss can be straghtforwardly extended to the general case of more paths. We denote by N A N B the sets of secondary users belongng to path A path B respectvely. A. Rsk Analyss Snce there are two paths we consder the followng rsk defned as where R -WA log P(path A s not blocked) WB log P(path B s not blocked) where WA WB are weghtng factors balancng the mportance of the two paths. Usng the same defnton of the allocaton vector x == (Xl... XM) t s easy to verfy that the rsk can be rewrtten as exp (R (x)) == 1 - (1 - e- Zn ) N n=l (8) (9) C. Channel Assgnment: Decentralzed Case Snce the computaton of the cut set hazard only requres local nformaton about the relabltes of dfferent channels where N B (10) f n E N A n ~ f n E N B n ~ N A (11) f n E N A nn B

4 4 reused channel M Y n = L L SmXm tee ; m =l Sm = - log (1 - r n m ) B. Channel Assgnment (12) (13) Due to the equvalence of (3) (9) the algorthms n Proc edures (2) can stll be used n the multple path case. The only dfference s the changed defnton of cut set hazard n (10). A. Rsk Analy ss Parallel-seres system wth channel reuse Equvalent system Fg. 2: An example of the mpact of correlated falures. V. R ED UND A NCY A LLOCATON W TH CHAN NEL R EUSE n ths secton we con sder the channel assgnment wth channel reuse. Obvously channel reuse may ncur dependency among the channel falures. We wll frst analyze the mpact of dependency on the system rsk. Then we dscuss the correspondng channel assgnment algorthm. For smplcty we consder only a sngle path. The multple path case can be extended smlarly to Secton V. n prevous sectons we assume that each channel can be assgned to only one secondary user. Th s s reasonable for small sze cogntve rado networks. However for a large cogntve rado network such a unque channel assgnment cannot be satsfed even though cogntve rado can prov de many aval able channels. Therefore channel reuse should be consdered when the network sze s large. Typcally the conflct rang e of secondary user s s smaller than the nterrupton range of prmary users. Then we have the followng rule s f two secondary users are wthn the confl ct range denoted by de.e. G j = 1 for secondary users j they cannot use the same channel. f two secondary users are out of the confl ct range de ( G j=o) but wthn the nterrupton range d these two secondary users can use the same channel; however the spectrum occupances of the channel are the same at the two secondary users. f two secondary users are out of the nterrupton range d ths channel can be consdered as two ndependent channels at the two secondary users. Now we con sder the mpact of the correlaton of falure f two secondary users employ the same channel wth n the nterrupton range d. Suppose two secondary users 2 along the path are assgned channels [21 = {l k 1... kq-d [22 = {l ml... mq-d respectvely. The only common channel s channel. Then the parallel-seres system can be equalzed as the system n Fg. 2. Obvously the system rel ablty s mproved snce a parallel path s establshed. The detaled analyss s gven below: f consderng channel as two ndependent channels at the two secondary users the system rsk s gven by (suppose that there are only two secondary users along the path ; for smplcty we assume that the channel falure probablty s ndependent of the locatons) R' x 1-(1-U(1- r)) (1 -!1(1 -r)) n (1 - rk) + n (1 - rk ) kerl! kerl 2 n (1 - rk) n (1 - rk). k Erl! k Erl2 R l - r 1-(1 - r 1)( - n (l - r k ) ) k Erl! k # l x (-Jl "(1 - r ) n (1 - rk ) + n (1 - rk) kerl! k Erl2 TkErl! (1 - rk) [1k Erl 2 (1 - rk) 1 - rl Then the dfference of the rsk s gven by (14) When chann el at the two secondary users has the same spectrum occupancy the system rsk s gven by ( 15) whch s postve snce rl < 1. The relatve dfference s gven

5 5 by 0.9 R' -R R' --- (1 - rk) Tk Ell2 (1 - rk) R'(1 - r ) r Tk Ell t (1 - rk) T k Ell 2 (1 - rk) (1 - r) (Tk Ellt (1 - rk) + Tk Ell2 (1 - rk)) r Tk Ell t (1 - rk) Tk Ell2 (1 - rk) (1 - r l ) mn {T k Ellt (1 - rk) T k Ell2 (1 - rk)} 0.7 r Tk Ell t < U U 0.4 -" ntellgent assgn Rm;n=0.9 :' ntellgent assgn Rm;n=0.95.f 0.1 rl max { T k Ellt k"" l (1 - rk) T (1 - rk) }(17)./.""' ~ """ rom assgn Rm;n=0.9.. rom assgn Rm;n=0.95 2~ Obvously when all channels are reasonably relable.e. 5 x ~ rsk kell2k""l Fg. 3: CDF curves of rsks n a sngle path. rk s close to 1 for each k the relatve reducton of rsk (R' - R) / R' s very small due to (17). For example when = r2 = r 3 = 0.9 (n = 3) the relatve reducton of rsk s less than 0.9%. Therefore although the dependency of the channel falure can reduce the rsk the relatve change s almost neglgble whch mples that we can gnore the dependency consder the correlated falures of the same channel as ndependent. Note that ths concluson s vald for only the smple case. When there are many nodes along the path many channels can be reused as wll be demonstrated n numercal smulatons the relablty wll be sgnfcantly mproved compared wth the case of no channel reuse. B. Channel Assgnment Then we extend the algorthm n (1 to the channel reuse case. Procedure 3 Centralzed Procedure of Channel Assgnment for Sngle-path Data Flow wth Channel Reuse : ntalze the channel sets [ n n = 1... N to be empty. 2: For each secondary user n set the resdual channel set S n n = 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: S: 1...N. for Secondary users n n = 1... N do Choose the channel m havng the hghest r n m n the resdual Assgn channel m to secondary user n.e add m to [ n. Remove m from the resdual channel set Sk f Cn k = 1. end for Compute the cut set hazards for all secondary users. for The resdual channel set S s nonempty do Choose the secondary user n havng the hghest cut set hazards l[ln < Q. Choose the channel m havng the hghest T n m n the resdual channel set S. Assgn channel m to secondary user n.e. add m to [n. Remove m from the resdual channel set S» f Cnk = 1. Update the cut set hazard for secondary user n. end for.' C'\....~ ' rl #..::.~" 0.9 t.' (. e. U- S 0.5 " ; 0.4 r' "" 0.7 _ ntellg ent assgn R. =0.9 ntellg ent assgn Rmn=0.95 nun ''' '' ' r om assgn Rm;n=0.9 '.. rom assgn Rm;n=0.95./ varance of cut set hazard Fg. 4: CDF curves of the varances of cut set hazards n a sngle path. A. Sngle Path wthout Channel Reuse We frst consder the sngle path case. We assume that N = 10.e. there are 10 secondary users along the path Q = 3.e. each secondary user s equpped wth three channels. The relabltes of the channels are generated unformly wthn [R m n 1]. We set R m n to n two sets of smulatons. The CDF curves of the rsks obtaned from the algorthm n Procedure 1 (marked as 'ntellgent assgnment') from rom channel assgnment are plotted n Fg. 3. We observe that the proposed algorthm of channel assgnment sgnfcantly mproves the network relablty. We also plotted the CDF curves of the varances of cut set hazards n Fg. 4 (the varance s for the cut set hazards wthn the same realzaton of channels). We observe that the varances are much smaller when the proposed algorthm s adopted than those of the rom channel assgnment. B. Multple Paths wthout Channel Reuse V. NUMERCAL RESULTS n ths secton we use numercal smulatons to demonstrate the performance of the proposed algorthms. Each result s obtaned from 1000 realzatons of the falure probabltes of dfferent channels. For the two path case we assume W A = 1 W B = 2. Each path has 10 nodes. There s one common node for the two paths. Other setups are the same as those n Fg. 3. The CDF curves of the correspondng rsks defned n (8) are plotted n Fg. 5. Agan we observe the sgnfcant performance gan

6 6 sngle path case to multple paths as well as the scenaros n whch channel can be reused. Numercal smulatons have demonstrated the mprovement of relablty ncurred by the channel assgnment redundancy allocatons R E F ER ENC ES u 00.5 U [) L. A. Baxter F. Harche "On the optm al assumbly of seres-parallel 0.4 " "" '"' " ntellgent assgn R. =0.9 ntellgent assgn R::~ =0.95 rom assgn Rmn=0.9 rom assgn Rmn= Fg. 5: CDF curves of rsks n multple paths. 1'0 _»r.-". ". 0.7 u.c'':"..'" _. :~ 0.9 '! 80.5 _f 0.4 -" """ '.. _ f 0.1 : ntellgent assgn R. =0.9 ntellgent assgn R::~=0.95 rom assgn Rmn =0.9 rom assgn Rmn = rsk Fg. 6: CDF curves of rsks n a sngle path wth channel reuse. of the proposed algorthm wth the defnton of cut set hazard n (10). C. Sngle Path wth Channel Reuse Now we consder the case n whch the there s a sngle path wth ten nodes the channels can be reused. We assume that nodes that are wthn two hops (ncludng two hops) from each other cannot transmt over the same channel. All other confguratons are the same as those n Fg. 3. The CDF curves of rsks are shown n Fg. 6. We observe that the channel reuse can mprove the path relablty compared wth Fg. 3. V. CONCLUSONS t s challengng to transmt realtme data over cogmnve rado networks due to the nterruptons from prmary users. We have dscussed how to use the large bwdth brought by cogntve rado to mprove the relablty of cogntve rado networks thus enablng many applcatons wth realtme data transmsson. The key prncple s to allocate redundancy.e. more channels than that a secondary user can use for transmsson to each secondary user. We have appled the theory of relablty desgn n ndustral engneerng. A heurstc algorthm has been proposed to assgn channels based on the concept of cut set hazard whch has been extended from systems " Operatons Research Letters vol.ll pp [2] T. Bedford R. Cooke Probablstc Rsk Analyss : Foundatons Methods Cambrdge Unversty Press [3] K. Ban J. Park "Segment based channel assgnment n cogn tve rado ad hoc networks " n Proc. of Cogntve Rado Orented Wreless Networks Communcatons (CrownCom) [4] C. Derman G 1. Leberman S. M. Ross "On optm al assembly of systems" Naval Research Logstcs Quarterly vo1.21 pp [5] E. E-Neweh F. Proschan J. Sethur aman "Optmal allocaton of components n parallel-seres systems" Journal of Appled Probablty vo1.23 pp [6] E. Hossan D. Nyato Z. Han Dynamc Spectrum Access n Cogntve Rado Networks. Cambrdge Unversty Press UK [7] W. Kuo V. R. Prasad F. A. Tllman C. Hwang Optmal Relablty Desgn: Fundamentals Applcatons Cambrdge Unversty Press [8] L. B. Le E. Hossan "Resource allocaton for spectrum underlay n cogntve rado networks " EEE Trans. Wreless Communcatons vol. 7 pp Dec [9] X. L S. A. Zekayat "Dstrbuted channel assgnment n cogntve rado networks " n Proc. of nternatonal Conference on Wreless Communcatons Moble Computng [10] X. Lu Z. Dng "ESCAPE: A channel evacuaton protocol for spectrum-agle networks " n Proc. of EEE Symposum on New Fronters n Dynamc Spectrum Access Networks (DySPAN) [11] J. Mtola "Cogntve rado for flexble moble multmed a communcatons" n Proc. EEE nt. Workshop Moble Multmeda Communcatons pp [12] A. Saha R. Tra M. Mshra N. Hoven "Fundamental desgn tradeo ffs n cognt ve rado systems " ACMoog TAPAS Aug [13] S. Tang B. L. Mark "Analyss of opportunstc spectrum sharng wth Markovan arrvals phase-type servce " EEE Trans. Wreless Commun. to appear. [14] D. Xu E. Jung X. Lu "Opt mal bwdth selecton n multchannel cogn tve rado networks : How much s too much?" n Proc. of EEE nternatonal Symposum of New Fronters n Dynamc Spectrum Access Networks (DySPAN) [15] C. Xn L. Ma CoCo Shen "A path-centrc channel assgnment framework for cogntve rado wreless networks " Moble Networks Applcatons (Kluwer) vol. 13 pp Oct [16] Q. Zhao A. Swam "A decson-theoretc framework for opportunstc spectrum access" EEE Wreless Communcatons Magazne vol. 14 pp Aug