Sesig Strategies for Chael Discovery i Cogitive Radio Networks (Ivited Positio Paper) Abdulkadir Celik, Ramzi Saifa, Ahmed E. Kamal Dept. of Electrical ad Computer Eg., Iowa State Uiversity, Ames, IA 50011 Dept. of Computer Eg., The Uiversity of Jorda, Amma, Jorda 11942 Abstract We cosider spectrum sesig strategies used to discover available spectrum i Cogitive Radio Networks (CRNs), usig both o-cooperative sesig ad cooperative sesig approaches. After itroducig the backgroud to sesig techiques, this positio paper focuses o strategies ad algorithms for coductig sesig such that the sesig time ad eergy are miimized, ad the likelihood of fidig available spectrum is maximized. The paper maily focuses o two approaches. The first is the orderig of chaels to be sesed, ad the secod is cooperative spectrum sesig. After discussig the available strategies uder each of these two approaches, we itroduce our ow proposed approaches. We first itroduce a method for sortig the chaels to be sesed i order to optimize the sesig time, while satisfyig PUs protectio ad false alarm costraits. The, we itroduce a framework for cooperative sesig of multiple PUs chaels by a group of SUs. The framework icludes strategies for assigig differet SUs to sese differet PUs chaels, selectio of the fusio ceter for each of the SUs clusters, ad routig sesig data withi the cluster from the SUs to the fusio ceter. We show how this framework is capable of optimizig differet objective fuctios. Several ope problems ad future research directios are also itroduced. I. INTRODUCTION Cogitive Radio Networks (CRNs) were itroduced to solve the problem of the uder utilizatio of the wireless spectrum, which has already bee exhausted due to allocatio to licesees [1]. I CRNs licesed users, called Primary Users (PUs), should be able to use their licesed spectrum bads wheever they wat, ad i the licesed localities. However, if the PUs are ot active, ulicesed users, termed Secodary Users (SUs), may use the PUs spectrum bads, but they must also moitor these bads for resumed PUs activities to vacate the spectrum bads i a timely maer, hece avoidig iterferece with the PUs. The above requires that the SUs be aware of the PUs chaels status, ad this is doe by sesig the PUs chaels. There are two modes of sesig: 1) out-of-bad sesig, which refers to sesig PUs chaels to determie whether PUs are active or ot, ad if ot active, determie that the chaels are usable by the SUs; ad 2) i-bad sesig, or moitorig, which refers to moitorig the status of the chaels used by the SUs to determie if the ower PUs have become active agai or ot. This paper focuses o out-of-bad sesig, which is the discovery of usable chaels. I this positio paper, we cosider the problem of out-ofbad sesig, ad discuss the properties that the sesig fuctio must satisfy. We also survey the most promiet chael sesig techiques. However, this paper is more focused o the sesig strategies, which deal with issues such as determiig the chaels to be sesed, ad their order, ad also determiig the sesig times that will satisfy the required properties ad costraits. Therefore, we discuss the state-of-the-art i the developmet of sesig strategies ad algorithms, ad discuss the advatages ad disadvatages of such techiques. We the itroduce two of our group s cotributios. The first oe is a algorithm to sort PUs chaels for sesig, such that the likelihood of fidig a available chael is maximized, while spedig the miimum sesig time ad eergy. The secod oe is a framework for cooperative spectrum sesig i the presece of multiple PUs, which optimizes the assigmet of SUs to PUs chaels. The approach also optimizes the selectio of the fusio ceter withi each cluster of SUs sesig a PU chael, ad optimizes the routig of sesig iformatio withi this cluster. Several ope research problems will also be itroduced. II. SPECTRUM SENSING TECHNIQUES Spectrum sesig is the task of achievig the spectral awareess about the PU occupacy i the sesig space with spectral, spatial ad temporal dimesios. We defie biary hypotheses H 0 ad H 1 which represet idle ad busy states of the chael, respectively. The, the purpose of sesig is to determie which hypothesis is valid. Cotiget upo the available iformatio about the primary sigal characteristics, a variety of spectrum sesig methods are studied i the literature. If the receiver has a absolute a priori kowledge about primary sigal, matched filters (MFs) are kow to be the optimal method for detectio withi a short sesig time to achieve a certai processig gai [2]. Cyclostatioary feature detectors (CFDs) exploit the kow statistical properties of primary sigals which arise from the spectrum redudacy caused by periodicity of modulated ad/or coded sigals. CFDs have the ability of recogizig the distictive features of differet primary sigals ad relatively better performace uder low SNR regimes [3]. Covariace-based sesig employs the fact that the statistical covariace matrices of primary sigal ad oise are differet from each other. Thus, it is robust agaist oise estimatio ucertaity. I particular, it gives a superior performace for detectig correlated sigals [4]. The techiques metioed above either deped upo the accurate kowledge regardig primary sigal characteristics or some other assumptios which are ot always readily available i practice. I the absece of a priori kowledge of primary sigals, however, eergy detectio has bee show to be robust to the ukow dispersed chaels ad fadig. To detect a primary sigal, eergy detector (ED) simply measures the received sigal eergy for a time iterval ad compares it with a predetermied threshold to decide o the PU activity. Uder eergy detectio, the k th sample of the received primary sigal take by SU m durig the sesig period T m, o chael with badwidth W is give as { v (k), H 0 y m, (k) (1) h m, s (k) + v (k), H 1
where v (k) is additive white Gaussia oise (AWGN), s (k) is the primary sigal, ad h m, is the covex evelope of the chael gai uder the slow fadig assumptio. The, ED measures the test statistic T m, (y) which is eergy of the received sigal ad compares it with a threshold λ m, to decide o PU presece/absece. I [5], T m, (y) has bee show to have cetral ad o-cetral chi-square distributio uder H 0 ad H 1, respectively. I the case of determiistic h m,, the probabilities of false alarm, ad detectio are give as [6] Pm, f = P [H 1 H 0 ] = Γ (N m,, λ m, /2) Γ (N m, ) ( 2Nm, Pm, d = P [H 1 H 1 ] = Q Nm, γ m,, ) λ m, where N m, = T m, W is the time-badwidth product, Γ ( ) is the gamma fuctio, Γ (x, a) = x e t t a 1 dt is the icomplete gamma fuctio, ad Q m (x, a) is the geeralized Marcum-Q fuctio defied as Q m (x, a) = 1 a m 1 x tm exp t 2 +a 2 2 I m 1 (at) dt where I m 1 is the (m 1) th order modified Bessel fuctio of the first kid. I the case of Rayleigh fadig, the closed form expressio for equatio (3) is derived i [7]. Out of the above sesig techiques, eergy detectio is usually the preferred approach ad this is due to a umber of desirable properties, icludig: 1) its low computatioal complexity; 2) applicability to ay sigal shape; ad 3) it does ot require ay a priori kowledge about the PUs ad their trasmissio characteristics [8]. Therefore, i the rest of this paper, we oly cosider spectrum sesig usig eergy detectio. III. SENSING TIME AND THRESHOLD OPTIMIZATION The most sigificat purpose of cogitive radio techology is to icrease the spectral efficiecy of wireless etworks i a opportuistic maer. Therefore, the first tred i the sesig optimizatio studies has focused o maximizig the achievable throughput subject to detectio errors: probabilities of misdetectio (P m = P [H 0 H 1 ]) ad false alarm (P f = P [H 1 H 0 ]). While miimizig the former result i a higher level of PU protectio from SU iterferece, miimizig the latter is the key part to maximize uused spectrum utilizatio. Furthermore, sesig for loger duratio provides more measuremets for the decisio maker, hece decreasig the error probabilities with icreasig the measuremets. If a slotted time frame is cosidered, sesig for a loger duratio results i achievable throughput reductio. If the eergy detectio is chose for sesig white space, threshold determiatio impacts P f. Moreover, P m decreases as the sesig duratio icreases for a give P f ad received SNR. Thus, required detectio threshold should be joitly optimized alog with sesig duratio i order to maximize the achievable throughput whe the optimizatio is costraied o PU protectio ad spectrum utilizatio. I this paper, we cosider path loss ad Rayleigh fadig for both cotrol ad sesig chaels. If we cosider SU m sesig chael, based o received SNR γ m, ad correspodig threshold λ m,, each SU ca locally fid its ow (2) (3) optimal sesig time subject to a PU protectio ad spectrum utilizatio threshold. Assumig sesig power is costat for every PU ad SU pair, i.e., P s m, = P s, m,, the the optimal eergy cosumed by SU m for sesig chael is give by ε m, = P s T m,. Accordigly, the optimal local sesig eergy ε m, is calculated usig Algorithm 1 where P d ad P f are required thresholds for detectio ad false alarm probability, respectively. The costraits i Lies 2 ad 3 protect PUs from SU iterferece, ad esure adequate spectrum utilizatio by SUs, respectively. Algorithm 1 : Optimal sesig eergy of the SU m at chael 1: Mi ε m, 2: s.t. P d m, P d 3: P f m, P f IV. CHANNEL SORTING Chael sortig is a approach to fid the sequetial order of the chaels to be followed durig searchig a idle chael. Sortig criteria may differ from applicatio to applicatio. Some sortig techiques may favor sortig the chaels based o chael capacity. Chael sortig techiques which reduce search time should ideally take three factors ito cosideratio: 1) The probability of the chael beig idle, P(H 0 ), which ca also be coditioal o the last sesed status ad time sesig. This ca also be based o modelig the chael activities, usig either parametric, or o-parametric statistical models. 2) Chael sesig time, which is iflueced by the characteristics of the chaels betwee the PUs ad the SUs, as described i Sectio III. Ad, 3) Switchig times betwee the chaels that are sesed, which is depedet o the differece betwee the cetral frequecies of these chaels, ad is also depedet o the techology of the Phase-Locked Loops (PLL) used. Switchig times ca be sigificat, ad therefore, they have to be take ito cosideratio. The literature icludes three basic approaches for chael sortig to miimize search time: The first approach is sequetial searchig, i which the chaels are searched sequetially, typically startig from the lowest frequecy chael[9]. Although it provides a miimized switchig time, this approach suffers from the fact that the chael sortig does ot take ito cosideratio the chael availability likelihood, e.g., i terms of P(H 0 ), or the chaels characteristics, which impact the sesig time. The secod approach cosiders the likelihood that the chaels will be idle. Kim ad Shi [10] itroduced such a approach where sesig-sequece sorts chaels i descedig order of the probability of beig idle. Also, [11] fids a search sequece that helps i fidig spectrum opportuities with miimal delay. To achieve their goal, [11] maitais two chael lists: back-up chael list (BCL) ad cadidate chael list (CCL). Both of these two approaches do ot optimize the sesig
time per chael, ad they also do ot take chael switchig times ito cosideratio. The third approach sorts chaels radomly. We believe that a sesig strategy that takes all above three factors ito cosideratio will result i better performace, i terms of faster discovery of available chaels, ad miimum sesig eergy cosumptio. However, this problem is hard, ad ca oly be solved offlie. Hece, developig algorithms for sortig chaels, while takig ito cosideratio all three factors, is a importat problem. Our group has developed a heuristic algorithm for chael sortig that takes all above factors ito accout, which is show i Algorithm 2. Algorithm 2 : Fidig the best sequece of chaels 1: For i = 1 up to M 2: Mi=, MiIdex=-1 3: For s = i up to M 4: Mi t(s) = [ts(s) + t sw(f 0, f s)] P r s(h1) 5: s.t. P r(h1 H1) P d (s) 6: P r(h1 H0) 0.1 7: if (t(s) Mi) 8: Mi=t(s) 9: MiIdex=s 10: Ed if 11: Ed For 12: Temp=f(i) 13: f(i)=f(miidex) 14: f(miidex)=temp 15: f 0 = f(miidex) 16: Ed For The algorithm miimizes the sesig plus switchig time amog the remaiig chaels, ad it works i iteratios. I iteratio i of the outer for loop, a chael that miimizes the sesig + switchig time will be foud. The ier for loop searches the M i chaels to fid the chael which miimizes the sesig plus switchig time ad makes it the i th chael to be sesed. Lies 4-6 fid the miimum sesig + switchig time for each chael give the curret chael. Lies 7-10 keep track of the chael that miimizes the sesig + switchig time. Lies 12-15 swap the ext chael with the chael that miimizes sesig + switchigtime. A. Search Sequece Results Fig. 1: Compariso of search times for differet switchig times We compare our approach of sortig the chaels with: 1) searchig the chaels sequetially which does ot cosider ay other properties of the chaels like P(H 0 ), SNR, or required sesig time; 2) the approach that sorts the chaels accordig to the P(H 0 ). We simulate 51 chaels i the rages of 470MHz to 770 MHz. Each chael is 6MHz wide. Each chael has: 1) radom SNR betwee -10 db ad -20 db, 2) radom P(H 0 ) betwee 0.2 ad 0.8, ad 3) radom required detectio probability P d betwee 0.92 ad 0.99. We cosider differet switchig times that ca rage from 10µs/1M Hz up to 0.1ms/1MHz. Figure 1 compares our approach to the other two approaches. It is clear that our approach is better tha the other approaches because our approach cosiders both the switchig time ad the probability of beig idle. Sortig accordig P(H 0 ) takes the logest time. This is because P(H 0 ) does ot take ito cosideratio sesig ad switchig times. V. COOPERATIVE SPECTRUM SENSING (CSS) The use of eergy detectio for chael sesig is based o a uderlyig assumptio of perfect oise power estimatio. Therefore, the ucertaity i oise results i SNR wall ad high false alarm probability. Furthermore, receiver ucertaity ad hidde termial problem caused from radio propagatio characteristics are other matters of challege for EDs [3]. CSS ca alleviate the shortage of idividual SUs by gettig beefits of spatial diversity of SUs sice it is highly ulikely for spatially distributed SUs to cocurretly suffer from similar chael impairmets. CSS ca be grouped ito subcategories based upo the cooperatio method withi the etwork (cetralized ad distributed) ad the shared data type (soft data fusio ad hard decisio fusio). Eve though exploitig the soft data fusio results i a superior performace, sharig large amout of measuremet data eds up with commuicatio overhead which caot be sustaied by a badwidth limited CC. Hece, hard decisio fusio surpass the soft data fusio with its low reportig overhead. Noetheless, as the umber of cooperatig SUs ad the geographical area of the etwork icrease, CC still experieces badwidth isufficiecy alog with reportig ureliability, power cosumptio ad delay due to log distaces. To surmout these problems, groupig SUs ito clusters is a favorable ad effective techique to reduce cooperatio rage ad commuicatio overhead [12], [13]. I particular, a eergy efficiet clusterig method plays a vital role for extedig the battery life of SUs if the mobility ad power resource limitatios of SUs are take ito cosideratio. If we defie the spectrum utilizatio ad eergy cosumptio as currecy ad commodity, respectively, a eergy ad throughput efficiet desig would be clusterig SUs such that commodity per currecy is maximized subject to a PU protectio level. For eergy efficiecy, the total eergy cosumptio withi each cluster will be miimized i.e. itracluster eergy miimizatio. For throughput efficiet desig, we will miimize the maximum sesig duratio withi each cluster to maximize remaiig time for secodary data trasmissio. This objective is based o the fact that a cluster head would ot diffuse back the fial decisio util the SU with logest sesig time fiish ad report its sesig results. Furthermore, fairess is aother desig factor to be focused o because a SU would like to get a fair beefit i retur for spedig eergy for others. Sice sesig eergy cosumptio is proportioal to sesig duratio, a fair eergy efficiet clusterig may be achieved by miimizig the total eergy cosumptio differece amog clusters i.e. iter-cluster eergy miimizatio. Similarly, a fair throughput efficiet desig may be obtaied by miimizig the achievable throughput
differece amog clusters. Cosiderig the objectives ad costraits above, plaig the selectio of SUs ito clusters is a otrivial task, especially whe geolocatio iformatio is ot available. Eve if the optimal clusterig of a CRN is give, pickig a optimal cluster head (CH) amog cluster members is still a desig issue. Decisio fusio rules employed by each CHs is also required to be desigated uder imperfect CC coditios. Moreover, if there exists multiple chaels, the matters give above become a complicated optimizatio problem. I the followig, we itroduce a framework for addressig all the issues above, which is based o our recet work i [14]. A. Phases of Cooperatio Assume that for a give sesig period, there exists M SUs available to help with sesig ad there exists N potetial PU chaels to sese, we propose a CSS process that cosists of three phases: 1) Sesig Phase: This is doe usig the procedure ad algorithm described i Sectio III based o received SNR γ m, ad correspodig threshold λ m,, for SU m ad chael. Each SU ca locally fid its ow optimal sesig time subject to a PU protectio ad spectrum utilizatio threshold. 2) Reportig Phase: Uder oisy CC ad maximum trasmissio power limitatio, sigle-hop reportig liks betwee SUs ad CHs may ot always yield a reliable ad eergy efficiet collaboratio amog SUs. Preferably, employig a multi-hop method for the reportig phase does ot oly mitigate the commuicatio rage limitatio but also gives a opportuity for exploitig a algorithm which fids the multi-hop path with miimum error probability from cluster members to a specific CH. Let us cosider a asymmetric directed graph of cluster, G (C, L ), with the set of vertices C represetig SU odes ad the set of liks represetig the direct hop betwee SU odes i ad j. Deotig the bit error probability (BEP) of the lik l i,j as p i,j = 1 q i,j, ay multi-hop path from SU i to SU j, i j, has the bit success probability (BSP) of q i j = k,l i j q k,l. Ideed, maximizig q i j is equivalet to miimizig the egative sum of logarithm of q i j. By doig so, Dijkstra s algorithm ca be employed to calculate the route with miimum path cost from SU i to SU j. Hece, the best CH amog members of cluster with miimum BEP ca be determied as follows CH = argmi j C D i j (4) i C i j where i j ad D i j are Dijkstra path ad its cost, respectively. 3) Decisio Phase: After the fial CH assigmet, each SU withi cluster reports its fial biary decisio u i = {0, 1} to CH over the route i j. Defiig the radom variable k = i C u i, k is biomially distributed uder perfect reportig chael ad i.i.d. SU reports, which is a.k.a. k- out-of-n rule. Uder the k-out-of-n rule, CH decides o H 1 for PU if at least k of SUs report 1, i.e. k k. Although all local observatios are i.i.d. before the reportig phase, sice each multi-hop path has a differet success rate, CH receives o-idetical detectio ad false alarm probabilities which are deoted by P i, d ad P f i,, respectively. For idepedet ad oidetically distributed (i..d.) SUs, k has Poisso-Biomial distributio [15]. The optimal k ( k ), however, may ot be the same for all scearios. Therefore, we umerically fid ( k which miimizes the total error rate, Q T ( k) = Q f ( k) ( k)) + 1 Q d. B. Multi-objective Clusterig Optimizatio (MOCO) To fulfill the objectives metioed earlier, we defie the fuctio I (m) which idicates the membership of SU m [1, M] i cluster [1, N ]. For each cluster, three types of objective vectors are defied to be miimized: F R N, G R N, ad H R 2 with elemets F = ε m,, G = max (T m, ), m C m C H 1 = max (F ) mi (F ), H 2 = max (G ) mi (G ) where F is for itra-cluster total eergy cosumptio miimizatio withi cluster, G is for itra-cluster maximum sesig time miimizatio withi cluster, such that the time available after sesig phase is maximized for maximizig the achievable throughput. H 1 ad H 2 hadle the iter-cluster total eergy cosumptio ad throughput balace, respectively. Based o these objectives, we formulate Algorithm 3 which clusters the etwork as follows: Algorithm 3 : MOCO 1: Mi F, G, H 2: s.t. N =1 I(m) 1, m 3: M m=1 I(m) 1, 4: Q d (k ) Q d, 5: Q f (k ) Q f, 6: T m, τ, m, Sice, a SU ca sese at most oe chael durig a sesig period, N =1 I (m) 1 i Lie 2. Moreover, Lie 3 makes sure that each PU chael is sesed by at least oe SU. Lies 4-5 are global decisio probability costraits which are eeded to be satisfied for reportig ad decisio phase reliability. The costrait i Lie 6 o the sesig time is especially beeficial to take SUs with uecessarily log sesig duratio out of cosideratio. C. Results ad Aalysis Algorithm 3 is a multi-objective mixed-iteger combiatorial optimizatio problem which is NP-hard, therefore, employig meta-heuristic methods to obtai a sufficiet solutio withi a reasoable time frame is preferable i practice. Hereupo, we will use the Nodomiated Sortig Geetic Algorithm-II (NSGA-II) [16] for solvig MOCO. Fig. 2 shows the error performace ehacemet which comes with the method proposed i the reportig phase, where the gree dashed lie, red dashed lie ad red solid lie show the total reportig error of proposed multi-hop techique, the worst ad the best case of sigle-hop techique, respectively. As we expect, a superior performace is obtaied through the proposed
1 2 3 4 5 6 7 8 9 Total Reportig Error 10 0 10 1 10 2 10 3 10 4 Sigle hop Worst CH Sigle hop Best CH Multi hop Dijkstra CH Clusters Fig. 2: Compariso betwee sigle-hop ad multi-hop approach method. For the populatio size of 50 ad geeratio size of 20, the results for MOCO objective fuctios ad clusterig topology of the etwork usig NSGA-II are show i Fig. 3(a) ad Fig. 3(b), respectively. At the bottom of the Fig. 3(a), colorbar rages from 1 to 50 represets the populatios of geeratios. I Fig. 3(b), the amoeba-like shapes represet the clusters i each of which square shape represets the PU with the umber iside, diamod shapes represet cluster members with SNR values i db, ad hexago shapes represets CH selected by the proposed techique. Fig. 3: (a) MOCO Results for differet objectives ad (b) Fial clustered etwork topology VI. OPEN RESEARCH ISSUES Although the problem of spectrum sesig has bee extesively studied i the literature, there are still ope issues that eed to be dealt with. We outlie some of these research issues here: Uder CSS, SUs are expected to participate i the sesig process, ad they fid chaels which may the be used by other SUs, which requires a motivatio or icetive. Game theory has bee used i the literature to facilitate participatig i cooperative sesig, e.g., [17], ad it was show that this ca result i improvig SUs throughput. However, there are still ope issues whe applyig icetives to facilitate CSS. These iclude the sesig eergy cosumptio, especially whe SUs are battery operated, ad how this affects their participatio i sesig. These also iclude the level of traffic that each of the SUs geerates, ad how this will be related to its participatio i sesig. Aother issue is the dyamic chael sesig ad schedulig of sesig. I our framework i Sectio V, we cosidered the case of the SUs beig allocated to sese a group of PUs chaels. I reality, there may be a very large umber of chaels ad the cluster formatios may ot be able to cover all chaels while guarateeig effective sesig. I particular, uder the scarcity of available SUs to cooperate, there may ot be sufficiet SUs to search PU chaels. Hece, assigig SUs with better chael qualities to differet clusters i differet sesig rouds would result i a feasible ad more eergy efficiet schedulig scheme. Therefore, assigmet of SUs to clusters ad schedulig the clusters to perform sesig is aother hard ope problem. Related to the above problems is the problem of the trust of sesor odes. If a sesor ode, that is ivolved i CSS, has bee compromised, the this ode may sed icorrect sesig iformatio which may chage the sesig outcome. Therefore, strategies to detect ad filter out sesig results from compromised odes eed to be developed. Chael sortig discussed above oly cosidered from a sigle SU s perspective. 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