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Protocol design and stability/delay analysis of half-duplex buffered cognitive relay systems PDF

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1 Protocol Design and Stability/Delay Analysis of Half-Duplex Buffered Cognitive Relay Systems Yan Chen, Vincent K. N. Lau, Shunqing Zhang, and Peiliang Qiu Abstract—Inthispaper,wequantifythebenefitsofemploying relay station in large-coverage cognitive radio systems which opportunistically access the licensed spectrum of some small- coverage primary systems scattered inside. Through analytical 0 study, we show that even a simple decode-and-forward (SDF) 1 relay, which can hold only one packet, offers significant path- 0 loss gain in terms of the spatial transmission opportunities 2 and link reliability. However, such scheme fails to capture the n spatial-temporal burstiness of the primary activities, that is, a when either the source-relay (SR) link or relay-destination (RD) J link is blocked by the primary activities, the cognitive spectrum accesshastostop.Toovercomethisobstacle,wefurtherpropose Fig. 1. An example of large-coverage CRS opportunistically access the 3 buffered decode-and-forward (BDF) protocol. By exploiting the licensedspectrumofsomerandomlydistributedsmall-coveragePUsystems. infinitelylongbufferattherelay,theblockagetimeoneitherSR ] T orRDlinkissavedforcognitivespectrumaccess.Thebuffergain I isshownanalyticallytoimprovethestabilityregionandaverage the impact of PU activities and dynamic spectrum-sharing. s. end-to-end delay performance of the cognitive relay system. Moreover,intheexistingworks,thecoverageofthePUsystem c is assumed to be much larger than the SU’s, so the spatial [ I. INTRODUCTION burstiness of the primary traffic and its impact on the CRS 1 have not been fully investigated. The core idea behind the cognitive transmission is to let v In this paper, we try to shed a light on the protocol design the secondary users (SUs) exploit the under-utilized spec- 6 of CRS that addresses the above issues. We are interested 4 trum holes left by the primary communication systems [1]– in the scenario where the CRS coverage is much larger than 3 [3], either in temporal, frequency or spatial domain, without 0 interferingtheregulartransmissionsoftheprimaryusers(PU). the PU coverage and try to design compatible cognitive relay . protocols that could effectively deal with the uncertainty of 1 One key issue of the cognitive radio (CR) system is on the PU locations and the spatial burstiness of PU activities. In 0 efficiency of spectrum sharing with the PU system. Direct 0 addition, we study the stability region and the average end-to- transmission, which demands large transmit power, ends up 1 enddelayoftheCRSunderdifferentrelayingprotocols,which with small opportunity of access and hence low spectrum : are critical for delay-sensitive applications. We shall show v sharing efficiency. As such, CR combined with relay station i that the introduction of a cognitive relay provides two levels X (RS), referred to as cognitive relay system (CRS), appears as of potential gains. In particular, a conventional decode-and- an attractive solution to boost the spectrum sharing efficiency. r forward(DF)relayunderasimpleDF(SDF)protocolprovides a The majority of the existing works on CRS focused on the increasedspatialtransmissionopportunitiesandenhancedlink physical layer aspects of the problem [4]–[6]. For example, a reliability, which is referred to as path-loss gain. On top of distributed algorithm for channel access and power control it, by enabling buffering at the relay, the blockage time on was proposed for cognitive multi-hop relays in [6], and a either the source-relay or relay-destination link can be saved channelselectionpolicyformulti-hopcognitivemeshnetwork to further increase spectrum access opportunities and reduce was considered by [5]. When delay-sensitive applications are the end-to-end delay. This is referred to as buffer gain and considered, other performance measures such as the stability is shown via the analysis of our proposed buffered DF (BDF) region and the average end-to-end packet delay become criti- protocol.Wederivetheclosed-formexpressionsofthestability cal. In [7], the authors analyzed the delay of a cognitive relay regionandtheaverageend-to-enddelayforeachprotocoland assisted multi-access network, however, they did not consider quantify the two types of gains based on the derived results. Manuscript received 1 Dec 2008; revised 7 May 2009 and 3 Sep 2009; accepted 11 Nov 2009. The associate editor coordinating the review of this II. SYSTEMMODEL paperandapprovingitforpublicationwasProf.AshutoshSabharwal. YanChenandPeiliangQiu(e-mail:qiupl418,[email protected]) WeconsiderascenariowherethecoverageoftheSUsystem are with Institute of Information and Communication Engineering, Zhe- is much larger than that of the PU systems. One example of jiang University, Hangzhou, China. Dr. Yan Chen is now working in Huawei Technologies, Shanghai, China. V. K. N. Lau and S. Zhang (e- such CR network is the WRAN system covering a suburb mail:eeknlau,[email protected])iswithDepartmentofElectronicand college town or rural areas, whose cell radius ranges from 2- Computer Engineering, Hong Kong University of Science and Technology 10 km or even larger. While the PU systems inside are Part74 (HKUST),ClearWaterBay,Kowloon,HongKong. ThispaperisfundedbyRGC615407. devices (wireless microphone), whose transmission ranges are 2 is the white Gaussian noise at receiver j, i.e. Z ∼N(0,σ2) j j and we assume σ2 =σ2, ∀j. Further define the instantaneous j received signal-to-interference-and-noise ratio (SINR) on link ij as γ = a(P ) · C · Pij · H , j = D and γ = ij ij 0 Dα ij SR ij a(P )·C G · PSR ·H , respectively, where C = κ0Gt SR 0 r Dα SR 0 σ2+σ2 isaconstantindepeSnRdentofthetransmitpower.Moreover,wIe assumethemaximumtransmitpowerconstraintforSU-Txand SU-RS are both P respectively. max B. Assumptions for PU Distribution and Activities WeassumethePUsareuniformly(randomly)distributedon the two-dimensional plane with density ρ. In any given slot, each PU can be either active (ON) (with probability π ) or 1 inactive(OFF)(withprobabilityπ =1−π ).Bytheindicator 0 1 Fig.2. IllustrativediagramoftheCRSunderthreeprotocols. variablea(P ),wehaverelatedtheimpactofPUactivitiesto ij receivedSINRsonlinkij.WhentransmittingwithpowerP , ij theaverageinterference-to-noiseratio(INR)receivedbyaPU about 100-200 m. So the transmission between a pair of SU D distance away is γ¯ (P ,D ) = C · Pij . When nodes may affect multiple PU systems simultaneously. SP SP ij SP 0 σ2Dα the INR is higher than threshold γ , the PUPtraSnPsmission th would be interfered. Setting γ¯ (P ,D∗ ) = γ , we can A. Assumptions for SU Transmission SP ij SP th findtheradiusofthemaximuminterferenceregionasD∗ = We consider a CRS with a SU transmitter (SU-Tx), a SU 1/α SP receiver (SU-Rx), and a half-duplex cognitive RS (SU-RS), σP2Cγ0th ·Pij .Sincethedirectionalbeamwithbeamwidth as shown in Fig. 2. The links between SU-Tx and SU-Rx, (cid:16)θ rad can be(cid:17)approximated by a sector with angle θ , the 2π SU-Tx and SU-RS, SU-RS and SU-Rx are referred to as area of the interference region can be approximated by the SD, SR and RD links, respectively. In order to reduce the area of that sector with radius D∗ , which is A (P ) = SP SP ij interference region caused by SU transmission, we assume πD∗ 2· θ .Accordingtotheuniformdistributionassumption, SP 2π that antenna arrays are equipped at both SU-Tx and SU-RS theaveragenumberofPUsintheinterferenceregioncanthus for beamforming 1 with beamwidth θ and transmit antenna becalculatedasN(P )=ρ·A (P ).TheSUtransmission ij SP ij gain G . Since SU-RS works in half-duplex mode, it uses the onlinkij is“blocked”ifanyoftheN(P )PUsisactiveand t ij antenna array to obtain receiving antenna gain G . At SU- a(P ) = 0. Recall S is the activity state of the k-th PU in r ij k Rx, however, only one omnidirectional antenna is available. the region and the probability that the SU transmission with Further assume the transmission time of the CRS is slotted. power P would not be blocked is ij In any slot, using power P to transmit signal X (with unit ij signal energy) on link ij, the received signal at j is Pr{a(Pij)=1}=π0N(Pij) =exp −C1(ρ,π0)·Pi2j/α n o a(Pij)hij PijLijGtX +Ij +Zj, i=S,R,j =D 2/α Yj =(a(Pij)hijpPijLijGtGrX +Ij +Zj, i=S,j =R where C1(ρ,π0) = ρ2θ σP2Cγ0th lnπ10 > 0 is a constant independent of the trans(cid:16)mit pow(cid:17)er Pij but directly related to respectively, whepre a(Pij) is an indicatior variable and is a the PU distribution density ρ and activity intensity π0. functionofP .Itindicateswhetherthetransmissionfromito ij j usingpowerP isblockedbyanyPU,a(P )=0indicates ij ij C. Probability of Successful Transmission over a Link the transmission is blocked and a(P ) = 1 otherwise. h ij ij stands for the channel fading coefficient, which is assumed We assume the data of the SU system is encapsulated into to be flat Rayleigh so that the power gain on the link ij, i.e. small packets with M bits each. For each time slot, at most Hij = |hij|2, is exponentially distributed with parameter 1. onepacketcanbetransmittedwhichrequireschannelcapacity Hij is assumed to be quasi-static within a slot but identically larger than M. Using Shannon formula, the channel capacity and independently distributed (i.i.d) between different slots. between node i and j can be expressed as Φ =Blog (1+ ij 2 Lij = κ0·Di−jα is the large-scale path-loss between i and j, γij), where B is the bandwidth of the channel and γij is whereDij isthedistancebetweeniandj,κ0 andαarepath- the SINR at receiver j. Thus, the probability of successful loss coefficient and exponent, respectively. Ij stands for the transmission of a packet over link ij, denoted as psijucc, is sum signals received from all neighboring active PUs at node j. Since the PU’s coverage is much smaller and we assume psijucc(Pij)=Pr{Blog2(1+γij)>M} SU-Rx is not inside the coverage of any active PU, then we (2M/B −1)Dα can treat Ij as white noise with power E[Ij] = σI2, ∀j. Zj =Pr Hij > C P ij ·Pr{a(Pij)=1} ( 0 ij ) 1Beamforming increases the ave. Rx SNR at the SU-Rx but the instanta- (=1)exp −C (ρ,π )·P2/α−C (M/B,D )·P−1 ,(1) neousRxSNRstillfollowsRayleighfadingduetothelocalscatteringcluster. 1 0 ij 2 ij ij n o 3 for i = S,R,j = D, where C (M/B,D ) = (2M/B−1) · SimpleDecode-and-Forward (SDF)Protocol:IntheSDF Dα >0 is a constant independen2t of P biujt directlyCr0elated protocol, SU-RS can successfully receive a packet from SU- ij ij to the ratio of packet size over the channel bandwidth M/B TxistheSRlinkisnotblocked.Itdecodesthereceivedpacket and the distance between the two ends of the link D . Step and forwards to the SU-Rx as a conventional DF relay does. ij (1) is from equation (1). For the case j =R, The SU-RS can not receive new packet from SU-Tx before the currently holding packet has been successfully forwarded psucc(P )=exp −C1(ρ,π0) − C2(MB,DSR) . (2) to the SU-Rx. A packet can be removed from SU-Tx’s queue SR SR ( P−2/α GrPSR ) if an ACK is received from SU-Rx. SR Buffered Decode-and-Forward (BDF) Protocol: In BDF Property 1: For a given set of d , R, ρ, and π , there ij 0 protocol,infinitelylongbufferisalsoassumedatSU-RS.SU- exists a unique transmit power Popt > 0 that maximize ij Tx transmits a packet to SU-RS only when SU-RS is not the probability of successful transmission over link ij, i.e. transmitting on the RD link and the SR link is not blocked. ∃Popt, s.t. Popt = argmax psucc(P ).. The optimal ij ij Pij ij ij The packet is removed from SU-Tx’s queue if an ACK is transmit power for SD, SR and RD links (in the interference receivedfromSU-RS.Highertransmissionpriorityisassumed limited case, i.e. Popt <P ) are (i=S,R) ij max at SU-RS such that it transmits to SU-Rx whenever the RD α α link is not blocked. Moreover, we assume SU-RS has the αC (M,D ) α+2 αC (M,D ) α+2 Popt = 2 B iD Popt = 2 B SR (3) channel state information (CSI) of the RD link so that the iD 2C1(ρ,π0) ! SR 2GrC1(ρ,π0) ! channel outage time of the RD link can be further saved for SR link transmission. The packet is removed from SU-RS’s respectively, and the maximized probabilities of successful relay queue when an ACK is received from SU-Rx. transmission on SD, RD and SR links are (i=S,R) IV. ANALYSISOFSTABILITY/DELAYPERFORMANCE α 2 M psiDucc,opt =exp −C3C1α+2(ρ,π0)C2α+2(B ,DiD) (4) A. Queue Dynamics and Stability/Delay Definitions (cid:26) (cid:27) Queue Dynamics: We adopt a similar model used in psucc,opt =exp − C3 Cαα+2(ρ,π )Cα+22(M,D ) (5) [7], [8] to depict the buffer dynamics in a slotted system. SR 2 1 0 2 B SR ( Gα+2 ) Let Q (t),t = mτ,m = 0,1,... denote the queue length r S at the SU-Tx observed at the end of slot t. It evolves as where C3 = 1+ α2 α2 −αα+2 is a constant related to α. QS(t)=(QS(t−1)−YS(t))++XS(t),∀t. In the equation, Remark 1: For fixed transmit power P , the impact of PU (cid:0) (cid:1)(cid:0) (cid:1) ij XS(t)representsthenumberofpacketarrivalsinslott(cannot activity on the SU transmission is like a good/bad fading be transmitted in the same slot), which is assumed to be a process, with states a(Pij) = 1 (good) and a(Pij) = 0 Bernoulli process with mean E[X (t)] = λ, i.e. X (t) only S S (bad).However,itisdifferentfromatraditionalchannelfading takes value 0 or 1 with probability 1−λ and λ, respectively. process (ρ = 0, π = 1) when the transmit power can be 0 Y (t) denotes the number of packets that depart from SU-Tx S adjusted. Specifically, to combat a traditional channel fading, in slot t. According to the protocols, Y (t) also takes value S increasing the transmit power always helps to increase psucc, ij from {0, 1}, depending on the states of PU activities, channel while with random PU distribution and activities, psucc(P ) ij ij fading,andtheinteractionwiththequeuedynamicsatSU-RS. isnotamonotonicincreasingfunctionofP .Asshowninthe ij Since Q (t+1) only depends on Q (t) and X (t),Y (t) is Property1,thereexistaunique Popt thatmaximizepsucc(P ) S S S S ij ij t either 0 or 1, {QS} is a discrete time Markov Chain and for a specific link ij. its state transitions only happen between neighboring states, i.e. {Q } is a discrete time birth-death process (DTBDP). S III. PROTOCOLDESCRIPTIONS For n ≥ 0, let λn be the state transition probabilities from S Q (t)=n to Q (t+1)=n+1 and µn the state transition In each protocol, an infinitely long buffer is assumed at S S S probabilities from Q (t) = n to Q (t + 1) = n − 1 for SU-Tx and the first-in-first-out rule is applied. Recall that S S n≥1.Similarly,theevolutionforthequeue atSU-RScanbe the transmission time is slotted and the packet transmission defined as Q (t)=(Q (t−1)−Y (t))++X (t),∀t. Note starts at the beginning of a slot. In each slot, only one packet R R R R the arrival process X (t) depends on the departure process can be transmitted. When transmitting, SU-Tx and SU-RS are R of the source queue (i.e. Y (t)) and the half-duplex constraint supposed to use the optimal transmit power to maximize the S makes the interaction between Q (t) and Q (t) complicated. probability of successful transmission over a link. S R {Q } is also a DTBDP, whose state transition probabilities Baseline (BL) Protocol: In the BL protocol, SU-Tx trans- R canbedefinedinasimilarmannerasλn andµn,respectively. mits a packet directly to SU-Rx if the SD link is not blocked. R R Stability of a CRS: A queue Q is stable if and only if ThepacketisremovedfromSU-Tx’squeuewhenanacknowl- i lim Pr{Q (t)=0}>0 [8], for i=S,R. In the BL and edge (ACK) message is received from SU-Rx2. t→∞ i SDF protocols, when the queue at SU-Tx is stable, the whole system is stable, but in the BDF protocol, system stability 2A low rate control channel is assumed for control signal exchange, e.g. ACK/NACKmessagefromSU-RxorSU-RS.Wealsoassumeallthenodes requires both the queue at SU-Tx and the queue at SU-RS cansynchronizetheirbehaviorsviathischannel.Inaddition,sincetheuseof to be stable simultaneously. Denote by λ∗ the stability region microphonesisusuallyrestrictedwithinabuildingorasquare,theiractivity of the CRS in terms of the maximum exogenous arrival rate, statescanbesensedbysensorsplacedinthebuildingsoronthesquares.The sensingresultsareassumedknownatbothSU-TxandSU-RS. which has unit “packet/slot”. 4 End-to-End Delay of a CRS: The end-to-end delay of transmission, denoted as E{SR link successful}. Therefore3, a packet in the CRS is the time from a packet arrives at the queueofSU-TxtillthepacketreachesSU-Rx.Little’stheorem µSn≥1 =(1−λ)Pr E{SR link successful} [9] enables the study from the angle of average queue length. ×Pr E{RD link idle} E{Q 6=L} Pr E{Q 6=L} (cid:0) R (cid:1) R Given the exogenous arrival rate λ, the average end-to-end =(1−λ(cid:0)) qR0 +(1−qR0 (cid:12)−qRL)(1−psR(cid:1)uDcc)(cid:0)psSuRcc,opt (cid:1) delay for the three protocols can be defined as (unit: slots) (cid:12) λn≥1 =λ 1− (cid:2)q0 +(1−q0 −qL)(1−psucc)(cid:3)psucc,opt S R R R RD SR W = 1 lim Tt=1QS(t) = E[QS], (6) and λn=0n= λ.(cid:2)Using the same method as in o(cid:3)btaining (o8), BL λ1 T→∞PT TQ (t) 1 λ T Q (t) the steSady state probability of QS =0 is WSDF/BDF = λTl→im∞ t=1T S + λTl→im∞ t=1T R q0 =1− λ (11) E[Q ]+PE[Q ] P S q0 +(1−q0 −qL)(1−psucc) psucc,opt = S R (7) R R R RD SR λ which implies(cid:2)the stability region is (cid:3) where E is taken w.r.t the steady distribution of queue length. λ∗ = q0 +(1−q0 −qL)(1−psucc) psucc,opt. (12) R R R RD SR For {Q }(cid:2), due to the half-duplex constrai(cid:3)nt, packet arrival R and packet departure would not happen in the same slot. As B. Stability/Delay Analysis for the BL protocol theincreaseofQ haslowerprioritythanitsdecrease.Sothe R IntheBLprotocol,only{Q }isinvolved.Thequeuelength probability that Q deceases by one equals the probability S R increasesbyoneifanewpacketarrivesandnopackethasbeen of successful transmission on the RD link. Thus, the state successfully transmitted, and decrease by one if an existing transition probabilities of {Q } are R packet is successfully transmitted and no new packet has arrived,whichimpliesλn=0 =λandλn≥1 =λ·(1−psucc,opt), λnR=0 =(1−qS0)psSuRcc,opt, S S SD andµn≥1 =(1−λ)·psucc,opt.Wederivethestabledistribution λ1≤n≤L−1 =(1−q0)psucc,opt(1−psucc,opt), S SD R S SR RD of {QS} by solving the detailed balance equation related to µ1≤n≤L =psucc,opt. the DTBDP. Define qn as Pr Q =n , we have R RD S S So the steady state probability of Q =0 is R (cid:2) (cid:3) qS0 = 1n+−1nX∞=λ1knkY=−01µλkS+kS1!q−01 =1− pλsS(uD1cλc−,oppts,ucc,opt) n(8) qR0 =1+ PLk=1(cid:16)(1−q1S0−)psSpuRpcsRcsRuD,ucDoccpc,t,o(op1pt−tpsRuDcc,opt)(cid:17)k−1(.13) qn =q0 S = S SD (9.)   S SkY=0 µkS+1 1−psSuDcc,opt (1−λ)·psSuDcc,opt! ThesteadystateprobabilityofQR =kcanbefurtherobtained via similar calculations used in (9) as System stability requires q0 > 0, which implies λ∗ = passSuDacccc,ooprtd.iFnugrttohe(r6m).oTreh,etohreemenSd1-tsou-menmdadriezleadytchaenabbeovcealcreusluatletsd. qRk = 1−pqsR0ucc,opt (1−qS0)psSuRcc,opt(1−psRuDcc,opt) psRuDcc,opt k RD (cid:0) (cid:14) (cid:1) Theorem 1: Thestabilityregionandtheaverageend-to-end SinceqL isfunctionofq0,solvingthecombinedequationsof delay under the BL protocol are R R (11) and (13), we can get the solutions for q0 and q0, which S R further lead to the results of the stability region λ∗ and the λ∗BL =psSuDcc,opt, WBL = 1−λ / psSuDcc,opt−λ .(10) average end-to-end delay 4. We now apply the general results derived above to the SDF and BDF protocols, respectively. (cid:0) (cid:1) (cid:0) (cid:1) Special Case I - SDF Protocol: In this case, L = 1 and C. Stability/Delay Analysis for the SDF/BDF protocol {QR} reduces toa two-stateMarkov chain withqRL =1−qR0. Therefore, (11) and (13) reduce to In the following, we shall first analyze a general case of SU-RS having buffer length L. qS0 =1−λ/qR0psSuRcc,opt, General Case: Similar as in the BL protocol, the decrease q0 =psucc,opt (1−q0)psucc,opt+psucc,opt . R RD S SR RD in Q implies a packet has been successfully transmitted to S (cid:14)(cid:0) (cid:1) SU-RS and no new packet arrives. However, under the SDF 3Here we approximate Pr{QR(t)=m |QS(t)=n} as Pr{QR(t)= or BDF protocol, the departure process of Q (t) is related m}, which is asymptotically tight for large L case (e.g. the BDF case) but S is an upper bound on µn in the SDF case. As a result, the final expression to the dynamics of Q (t). The departure of a packet implies S R ofthestabilityregion(end-to-enddelay)oftheSDFcaseisanupperbound that the following three events must be true simultaneously: (lowerbound),whichisverifiedbythesimulationinSectionV. 1) The queue length at SU-RS is not L, denoted as E{QR 6= 4There is no closed-form expressions for qR0 and qS0 in the general case, whichinvolvesfindingtherootsofanpolynomialtoapowerofL.However, L}; 2) SU-RS is not transmitting on the RD link, denoted as for the two special cases L = 1 and L = ∞, the polynomials reduce to E{RD link idle}; 3) The SR link is able to support the packet quadraticformsandclosed-formsolutionsarereadytoget. 5 Solving the two equations, the steady state probabilities are as the throughput gain and power gain of the SDF protocol over the BL protocol, then the path-loss gain in throughput q0 = 1−λ/ psucc,opt−psucc,optλ psucc,opt , (14) S SR SR RD per Watt is thus given by ∆T = 1+∆T −1. Fig. 3 depicts qR0 = 1−λ/(cid:0)psRuDcc,opt, (cid:14) (cid:1) (15) the path-loss gain of a CRS ovPer the1+B∆LPsystem as a function of SU-RS’s location. Here we assume SU-Tx and SU-Rx are respectively. The stability region can be obtained from the fixed at (0,0) and (2,0) km while SU-RS is at (D ,0). It requirement q0 >0 and the average end-to-end delay can be SR S can be shown that setting Popt(D ) = Popt(D −D ) calculatedaccordingto(7).Theorem2summarizestheresults. SR SR RD SD SR achievesthepeakofthepath-lossgain,whichimpliesD∗ = SR delTahyeoforremthe2:SDThFepsrtoatboicliotyl areregionandtheaverageend-to-end (1P−roCp4e)rDtyS2D:,DThR∗eDpa=thC-lo4DssSgDai,nwahcehrieevCes4i=tsp1+eGaG−rk−r1/1wα/αhe.n SU- RS is located at (D∗ ,0), i.e., psucc,optpsucc,opt SR λ∗SDF = psRuDRccD,opt+SpRsSuRcc,opt (16) 1+∆T 1 psucc,opt C4α2+α2−1 WSDF = psSuRcc,opt−1−ppsSsuuRλcccc,,ooppttλ−λ + psRuDc1c,opt. (17) G∆iTveP∗n=su1ch+∆loPcat−ion1=ofGSrU−-αR2α+(cid:0)S2,(S1Dth−eCc4o(cid:1))nααd+2i2tio+nCf4oαrα+22ha−vin1g. RD Special Case II - BDF Protocol: In this case, L=∞ and positive path-loss gain is given by then for a stable system qRL =0. Cλorrespondingly, we have psSuDcc,opt < 2Gr−αα+2(1−C4)αα+22 +2C4αα+22 C4α2+1α2−1. q0 =1− , S 1−(1−q0)psucc,opt psucc,opt (cid:16) (cid:17) R RD SR B. Analysis of Buffer Gain (1−q0)psucc,opt qR0 =1− (cid:2)psucc,opt 1+S(1−SRq0)(cid:3)psucc,opt . The buffer gain is referred to the gain that comes from RD S SR enabling the buffering capability at SU-RS. We shall use Solving the two equations, w(cid:2)e get (cid:3) the results derived in section IV to illustrate this gain. In q0 =1−λ (1−λ)psucc,opt , q0 =1−λ psucc,opt(.18) particular, we shall show the relative increase in the stability S SR R RD regionandthereductionintheaverageend-to-enddelayunder respectively. T(cid:14)h(cid:2)e stability region(cid:3)can be obtaine(cid:14)d from satis- the BDF protocol (infinite buffer) compared with the SDF fying the requirements of both q0 > 0 and q0 > 0, and the protocol(singlepacketstorage).Thebuffergaininthestability S R average end-to-end delay can be calculated according to (7). region and in the average end-to-end delay are defined as Theorem 3 summarizes the above results. ∆λ∗ = λ∗ /λ∗ −1 and ∆W¯ = 1−W¯ /W¯ , BDF SDF BDF SDF Theorem 3: Thestabilityregionandtheaverageend-to-end respectively. delay for the BDF protocol are Property 3: Given SU-RS located at (D∗ ,0), and let SR 2α psucc,opt ζ=∆psucc,opt = psucc,opt C4α+2, the buffer gain λ∗BDF =min(1+SpRsSuRcc,opt,psRuDcc,opt), (19) in stRabDility r(cid:12)eDgRioDn=DanR∗dDin av(cid:0)erSagDe end(cid:1)-to-end delay are (cid:12) WBDF = (1−λ)1psS−uRcλc,opt−λ + psRuDc1c,−optλ−λ. (20) ∆λ∗ = 11−+ζζ >0, ∆W¯ = (ζ−1λ−λ2λ)((1ζ−−ζ)λ ) >0.(21) 1−λ V. ANALYSISOFPATH-LOSSGAINANDBUFFERGAIN The value of ζ in (21) depends on the system parameters suchasαandG aswellasPUdistributiondensityρandPU A. Analysis of Path-loss Gain r activity intensity π . Fig. 4 depicts how the buffer gain given Path-loss gain is referred to as the gain that a CRS obtains 0 by equation (21) varies with PU activity intensity π and PU from the reduction in path-loss over the BL system. We shall 0 distributiondensity.Fromthefigureweseethatthebuffergain use the metric called “throughput per Watt” to illustrate this increaseswhenthecognitiveenvironmentismoreunfavorable gain, which is defined as the average throughput (in bits/slot) (e.g. larger intensity of PU activity and higher density of PU of delivering a single packet from SU-Tx to SU-Rx divided distribution), which verifies that with the buffering capability by the transmit power needed. In this case, the SDF and BDF enabled at the cognitive relay, a CRS can better adjust to protocols behave alike, so we only compare the SDF protocol the environment and more efficiently deal with the spatial with the BL protocol. burstiness of the PU activities. To transmit a single packet with R bits on SD, SR, and RD links take 1/psucc,opt, 1/psucc,opt and 1/psucc,opt C. Numerical Discussions SD SR RD time slots, respectively, so the average throughput for the In this subsection, we shall discuss the end-to-end delay BL and SDF protocols are T = R · psucc,opt and BL SD performanceunderthethreeprotocolsandverifyouranalytical TSDF = 1/psucc,opt+R1/psucc,opt = Rps·pusScucR,cocp,to+ptppssRuuDcccc,,oopptt, respec- results via Monte Carlo simulations. The packet size M = tively. WhileStRhe transmRiDt power neSeRded forRtDhe two proto- 16 kbits and the channel bandwidth is B = 16 kHz. Other cols are Popt and Popt +Popt, respectively. Further define parameters are set as follows: κ = 1, α = 4, σ2 = σ2 = 1, SD SR RD 0 I ∆T = T /T −1 and ∆P = Popt+Popt /Popt−1 G =G =2,θ =π/3radandγ =1.Fig.5depictsthethe SDF BL SR RD SD t r th (cid:0) (cid:1) 6 0.8 6 30 BL simu. 0.7 G = 2 Gr = 2 SDF simu. r 5 25 BDF simu. n 0.6 wer gai 0.5 4 Gr = 1 delay20 analyλs=is0 .r2esults hroughput gain and po 000...234 Gr = 1 Path−loss gain23 Average end−to−end 1105 T 0.1 1 5 0 throughput gain power gain analysis results, λ=0.1 −0.1 0 0 0 0.5 1 1.5 2 0 0.5 1 1.5 2 1 1.5 2 2.5 3 3.5 4 Distance of SU−RS Distance of SU−RS PU distribution density ρ Fig. 3. Path-loss gain of CRS over BL system with different distances of Fig.5. Theaverageend-to-enddelayunderthethreeprotocolswithdifferent SU-RS.DSD =2km,ρ=2perkm2,π0=0.8. PU distribution density ρ per km2. DSD = 2 km and SU-RS is fixed at (DS∗R,0)=((1−C4)DSD,0)=(1.086,0)km,π0=0.8. 1 30 0.9 ρ = 1.5 Buffer gain in delay analysis results 0.8 λ = 0.2 λ = 0.2 Buffer gain in 25 0.7 stable region ρ = 2 ay Buffer Gain000...456 ρ = 1.5 ρ = 2 nd−to−end del1250 e Buffer gain in delay e 0.3 λ = 0.1 erag10 0.2 ρ = 1.5 ρ = 2 Av 0.1 5 BL simu. SDF simu. 00 .5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 BDF simu. analysis results, λ = 0.1 PU activity intensity π0 00 .5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 PU activity intensity π 0 Fig.4. Buffergaininbothstabilityregionandaverageend-to-enddelayof CRSundertheBDFprotocoloverthatundertheSDFprotocolwithdifferent Fig.6. Theaverageend-to-enddelayunderthethreeprotocolswithdifferent PUactivityintensityπ0.ρ=2perkm2,DSD =2km,andSU-RSisfixed PUactivityintensityπ0.DSD =2kmandSU-RSisfixedat(DS∗R,0)= at(DS∗R,0)=((1−C4)DSD,0)=(1.086,0)km. ((1−C4)DSD,0)=(1.086,0)km,ρ=2perkm2. performance of the average end-to-end delay with increasing REFERENCES PU distribution density, while Fig. 6 shows the trend that the [1] J.MitolaandG.Q.Maguire,“Cognitiveradio:makingsoftwareradios average end-to-end delay varies with decreasing PU activity morepersonal,”IEEEPersonalCommun.Mag.,vol.6,no.4,pp.13– intensity. We can see that the simulation results matches well 18,Aug.1999. withouranalyticalresults.Moreover,theBDFprotocolalways [2] S. Haykin, “Cognitive radio: brain-empowered wireless communica- tions,” IEEE J. Sel. Areas Commun., vol. 23, no. 2, pp. 201 – 220, achieveslargerstabilityregionandsmallerdelaythantheSDF Feb.2005. protocol, as claimed in Property 3. [3] Q. Zhao, L. Tong, A. Swami, and Y. Chen, “Decentralized cognitive mac for opportunistic spectrum access in ad hoc networks: A pomdp framework,” IEEE J. Sel. Areas Commun., vol. 25, no. 3, pp. 589 – 600,Apr.2007. VI. CONCLUSION [4] K.LeeandA.Yener,“Outageperformanceofcognitivewirelessrelay networks,”inProc.IEEEGLOBECOM’06,Nov.2006. We have shown two levels of gains provided by a CRS, i.e. [5] M. Sharma, A. Sahoo, and K. D. Nayak, “Channel selection under interferencetemperaturemodelinmulti-hopcognitivemeshnetworks,” path-lossgainandbuffergain.Thepath-lossgainsubstantially inProc.IEEEDySPAN’07,Apr.2007,pp.133–136. increases the spectrum access opportunities by reducing the [6] Y.T.Hou,Y.Shi,andH.D.Sherali,“Spectrumsharingformulti-hop transmit power while the buffering capability at the relay networkingwithcognitiveradios,”IEEEJ.Sel.AreasCommun.,vol.26, no.1,pp.146–155,Jan.2008. further saves the blockage time of either the SR or RD [7] A. K. Sadek, K. J. R. Liu, and A. Ephremides, “Cognitive multiple link and reduces the end-to-end delay to a larger extent. 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