Jont Channel Assgnment and Opportunstc Routng for Maxmzng Throughput n Cogntve Rado Networs Yang Qn*, Xaoxong Zhong*, Yuanyuan Yang +,Yanln L* and L L* *Key Laboratory of Networ Orented Intellgent Computaton, Shenzhen Graduate School, Harbn Insttute of Technology, Shenzhen, 58055, P. R. Chna + Department of Electrcal and Computer Engneerng, Stony Broo Unversty, Stony Broo, NY 79, USA Emal: {xxzhong, yqnsg, lyanln0}@gmal.com, yuanyuan.yang@stonybroo.edu, ll8503@alyun.com Abstract-In ths paper, we consder the jont opportunstc routng and channel assgnment problem n mult-channel mult-rado (MCMR) cogntve rado networs (CRNs) for mprovng aggregate throughput of the secondary users. We frst present the nonlnear programmng optmzaton model for ths jont problem, tang nto account the feature of CRNs-channel uncertanty. Then consderng the queue state of a node, we propose a new scheme to select proper forwardng canddates for opportunstc routng. Furthermore, a new algorthm for calculatng the forwardng probablty of any pacet at a node s proposed, whch s used to calculate how many pacets a forwarder should send, so that the duplcate transmsson can be reduced compared wth MAC-ndependent opportunstc routng & encodng (MORE) []. Our numercal results show that the proposed scheme performs sgnfcantly better that tradtonal routng and opportunstc routng n whch channel assgnment strategy s employed. Keywords-Opportunstc routng; CRNs; channel assgnment I. INTRODUCTION The cogntve rado prncple has ntroduced the dea to explot spectrum holes (.e., bands) whch result from the proven underutlzaton of the electromagnetc spectrum by modern wreless communcaton and broadcastng technologes []. CRNs have emerged as a promnent soluton to mprove the effcency of spectrum usage and networ capacty. In CRNs, secondary users (SUs) can explot channels when the prmary users (PUs) currently do not occupy the channels. The set of avalable channels for SUs s nstable, varyng over tme and locatons, whch manly depends on the PU s behavor. Thus, t s dffcult to create and mantan the mult-hop paths among SUs through determnng both the relay nodes and the avalable channels to be used on each ln of the paths. Tang the advantage of the broadcast nature and specal dversty of the wreless medum, a new routng paradgm, nown as opportunstc routng (OR) [2], has been proposed n the ExOR protocol. Instead of frst determnng the next hop and then sendng the pacet to t, a node wth OR broadcasts the pacet so that all neghbors of the node have the chance to hear t and assst n forwardng. OR provdes sgnfcant throughput gans compared to tradtonal routng. In CRNs, t s hard to mantan a routng table due to dynamc spectrum access. The pre-determned end-to-end routng does not sut for CRNs ether. Snce opportunstc routng does not need pror setup of the route, t s more sutable for CRNs wth dynamc changes of channel avalablty dependng on the PU s behavor. The effects of opportunstc routng on the performance of CRNs have been nvestgated n [3-8]. In 2008, Pan et al. [3] proposed a novel cost crteron for OR n CRNs, whch leverages the unlcensed CR lns to prortze the canddate nodes and optmally selects the forwarder. In ths scheme, the networ layer selects multple next-hop SUs and the ln layer chooses one of them to be the actual next hop. The canddate next hops are prortzed based on ther respectve lns pacet delvery rate, whch n turn s affected by the PU actvtes. At the same tme, Khalfe et al. [] ntroduced a novel probablstc metrc towards selectng the best path to the destnaton n terms of the spectrum/channel avalablty capacty. Consderng the spectrum avalablty tme, Badarneh et al. [5] gave a novel routng metrc that jontly consders the spectrum avalablty of dle channels and the requred CR transmsson tmes over those channels. Ths metrc ams at maxmzng the probablty of success (PoS) for a gven CR transmsson, whch consequently mproves networ throughput. Ln et al. [6] proposed a spectrum aware opportunstc routng for sngle-channel CRNs that manly consders the fadng characterstcs of hghly dynamc wreless channels. The routng metrc taes nto account transmsson, queung and ln-access delay for a gven pacet sze n order to provde guarantee for end-to-end throughput requrement. Tang heterogeneous channel occupancy patterns nto account, Lu et al. [7] ntroduced opportunstc routng nto the CRNs where the statstcal channel usage and the physcal capacty n the wreless channels are exploted n the routng decson. Lu et al. [8] further dscussed how to extend OR n mult-channel CRNs based a new routng metrc, referred to as Cogntve Transport Throughput (CTT), whch could capture the potental relay gan of each relay canddate. The locally calculated CTT values of the lns (based on the local channel usage statstcs) are the bass for selectng the next hop relay wth the hghest forwardng gan n the Opportunstc Cogntve Routng (OCR) protocol over mult-hop CRNs. However, none of the above schemes systematcally combnes the channel assgnment wth OR to model CRNs. The number of canddate forwarders and the performance of OR wll decrease, f usng exstng channel assgnment algorthms for MCMR OR. A Worload-Aware Channel Assgnment algorthm (WACA) for OR s desgned n [9].
WACA dentfes the nodes wth hgh worloads n a flow as bottlenecs, and tres to assgn channels to these nodes wth hgh prorty. WACA s the frst statc channel assgnment for OR. However, t deals wth channel assgnment for sngle flow. Assumng that the number of rados and the number of channels are equal, a smple channel assgnment for opportunstc routng (SCAOR) s proposed n [0]. It selects a channel for each flow. SCAOR s for multple flows but assumes that the number of rados and the number of channels are equal. Nether of them s a feasble soluton for OR n MCMR CRNs due to channel uncertanty of SUs. In ths paper, we combne channel assgnment and opportunstc routng, and analyze the mpact of PU s behavor and buffer sze on throughput. The contrbutons of ths paper can be summarzed as follows. Frst, we propose a new scheme to select proper forwardng canddates for opportunstc routng, whch consders the queue state of a node and channel avalablty. Second, a new algorthm for calculatng the forwardng probablty of any pacet at a node s proposed, whch s used to calculate the number of pacets a forwarder should send. Fnally, we formulate an optmzaton problem for combnng opportunstc routng and channel assgnment for CRNs, and compare the performance of our scheme, ntra-sesson networ codng-based opportunstc routng (ORNC), wth shortest path routng (SINGLE), MORE [], and ExOR n CRNs under dfferent number of channels and buffer sze. The rest of ths paper s organzed as follows. In Secton II, we descrbe the CRNs model used n ths paper. In Secton III, we formulate an optmzaton problem for jont opportunstc routng and channel assgnment for CRNs. The numercal results are presented n Secton IV. Fnally, Secton V concludes ths paper. II. SYSTEM MODEL We model the CRNs as a drected graph denoted by G = ( V, E), where V s the set of N SUs and E s the set of lns connectng any par of nodes. The source node s denoted as S, and the destnaton s denoted as D. We consder a tme slotted CRNs wth K lcensed orthogonal channels belongng to an nterweave model [2]. There are N SUs and M PUs n ths CRN. Each node s equpped wth the same number of rados R n half-duplex model. Each SU s capable of sensng the locally avalable channels and has the capablty of channel changng at pacet level for data transmsson. In CRNs, the SU s transmsson range s d s and the nterference range s d I. Let d j denote the dstance between node and node j. If d j < d s, we say nodes and j are neghbors. Node and node j can communcate wth each other f they are neghbors and they are operatng on the same channel. In OR, each node has multple canddate forwarders denoted as CFS. For any two nodes, and j, <j ndcates that node s closer to the destnaton node than node j, or n other words, has a smaller ETX (expected transmsson count) [3] than j. We summarze the notatons used n ths paper n TABLE I. Symbol Meanng G = ( V, E) the CRN topology graph S the source node D the destnaton node ψ + ψ ρ j TABLE I SUMMARY OF KEY NOTATIONS the set of node s n-edge on the channel the set of node s out-edge on the channel the loss rate of ln e j (e j E) on the channel Ο the probablty that node can transmt data pacets usng channel on tme slot t θ the probablty that node can use the channel on tme slot t P the amount of pacets that node has sent on channel µ j the probablty of e j that transmts data pacets usng the channel on tme slot t f the number of data pacets that e j transmts on channel j B the maxmum transmsson rate on a channel III. PROBLEM FORMULATION In ths secton, we formulate the problem of jont channel assgnment and OR as a nonlnear programmng problem. Let h {0,} denote whether node and node j can j communcate wth each other through channel. If h j =, t means that nodes and j can communcate wth each other and h = 0, vce versa. j We adopt the protocol nterference model []. If d uj d s, t means that node j s n u s transmsson range. When nodes and u smultaneously transmt data pacets, the transmsson of to j wll nterfere wth the transmsson of u to v n tme slot t. Smlarly, when d v d s, the transmsson of node to node j wll nterfere wth the transmsson of nodes u to v n tme slot t. Thus, we can calculate the nterference ln set I j of ln e j, Ij = { < u, v > < u, v > E, duj ds or dv ds}, and have µ + µ, < u, v > I () j uv j where u s the probablty of ln e j that transmts data j pacets usng the channel n tme slot t. In CRNs, uj s affected by the PU s actvty. If two lns are concurrently usable at the same channel n tme slot t, they should ether share the same transmtter or not nterfere wth each other. Hence, we can obtan µ mn, < m, n > Ij, <, j > E (2) < m, n> Ij Channel can be allocated to ln e j n tme slot t only when channel s avalable. Thus, we have
µ h, <, j > E (3) j j For each node, t can partcpate n at most R smultaneous communcatons n any gven tme T (T ncludes some mn-slots t). Ths can be formally represented by µ j θ, <, j > ψ µ g θ, < g, > ψ θ R 0 θ where θ s the probablty that node can use the channel n tme slot t, ψ + s the set of node s n-edge on channel, andψ s the set of node s out-edges on channel. In MORE, the canddate forwarder s selected accordng to ETX. However, snce n real world the buffer of a node s lmted, t s reasonable to consder the buffer sze n pacet forwardng scheme. Thus, we should tae buffer sze constrant nto account to select forwardng canddate. Durng tme slot T, node sends P pacets on channel. Then the queue length of at tme (T+), Q (T+), can be expressed as Q ( T + ) = Q ( T ) P + ( f ( ρ ) µ ) g g g t + < g, > ψ + () (5) where ρ s the loss rate of ln e g on channel, f s the g number of data pacets that e g transmts on channel, P s the number of pacets that node has sent on channel durng tme slot T+, and ( f ( ρ ) µ ) s the t + < g, > ψ g g g amount of recevng pacets of node durng tme slot T+. Consderng the queue baclog of node, we use the summaton of queue baclog and ETX as the forwardng canddate selector crteron, whch can be expressed as H ( T ) = χq ( T ) + γ ETX (6) where χ and γ are the weghts, constraned by χ + γ =, whch are set to be 0.5 and 0.5 n our analyss. In (6), we consder the queue length and channel avalablty n forwardng scheme. The smaller H (T) node has, the hgher probablty the node to be selected as a forwardng canddate. If the queue of a node s almost full, whch means pacet loss wll occur at the node, the node should not receve more pacets. For a gven tme T, the ncomng pacets of node are the same as the outgong pacets of node on channel to eep traffc balance. Also, the total number of data pacets that e j transmts on channel are not exceedng the maxmum transmsson rate of the channel. Therefore, we have g 0 fj µ j B, <, j > E t f g ( ρ g ) αg = P + Q ( T ),, g V, S) + < g, > ψ where B s the maxmum transmsson rate on a channel, and αj s the forwardng probablty that node j forwards the pacet receved from node over channel, to j s next hop. Generally, the channel avalablty s heterogeneous n CRNs due to PU s actvty. So, n our scheme, n each ntermedate node, we attach the forwardng probablty αj to each data pacet, whch can reduce duplcate transmsson. In the followng, we gve the algorthm to calculate α. Algorthm Calculate αm n CFS : β 0, temp 0, A m 2: for all node m n CFS do 3: calculate the probablty β () accordng to (8) : calculate the probablty β (2) accordng to (9) 5: β β () + β (2) m m m βm + 6: temp 7: end for 8: for all node m n 9: α β / temp CFS m m temp 0: A A { α m } : end for 2: return A do The probablty that only node m has receved the pacet s m m m 2 m m m+ l m (7) β () = ρ ρ ρ ( ρ ) ρ ρ (8) where ρ corresponds to node whose ETX s the least n CFS, ρ 2 s node 2 whose ETX 2 s n the second place, and so on, and l s the number of canddates n CFS. All nodes, from to l, are ordered by ther ETX. The probablty that node m and at least one node n CFS (m+, l) have receved the pacet s β (2) = ρ ρ ρ ( ρ )( ρ ρ... ρ ) (9) m 2 m m m+ m+ 2 l We now gve an example for the algorthm. In Fg., there are four nodes,, 2, 3 and, n node 0 s CFS0 on channel n a tme slot, and the nodes are ordered by ther ETX. The pacet loss rate of ln (0, ) s ρ 0, smlarly, ρ02 for ln (0, 2), ρ03 for ln (0, 3), and ρ0 for ln (0, ).
s.t. Fg.. An example for calculatng α. Accordng to Algorthm, we can obtan β0 = ( ρ0) ρ02ρ03ρ0 + ( ρ0)( ρ02ρ03ρ0 ) β02 = ρ0( ρ02 ) ρ03ρ0 + ρ0( ρ02)( ρ03ρ0) β03 = ρ0ρ02( ρ03) ρ0 + ρ0ρ02 ( ρ03)( ρ0 ) β0 = ρ0ρ02ρ03( ρ0) j (0) Node wll forward the pacet receved from node 0 wth probablty β0 / β0 to ts next hop. Smlarly, node 2 wll = forward the pacet wth β 02 / β0 =, node 3 wll forward the pacet wth β03 / β0, and node wll forward the pacet wth β 0 / β0 =. = Note that our scheme adopts networ codng [5, 6, 7, 8, 9, 20], and the codng operatons are smlar to the ntrasesson networ codng n MORE. And, smlar to WACA, we mantan K credt counters for each node. Each credt counter corresponds to a channel. In our scheme, we consder the mpact of channel avalablty of CRNs on credt calculatng, whch s shown as P credt =,, g V, S ( f ( ρ ) µ ) t + < g, > ψ g g g () In Eq. (), the parameter µ g s the channel avalablty dependng on PU s behavor n CRNs. If the credt becomes postve, the node creates a coded pacet, broadcasts t on channel, and then decrements the credt counter. In ths paper, our goal s to maxmze the aggregate throughput at destnaton node D. Thus, puttng all the above constrants together, the objectve functon of the formulaton s expressed as jd jd (2) + < j, D> ψ D max f ( ρ ) 0 uj, <, µ mn, < m, n > Ij, <, < m, n> I j uj θ, <, j > ψ,, j V, D + ug θ, < g, > ψ, g, V, S θ R 0 θ 0 αg (3) 0 < ρj < uj hj, <, 0 fj uj B, <, t fg ( ρg ) αg = P + Q ( T), g, V, S + < g, > ψ hj {0,} K, t T,, j, g V Ths s a nonlnear programmng problem, and we can use the IBM ILOG CPLEX 2. 2 [2] to solve t. IV. NUMERICAL RESULTS We compare the aggregate throughput among ORNC, SINGLE, ExOR and MORE n CRNs under dfferent number of channels and buffer sze. In the smulaton, we randomly deploy 30 SUs and PUs n a rectangle area of 500 unts by 500 unts. The nterference range of SUs, d I, s 8 unts. The transmsson range of SUs, d s, s unts, whle nterference range of PUs s 2 unts and the transmsson range s 6 unts. Each T ncludes 5 tme slots. The batch sze s 0. Each ln capacty s set to be 00 unts. We set the pacet loss rate ρ [0., 0.3]. j In Fg. 2 and Fg. 3, the buffer sze s 00 unts. We can see that as the number of channels ncreases, there would be more avalable channels for CRNs, so the throughput of each scheme ncreases. ORNC, ExOR and MORE acheve hgher throughput than SINGLE. The reason s that these three schemes tae advantage of the nherent property of ORopportunstc forwardng by usng multple forwardng canddates, whle SINGLE always uses the same route consstng of a forward canddate. ORNC performs better than ExOR and MORE. Ths s because we explot a new method for selectng forwardng canddates for ORNC n CRNs, whch consders the queue length and channel avalablty. In addton, networ codng n ORNC can reduce the retransmssons over forwarders data transmsson. The X3R (X: ORNC, MORE, ExOR, SINGLE) schemes, as shown n Fg. 2, perform clearly better than XR, as shown n Fg. 3 whch explots possble concurrent transmssons by multrado nodes over the orthogonal channels of CRNs.
Throughput (Unts) 30 25 20 5 0 5 ORNC-3R MORE-3R ExOR-3R SINGLE-3R 0 2 3 5 6 7 8 9 0 Number of Channels Fg. 2. Throughput comparson vs. Number of channels-wth 3 rados. Throughput (Unts) 30 25 20 5 0 5 ORNC-R MORE-R ExOR-R SINGLE-R 0 2 3 5 6 7 8 9 0 Number of Channels Fg. 3. Throughput comparson vs. Number of channels-wth rado. Throughput (Unts) 8 6 2 0 8 ORNC-3R MORE-3R ExOR-3R SINGLE-3R 6 00 200 300 00 500 Buffer Sze (Unts) Fg.. Throughput comparson vs. Buffer sze. In Fg. (R=3, K=), we can see that as buffer sze ncreases, the throughput ncreases and fnally the growth s slowed down. Ths s due to the fact that for large buffer sze, the pacet loss s low. However, when the buffer sze goes up to a certan value, the throughput ncreases slowly, as shown n Fg.. It s observed that the ORNC acheves much hgher throughput than MORE, ExOR and SINGLE. Ths s because t consders the queue length and channel avalablty for selectng forwardng canddates n ORNC; also t explots networ codng technology n ORNC, whch can reduce the retransmssons over mult-hop CRNs. V. CONCLUSION In ths paper, a novel scheme, ORNC, that jontly consders channel assgnment and OR, s proposed for maxmzng the aggregate throughput n mult-hop CRNs. In ORNC, we present a novel routng metrc by consderng queue state, ETX of a node and channel uncertanty. In addton, we propose a new algorthm for calculatng the forwardng probablty of any pacet at a node that a pacet can be sent at the node, whch can reduce the duplcate transmsson compared wth MORE. And then, we formulate the jont problem as a nonlnear programmng problem, and use ILOG CPLEX Optmzer to solve t. It s valdated by numercal results that the proposed jont scheme ORNC acheves hgher throughput than SINGLE, ExOR and MORE consderng channel assgnment. In future wor, we wll consder how to deal wth the congeston n CRNs under opportunstc routng scenaro. ACKNOWLEDGMENT Ths wor was supported by the Scence and Technology Fundament Research Fund of Shenzhen under grant JC2009032089A,JC2000526083A, ZYA200607003A. We would le to acnowledge the revewers whose comments and suggestons sgnfcantly mproved ths paper. REFERENCES [] S. Hayn, Cogntve rado: Bran-empowered wreless communcatons, IEEE Journal on Selected Areas n Communcatons, vol. 23, no. 2, pp. 20-220, 2005. [2] S. Bswas and R. Morrs, ExOR: Opportunstc mult-hop routng for wreless networs, n Proc. ACM SIGCOMM 2005, vol.35, pp.33-. [3] M. Pan, R. Huang and Y. Fang. Cost desgn for opportunstc mult-hop routng n cogntve rado networs, n Proc. IEEE MILCOM 2008, pp.-7. [] H. Khalfe, S. Ahuja, N. Malouch and M. Krunz, Probablstc path selecton n opportunstc cogntve rado networs, n Proc. IEEE GLOBECOM 2008, pp.-5. [5] O. S. Badarneh and H. B. Salameh, Opportunstc routng n cogntve rado networs: Explotng spectrum avalablty and rch channel dversty, n Proc. IEEE GLOBECOM 20, pp.-5. [6] S.-C. Ln and K.-C. Chen, Spectrum aware opportunstc routng n cogntve rado networs, n Proc. IEEE GLOBECOM 200, pp.-6. [7] Y. Lu, L.X. Ca, X. Shen and J. W. Mar, Explotng heterogenety wreless channels for opportunstc routng n dynamc spectrum access networs, n Proc. IEEE ICC 20, pp.-5. [8] Y. Lu, L.X. Ca and X. Shen, Spectrum-aware opportunstc routng n mult-hop cogntve rado networs, IEEE Journal on Selected Areas n Communcatons, vol.30, no.0, pp.958-968, 202. [9] F. Wu, and N. Vadya, Worload-aware opportunstc routng n multchannel, mult-rado wreless mesh networs, n Proc. IEEE SECON 202, pp.3-352. [0] S. He, D. Zhang, K. Xe, and H. Qao and J. Zhang, A smple channel assgnment for opportunstc routng n mult-rado mult-channel wreless mesh networs, n Proc. IEEE MSN 20, pp. 20-208. [] S. Chachuls, M. Jennngs, S. Katt, and D. Katab, Tradng structure for randomness n wreless opportunstc routng, n Proc. ACM SIGCOMM 2007, pp.69-80. [2] A. Goldsmth, S. A. Jafar, I. Marc, and S. Srnvasa, Breang spectrum grdloc wth cogntve rados: an nformaton theoretc perspectve, Proceedngs of the IEEE, vol.97, no.5, pp. 89-9,2009. [3] D. S. J. De Couto, D. Aguayo, J. Bcet, and R. Morrs, A hghthroughput path metrc for mult-hop wreless routng, n Proc. ACM MOBICOM 2003, pp.3-6. [] P. Gupta, and P. R. Kumar, The capacty of wreless networs, IEEE Transactons on Informaton Theory, vol. 6,no.2, pp.388-0, 2000. [5] R.Ahlswede, N.Ca, S,-Y.R.L, and R.W.Yeung, Networ nformaton flow, IEEE Transactons on Informaton Theory, vol.6, no., pp.20-26, 2000. [6] M. Yang and Y. Yang, Peer-to-peer fle sharng based on networ codng, n Proc. IEEE ICDCS 2008, pp.68-75.
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