Opportunistic Spectrum Access for Mobile Cognitive Radios

Transcription

1 Opportunstc Spectrum Access for Moble Cogntve Rados Alexander W. Mn, Kyu-Han Km, Jatnder Pal Sngh, and Kang G. Shn Real-Tme Computng Laboratory, Dept. of EECS, The Unversty of Mchgan, Ann Arbor, MI 489 Deutsche Telekom Inc. R&D Lab USA, Los Altos, CA 9422 {alexmn, {kyu-han.km, Abstract Cogntve rados (CRs) can mtgate the mpendng spectrum scarcty problem by utlzng ther capablty of accessng lcensed spectrum bands opportunstcally. Whle most exstng work focuses on enablng such opportunstc spectrum access for statonary CRs, moblty s an mportant concern to secondary users (SUs) because future moble devces are expected to ncorporate CR functonalty. In ths paper, we dentfy and address three fundamental challenges encountered specfcally by moble SUs. Frst, we model channel avalablty experenced by a moble SU as a two-state contnuous-tme Markov chan (CTMC) and verfy ts accuracy va n-depth smulaton. Then, to protect prmary/ncumbent communcatons from SU nterference, we ntroduce guard dstance n the space doman and derve the optmal guard dstance that maxmzes the spato-temporal spectrum opportuntes avalable to moble CRs. To facltate effcent spectrum sharng, we formulate the problem of maxmzng secondary network throughput wthn a convex optmzaton framework, and derve an optmal, dstrbuted channel selecton strategy. Our smulaton results show that the proposed spectrum sensng and dstrbuted channel access schemes mprove network throughput and farness sgnfcantly, and reduce SU energy consumpton for spectrum sensng by up to 74 %. I. INTRODUCTION The recent advent of cogntve rado (CR) technology promses sgnfcant mprovement n spectrum effcency by allowng secondary (unlcensed) devces or users (SUs) to opportunstcally utlze the lcensed spectrum bands. Such opportunstc spectrum access has attracted consderable nterest due to ts ablty to allevate the spectrum scarcty problem that we may face soon because of the rapd ncrease n wreless spectrum demand and the neffcency of current statc spectrum allocaton polces. The man goal of opportunstc spectrum access s to allow CR-equpped SUs to safely coexst wth legacy prmary devces or users (PUs) wthout dsruptng PU communcatons. To acheve ths goal, varous aspects of opportunstc spectrum access, such as spectrum sensng [] [3], spectrum sharng [4], [5], and securty [6], have been studed extensvely. Most exstng efforts, however, focus on statonary cogntve rado networks (CRNs), n whch both PUs and SUs are statonary, and thus, they may not be sutable when SUs are moble. We envson that future moble devces wll ncorporate CRfunctonalty and wll be capable of dynamc and flexble spectrum access. Meanwhle, varous standardzaton efforts for moble CRs are beng developed to utlze spectrum whte spaces, such as 82.af [7] and Ecma 392 [8]. Enablng opportunstc spectrum access for moble SUs, however, entals new practcal challenges, and remans an open problem. Alexander W. Mn was a Research Intern at Deutsche Telekom Inc. R&D Labs USA whle ths work was conducted. In ths paper, we study the problem of enablng opportunstc spectrum access for moble CR devces by dentfyng and addressng three fundamental challenges. Frst, exstng spectrum-avalablty models are derved based solely on PUs temporal traffc statstcs and mght thus be unsutable for CRNs wth moble CRs/SUs. Unlke n statonary CRNs (e.g., [9]), n whch the spectrum opportunty (or avalablty) s mostly affected by PUs temporal channel usage patterns, n moble CRNs, avalablty can also change as SUs move towards or away from PUs that are actvely transmttng data. To overcome ths lmtaton, we model channel avalablty that reflects the fluctuaton of spectrum opportuntes nduced by the SU moblty as a two-state contnuous-tme Markov chan (CTMC) and verfy ts accuracy va n-depth smulaton. Second, protectng PUs from the SU moblty-nduced nterference s a challengng problem that calls for an effcent spectrum-sensng strategy talored to moble CRNs. Moble SUs may need to sense spectrum more frequently to avod nterferng wth PU communcatons. However, frequent spectrum sensng may not only ncur sgnfcant tme overhead [], but also quckly dran the battery of moble CR devces due to the power-ntensve nature of spectrum sensng [], []. To address ths challenge, we propose the use of guard dstance to mnmze the requred spectrum sensng for moble SUs, whle provdng suffcent protecton to prmary communcatons. Guard dstance s an addtonal separaton between PUs and SUs to prevent moble SUs from causng excessve nterference. Further, based on our proposed channelavalablty model, we jontly optmze the guard dstance and spectrum-sensng nterval to maxmze the reuse of spectrum opportuntes n the space and tme domans. Thrd, moble SUs wll experence heterogeneous spectrum opportuntes across the space and tme domans based on the geographcal dstrbuton of PUs and SUs moblty patterns. To better utlze such heterogeneous spectrum opportuntes, we derve an optmal, dstrbuted channel-access strategy n a closed form wthn the convex optmzaton framework. Our channel-access strategy ncorporates the three key factors that dversfy spectrum access opportuntes across dfferent channels: () SU-moblty-aware spectrum sensng adaptaton, () heterogenety n PUs spatal dstrbutons and channel-usage patterns, and () spectrum sharng among SUs. Our proposed channel-access strategy s shown to sgnfcantly mprove the secondary network throughput, farness and energy-effcency n spectrum sensng. The three challenges mentoned above are nter-related. Hence, to fully realze the benefts of opportunstc spectrum access for moble SUs, they must be consdered jontly. To the best of our knowledge, our work s the frst to extensvely

2 nvestgate SU moblty n regard to the channel-avalablty model, spectrum sensng and access strateges. The remander of ths paper s organzed as follows. Secton II overvews related work, and Secton III ntroduces the system models that wll be used throughout the paper. Secton IV presents our new channel-avalablty model for moble SUs. Sectons V and VI detal the desgn of spectrum sensng and access schemes that maxmze the secondary network throughput. Secton VII evaluates the performance of the proposed schemes, and Secton VIII concludes the paper. II. RELATED WORK Spectrum sensng has been studed extensvely as a key technology for prmary detecton and protecton [], [2], [2] [6]. Most exstng work, however, focuses on optmzng the sensng nterval based on PUs temporal channel-usage statstcs. To valdate such channel models, Wellens et al. [6] studed the mpact of channel-occupancy statstcs obtaned from extensve measurements on the performance of MAClayer sensng schemes. They showed that the channels wth longer busy/dle perods follow exponental dstrbutons and that spectrum sensng and access strateges desgned under the assumpton of exponentally-dstrbuted PU traffc are hghly effcent. However, such models hnge on the assumpton of statonary CRNs, n whch both PUs and SUs are statonary. Thus, they may not be sutable for moble CRNs, n whch channel avalablty depends on dynamcally changng SUs locatons. By contrast, we model channel avalablty from a moble SU s perspectve by ncorporatng the mpact of SU moblty (e.g., speed). Despte ts practcal mportance, the problem of allowng moble SUs n CRNs has receved lttle attenton. The IEEE standard draft provdes a two-stage sensng (TSS) mechansm [7], but t s desgned exclusvely for the detecton of a statonary TV transmtter, and does not specfy any effcent mechansms for spectrum sensng for portable/moble CRs. Recently, the FCC [8] mposed a mnmum sensng nterval of 6 seconds for TV band devces (TVBD). However, ths may not be suffcent to protect PUs from the nterference nduced by SU moblty. Moreover, whle most prevous work focused on ether schedulng spectrum sensng [2] or spatal CR deployment [9], [2] for prmary protecton, we jontly explot the guard dstance and the sensng nterval to maxmze spato-temporal spectrum opportuntes for moble SUs. III. SYSTEM MODEL In ths secton, we present a moble CRN model, along wth dstrbuted spectrum sensng and channel-access models. A. Moble CRN Model We consder a CRN wth nfrastructure-based fxed prmary networks and moble ad-hoc secondary networks n the same geographcal area, as shown n Fg.. We assume that each cell of the prmary system conssts of a sngle central node (e.g., access pont) and recevers. From now on, we refer to each prmary cell as a PU. We assume that there s a non-empty set K of lcensed channels, and that PUs operatng on the same channel belong to the same type of system and have the same temporal channel-usage statstcs, e.g., channel busy/dle Fg.. Illustraton of a moble CRN: Moble CR devces (sold dots wth arrow) can opportunstcally use the lcensed channels only when the dstance from any actve PUs (trangles and rectangles) s greater than a certan threshold (.e., protecton regon) so as to avod excessve nterference to PUs. The crcles wth sold (dotted) lnes ndcate the protecton regon of actve (nactve) PUs wth (wthout) data transmsson. duratons. Prmary transmtters are assumed to be dstrbuted, followng a pont Posson process wth a dfferent average densty for each channel,.e., n p, Posson(k; ρ p, ), where n p, s the number of prmary transmtters and ρ p, s the average PU densty on channel K. We assume that prmary transmtters on the lcensed channel K are separated by at least twce ther transmsson range n order to avod nterference [2]. Such a PU dstrbuton can be obtaned by elmnatng overlappng PUs n the orgnal Posson process, resultng n a Marten Hardcore Process [22]. We assume that SUs know the average densty of PUs on each channel, and PUs temporal channel-usage characterstcs. We further assume that SUs do not know the avalablty of a channel at specfc tme and locaton unless they perform spectrum sensng. B. Dstrbuted Spectrum Sensng & Access Models We assume that SUs are moble devces wth CRfunctonalty that allows them to access any lcensed channels n the set K. However, they do not have the capablty of accessng a geo-locaton spectrum database to obtan local spectrum-avalablty nformaton. 2 Therefore, we assume that SUs rely on local spectrum sensng (e.g., feature detecton) to detect channel avalablty.e., the presence/absence of prmary sgnals at a gven tme and locaton. SUs are assumed to use feature detecton (e.g., [23]) for PHY-layer sensng. Feature detecton s known to provde hgh accuracy wthout collaboraton amongst SUs even at a low SNR [24]. Thus, t s better suted for ad-hoc secondary networks, n whch SU collaboraton may not be feasble due to the needs for nformaton exchange and global tme synchronzaton [25]. Once an SU dentfes avalable channels va spectrum sensng, t contends wth neghborng SUs to access the channel va a random access scheme such as CSMA. SU channel access behavor s depcted n Fg. 2. We assume that SUs We use the terms busy/dle to ndcate PUs temporal traffc patterns, and use ON/OFF to ndcate the avalablty of a channel seen from a moble SU s perspectve. 2 The FCC specfes two types (Mode I and II) of portable devces that can access TV whte space [8]. Mode I devces are requred to access the geo-locaton database, whereas Mode II devces are not requred such access capablty.

3 ch ch2 ch3 ch4 t sensng t t2 t3 swtchng channel access epoch Fg. 2. Opportunstc channel access model: An SU perodcally senses ts current operatng (n-band) channel (the gray block) untl t detects a prmary sgnal, followed by channel swtchng (the black block). The sensng nterval s dynamcally adapted based on the SU s speed and PUs spato-temporal channel usage statstcs. always have packets to transmt and always use the maxmum transmsson power allowed by a regulatory body. IV. MODELING CHANNEL AVAILABILITY FOR MOBILE SECONDARY USERS In ths secton, we characterze the spectrum opportunty that corresponds to PUs spato-temporal channel usage patterns, propose a new SU moblty-aware channel avalablty model, and demonstrate ts accuracy va smulaton. A. Characterzng Spato-Temporal Spectrum Opportunty We frst ntroduce the keep-out-radus and guard dstance for protectng PUs from ncreased nterference caused by SU moblty. We then quantfy the spato-temporal spectrum opportuntes avalable to moble SUs. Defnton (Keep-out radus) The keep-out radus s defned as the mnmum dstance between a prmary transmtter and SUs under the nterference temperature lmt (ITL) set by the regulatory body (e.g., the FCC),.e., n o R e, = nf d R I tot(ρ s,, d) ITL, () where I tot (ρ s,, d) s the average nterference generated by SUs (separated by least dstance d from the prmary transmtter) at a prmary recever located at the edge of the prmary coverage area and ρ s, s the densty of SUs on channel. The aggregate SU nterference at a prmary recever located at the edge of the prmary transmsson range (.e., at dstance R o from the prmary transmtter) can be bounded as [9]: I U (ρ s,, R e,) = 2πPodα o ρ s, `Re, R o 2 α, (2) α 2 where s the transmsson power of SUs, d o the short reference dstance (e.g., 5 m), α the path-loss exponent, ρ s, the average SU densty on channel, R o the PUs transmsson range, and R e, the prmary keep-out radus. From Eq. (2), the keep-out radus necessary for channel to meet the nterference constrant, I U ITL, s gven as: R e,(ρ s,) =» (α 2) 2πd α o ρ s, ITL 2 α tme + + R o, (3) where [ ] + max{, }. One mportant observaton from Eq. (3) s that the keepout radus of channel ncreases wth the densty of channel- SUs, ρ s,, as shown n Fg. 3(a). Ths s because as SU densty ncreases (.e., more SUs access channel ), the keep-out radus must be expanded to meet the nterference constrant. The keep-out radus n Eq. (3), however, assumes statonary SUs, and thus, t may not be suffcent to protect PUs from nterference caused by moble SUs. To protect PUs further keep out radus (m) = 25 mw = 5 mw = mw average SU densty (per m 2 ) (a) Keep-out radus fracton of PPR ( χ) = 25 mw = 5 mw = mw average SU densty (per m 2 ) (b) Fracton of avalable area Fg. 3. Impact of SU densty on spatal spectrum opportunty: The keepout radus for prmary protecton (a) ncreases wth ncreasng SU densty, and thus (b) spatal spectrum opportunty decreases. The smulaton parameters are set to R o=25 m, ITL=. mw, ρ p =/km 2, and α=4. from such SU moblty-nduced nterference, we ntroduce an addtonal protecton layer (guard dstance), denoted by ǫ. Defnton 2 (Prmary protecton regon) Let P denote a set of prmary transmtters on channel. A prmary protecton regon (PPR) of prmary transmtter j P, denoted as Ω,j, s defned as a unt dsk centered at the prmary transmtter j located at (x,j, y,j ),.e., o Ω,j = n(x,y) R 2 (x,j, y,j) (x, y) R e, + ǫ, (4) where R e, s the keep-out radus, and ǫ s the guard dstance. Thus, f an SU s located wthn a PPR of actve PUs on channel, t refrans from usng the same channel to avod causng nterference. Then, the average fracton of the unon of PPRs on channel n the entre network s [26]: χ (ρ s,) = e ρ p,π(r e, (ρ s, )+ǫ ) 2, (5) where ρ s, s the average SU densty on channel. The average fracton of areas where the channel s avalable at any gven tme can be approxmated as: γ ( χ ) + χ dle, = χ busy,, (6) where dle, = busy, s the steady-state probablty that a PU on channel s n dle state,.e., not transmttng data. B. Assumptons for Modelng Channel Avalablty To model channel avalablty from a moble SU perspectve, we make the followng three man assumptons: A) PUs traffc statstcs,.e., busy/dle perods follow exponental dstrbutons. A2) The tme nterval that an SU moves nsde a PPR follows exponental dstrbutons. A3) The tme durng whch an SU s located wthn a PPR follows exponental dstrbutons. Regardng A), the exponental dstrbuton s the most wdely used for modelng PU traffc patterns n CRNs. A recent measurement study [6] ndcates that the PU channelusage pattern can ndeed be accurately approxmated as an exponental dstrbuton unless the average busy/dle perods are very long. 3 3 For such channels wth long busy/dle perods, a long-tal dstrbuton, such as log-normal dstrbuton, s more sutable.

4 ON λ busy BUSY λ dle v(r e+ε) - IDLE CDF CDF (R e+ε)vρ pϖ busy PPR OFF 2(R e+ε)vρ pϖ dle Fg. 4. Moblty-aware channel avalablty model as a contnuous-tme Markov chan (CTMC): A channel s avalable for a (moble) SU ether when () the SU located outsde the PPRs (denoted as PPR) or () the prmary transmtter of the PPR that the SU belongs to s n dle state. Regardng A2), let T ht denote the frst (httng) tme that a moble SU n moves nto an actve PU s PPR (.e., n busy state). Then, the analyss of T ht s analogous to the httng tme of a statonary object n wreless sensor networks, whch can be consdered as a PU n a moble CRN. By borrowng the analyss n [26], T ht can be approxmated as [26]: T ht,n Exp(2(R e, + ǫ ) v nρ p, busy, ), (7) where v n s the average speed of SU n. Regardng A3), the tme duraton n whch an SU stays wthn a PPR can be derved from the lnk-lfetme dstrbuton analyss n moble ad-hoc networks [27]. Accordng to [27], the lnk lfetme,.e., the tme duraton durng whch the transmtter-recever par are located closer than a transmsson range, can be accurately approxmated as an exponental v dstrbuton wth ntensty, R, where v s the average relatve speed of the transcever and R s the transmsson range. C. Moblty-Aware Channel Avalablty Model We now opt to desgn a moblty-aware channel avalablty model for moble CRNs. For ths, we frst defne three states.e., busy, dle, and PPR based on the SU s locaton relatve to the PPRs and PUs traffc patterns, as shown n Fg. 4. We assume that channel s avalable (.e., OFF state) when a moble SU s located outsde the PPR of any actve prmary transmtters on channel (.e., dle or PPR); otherwse, the channel s not avalable (.e., ON state). We can thus reduce the Markov chan nto a two-state model by mergng the states dle and PPR nto an OFF state, as shown n Fg. 4. The ON/OFF state transtons occur n the followng cases. ON OFF: An SU moves out of the protecton regon of an actve PU or a PU stops transmttng data. OFF ON: An SU moves nto the protecton regon of an actve PU or a PU starts transmttng data. We now derve the dstrbutons of ON and OFF duratons based on the Markov model n Fg. 4. ) Dstrbuton of ON Perod: The sojourn tme of the ON state of channel follows an exponental dstrbuton [27]: v n T on, Exp λ busy, +, (8) R e, + ǫ where λ busy, s the rate at whch a PU resumes data transmsson, v n the average speed of an SU, 4 and R e, and ǫ 4 Although the speed of an SU can vary depends on ts movement pattern, we consder average speed n the analyss for mathematcal tractablty..2 analyss smulaton OFF tme duraton (s) (a) OFF perod.2 analyss smulaton ON tme duraton (s) (b) ON perod Fg. 5. Comparson of channel ON/OFF duraton dstrbutons: Our analyses on channel ON/OFF duratons closely match the smulaton results, thus corroboratng the valdty of the proposed channel model. In the smulaton, we use the Random Waypont model wth no pause tme where an SU unformly chooses ts speed n [, ] m/s and destnaton wth a fxed nterval of 6 seconds. The average PU and SU denstes are set to 2 and (per km 2 ), respectvely. We set dle, =.4 and λ dle, =. K. are the keep-out radus and the guard dstance on channel, respectvely. 2) Dstrbuton of OFF Perod: The OFF perod duraton can be thought of as the httng tme of the busy state, havng ether dle or PPR as an ntal state. The OFF ON state transton rate, λ off, can be derved usng the detaled balance equaton,.e., on, λ on, = off, λ off,, based on the statonary dstrbutons of ON/OFF states, whch can be approxmated from Eq. (6),.e., on, = γ and off, =γ, and the ON OFF transton rate λ on, n Eq. (8),.e., λ off, = χ busy, λ busy, + χ busy, v n, (9) R e, + ǫ and thus, the sojourn tme of the OFF state s gven as: T off, Exp(λ off, ). () The above analyss for channel modelng wll be used for desgnng effcent spectrum sensng schedulng and dstrbuted access strategy n Sectons V and VI. 3) Model Verfcaton: To show the accuracy of the proposed channel-avalablty model, we measure the channel ON/OFF perods observed from a moble SU va smulaton for 2 4 seconds. Fg. 5 shows that the emprcal results closely match the analytcal results, ndcatng the accuracy of the proposed model. To further quantfy the accuracy, we measure the smlarty between the emprcal c.d.f. and the analytcal c.d.f. usng Kullback-Lebler Dvergence (KLD) [28]. The KLD for two exponental dstrbutons wth ntenstes µ o and µ can be calculated as: D KL(µ o µ ) = log(µ o) log(µ ) + µ µ o. () Table I summarzes the average and standard devaton of KLD for the ON/OFF duratons whle varyng the maxmum speed of SUs n the range of [2, ] m/s. It shows that the KLD remans low for all smulated scenaros. In fact, the case where v max = m/s corresponds to the case n Fg. 5. V. PRIMARY PROTECTION VIA JOINT OPTIMIZATION OF SPECTRUM SENSING INTERVAL AND GUARD DISTANCE In ths secton, we jontly desgn the sensng nterval and guard dstance to protect PU communcatons from moble SUs. We frst derve the mnmum spectrum sensng nterval

5 TABLE I KULLBACK-LEIBLER DIVERGENCE FOR CHANNEL MODEL D KL,OF F D KL,ON v max (m/s) mean std mean std for moble SUs, and then the optmal guard dstance that maxmzes spato-temporal spectrum opportuntes. A. Moblty-Aware Spectrum Sensng In order to avod causng excessve nterference to prmary communcatons, SUs must perform spectrum sensng frequently enough to detect a prmary sgnal before they move nto the PPR of actve PUs. We assume that SUs can perfectly detect the presence of a prmary sgnal va spectrum sensng when they are located wthn the PPR of any actve PU. In practce, SUs may need to adjust the sensng parameters to dentfy ther locatons relatve to the PPRs, but ths s not wthn the scope of ths paper. There are two condtons under whch an SU performs spectrum sensng: () when the c.d.f. of the channel OFF state at a gven tme exceeds a predefned threshold, ξ (<ξ<), to detect the returnng PUs, or () when an SU travels a certan dstance snce the prevous sensng tme, to prevent an SU from movng nto the keep-out radus, whchever comes frst. Then, the mnmum sensng nterval requred on channel s gven as: t = max j j T s,,mn ffff ln( ξ), ǫī, (2) λ off v where λ off s the ntensty of the channel OFF perod dstrbuton n Eq. (9), ǫ the guard dstance, and v the average speed of an SU. Note that a lower probablty ξ wll lead SUs to sense the channel more frequently. Eq. (2) ndcates that the mnmum sensng nterval depends not only on temporal features such as prmary traffc statstcs, but also on spatal features such as the SUs average speed v n and the PU densty ρ p,. Fg. 6(a) shows that when an SU moves slowly (Regon I for the case ǫ=4 m), the sensng nterval wll be determned by PU traffc patterns,.e., λ busy and λ dle, whereas, when t moves quckly (Regon II), the nterval wll be determned by the speed of SUs. We have made a smlar observaton regardng PU densty n Fg. 6(b). B. Desgn of Optmal Guard Dstance The selecton of guard dstance, ǫ, entals an nterestng tradeoff n explorng the spectrum opportuntes n the tme and space domans. That s, a larger guard dstance (thus enlargng the areas of PPRs) wll reduce the spatal spectrum opportuntes. However, ths allows SUs to perform sensng less frequently and spend more tme for data transmsson, thus ncreasng the spectrum opportuntes n the temporal doman. sensng nterval (s) I II ε = 2m ε = 4m ε = 6m average speed (v) (m/s) (a) Impact of SU moblty sensng nterval (s) I II PU densty (ρ p ) (per km 2 ) (b) Impact of PU densty Fg. 6. Mnmum sensng nterval: Sensng nterval depends on (a) the SUs average speed, v, and (b) the average PU densty, ρ p. In our smulaton, we set the parameters ξ =.3, ǫ=4 m, ρ s =/km 2, ρ p =/km 2, R o =25 m, v=5 m/s, λ dle, =., and dle, =.4 K. Defnton 3 (Average channel utlzaton) Average channel utlzaton s defned as the average fracton of tme a moble SU can access the channel K,.e., j u,n = E P Ns,,n j= T s, T sw, T ff, (3) where N s,,n s the number of tmes SU n performs spectrum sensng wthn the channel access epoch T. T s, and T sw, are the tmes spent for a one-tme sensng and swtchng for channel, respectvely. Wthout loss of generalty, we assume T s =T s, and T sw =T sw,. Defnton 4 (Spato-temporal spectrum opportunty) The avalablty of channel K n the spato-temporal doman, denoted as Λ, s defned as the long-term average fracton of the tme a moble SU can access the channel,.e., Λ = γ u where γ and u are defned n Eqs. (6) and (3), respectvely. Fg. 7(a) plots the spato-temporal channel avalablty Λ for varous guard dstances ǫ. As shown n the fgure, when ǫ s too small (.e., ǫ <3 m), Λ s because of the need to sense the channel contnuously,.e., t =T s,. When ǫ s relatvely small, Λ suffers from a large (temporal) sensng overhead, whereas when ǫ s too large, Λ suffers from decreased spatal spectrum opportuntes. Proposton (Optmal guard dstance) The optmal guard dstance ǫ that maxmzes spato-temporal spectrum opportunty, Λ, s gven as: q R e, v T s, + (R e, vt s,) vt s,(r e, v T s, ) ǫ πρ p, busy, =, (4) 2(R e, vt s,) where R e, s the keep-out radus, v the average speed of SUs, T s, the sensng tme, ρ p, the prmary densty, and busy, the steady-state probablty of a busy state for channel. ǫ Proof: The average fracton of area whch s not covered by the PPRs can be approxmated as γ (ǫ ) e f(ǫ) from Eq. (6) where f(ǫ ) = ρ p, busy, π(r e, + ǫ ) 2. Assumng the swtchng overhead s neglgble compared to the average OFF perod,.e., T sw λ off, u can be approxmated as v Ts, u. Then, the channel avalablty n the spatotemporal doman can be expressed as: Λ (ǫ ) γ (ǫ )u (ǫ ) e f(ǫ ) v Ts, ǫ. (5)

6 channel avalablty (Λ) ρ p = /km 2 ρ p = 2/km 2 ρ = 4/km 2 p guard dstance (ε) (m) (a) Impact of guard dstance optmal guard dstance (ε * ) analyss smulaton average speed (v) (m/s) (b) Optmal guard dstance (ǫ ) Fg. 7. Optmal guard dstance (ǫ ): (a) The channel avalablty Λ depends sgnfcantly on the desgn of guard dstance, and (b) the optmal guard dstance dffers for dfferent SU mobltes. The parameters are set to ρ s =/km 2, λ dle, =., dle, =.4 K, and ρ p =2/km 2 n (b). 2 Λ (ǫ ) ǫ 2 It can be easly shown that <. By takng the frst-order dervatve of Λ(ǫ ) and settng t to zero, we have: Λ (ǫ ) = ǫ e f(ǫ ) 2ρ p, busy, π(r e, + ǫ ) v Ts, ǫ + «v Ts, =. ǫ 2 (6) For mathematcal smplcty, we assume that the term 2ρ p, busy, πǫ can be approxmates as n Eq. (6), whch provdes the followng quadratc equaton: (R e, v T s,)ǫ 2 R e,t s,ǫ v T s, 2πρ p, busy, =. (7) Then, by solvng Eq. (7), the proposton follows. Interestngly, Fg. 7(b) shows that, the optmal guard dstance ncreases as SUs average speed ncreases, whch result from balancng the tradeoff between temporal and spatal spectrum opportuntes.e., t s better to ncrease the guard dstance at the cost of reduced spatal spectrum opportunty, rather than reducng the sensng nterval. The fgure shows that our analytcal results closely match the exhaustve-searchbased smulaton results. VI. DISTRIBUTED SPECTRUM ACCESS STRATEGY IN MOBILE CRNS We now derve an optmal channel selecton (access) strategy that maxmzes each secondary lnk s throughput. In mult-user CRNs, t s mportant to consder the channel contenton overhead, as t can affect the achevable throughput sgnfcantly. However, t may be nfeasble for moble SUs to estmate the nterference on each channel n real tme. Thus, we assume that all the SUs n the network follow the same channel access strategy, and derve the optmal strategy by takng nto account SUs moblty-dependent spectrum opportunty as well as channel access contenton among SUs as follows. Let us denote the mxed channel selecton vector by p = [p, p 2,..., p K ] T where K p. Then, the total number of SUs selectng channel n the network can be approxmated as Np, where N s the total number of SUs n the network, whch can be estmated as N ρ s A. A s the entre network coverage area and ρ s s the average SU densty. The probablty that an arbtrarly-chosen SU on channel has m N nterferng neghbors, that have chosen the same channel, follows a Bnomal dstrbuton,.e., M B(m; Np, f ). Here, f = πr2 I, A s the rato of the SU s nterference regon to the total network area, where R I, s the nterference range of an SU on channel. The expected throughput of secondary lnk n can then be expressed as:! Np X Λ Np E[R n] = p f m ( f ) Np m m + m = N m= Λ ( f) Np f, (8) where K = K s the total number of lcensed channels. Then, the problem of fndng an optmal channel selecton strategy p can be cast nto the followng optmzaton problem (P): mnmze subject to F(p) = Λ fnp f p = and p, where f = f for brevty. To fnd the optmal sensng strategy p, we frst show the convexty of F(p) by examnng the second-order dervatve of F(p) w.r.t. p,.e., 2 F(p ) p 2 = f Np (ln( f N )) 2 >. (9) The nequalty n Eq. (9) s straghtforward. Hence, F(p) s convex n p [, ] K. Snce the objectve functon s convex and constrants are affne, we now have a convex optmzaton problem. The Lagrangan wth multplers λ R K and ν R s gven as: L(p, λ, ν) = = Λ ( f Np ln( f N ))) λ p + ν( p ) ((λ ν)p Λ ( f Np ln( f N )) ν, where λ and ν =. Then, the Lagrange dual functon,.e., the mnmum value of the Lagrangan over p, s gven as: g(λ,ν) = nf L(p, λ, ν) p = nf p ( (λ ν)p + Λ( f Np ln( f N ))) ν. It can be easly shown that there exsts p such that the constrants hold wth strct nequalty,.e., p > K and K p. Therefore, accordng to Slater s condton, strong dualty holds wth zero optmal dualty gap. The Karush-Kuhn-Tucker (KKT) condtons are gven as: p, p = (2) p λ + Λ f f Np ln( f N ) = (2) λ + f f Np ln( f N ). (22)

7 Algorthm OPTIMAL CHANNEL-SELECTION ALGORITHM : // Intalzaton 2: p [ K,..., K ]T // p s channel-selecton probablty 3: p prev p 4: 5: ε. // condton for the convergence 6: whle ( > ε) do 7: Update the SU densty on each channel ρ s, ρ sp 8: Update the keep-out radus R e, usng Eq. (3) 9: Update the optmal guard dstance ǫ usng Eq. (4) : Update the spato-temporal channel avalablty Λ (ǫ ) : Update the channel-selecton vector p usng Eq. (23) 2: p p prev 3: p prev p 4: end whle 5: return p By solvng the above system of equatons, we can derve the optmal channel-selecton strategy, p, as descrbed n the followng proposton. Proposton 2 (Optmal channel-selecton strategy) The optmal channel-selecton vector p that maxmzes the expected secondary network throughput s: ( h ln(λ p )+ln(f )+ln( N ln( f )) ln(λ + ) = N ln( f ) f dle, > f dle, =, (23) where Λ =γ u K and λ s a constant s.t. K p. Eq. (23) ndcates that the channel-selecton probablty p ncreases as the channel avalablty Λ ncreases, thus confrmng our ntuton. Interestngly, the optmal channelselecton vector p n Eq. (23) depends on SU densty on each channel as the number of SUs affects the selecton of guard dstance (n Eq. (6)), nfluencng the amount of spatal spectrum opportunty. Ths couplng between channelselecton strategy and spatal channel avalablty requres an teratve algorthm to fnd the optmal strategy, as descrbed n Algorthm. Proposton 2, however, provdes the followng counterntutve observaton: Corollary The optmal channel-selecton probablty becomes more unform as the number of SUs n the network ncreases,.e., K, p as N, (24) K where K s the number of lcensed channels, and N s the total number of SUs n the network. Corollary ndcates that the optmal channel-selecton probablty becomes almost ndependent of spato-temporal spectrum opportuntes as SU densty approaches nfnty. The s because, when there exsts a large number of SUs, the beneft from heterogeneous spato-temporal spectrum opportuntes becomes neglgble due to hgh level of nterference among SUs. VII. PERFORMANCE EVALUATION We evaluate the performance of the proposed spectrum sensng and dstrbuted channel-selecton schemes. We frst descrbe the smulaton setup, channel-selecton schemes for performance comparsons and performance metrcs. Then, we present key evaluaton results. A. Smulaton Setup We consder a CRN n whch moble SUs coexst wth PUs n a 5 km 5km area. Throughout the smulaton, we assume that there are 5 lcensed channels, 5 and that the average channel dle probablty s n the range of [.3,.7], unless specfed otherwse. We also assume that λ dle s. for all the channels and that average densty of SUs ρ s ranges n [, ]/km 2. We assume that the path-loss exponent α s 4, the SUs transmt power s mw, the reference dstance d o s m, the PUs transmsson range R o s 25 m, the nterference temperature lmt (ITL) s. mw, and the sensng trggerng threshold ξ s.3. We further assume that channel sensng and swtchng tmes are T s =.5 s and T sw = s, respectvely. To comparatvely evaluate the effcacy of the proposed channel-selecton scheme, we compare the followng: () random channel selecton (RAND), () optmal channel selecton strategy based only on PUs temporal channel usage statstcs (OPT-T), and () optmal channel selecton strategy based on PUs spato-temporal channel usage statstcs (OPT-ST). In RAND, SUs randomly select a channel wth an equal probablty. In OPT-T, SUs use the channel-selecton probablty n Eq. (23) whle settng γ = dle, K (thus elmnatng the mpact of heterogeneous PU densty on channels). On the other hand, InOPT-ST, SUs fully explots the spato-temporal channel-usage characterstcs of PUs. To quantfy the effcacy of the proposed algorthms, we use the followng three man performance metrcs: normalzed secondary network throughput,.e., P n Rn N, throughput farness (Jan s ndex [29]),.e., (P n Rn)2 N P, and n R2 n normalzed energy consumpton n spectrum sensng,.e., the fracton of tme a CR devce spent on sensng durng channel access, where R n s the throughput of secondary lnk n, and N s the total number of secondary lnks n the network. B. Optmal Channel Selecton ) Impact of Temporal Channel Avalablty: We frst study the mpact of PUs temporal channel-usage statstcs on the optmal channel-selecton strategy. For ths, we fx the PU densty at ρ p, = /km 2 K and set dfferent channel dle probabltes,.e., dle =[.3,.4,.5,.6,.7] ( dle ncreases wth ncreasng channel ndex). Fg. 8(a) shows SUs preference to access channels wth a hgher average channel dle probablty,.e., p > p j when dle, > dle,j. Interestngly, when SUs are densely populated,.e., ρ s = /km 2, the mpact of PUs temporal channel-usage statstcs on the channel-selecton strategy decreases. Ths s clearly shown n Fg. 8(b) where the largest dfference n the channel-selecton probablty (.e., max(p ) mn(p ) ) decreases wth the ncreasng SU densty. Intutvely, as the number of SUs n the network ncreases, ther channel access tme decreases due to the need for sharng the channel. Thus, as the densty tends to nfnty, the achevable throughput of SUs becomes close to, regardless of the PUs channel usage statstcs. 5 Although the number of avalable channels depends on the wreless envronments, we observed smlar results for dfferent numbers of channels.

8 channel selecton probablty (p * ) ρ s = /km 2 ρ s = /km channel ndex (a) Impact of channel avalablty max(p * ) mn(p * ) average SU densty (ρ s ) (per km 2 ) (b) Impact of SU densty Fg. 8. Optmal channel-selecton probablty: (a) The optmal channel-selecton strategy depends on the average channel avalablty ( dle ), but (b) the effects of PU traffc statstcs decreases as SU densty ncreases. The parameters are set to dle =[.3,.4,.5,.6,.7], v s fxed at 4 m/s, and ρ p, =/km 2 K. p * SU densty (ρ ) 2 s channel ndex Fg. 9. Impact of PU densty on p : Spatal dstrbuton of PUs affects the optmal channel-selecton probablty. ρ p = [.,.2,.5,, 2]/km 2 (p ncreases wth ncreasng channel ndex), dle, =.4 and λ dle, =. K. Λ p channel ndex (a) v = m/s channel ndex (c) v = m/s Λ p channel ndex (b) v = m/s channel ndex (d) v = m/s Fg.. Impact of SUs speed on Λ and p : The spato-temporal channel avalablty depends on the SUs speed, thus affectng the optmal channel-selecton strategy p. The parameters are set to ρ p = [.,.2,.5,, 2]/km 2, ρ s =/km 2, and dle, =.4 K. 2) Impact of Spatal Channel Avalablty: Fg. 9 shows the mpact of PU densty on the optmal channel-selecton strategy. In the smulaton, we assume a dfferent PU densty on each channel, whle assumng the temporal channel usage statstcs,.e., dle, are the same for all channels. The fgure ndcates that, the lower the PU densty (channel ndex), the hgher the channel-selecton probablty. However, the PU densty becomes less nfluental as the average SU densty ncreases, smlar to the case n Fg. 8(b). 3) Impact of SUs Speed: Fg. shows the mpact of SUs average speed on spato-temporal channel avalablty Λ (n Fgs. (a)-(b)), and on the optmal channel-selecton strategy p (Fgs. (c)-(d)). As shown n the fgures, the SUs speed has dfferent consequences on channel avalablty (Λ), dependng on the densty of PUs on each channel; Λ decreases faster when PU densty s hgh. As a result, the SUs preference to access channels wth a low PU densty ncreases as ther speed ncreases. The smulaton settngs are descrbed n Fg.. C. Performance Comparson Next, we compare the performance of the three channelselecton schemes (.e.,rand,opt-t, andopt-st) n terms of throughput, farness, and energy-effcency. In the smulatons, we set the average PU densty on each channel to ρ p = [.,.2,.5,, 2]/km 2. The channel dle probabltes dle are randomly selected n [, ] such that K dle, = for each network topology. The results are obtaned from smulaton runs over 3 randomly-generated topologes. Fgs. and 2 plot the average and ±.25 σ ntervals of throughput and farness, under varous SUs speed and densty. ) Throughput and Farness: Fg. (a) shows that the proposed OPT-ST outperforms the other channel-selecton schemes (.e., OPT-T and RAND) under all smulated scenaros, thanks to ts ablty to optmally select channels by explotng the heterogeneous spatal/temporal spectrum opportuntes of each channel. On the other hand, the performance ofopt-t decreases as SU speed ncreases, because the spatal spectrum opportunty becomes more dverse wth hgher SU moblty (see Fg. ), whch s not consdered n OPT-T. Fg. (b) ndcates that OPT-ST acheves the hghest farness among the three channel-selecton schemes, as t correctly ncorporates the mpacts of heterogeneous spectrum opportuntes and channel access contenton among SUs n the optmal channel selecton strategy. Fg. 2 shows the mpact of SU densty on throughput performance. As shown n the fgure, the throughput degrades as SU densty ncreases, manly because of the ncreased level of SUs contenton for channel access. In addton, the performance of OPT-ST becomes close to RAND s as the densty ncreases, snce the optmal channel-selecton strategy tends to become smlar to a unform dstrbuton, whch can be seen n RAND, n a dense network, as observed n Fg. 9. 2) Energy Savng n Spectrum Sensng: Fnally, we study the energy-savng perspectve n spectrum sensng. Frequent spectrum sensng can consume a consderable amount of energy, especally n battery-powered moble CR devces. Fg. 3 plots the CR s normalzed energy consumpton n dfferent settngs: use of a fxed guard dstance (.e., ǫ=2, 4 m) and use of the optmal guard dstance (ǫ ). The fgure ndcates that energy consumpton due to spectrum sensng n moble CR devces can be reduced by up to 74 % whle ensurng prmary protecton. VIII. CONCLUSION Takng moblty nto consderaton s vtally mportant for full realzaton of the benefts of opportunstc spectrum access

9 normalzed throughput RAND OPT T OPT ST average speed (m/s) (a) Throughput farness ndex RAND OPT T OPT ST average speed (m/s) (b) Farness Fg.. Performance of the proposed dstrbuted channel-selecton algorthm: OPT-ST outperforms other channel-selecton schemes n terms of (a) network throughput and (b) farness (Jan s ndex), under all smulated scenaros. In the smulaton, the average SU densty was fxed at ρ s =/km 2. normalzed throughput RAND OPT T OPT ST average SU densty (ρ ) (per km 2 ) s Fg. 2. Impact of SU densty on throughput performance: The performance of OPT-ST decreases as the average SU densty ncreases. In the smulaton, the SUs speed s fxed at 4 m/s. normalzed energy consumpton ε = 2m ε = 4m ε * (optmal) average speed (v) (m/s) Fg. 3. Energy savngs va the use of optmal guard dstance: SUs can save energy sgnfcantly due to spectrum sensng va the optmal guard dstance, whle meetng the prmary nterference constrants. n CRNs. In ths paper, we consdered the case of a CRN wth moble SUs. We dentfed and addressed the three fundamental challenges n maxmzng spectrum effcency n moble CRNs. In partcular, we presented a novel channel-avalablty model, a moblty-aware spectrum-sensng strategy, and an optmal dstrbuted channel-selecton (or access) strategy talored to moble CRNs. Our evaluaton results verfed the correctness of our channel-avalablty model under varous SU moblty patterns. Our performance comparson study has also shown that the channel-access strategy mproves the throughput and farness of moble SUs sgnfcantly over the conventonal strategy that reles solely on PUs temporal channel-usage statstcs. REFERENCES [] Y.-C. Lang, Y. Zeng, E. C. Peh, and A. T. Hoang, Sensng-Throughput Tradeoff for Cogntve Rado Networks, IEEE Trans. Wreless Commun., vol. 7, no. 4, pp , Aprl 28. [2] A. W. Mn and K. G. Shn, An Optmal Sensng Framework Based on Spatal RSS-profle n Cogntve Rado Networks, n Proc. IEEE SECON, June 29. [3] A. W. Mn, X. Zhang, and K. G. Shn, Spato-Temporal Fuson for Small-scale Prmary Detecton n Cogntve Rado Networks, n Proc. IEEE INFOCOM, March 2. [4] Q. Zhao, L. Tong, A. Swam, and Y. Chen, Decentralzed Cogntve MAC for Opportunstc Spectrum Access n Ad Hoc networks: A POMDP Framework, IEEE J. Sel. Areas Commun., vol. 25, no. 3, pp , Aprl 27. [5] A. W. Mn and K. G. Shn, On Sensng-Access Tradeoff n Cogntve Rado Networks, n Proc. IEEE DySPAN, Aprl 2. [6] A. W. Mn, K. G. Shn, and X. Hu, Attack-Tolerant Dstrbuted Sensng for Dynamc Spectrum Access Networks, n Proc. IEEE ICNP, Oct 29. [7] IEEE Workng Group on Wreless Local Area Networks, [8] J. Wang et al., Frst Cogntve Rado Networkng Standard for Personal/Portable Devces n TV Whte Spaces, n Proc. IEEE DySPAN, Aprl 2. [9] IEEE Workng Group on Wreless Regonal Area Networks, [] A. T. Hoang, Y.-C. Lang, D. T. C. Wong, and R. Zhang, Opportunstc Spectrum Access for Energy-constraned Cogntve Rados, IEEE Trans. Wreless Commun., vol. 8, no. 3, pp. 26 2, March 29. [] A. Dejonghe et al., Versatle Spectrum Sensng on Moble Devces? n Proc. IEEE DySPAN, Aprl 2. [2] N. B. Chang and M. Lu, Optmal Channel Probng and Transmsson Schedulng n a Multchannel System, n Proc. ACM MobCom, Sep 27. [3] A. T. Hoang and Y.-C. Lang, Adaptve Schedulng of Spectrum Sensng Perods n Cogntve Rado Networks, n IEEE Globecom, Nov 27. [4] T. Shu and M. Krunz, Throughput-effcent Sequental Channel Sensng and Probng n Cogntve Rado Networks Under Sensng Errors, n Proc. ACM MobCom, Sep 29. [5] S. Huang, X. Lu, and Z. Dng, Optmal Sensng-Transmsson Structure for Dynamc Spectrum Access, n Proc. IEEE INFOCOM, Aprl 29. [6] M. Wellens, J. Rhjärv, and P. Mähöne, Evaluaton of Adaptve MAC- Layer Sensng n Realstc Spectrum Occupancy Scenaros, n Proc. IEEE DySPAN, Aprl 2. [7] D. Cavalcant and C. Cordero, Proposed Resoluton for Comments Related to the Superframe and Sensng, IEEE /76r, Aprl 27. [8] FCC, Second Report and Order, FCC 8-26, Nov 28. [9] M. Vu, N. Devroye, and V. Tarokh, On the Prmary Exclusve Regon of Cogntve Networks, IEEE Trans. Wreless Commun., vol. 8, no. 7, pp , July 29. [2] M. F. Hanf, M. Shaf, P. J. Smth, and P. Dmochowsk, Interference and Deployment Issues for Cogntve Rado Systems n Shadowng Envronments, n Proc. IEEE ICC, June 29. [2] Y. Yang, Y. Lu, Q. Zhang, and L. N, Cooperatve Boundary Detecton for Spectrum Sensng Usng Dedcated Wreless Sensor Networks, n Proc. IEEE INFOCOM, Aprl 2. [22] D. Stoyan, W. S. Kendall, and J. Mecke, Stochastc Geometry and ts Applcatons. Chchester: John Wley & Sons, 986. [23] A. Fehske, J. Gaeddert, and J. H. Reed, A New Approach to Sgnal Classfcaton Usng Spectral Correlaton and Neural Networks, n Proc. of IEEE DySPAN, Nov 25. [24] R. Tandra and A. Saha, SNR Walls for Feature Detectors, n Proc. IEEE DySPAN, Aprl 27. [25] J. Nemnen, R. Jäntt, and L. Qan, Prmary User Detecton n Dstrbuted Cogntve Rado Networks under Tmng Inaccuracy, n Proc. IEEE DySPAN, Aprl 2. [26] B. Lu, P. Brass, O. Dousse, P. Nan, and D. Towsley, Moblty Improves Coverage of Sensor Networks, n Proc. ACM MobHoc, May 25. [27] W. Wang and M. Zhao, Jont Effects of Rado Channels and Node Moblty on Lnk Dynamcs n Wreless Networks, n Proc. IEEE INFOCOM, Aprl 28. [28] S. Kullback, Informaton Theory and Statstcs. John Wley and Sons, 959. [29] R. Jan, W. Hawe, and D. Chu, A Quanttatve Measure of Farness and Dscrmnaton for Resource Allocaton n Shared Computer Systems, Dgtal Equpment Corporaton, Tech. Rep. DEC-TR-3, Sep 984.