A Fuzzy-based Routing Strategy for Multihop Cognitive Radio Networks

Transcription

1 74 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 3, No., Aprl 0 A Fuzzy-based Routng Strategy for Multhop Cogntve Rado Networks Al El Masr, Naceur Malouch and Hcham Khalfé 3 Troyes Unversty of Technology, Troyes, France Unversté Perre et Mare Cure (UPMC), Pars, France 3 Unverty of Bordeaux, Bordeaux, France al.el_masr@utt.fr, naceur.malouch@lp6.fr, hcham.khalfe@labr.fr Abstract: Cogntve rado networks represent a new class of wreless networks where the channels are not permanently avalable, dependng on the traffc actvty of lcensed users who have the prorty to use these channels. We desgn a novel routng procedure for multhop cogntve rado networks composed of adequate metrcs and a strategy to combne these metrcs. The objectve s then to ncrease channel avalablty when the routes are establshed. Two global metrcs are defned. The stablty metrc evaluates the utlzaton effcency of channels by capturng ther sporadc avalablty to cogntve users. The predcted power metrc estmates the spectrum capabltes for the on-gong transmsson wthout nterruptng lcensed users. We use fuzzy logc theory to compute and combne these metrcs n order to make sutable routng decsons. Our procedure conssts of two phases. In the frst phase we compute the route to the destnaton, and n the second we examne the ablty of ths route to satsfy the requred type of connecton at the source. Numercal analyss and smulaton results show that our procedure s able to fnd the route that goes through the nodes wth better channel condtons. Fuzzy logc seems then to be an approprate technque to decde the routes to establsh n multhop cogntve rado networks. Keywords: Cogntve rado networks, Multhop, Routng, Fuzzy Logc Controllers.. Introducton Cogntve Rado s an emergng and promsng technology that ams to ncrease the overall utlzaton of rado resources by enablng the dynamc allocaton of some porton of the wreless spectrum. Unlcensed users, through cogntve rado devces, can opportunstcally operate over the current unused parts of lcensed bands called whte spaces, spectrum holes, or spectrum opportunty []. The unlcensed users should have new smart and programmable rados that allow them to sense large portons of the spectrum, learn ts surroundng envronment, analyze and make ntellgent decsons, dentfy the nstantaneous unused channels, use multple channels n parallel, dynamcally reconfgure ther transmsson parameters to adapt n real tme to the current unused parts of the lcensed bands. Proposed tradtonal routng solutons n mult-channel multhop ad hoc and mesh networks are not approprate to cogntve rado networks. Frst, there s no statc spectrum allocaton and hence there s no set of channels accessble at any tme by each node n the network. Therefore, the channel selecton must be part of the routng decsons and must be taken at the network layer jontly wth the MAC (Medum Access Control) layer. Second, the transmsson of unlcensed users can be nterrupted at any tme when a lcensed user appears. It then needs to be swtched to another channel accordng to the nstantaneous unused parts of the lcensed bands. Therefore, the unlcensed users should permanently scan the spectrum and choose carefully whch route to follow before startng the transmsson, n partcular, n order to avod as much as possble route handover. Thrd, the unlcensed users should adapt ther transmsson power to avod any nterference wth the lcensed users who have the absolute prorty of usng the channels. In ths paper, we ntroduce a novel routng procedure based on the nferred behavor of lcensed users over ther channels whle assumng that ther behavor s measured only n the past by sensng technques. Each channel at each node s evaluated by two metrcs. Frst, the stablty metrc ams to reflect the utlzaton effcency of the spectrum by studyng the sporadc avalablty of the lcensed bands to the unlcensed users. Second, the transmsson power estmaton metrc ams to characterze the allowed transmsson power and ts varaton over tme. Ths metrc ams to reflect the state of the spectrum durng the on-gong transmsson. We use Fuzzy Logc theory [][3] to combne these metrcs n order to make good routng decsons. In general, Fuzzy Logc allows the partal membershp of a varable x n a set A. The degree of membershp s specfed usng membershp functons and lngustc varables. A membershp functon s a curve whch assgns a real value n [0,] for each measure of a lngustc varable such as age or speed. Fuzzy Logc also provdes a mathematcal tool called Fuzzy Logc Controllers used to determne and control varables va a set of rules to handle ther complex relatons. Fuzzy Logc theory s an adapted technque to solve the uncertanty, the heterogenety, and the nformaton ncompleteness of routng problems n cogntve rado envronment. Partcularly, even f the propertes of channels are well dentfed, t s stll dffcult to assess wth certanty the mpact of these propertes on the performance of a gven route. The contrbuton of ths paper s twofold. Frst, n presentng routng metrcs that characterze the dynamc and unstable aspects of cogntve rado networks and second n proposng a technque that avods combnng these parameters through nflexble methods smlar to the weghted sum. Indeed the fuzzy logc allows partal membershp of a channel to a metrc and a metrc to a path thus capturng the dynamc behavor observed n cogntve rado networks. Practcally wth the consdered metrc, and the combnaton technque we prvlege paths avalable for long perods of tme. These paths are sutable for applcaton requrng nterrupted servces such as data or vdeo exchange. Besdes, we valdate

2 75 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 3, No., Aprl 0 our metrcs and routng procedure wth smulatons and show that our routng ensures long term stablty by accountng for nstantaneous varatons. The remanng of ths paper s organzed as follows. The related work s revewed n Secton. In Secton 3, we wll brefly summarze the man concepts of Fuzzy Logc theory. We present our routng metrcs n Secton 4. In Secton 5, we descrbe the two phases of our routng protocol. Performance evaluaton and numercal results are provded n secton 6. Fnally, we draw our conclusons and we brefly hghlght the possble future works n Secton 7. In the sequel, we note by Prmary Rados (PRs) the lcensed users and by Cogntve Rados (CRs) the unlcensed users.. Problem Formulaton. Routng n Cogntve Rado Networks Because n Cogntve Rado Networks channels are not permanently avalable, proposed routng technques for mult-channel mult-hop ad hoc or mesh networks cannot be reused for CRNs. Any proposed routng strategy n CRNs should characterze the non-permanent avalablty and descrbe the sporadc accessblty of the spectrum bands. Other CRN routng proposals address the above ssue by smply computng the percentage of avalablty for each channel [5][6].. Objectve We consder a multhop cogntve rado network where data s forwarded through multple cogntve rado nodes between a source and a destnaton. Cogntve nodes try to share several channels occuped by lcensed users belongng to dfferent networks and thus havng dfferent propertes. The objectve s then to desgn an approprate routng strategy that bulds a sngle path from a source node to a destnaton usng only cogntve rado nodes as ntermedate relays. The steps of the desgn are as follows: Gven a multhop cogntve rado network, fnd the best routng metrcs that best characterze the avalablty and usablty of the channels. Gven a number of computed metrcs, propose a flexble method of combnng parameters able to capture uncertanty and varatons of the computed metrcs. Gven the metrcs and ther combnaton, fnd the best path between a source node and a destnaton. The path s composed of an aggregated set of channels on every hop. 3. Related Work Some routng algorthms or protocols for multhop cogntve rado networks were proposed n prevous works. They are manly based on technques developed frst for ad-hoc or mesh networks. Here, we present some works that are close to our proposal. Sharma et al. proposed n [4] a way to ntegrate the nterference temperature nto routng decsons. A smple weghted sum s used to combne nterference wth other routng metrcs. Yet, ths way s not flexble enough and t was not evaluated by smulaton or models. Also, t s not clear how the weghts are computed and how the CR nodes estmate the nterference at the PR nodes. SAMER s a routng scheme proposed n [5] to provde a tradeoff between long-term parameters such as hop count and short-term parameters such as spectrum avalablty. Also, SAMER provdes a compromse between the local spectrum condtons at the forwardng nodes and the global spectrum vew of the entre routng path. However, the spectrum avalablty does not appear well n the calculaton of routng metrcs except by the percentage of tme durng whch channels are avalable for CR nodes. We show later that ths s not suffcent. Akyldz et al. proposed n [6] STOD-RP an on-demand routng protocol. In STOD-PR, CR nodes are dvded nto groups nterconnected by overlappng nodes where each group uses only one channel. A recovery mechansm s proposed to fnd a new channel for a group after the loss of the old one due to a PR actvty. The framework desgned n ths work s realstc especally when used n cogntve rado mesh networks. However, ths protocol presents few ssues. Frst, the throughput s much reduced wthn each group due to the use of just one channel per group. Second, the overlappng nodes become quckly bottleneck lnks. Accordng to [7], the next forwardng node s the node that requres the mnmal consumpton power. Hence, the next forwardng node s usually the nearest neghborng node; and then the optmal route s much longer than the route of mnmum hop count. Moreover, the percentage of channels avalablty s not taken nto consderaton durng the channel selecton. In [8] a new routng metrc was proposed based on a probablstc defnton of the avalable capacty over channels. Ths defnton ams at fndng the most probable route or the route wth the hgher probablty of avalablty. After the route assgnment, the source examnes f ts throughput capacty satsfes the throughput demand and t adds, when needed, other channels for transmsson untl the throughput demand s satsfed. Probablstc throughput computaton s adequate to ncrease the long term avalablty and the overall statstcal utlzaton of the network. However, ths approach may not be adapted for short connectons. In [9], several routng metrcs are proposed based on the nterference at PR lnks due to CR actvtes, and based on the lfe tme of CR lnks. In fact, the defnton of routng metrcs s functon of the usage pattern proposed for PR nodes and t wll not reman vald f ths usage pattern changes. In addton, the duraton of the lfe tme of CR lnks s dffcult to specfy. Our work dffers from prevous proposals n two aspects: Frst, by presentng a new flexble and effcent way to combne routng metrcs n cogntve rado networks. Second, by proposng new routng metrcs able to capture the uncertan, dynamc and sporadc avalablty of lcensed bands. 4. Fuzzy Logc In ths Secton, we gve a bref overvew of the Fuzzy Logc theory to help the unfamlar reader to understand the rest of the paper. Exhaustve descrpton can be found n the lterature [][3]. 4. Fuzzy Sets Fuzzy sets represent a modernzaton of tradtonal crsp sets where the membershp of an object x n a set A s evaluated by 0 (false) or (true). True means that x s member of A

3 76 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 3, No., Aprl 0 and false means that x s non-member of A. Fuzzy sets allow the partal membershp of x n A. The degree of membershp has a real value n [0, ], where 0 and correspond respectvely to the full non-membershp and membershp of x n A. If A s a fuzzy set n a unverseu, the membershp of x n A s evaluated by the membershp functon µ as followng: A µ : U [0,] () A Each u U has a degree of membershp n A equals to µ (u A ). An object x s defned as a lngustc varable such as dstance or speed, and a fuzzy set A s defned as a lngustc term such as far or hgh. 4. Fuzzy Logc Controllers A Fuzzy Logc Controller (FLC) s a tool used to compute the value of an output based on several nputs havng between them a complex relaton, whch cannot be solved va tradtonal mathematcal tools such as weghted sum. The structure of FLC s shown n Fgure. To compute the value of the output of the FLC, the followng steps must be appled. dsposed n tme, such as the dstance between two successve perods and the dfference n ther duratons. We call a channel stable when t swtches between long avalable perods and/or long unavalable perods. When unavalable perods are small the channel s of course excellent to use, but long unavalable perods also provde us a good nformaton whch s avodng to use the channel for sure. An unstable channel swtches quckly between avalablty and unavalablty. The degree of stablty can be specfed accordng to ts poston between a channel that s almost statc and a hghly unstable channel. In ths work, we use 3 parameters to compute the stablty of channels: The frequency of transtons between avalablty and unavalablty, the devaton n the duraton of avalable perods and the devaton n the duraton of unavalable perods. In the followng we descrbe the mpact of each parameter on the stablty. Fgure shows an example of the mpact of the frequency of transtons between avalable and unavalable perods on the stablty of channels. It s clear that for the same percentage of channel avalablty, the degree of stablty decreases proportonally wth the ncrease of the frequency of transtons. Fgure. Fuzzy Logc Controller Frst, we compute or measure from the external envronment the value of each nput. Second, these values are converted by the fuzzfer nto fuzzy varables ready to be used by the nference engne. Ths step s called fuzzfcaton and t s executed based on the membershp functons of each nput. An example of membershp functons s shown n Fgure 5. Thrd, the nference engne apples every rule of the fuzzy rule base to the nput fuzzy varables to compute an output fuzzy varable. An example of a fuzzy rule base s shown n Table. The rules of the fuzzy rule base have the followng form: IF (Input s X and Input s X and Input 3 s X 3 ) THEN (Output s Y). Fourth, the output fuzzy varables of all the rules are connected to compute the fnal output fuzzy varable. Fnally, the fnal output fuzzy varable s converted by the defuzzfer nto a crsp output ready to be used n the external envronment. 5. Routng Metrcs 5. Stablty The goal of the stablty metrc s to capture the actvty behavor of PR nodes over the lcensed channels and hence the sporadc avalablty of these channels to CR nodes. In other words, the stablty ams to descrbe how the avalablty of channels s dstrbuted over tme. The dstrbuton model of channels avalablty can be descrbed by the number of perods durng whch channels are avalable to CR transmssons and the manner these perods are Fgure. Impact of frequency of transtons on stablty Fgure 3 shows that two channels wth the same percentage of avalablty and the same frequency of transtons can have two dfferent degrees of stablty. Ths can be captured by the devaton of avalable perods. We notce that when the value of devaton n the duraton of avalable perods ncreases, the dstrbuton model of channel avalablty s more smlar to the stable case. In fact, the avalablty of the channel n Fgure 3(a) s composed of one long and several short avalable perods. The long perod s smlar to the long avalable perod n the orgnal stable case n Fgure (a) and the short perods are almost not useful and can offer n the rest of the tme the same performance as the long unavalable perod n Fgure (a). In Fgure 4 two dfferent degrees of stablty are gven to two channels that have the same percentage of avalablty, the same frequency of transtons, and the same devaton of the duraton of avalable perods (devaton = 0). We remark that when the value of the devaton of the duraton of unavalable perods ncreases, the dstrbuton model of channel avalablty s more smlar to the stable case due to the same reasons already explaned n the prevous case. To compute the degree of stablty of each channel, we combne the 3 parameters usng the Fuzzy Logc Controller FLC. The FLC conssts of 3 nputs lngustc varables (frequency of transtons between avalablty and unavalablty (Input ), devaton n the duraton of avalable perods (Input ), and devaton n the duraton of unavalable perods (Input 3 )), characterzed by the membershp functons depcted n Fgure 5(a), and one output lngustc varable

4 77 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 3, No., Aprl 0 (Stablty), characterzed by the membershp functon depcted n Fgure 5(b). Each nput lngustc varable s characterzed by a term of three fuzzy sets, {T(Input)} = {[Low, Medum, Hgh]}. The output lngustc s characterzed by a term of four fuzzy sets, {T(Output)} = {[Very Low, Low, Medum, Hgh]}. Fgure 3. Impact of avalablty devaton on stablty Fgure 4. Impact of unavalablty devaton on stablty The Output s a value between 0 and 00. The fuzzy Rule Base of the FLC s shown n Table. The table s a proposal for the FLC determned va the analyss n the prevous secton but also va observatons durng smulatons. Note that the rule base s malleable enough so that other researchers can argue and propose dfferent rules for dfferent reasons. For nstance, f the frequency of transtons s medum and the devatons are very hgh, one can consder that the stablty s hgh rather than medum. Fgure 5. Membershp functon of the FLC 5. Transmsson Power Estmaton The stablty metrc characterzes the spectrum holes to be used by cogntve rado transmssons. Nevertheless n order to explot these whte spaces, CRs must judcously compute ther transmsson power n a way not to dsturb prmary rados actvty. Moreover, snce nterference at PRs s addtve, the estmated transmsson power should also account for neghborng CRs actvty over the channel. Consequently every CR should contnuously estmate the mum allowed transmsson power P over every avalable channel. Practcally, the estmated transmsson power dctates the set of CR recevers on every channel.e. the obtaned CRN topology. For ths reason, our second metrc captures the estmated transmsson power and ts varaton. The predcted P whch s gong to be consdered for next transmssons can be computed based on a set of prevously measured values of P, n addton to the current measured value. Many methods exst n the lterature to predct the next value of random varables such as regresson models or Kalman flters. The approprate predcton method to use s out of the scope of ths work. We rather focus on how we can beneft from the results obtaned from the predcton method by consderng a general output from the predcton module. Consder the predcton module n Fgure 6. It has three nputs: The current measured value of P, the hstory of past measured values, and the number of past values. These three nputs are combned by the predcton method to obtan two outputs: The predcted value P Pr edcted of P and the confdence nterval [ P Pr β, P Pr + β ]. Number of trans. edcted edcted Table. FLC Fuzzy Rule Base σ IF ON Perods σ OFF Perods THEN Stablty Hgh Hgh Hgh Low Hgh Hgh Medum Low Hgh Hgh Low Low Hgh Medum Hgh Low Hgh Medum Medum Very Low Hgh Medum Low Very Low Hgh Low Hgh Very Low Hgh Low Medum Very Low Hgh Low Low Very Low Hgh Hgh Hgh Medum Medum Hgh Medum Medum Medum Hgh Low Medum Medum Medum Hgh Medum Medum Medum Medum Low Medum Medum Low Low Medum Low Hgh Low Medum Low Medum Low Medum Low Low Low Low Hgh Hgh Hgh Low Hgh Medum Hgh Low Hgh Low Hgh Low Medum Hgh Hgh Low Medum Medum Hgh Low Medum Low Hgh Low Low Hgh Hgh Low Low Medum Hgh Low Low Low Hgh By means of the Fuzzy Logc Controller FLC each CR node computes the fnal result of the predcted power (Fnal Predcted Power) for each channel based on the two outputs of the predcton method ( P Pr edcted, β ). The polcy of FLC s based on sx smple rules shown n Table. Rules, 3, and 5 ndcate that the fnal result of the predcted power (Fnal Predcted Power) s proportonal to the value of P Pr edcted. Rules, 4, and 6 ndcate that the fnal result of the predcted power (Fnal Predcted Power) of a channel wth a hgh value of β must be lower than that of channel wth a comparable value of P Pr edcted and smaller value of β.

5 78 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 3, No., Aprl 0 Fgure 6. Inputs and outputs of the predcton operaton Fnally, note that P Pr edcted s the mum allowed transmsson power beyond whch prmary users are dsturbed. It s not the power that s gong to be used when transmttng whch depends manly on the locaton of the recever node. The FLC conssts of two nputs lngustc varables ( P Pr edcted and β ) characterzed by the membershp functons depcted n Fgure 7(a) and Fgure 7(b), and one output lngustc varable (Fnal Predcted Power), characterzed by the membershp functon depcted n Fgure 7(c). P Pr s edcted characterzed by a term of three fuzzy sets, {T( P Pr edcted )} = {[Low, Medum, Hgh]}, and β s characterzed by one fuzzy set, {T( β )} = {[Hgh]}. The output lngustc s characterzed by {T(Output)} = {[Very Low, Low, Medum, Hgh]}. The exact output power can be computed n Watts by normalzaton but ths operaton s not necessary snce the output s used for comparson between channels. Table. FLC Fuzzy Rule Base n IF THEN P Pr β Fnal Predcted Power edcted Hgh Hgh Hgh Hgh Medum 3 Medum Medum 4 Medum Hgh Low 5 Low Low 6 Low Hgh Very Low channel at each node. The best channel s the most stable channel wth a hgh Fnal Predcted value of P (greater than the mnmum needed for transmsson). The hgher the fnal predcted power, the hgher the number of neghbors and thus the hgher the route possbltes to select. Also, a hgher fnal predcted power provdes a securty margn before volatng t. Other fner rules can be defned and they are summarzed n Table 3. The global FLC of the channel grade computaton s llustrated n Fgure 9. The FLC3 conssts of two nputs lngustc varables (Stablty and Fnal Predcted Power) characterzed by the membershp functons depcted n Fgure 8(a) and Fgure 8(b), and one output lngustc varable (Channel Grade), characterzed by the membershp functon depcted n Fgure 8(c). Stablty s characterzed by a term of three fuzzy sets, {T(sStablty)} = {[Low, Medum, Hgh]}, and Fnal Predcted Power s characterzed by one fuzzy set, {T(Fnal Predcted Power)} = {[ Low, Medum, Hgh]}. The output lngustc s characterzed by {T(Channel Grade)} = {[Very Low, Low, Medum, Hgh, Very Hgh]}. Fgure 8. Membershp functons of FLC 3 Fgure 9. The global FLC of the channel grade computaton Table 3. FLC 3 Fuzzy Rule Base Fgure 7. Membershp functons of FLC 5.3 Channel Grade After computng for each channel the degree of stablty accordng to the method explaned n Secton 5., the fnal predcted value of P accordng to the method explaned n Secton 5., the Fuzzy Logc Controller FLC3 combnes these two routng metrcs to compute the grade of each IF THEN Stablty Fnal Predcted Power Channel Grade Hgh Hgh Very Hgh Hgh Medum Medum Hgh Low Very Low Medum Hgh Hgh Medum Medum Medum Medum Low Low Low Hgh Low Low Medum Low Low Low Low

6 79 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 3, No., Aprl 0 6. Route Constructon Procedure 6. Route Computaton The computaton of all the routng metrcs must take place for each channel n all the routes from the source to the destnaton. The grade of a lnk between two CR nodes s equal to the sum of the grades of all channels that are gong to be used for transmsson by the cogntve rado between these two nodes. As for the grade of a route we am at ncludng n the fnal grade also the number of hops. To do so, the lnk grades are nverted, then the fnal grade s the nverse of ther sum. The route wth the hghest grade s the best route from the source to the destnaton. More formally, f we denote by R the set of all routes between a source node S and a destnaton D, and by n r the number of lnks that consttutes route r, r R, then computng the best route based on the grades of routes between S and D can be wrtten as n r ( r ) () r R g l= l r where gl s the grade of lnk l n route r ( l n r, r R ). There are several reasons that justfy ths way of computaton. Frst, the hghest nverted route grade corresponds to the lowest sum of the nverted lnk grades whch also ntrnscally tends to reduce the number of hops. Second, lnk grades do not correspond only to bandwdth avalablty. Thus takng the mum of the mnmum lnk grade through the route as a fnal grade n order to capture a sort of bottleneck may not be suffcent. Thrd, f the mum of the mnmum approach or another approach s used, an addtonal technque to nclude the number of hops must be added. Nevertheless, ths s stll feasble. A comparson between the sum and -mn approaches has been studed before. See for nstance [0]. When the source wants to establsh a connecton, t s possble to ncorporate the computaton of the route grades n an AODV-lke [][6] or a DSR-lke [] routng protocol that allows also to reach the destnaton. Every CR node can compute ts local lnks grades and add t to the cumulatve grades receved from ts neghbors. Durng the computaton, CR nodes must take nto consderaton the fact that the computed bandwdth accounts for the nterference between consecutve lnks whch dvdes the bandwdth among neghborng lnks, but does not change the avalablty percentage snce t depends only on PR actvty. Furthermore, the predcted mum allowed power for transmsson should be updated whle the route s constructed towards the destnaton. Ths s because the addton of a channel to the route actvates the channel for transmsson and wll add possbly nterference at PR recevers. The predcted power s then possbly reduced for the same channel of next lnks n the route. Ths update cannot use the recent measured powers receved from the sensng module of the cogntve rado snce the transmsson s not yet started. The deployment of a procedure that updates the mum power durng route constructon s challengng and ncreases the complexty of the route establshment especally that t would requre message exchange between CR nodes and dstrbuted power computatons. However, n our case, channels wth hgher mum power are chosen frst whch reduces the probablty of volatng t f more than one CR node uses the same channel n the route. Practcally, ths wll not affect PR transmssons but t causes the route to be establshed, then some CR nodes wll not be able to transmt as predcted. Desgnng a lghtweght procedure to update the mum power dynamcally s one of our future works. 6. Route Examnaton The goal of ths second phase s to examne f the route selected n the frst phase responds or not to the type of connecton at the source. For example, a route can be accepted for an ftp connecton whle t may not be adequate for an nteractve connecton. To acheve the goal of ths phase, we propose a new method to analyze how the average throughput computed n the frst phase wll be provded to a gven connecton. Let's consder that between two CR nodes ( CR and CR ) we have n channels to n. The percentages of avalablty of each channel are respectvelyα, α,..., and α n whle the throughput capactes are D, D,..., and D n. Hence, channel offers the throughput D durng α percent of the tme. If one of the channels between CR and CR offers the throughput D durng α percent of the tme, then the lnk between CR and CR offers at least the throughput D durng α percent of the tme. We denote by A the state where the channel s avalable to CR nodes. Hence, the probablty of the state A s p( ) = α and ts throughput s D whle the probablty of the state A A s and ts throughput s 0. Also, the state p( A ) = α A I A I A represents the overall tme durng whch the channels and j are avalable whle the channel k s not, and the probablty of ths state s p A I A I A ) = α α ( α ) and ts throughput s j ( j k j k D + D. In fact, at any moment the lnk between CR and CR s n one of the followng states: A I A I... I A n, A I A I... I An,... A I A I... I An. The probablty of each composed state s equal to the product of the probablty of ts states f we assume that channels are ndependent. The throughput of each composed state s equal to the sum of the throughputs. The sum of the probablty of all the states s equal to. In consequence, for each lnk between two CR nodes consstng of n channels, n we have states. Thus, we can compute for the lnk a set of offered throughputs by the channels of the lnk and ther percentages of avalablty. From that, t s possble to determne f ths lnk s adequate to a gven type of applcaton accordng to ts requred throughput(s). For example, f we have a lnk where the throughput Mbps s avalable 0.9 of the tme, we can consder that ths lnk s adequate for a VoIP talk spurt f Mbps s the requred servce rate to satsfy the delay constrant. In the case of routes wth several lnks, the fnal result s the mnmum of the results of all lnks. j k

7 80 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 3, No., Aprl 0 Consder the followng numercal example whch consst of two nodes connected through 3 channels ( X,Y and Z ). The throughput capacty of each channel s 80 Kbps. Avalablty percentages are 0.7, 0.5 and 0.4 respectvely. The source node runs the followng steps. Frst, t constructs the lnk table (Fgure 0) where each combnaton of channels (state of channels) s represented wth ts throughput capacty and ts probablty of avalablty. Second, t selects from the table the combnatons that satsfy the throughput demand, say for nstance 60 Kbps. Thrd, t computes the sum of the probabltes of all selectng combnatons. The result represents the probablty of tme durng whch the throughput demand s avalable permanently (at each moment). In ths case, 60 Kbps s avalable permanently for = 0.55 of the tme. All computatons are shown n Fgure 0. not always selected. For nstance, f two channels have close values of P Pr edcted, a CR node chooses the channel whch has the lowest value of β. In other words, the chosen channel s the one whose operaton of predcton gves the hghest level of confdence. Such result cannot be obtaned through the classcal β functon. P Pr edcted Fgure. Fnal predcted power as a functon of predcted power and predcted error Fgure 0. Examnaton Table: Throughputs greater than 80 Kbps are avalable permanently for 9% of the tme. Throughputs between 80 Kbps and 60 Kbps are avalable permanently for 55% of the tme. etc. It s worthwhle notcng that f the number of channels s very large then the computatons are not scalable whch s a drawback of ths method. To allevate ths problem, channels can be gathered nto dfferent groups before the computatons. Also, low grade channels can be wthdrawn frst. 7. Performance Evaluaton 7. Metrcs Analyss Before smulatng the whole routng procedure, we frst valdate the effectveness of usng the fuzzy logc wthn the proposed metrcs. Snce our proposed metrcs are based on IF-THEN rules and not on mathematcal equatons, we show how these metrcs change wth the varaton of the FLCs nputs. We consder here a smple one hop network snce the objectve s to show that the developed metrcs capture effcently the cogntve rado envronment. All numercal computatons and smulatons were conducted usng MATLAB. 7.. Transmsson Power Estmaton Fgure represents how the output of the FLC (Fnal Predcted Power) changes as a functon of ts two nputs ( P Pr edcted and β ). It s clear that the Fnal Predcted Power s proportonal to the P Pr edcted obtaned through the predcton operaton. However, f a CR node compares between two channels, the channel that has the hghest value of P Pr s edcted 7.. Channel Grande Fgure shows how the channel grade vares based on the stablty and the Fnal Predcted Power. Note that f the stablty s very low, the channel grade s also low regardless of the Fnal Predcted Power value. However, f the stablty s hgh, the channel grade swtches between very hgh and very low levels and t s hghly dependent on the Fnal Predcted Power. The two prevously obtaned results typcally express the relaton between the stablty and the Fnal Predcted Power. In fact, a stable channel should be selected based on the Fnal Predcted Power snce the current state of the channel wll mostly contnue n the future for a sgnfcant perod of the tme. On the other hand, an unstable channel wll probably swtch several tmes between avalablty and unavalablty durng a short perod, and then the mpact of the current state on channel selecton s wdely reduced. It s also remarkable that durng unavalablty perods, an unstable channel s preferred over a stable one snce the former allows startng the transmsson faster than the latter one and provdes at least some throughput guarantee even wth ntermttent connectvty. Ths example shows agan the flexblty provded by the fuzzy logc to control carefully the channel selecton. Such fgure cannot be obtaned usng a tradtonal weghted sum equaton. Fgure. Channel Grade as a functon of Stablty and Fnal Predcted Power 7. Route Constructon Smulatons In order to smulate the routng procedure, we use 64 nodes placed n a grd topology (Fgure 3). The source node s the node placed n the top left corner of the grd whle the destnaton node s the one placed n the bottom rght corner. There are 6 lcensed channels between every two nodes. For all the smulatons, all channels have 50% avalablty rato n

8 8 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 3, No., Aprl 0 the long term and a untary bandwdth. We smulate three types of channel models correspondng to dfferent degree of stablty. These types are placed n the network n order to creates three regons of channels n the network as shown n Fgure 3. Fgure 5. The case where the frst constructed routes start from the hgh stablty regon of the network Fgure 3. Smulated network topology The channels of the bottom regon behave randomly from three low actvaton rates of PR nodes. The channels of the top regon behave randomly from three actvaton rates of PR nodes. Fnally, the channels of the mddle regon behave randomly from three medum actvaton rates of PR nodes. Ths confguraton wll show clearly how routes are chosen through dfferent lnks wth dfferent condtons. Frst, we run the routng algorthm to fnd the best route from the source to the destnaton. Fgure 4 shows the route constructed through lnks wth hghest grades. Also, t appears that the number of hops s consdered n the route constructon that s why the route s close to the moderate stablty regon. Hence, the chosen route s a good trade-off between the qualty of lnks and the route hop count. Fgure 4. Route constructon through lnks wth hgh grades Second, we contnue runnng the algorthm between the same source and the same destnaton but for new connectons up to 9 routes whch s the mum for ths topology. We do ths operaton several tmes whle we vary randomly and unformly the startng of each route establshment. The obtaned routes can be categorzed nto two types. Examples of these successve routes are shown n Fgures 5 and 6. In Fgure 5, we remark that the frst four constructed routes are n the bottom regon of the topology where the stablty s hgher, the routes 5, 6, and 7 are hybrd between the hgher and the moderate stablty regon, and fnally the last two routes are totally n the lower stablty regon. These types of routes look ndeed ntutve and valdate the routng algorthm n contrast to the second type shown n Fgure 6. Fgure 6. The case where the frst constructed routes start from the hgh stablty regon of the network In Fgure 6, the frst establshed routes n the network starts surprsngly from the unstable regon and they fnsh n the stable one. In fact, the routes wth stable channels have very low grades when the predcted power s low and/or β s hgh. These routes were ndeed establshed when the fnal predcted allowed power s too low or does not allow transmsson. Although the unstable lnks have low grades, these grades are stll greater than the grades of stable ones durng perods where the channels are not really avalable for transmsson. Thus, that s why they are chosen to construct the route. Evdently, ths s not suffcent and the algorthm should also choose the route that offers the better avalablty as shown n the next secton. Next, after the establshment of the frst nne routes n the network, we measure the offered avalablty of each route whch determnes also the average throughput offered by each one of them at the begnnng of the transmsson. We show the results that correspond to the two types of routes dentfed n the prevous set of smulatons. Fgure 7 (a) shows the avalablty average for the nne routes before the routng decson and the establshment of the route. By constructon, the avalablty s around 50%. Fgure 7 (b) shows the avalablty average for the nne routes after the routng decson. The two fgures correspond to the case where routes are establshed through lnks that are n ther majorty avalable for transmsson (correspondng to the frst type n the prevous smulatons, Fgure 5). That s why the measured avalablty s hgh and even close to 00% for the frst route. Then, for next routes the avalablty decreases untl 50%. However, for some routes, the avalablty can ncrease a lttle as t s the case for route 6 n Fgure 7 (b). It does not mply that route 6 s better than route 5. On the

9 8 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 3, No., Aprl 0 contrary, ths s qute normal because the channel grade takes nto account other metrcs and not only the avalablty. nterestng to test the beneft from desgnng a dstrbuted update of the mum allowed power durng the constructon of the route. Fnally, the second phase of the routng procedure should be enhanced so that the throughput computatons become more scalable wth the number of avalable channels between two nodes. References [] I. Akyldz, W. Y. Lee, and K. Chowdhury, CRAHNs: Cogntve Rado Ad hoc Networks, Computer Networs Elsever Scence, vol. 7, no. 3, Jul [] A. Kaufmann, Intoducton to Theory of Fuzzy Subsets. New York: Academc, 975. Fgure 7. Percentage of channels avalablty of the frst constructed routes before and after the routng decsons Same results are shown n Fgure 7 (c) and Fgure 7 (d) respectvely before and after the route establshment. Agan, here the route avalablty decreases for next routes wth very small varatons. So they are a good compromse between avalablty and the other metrcs. Nevertheless, n ths case the rato of avalablty after the route establshment s much lower than the case of Fgure 7 (b). In fact, these routes correspond to lnks havng stable channels but n an unavalablty perod or lnks havng unstable channels. In consequence, the average throughput capacty acheved by the on-gong transmsson s lower than the frst case (Fgure 7 (b)). Ths degradaton s mposed by the nstant when the route must be establshed. The algorthm, however, chooses the best alternatve among the possbltes n hand, and especally t avods choosng routes that are not avalable even f they have acceptable performance n the long term. Ths property s partcularly requred for nteractve applcatons or n general applcatons that need fast frst access. Ths s a key feature that s enabled by ncorporatng sgnal predcton n the computaton of routng metrcs. 8. Concluson and Future Work Ths paper proposes a new routng approach n multhop cogntve rado networks based on the sporadc avalablty of channels. Two routng metrcs are defned based on the power allocaton at cogntve rado nodes. These metrcs are computed and combned usng the fuzzy logc theory. Our proposed protocol computes the route to the destnaton and then checks f ths route s able to satsfy the requred type of connecton at the source. Numercal analyss and smulatons show that our routng procedure s able to explot adequately all types of channels whenever there are avalable spaces. The establshed routes acheve a good trade-off between avalablty, transmsson ablty and stablty. Based on our results, further nvestgatons can be made ncludng especally expermentng other fuzzy rules that can be tuned for a specfc applcaton requrements. Also, t s [3] W. Pedrycz and F. Gomde, An Intoducton to Fuzzy Sets: Analyss and Desgn. MIT Press, 998. [4] H. Sharma, M. Krunz, and O. Youns, Channel Selecton under Interference Temperature Model n Mult-hop Cogntve Mesh Networks, n Proceedngs of the IEEE DySPAN Conference, Apr [5] I. Pefkanaks, S. Wong, and S. Lu, SAMER: Spectrum Aware Mesh Routng n Cogntve Rado Networks, n Proceedngs of the IEEE DySPAN Conference, Oct [6] G. Zhu, M. D. Felce, and I. F. Akyldz, STOD-RP: A Spectrum-Tree Based On-Demand Routng Protocol for Mult-Hop Cogntve Rado Networks, n Proceedngs of the IEEE GLOBECOM Conference, Nov [7] C. Pyo and M. Hasegawa, Mnmum Weght Routng based on a Common Lnk Control Rado for Cogntve Wreless Ad hoc Networks, n Proceedngs of the IEEE IWCMC Conference, Aug [8] H. Khalfe, S. Ahuja, N. Malouch, and M. Krunz, Probablstc Path Selecton n Opportunstc Cogntve Rado Networks, n Proceedngs of the IEEE GLOBECOM Conference, Nov [9] G. Le, W. Wang, T. Peng, and W. Wang, Routng Metrcs n Cogntve Rado Networks, n Proceedngs of the IEEE ICCSC Conference, May 008. [0] H. Khalfe, Improvng end to end throughput n wreless multhop networks usng several control technques, Ph.D. dssertaton, Unv. of Pars VI, Pars, Nov [Onlne]. Avalable at: [] C. Perkns, E. Royer, and S. Das, Ad hoc on demand dstance vector (AODV) routng, IETF, RFC 356, 003. [] Johnson, D., Hu, Y., Maltz, D., The Dynamc Source Routng Protocol (DSR) for Moble Ad Hoc Networks for IPv4, IETF, RFC 478.