Voluntary Spectrum Handoff: A Novel Approach to Spectrum Management in CRNs

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1 Volutary Spectrum Hadoff: A Novel Approach to Spectrum Maagemet i CRNs Suk-U Yoo ad Eylem Ekici Departmet of Electrical ad Computer Egieerig The Ohio State Uiversity, Columbus, OH, USA Abstract I this paper, a ew spectrum maagemet scheme for CRNs called Volutary Spectrum Hadoff (VSH) is itroduced. The two mechaisms proposed uder VSH estimate opportue times to iitiate uforced spectrum hadoff evets to facilitate setup ad sigalig of alterative chaels without havig commuicatio disruptio, which occurs whe a secodary user is forced out of a operatig spectrum due to primary user activity. VSH has bee evaluated through extesive simulatios. Simulatio results idicate that VSH sigificatly reduces the commuicatio disruptio duratio due to hadoffs. Idex Terms Cogitive radio etworks; Hadoff maagemet; Primary user estimatio. I. INTRODUCTION The Cogitive Radio (CR) cocept has bee proposed to improve the spectrum usage efficiecy by exploitig the existece of spectrum holes [1]. Devices usig CRs referred to as Secodary Users (SUs), are aware of their spectrum eviromets ad chage their trasmissio ad receptio parameters to avoid iterferece with licesed spectrum users referred to as Primary Users (PUs). Networks cosistig of odes equipped with CRs are referred to as Cogitive Radio Networks (CRNs) [2], [3]. CRNs are etworks that have cogitive ad recofigurable properties ad the capability to detect uoccupied spectrum holes ad chage frequecy for ed-to-ed commuicatio [2], [4], [5]. I CRNs, spectrum mobility causes a ew type of hadoff referred to as spectrum hadoff [2]. I cellular etworks, mobile devices trasfer a ogoig coectio betwee base statios due to user mobility or chael degradatio. However, i CRNs, the umber ad characteristic of available spectrum at a ew locatio may vary with local PU behavior. Moreover, the spectrum hadoffs i CRNs icur loger delays or temporary commuicatio disruptios as SUs must search for spectrum holes ad discover a ew chael at every spectrum hadoff. To sese ad discover spectrum holes which have log life times, probabilistic ad adaptive spectrum sesig algorithms have bee proposed i the literature [6], [7], [8]. For opportuistic spectrum discovery, sesig-period adaptatio ad optimal sesig-sequecig schemes at chael switchig are preseted i [6]. A BTR (Busy Time Ratio)-based chael quality metric ad a distributed measuremet scheme are proposed i [7]. Opportuistic access schemes icludig frequecy hoppig are explored i [9]. I spectrum mobility This work is supported by NSF uder grat umber CCF maagemet, spectrum sharig is also a importat step to discover a commoly available chael o both trasmitter ad receiver SUs. To share sesig iformatio ad to setup commuicatio liks, commo cotrol chael cocepts are advocated i [10], [11]. I this paper, we propose a ew type of spectrum hadoff referred to as Volutary Spectrum Hadoff (VSH) to reduce temporary commuicatio disruptio time which is caused by spectrum hadoffs. VSH is ot ecessarily triggered by PU detectio as i covetioal spectrum hadoff, referred to as Forced Spectrum Hadoff (FSH) i this paper. Estimatig remaiig time util PU access, SUs volutarily chage the spectrum without coflictig with PUs. By volutarily chagig spectrum at estimated times, SUs ca reduce delays caused by spectrum hole search ad iformatio sharig by overlappig these fuctios i time with data commuicatio. First, we itroduce a ew method for PU spectrum usage estimatio. We propose two spectrum selectio algorithms, called Trasitio Probability Selectio (TPS) ad Reliability Based Selectio (RBS), to determie the spectrum bad to switch to. Our proposed algorithms ca be used for arbitrary probability distributios of PU chael occupacy. VSH reverts back to FSH i case a PU accesses a spectrum curretly used by a SU before a VSH occurs. Simulatio results idicate that SUs have shorter commuicatio disruptio duratios with VSH. II. ARCHITECTURE A. Prelimiaries PU chael occupacy is modeled as a ON-OFF process alteratig betwee ON (busy) ad OFF (idle) periods [6], [7]. We specifically focus o expoetial ad Erlag distributed ON-OFF periods. However, our methods ca be applied to arbitrary ON-OFF period distributios based o sesig data usig pdf estimatio methods described i [12]. For spectrum iformatio sharig ad commuicatio, our proposed work is based o a dedicated commo cotrol chael. B. Network Model The PUs operate o licesed bads ad are owers of such bads. SUs ca utilize uused licesed spectrum. SUs must vacate licesed spectrum as soo as PU activity starts. SUs ca access oe of N licesed chaels at a time. A Spectrum Server (SS) is used to log SU activity, which is the used to deduce past PU activity [13], [14]. The mai fuctioalities /10/$ IEEE

2 of the SS are to store spectrum usage iformatio of SUs ad to provide spectrum iformatio to other SUs upo request. Whe a SU seses the spectrum locally, it observes the combied spectrum usage iformatio of both PUs ad SUs. With the SU iformatio from SS, a SU ca estimate the spectrum usage of PUs as the differece betwee the locally sesed combied usage ad the iformatio from SS. III. SPECTRUM USAGE ESTIMATION VSH is primarily based o the estimatio of PU activity. Whe the PU traffic is more dyamic ad fast varyig as i cellular etworks, spectrum estimatio mechaisms should be more adaptive to reflect the traffic behaviors. Eve whe PU traffic behavior is statistically steady, PU spectrum usage may dyamically chage wheever the SU moves to ew locatios. To cope with spectrum usage behavior chages, we defie two sesig periods: sesig widow ad history widow. Sesig widow is the basic time uit over which spectrum usage is observed. A SU takes S samples of a chael s status durig a sesig widow T. Each sample is coverted to a biary value represetig primary user activity. SUs compute PU spectrum usage as the differece betwee the locally sampled biary values ad the biary values of SU spectrum usage provided by the SS. The average obtaied durig a sesig widow represets a short term statistics of the PU usage. For estimatios to be useful for VSH, statistics must be averaged over loger periods of time. We use a history widow of legth K, K T, for estimatio purposes. The value of K is icreased as log as the average estimated i a sesig widow does ot deviate more tha ɛ fractio of the average obtaied over the history widow. If the deviatio is more tha ɛ, the K is decreased aggressively to capture chages that occur i the PU spectrum usage behavior. A. Sesig Widow Size Selectio Sice a SU does ot kow the traffic behavior or rates of PUs, the spectrum sesig widow size must be iferred from the spectrum sesig data. To this ed, we adopt the followig approach. The spectrum usage is represeted as a sequece of busy (used) 1 ad idle (uused) states 0 [6], [7]. I the O-Off chael model, the sojour time of a ON period for chael is modeled as a radom variable TON with the probability desity fuctio f TON (y), y>0. Similarly, a OFF period is modeled as TOFF with f TOF (x), F x > 0 [6]. The observatio is based o the cycles of the spectrum states. We defie a spectrum cycle C as the time from the begiig of oe state to the ed of aother state. The average of l spectrum cycles Cl o chael is computed m k 1 +m k t=m k 1 +1 X [t] as Cl = l k=1 m k /l, m = l k=1 m k 2l, where X [t] is the biary chael observatio of chael at t, m k (m 0 =0) is the umber of samples o the k th spectrum cycle, ad m is the umber of total samples. The sesig widow size is chose such that var(cl ) α, where l l mi (a pre-determied value), ad α is tuig parameter. The geeral pdf of the PU activity duratios ca be estimated via pdf estimatio methods of [12]. Although our methods are applicable to arbitrary distributios, we focus o two example distributios, i.e., expoetial ad Erlag. The spectrum sesig time T for chael is determied as T = l [E{TON } + E{T OFF }]. B. Spectrum Usage Estimator A SU updates the spectrum usage estimate every T secods usig the sesig data ad iformatio obtaied from SS. The, the spectrum usage estimator calculates PU spectrum usage ratio with history widow data. The history widow size is icreased by oe or decreased by D fractio accordig to the deviatio criterio of Eq. 1. The estimated average o chael at time t (assumed as a iteger) ca be expressed as follows: X T = 1 T T i=1 X [t T + i], X K = 1 K K i=1 X [t K + i]. History widow size K o chael is computed usig Equatio 1: K = { mi(k +1,KMAX ),if X K XT ɛ XK max( K D K,T ), otherwise IV. SPECTRUM HANDOFF MANAGEMENT A. Volutary Spectrum Hadoff Volutary spectrum hadoff is triggered by reachig the threshold probability or time of PU presece predictio. Without PU detectio, a SU ca predict a future PU activity ad chage the spectrum bad which has lower probability of PU detectio. The volutary spectrum hadoff time which is called residual spectrum lifetime ca be estimated by the spectrum selectio algorithms. The purpose of VSH is to reduce commuicatio disruptio time caused by the sudde PU presece. If a SU kows the time to switch to aother chael, it prepares for chael switchig by searchig for spectrum holes ad sharig spectrum iformatio with other SUs i advace. I CRNs, the delay of FSH icludes spectrum hole searchig delay (t search ), spectrum iformatio sharig delay (t sharig ) amog SUs, chael orderig ad selectio delay (t decisio ), ad chael switchig delay (t switchig ). With VSH, a SU ca overlap the spectrum aalysis ad sharig time with the ogoig commuicatio. Cosequetly, the actual commuicatio of the SU cotiues while preparig for VSH. As a direct result, the commuicatio sessio is disrupted for shorter periods of time uder VSH tha uder FSH. The sessio disruptio duratio for FSH (D FSH ) ad VSH (D VSH )ared FSH = t search + t sharig + t decisio + t switchig, D VSH = t switchig. B. Spectrum Lifetime Estimatio Whe a SU predicts PU presece (or ed of the spectrum lifetime), it switches to a ew spectrum bad without detectig a PU. The spectrum lifetimes of target chaels for VSH are estimated by two algorithms. The proposed algorithms are based o the probability derived from the estimated pdfs with averages (E{TON } ad E{T OFF }) ad variaces (var(t ON ) ad var(toff )) of ON ad OFF periods, respectively. For (1)

3 other distributios, pdf estimatio methods such as [12] ca be adopted. The proposed two algorithms are as follows: TPS (Trasitio Probability Selectio) Derivatios of trasitio probabilities for the geeral ON/OFF processes usig Laplace trasform are itroduced i [10]. I particular, the trasitios probabilities for expoetially distributed ON/OFF periods are calculated as P 00(t) =(1 u )+u e (λ ON +λ OF F )t P 01(t) =u u e (λ ON +λ OF F )t, where, u λ = OF F λ. Similarly, the trasitios probabilities for Erlag-distributed (k=2) ON/OFF periods ON +λ OF F are P00(t) =1 1 (λ ON λ OF F )2 4 λ e 1 2 (λ ON +λ OF F )t sih( 1 2 Ct) ON C [ 4λ ON λ OFF (λ ON λ OFF )2 e (λ ON +λ OF F )t +(λ ON + λ OFF )2 e 1 2 (λ ON +λ OF F )t cosh( 1 2 Ct)](1 u ) P01(t) =1 P00(t), C = (λ ON )2 6λ ON λ OFF +(λ OFF )2 (3) With the trasitio probabilities P 00 (idle to idle trasitio) ad P 01 (idle to busy trasitio) from reewal theory, we ca estimate spectrum lifetime for VSH. We defie the spectrum life time t o chael as t = (2) argmax {t P00(t) P01(t)}. (4) 0<t (t Max K ) I the TPS algorithm, if the probability crossover does ot happe due to low PU activity, the SU stays o the same chael ad VSH reverts back to FSH. O the other extreme, if a short spectrum lifetime is estimated such as 0 <t oe sesig period, the spectrum lifetime t is set to oe sesig period ad SU switches to a ew chael due to the predictio of immiet PU presece oly if there are chaels with loger spectrum lifetime estimatios. RBS (Reliability Based Selectio) RBS is based o the reliability theory [15] ad estimates spectrum lifetime of the OFF periods. To derive a geeral equatio, we defie the followig; T : time util ext primary user detectio (r.v.), t: time after the detectio of o primary user, S(t): spectrum lifetime fuctio, F (t): cumulative distributio fuctio of T, f(t): probability desity fuctio of T. Spectrum lifetime fuctio is defied as S(t) =P (T > t) =1 P (T t) =1 F (t). S(t) is a curve describig the proportio of spectrum availability as a fuctio of t ad expressed i terms of cumulative distributio fuctio F (t) of the OFF process. PU detectio rate μ(t) is defied as the relative rate for spectrum lifetime fuctio declie: μ(t) = ds(t) S(t)dt = d l S(t) (5) dt From Eq. 5, the spectrum lifetime fuctio is computed as S(t) =e t 0 μ(u)du. For example, for expoetially distributed TOFF with rate λ OFF, the detectio rate ca be replaced by costat rate μ(t) = S (t) S(t) = λ OFF = cost. With the costat PU detectio rate, the spectrum lifetime fuctio ca be described by the expoetial distributio S(t) =e λ OF F t. Similarly, whe TOFF is Erlag-distributed, the detectio rate is expressed as μ(t) = (λ OFF )k t k 1 /(k 1)! k 1 m=0 (λ OFF t)m /m! With the spectrum lifetime fuctio, the spectrum lifetime t o chael is computed as t = (6) argmax {t S(t) S threshold }. (7) 0<t (t Max K ) S threshold determies the aggressiveess of the VSH attempts. C. Volutary Spectrum Hadoff Process Uder VSH, a SU uses spectrum lifetime estimatio to select a potetial chael to switch to. The SU selects a chael which has the logest spectrum life time t that is estimated by the proposed algorithms. The sequeces of evets leadig to a VSH are as follows: 1) Share the uused spectrum iformatio ad estimated spectrum lifetimes t betwee SUs. 2) Decide o a chael which has the maximum spectrum lifetime o both SUs. 3) Share ad cofirm the decisio results. 4) Whe spectrum lifetime expires, switch to the ew chael. Note that steps 1 3 occur without disruptig the commuicatio sessio of the SU uder VSH. If a PU is detected before estimated spectrum lifetime, these steps are repeated (as i FSH) i which case all 4 steps cotribute to the disruptio duratio. V. PERFORMANCE EVALUATION VSH is evaluated through simulatios. We assume N chaels ad a ON-OFF PU traffic source model. We assume that ON ad OFF periods are iid positive radom variables with expoetial or Erlag distributios. For the spectrum usage estimatio ad PU detectio, SU seses all N chaels every secod. Whe a SU detects PU presece, it vacates curret spectrum without further trasmissio ad searches for a empty spectrum bad. We cosider the followig two FSH algorithms for compariso: Radom Selectio (RS): Whe FSH is triggered, a SU radomly selects a chael amog curretly available oes. Lowest Average Selectio (LAS): Whe FSH is triggered, a SU selects the available chael with the lowest average spectrum usage o history widow (i.e., lowest BTR [7]). To evaluate our proposed schemes, we compare TPS ad RBS (S threshold =0.5) algorithms for VSH with RS ad LAS for FSH. I our simulatios, we cout the umbers of forced ad volutary spectrum hadoffs ad measure the Commuicatio Disruptio Ratio (CDR). CDR is calculated as disruptio periods/total commuicatio time. I our simulatios, the disruptio period of SU commuicatio icreases whe FSHs or VSHs are triggered, or whe there is

4 (a) CDR Compariso i IM (b) CDR Compariso i DM (c) CDR Compariso i SM (d) CDR Compariso i HM Fig. 1. CDR Compariso with Four Traffic Models o available chael. I the latter case, the SU waits util a spectrum hole emerges. Simulatio results about the chael switchig ad packet trasmissio delays are provided i several existig works [6], [7], [16]. I our system model, the delay compoets of FSH iclude t search, t sharig, t decisio, ad t switchig. I [6], the chael switchig delay icludig t search, t decisio, ad t switchig is reported betwee 80 msec ad 350 msec. I [16], the packet delay of a sigle hop commuicatio is reported as 100 msec, which ca be cosidered as t sharig /2. With these simulatio results, we assume that a SU s commuicatio is disrupted for D FSH =500 msec durig FSH to detect spectrum holes ad coect to aother SU. I case of VSH, we assume that SU s commuicatio is disrupted for 50 msec to switch to a ew spectrum. We choose a maximum history widow size of 1000 sec, which is five times larger tha the spectrum sesig widow of 200 sec. The total simulatio time is 5000 secods for each cofiguratio. The results have a trasiet period of 1000 sec, which are igored whe computig averages. A. Commuicatio Disruptio Ratio Compariso For various commuicatio scearios, we defie 4 traffic patters with Erlag distributio (k=2) such as Idetical Mode (IM), Dese Mode (DM), Sparse Mode (SM), ad Hybrid Mode (HM) which have differet chael usage. I each mode, the umber of chaels is 9. Idetical Mode: I idetical mode, all 9 chaels are cofigured with E{T ON } = 3.0 ad E{T OFF } = 3.0. I Figure 1(a), VSH schemes have aroud 10% disruptio ratios ad FSH methods have aroud 13%. This meas that durig 5000 secods simulatio, TPS ad RBS with VSH have 150 secods loger uiterrupted coectio time which is caused by 23% 35% fewer FSHs. The CDR performace is ordered as RBS > TPS > RS > LAS. Dese Mode: I dese mode, all 9 chaels are cofigured with E{T ON } = 9.0 ad E{T OFF } = 3.0 to simulate high spectrum usage behavior. From Figure 1(b), we ca see the TPS ad RBS have 11.5% ad 14.5% disruptio ratios, respectively, whereas RS ad LAS have 19% disruptio ratios. The 4.5% 7.5% performace gais of TPS ad RBS are obtaied from reducig FSH couts ad replacig them with VSHs. This meas that SUs ca have loger uiterrupted coectio times with VSH whe PU spectrum usage ratio is high. Amog VSH schemes, TPS has superior performace over more aggressive VSHs tha RBS. The CDR performace is ordered as TPS > RBS > LAS > RS. Sparse Mode: I sparse mode, all 9 chaels are cofigured with E{T ON } = 3.0 ad E{T OFF } = 9.0 to simulate low spectrum usage behavior. From Figure 1(c), all spectrum selectio algorithms icludig VSH schemes have similar disruptio ratios aroud 4.3% 4.8%. This meas the TPS ad RBS schemes deliver small beefits sice FSH occurs before estimated spectrum lifetimes are reached due to low PU spectrum usage. Hybrid Mode: To simulate heterogeeous spectrum usage behaviors, 3 chaels are cofigured with E{T ON } = 3.0 ad E{T OFF } = 9.0, 3 chaels with E{T ON } = 6.0 ad E{T OFF } = 6.0, ad 3 chaels with E{T ON } = 9.0 ad E{T OFF } = 3.0. I compariso results show i Figure 1(d), LAS, TPS, ad RBS have lower CDR tha RS. The CDR performace is ordered as RBS > LAS > TPS > RS. B. Effect of Primary User Spectrum Usage To show the effect of PU spectrum usage, we ra simulatios with varyig PU spectrum usage ratios betwee 0 (o PU activity) ad 1 (permaet PU activity) with expoetially distributed O-Off periods. The PU spectrum usage ratio o a chael is defied as E{T ON }/(E{T ON } + E{T OFF }). For every parameter combiatio, we average the results for 4000 sec. simulatio time. For CDR comparisos of all spectrum selectio algorithms with differet PU spectrum usages, the cotrol of PU spectrum usage ratios is achieved usig a variable λ ON =1/E{T ON } ad afixedλ OFF =1/E{T OFF } as 1/3. Figure 2(a) is the exteded versio of Figure 1(a) with a differet pdf (Expoetial) ad various PU spectrum usage ratios. Figure 2(a) shows that TPS ad RBS have lower disruptio ratios i most cases. Betwee 0.3 ad 0.9 of PU spectrum ratio, VSH schemes have beefits from volutary hadoffs by reducig forced hadoffs. Betwee VSH schemes, RBS has better performace i most cases. Betwee 0.3 ad 0.8 of PU spectrum ratio, RBS quite aggressively reduces FSH couts with active VSHs

5 (a) CDR with E{T OF F } =3 (b) CDR with RS/RBS (c) CDR with LAS/RBS (d) CDR with TPS/RBS Fig. 2. CDR Comparisos with PU Spectrum Usage Variatio ad has lower disruptio ratios tha TPS VSH scheme. The aggressive VSHs of RBS are caused by short spectrum lifetime estimatios. The sharp icrease i CDR betwee 0.8 ad 1 for all schemes is caused by the uavailability of chaels. To compare CDR performace amog spectrum selectio algorithms, we calculate the CDR ratios of RS/RBS, LAS/RBS, ad TPS/RBS. Sice RBS has relatively stable ad superior performace result with various traffic parameters, we choose RBS as a compariso base. I compariso results, ratios greater tha 1 mea that RBS has superior performace. I case of RS ad LAS comparisos i Figures 2(b) ad 2(c), the ratios are greater tha 1 i all rages. Betwee PU spectrum usage ratios 0 ad 0.3, the CDR ratios icrease slowly. Especially, RBS CDR has loger udisrupted coectio times betwee PU spectrum usage ratios 0.3 ad 0.9. Beyod PU spectrum usage ratio of 0.9, the CDR ratios coverge o 1 because there are o spectrum holes for SUs. I compariso of TPS with RBS i Figure 2(d), RBS has better performace betwee PU spectrum usage ratios 0.3 ad 0.7 with λ OFF 0.25 by iitiatig VSHs more aggressively tha TPS. The compariso results rapidly coverge to 1 betwee PU spectrum usage ratios 0.7 ad 0.8. VI. CONCLUSIONS We have itroduced a ovel spectrum hadoff scheme called volutary spectrum hadoff to miimize SU disruptio periods durig spectrum hadoff. To determie volutary spectrum hadoff time, we defie spectrum life time which is estimated by two spectrum selectio algorithms, i.e., TPS ad RBS. For spectrum usage estimatio, we propose to use a approach based o a fixed sesig widow ad a variable history widow. Simulatio results show that SUs ca reduce forced spectrum hadoff couts with VSH. With the reduced forced spectrum hadoffs, SUs ca have loger udisrupted coectio times. I the comparisos of each spectrum selectio algorithm, while TPS has superior performace for high PU activity, RBS has superior performace i other cases. I geeral, RBS shows superior performace o various PU spectrum usage ratios. I the future, we would like to explore a estimatio of PU spectrum usage distributios from real world data sets such as cellular ad WiFi usage statistics to build more realistic system models. REFERENCES [1] Simo Hayki, Cogitive radio: brai-empowered wireless commuicatios, IEEE Joural o Selected Areas i Commuicatios, pp , Feb [2] Ia F. Akyildiz, Wo-Yeol Lee, Mehmet C. Vura, Shatidev Mohaty, NeXt geeratio/dyamic spectrum access/cogitive radio wireless etworks: A survey, Computer Networks Joural (Elsevier), Vol. 50, No. 13, pp , September [3] Milid M. Buddhikot Uderstadig Dyamic Spectrum Access: Models, Taxoomy ad Challeges, IEEE DySPAN 2007, April [4] R. W. Thomas, L. A. DaSilva, ad A. B. Mackezie, Cogitive Networks, IEEE DySPAN 2005, pp , Nov [5] Rya W. Thomas, Daiel H. Fried, Luiz A. DaSilva, ad Alle B. MacKezie, Cogitive Networks: Adaptatio ad Learig to Achieve Ed-to-Ed Performace Objectives, IEEE Commuicatios Magazie, Volume 44, Issue 12, pp51-57, December [6] Hyoil Kim ad Kag G. Shi, Efficiet Discovery of Spectrum Opportuities with MAC-Layer Sesig i Cogitive Radio Networks, IEEE Trasactios o Mobile Computig [7] Guag-Hua Yag, Haitao Zheg, Ju Zhao, Li V.O.K., Adaptive Chael Selectio Through Collaborative Sesig, IEEE Iteratioal Coferece o Commuicatios, Jue [8] L. Ma, X. Ha, C.-C. She, Dyamic ope spectrum sharig MAC protocol for wireless ad hoc etwork, IEEE DySPAN 2005, pp , November [9] Sudhir Sriivasa ad Syed Ali Jafar, The Throughput Potetial of Cogitive Radio: A Theoretical Perspective, IEEE Commuicatios Magazie, May [10] S. Krishamurthy, M. Thoppia, S. Vekatesa, R. Prakash, Cotrol chael based MAC-layer cofiguratio, routig ad situatio awareess for cogitive radio etworks, IEEE MILCOM 2005, October [11] Papadimitratos P., Sakaraarayaa S., Mishra A., A badwidth sharig approach to improve licesed spectrum utilizatio, IEEE Commuicatios Magazie, Volume 43, Issue 12, pp , December [12] Mark Girolami ad Chao He, Probability Desity Estimatio from Optimally Codesed Data Samples, IEEE Trasactios o Patter Aalysis ad Machie Itelligece, VOL. 25, OCTOBER [13] M.M. Buddhikot, P. Kolody, S. Miller, K. Rya, J. Evas, DIMSUM- Net: ew directios i wireless etworkig usig coordiated dyamic spectrum access, IEEE WoWMoM 2005, pp , Jue [14] Ileri, O. Samardzija, D. Madayam, N.B., Demad resposive pricig ad competitive spectrum allocatio via a spectrum server, IEEE Iteratioal Symposium o DySPAN [15] Marvi Rausad ad Arljot Hylad, System Reliability Theory: Models, Statistical Methods, ad Applicatios, Wiley-Itersciece, [16] J. Zhao, H. Zheg, G.-H. Yag, Distributed coordiatio i dyamic spectrum allocatio etworks, IEEE DySPAN 2005, November 2005, pp