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

0.21 MB·English

by  Yan Chen

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.
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