and Wai-Choong (Lawrence) Wong, Senior Member, IEEE
Abstract—In this paper, we consider medium access control(MAC) protocol design for random-access cognitive radio (CR)networks. A two-level opportunistic spectrum access strategy isproposed to optimize the system performance of the secondarynetwork and to adequately protect the operation of the primarynetwork. At the first level, secondary users (SUs) maintain asufficient detection probability to avoid interference with primaryusers (PUs), and the spectrum sensing time is optimized to controlthe total traffic rate of the secondary network allowed for ran-dom access when the channel is detected to be available. At thesecond level, two MAC protocols called the slotted cognitive radioALOHA (CR-ALOHA) and cognitive-radio-based carrier-sensingmultiple access (CR-CSMA) are developed to deal with the packetscheduling of the secondary network. We employ normalizedthroughput and average packet delay as the network metrics andderive closed-form expressions to evaluate the performance of thesecondary network for our proposed protocols. Moreover, we usethe interference and agility factors as the performance parametersto measure the protection effects on the primary network. Forvarious frame lengths and numbers of SUs, the optimal perfor-mance of throughput and delay can be achieved at the samespectrum sensing time, and there also exists a tradeoff between theachievable performance of the secondary network and the effectsof protection on the primary network. Simulation results showthat the CR-CSMA protocol outperforms the slotted CR-ALOHAprotocol and that the PUs’ activities have an influence on the per-formance of SUs for both the slotted CR-ALOHA and CR-CSMA.
Index Terms—Cognitive radio networks, CR-ALOHA,CR-CSMA, opportunistic spectrum access.
Manuscript received July 27, 2010; revised December 23, 2010 andMarch 16, 2011; accepted March 20, 2011. Date of publication April 11, 2011;date of current version June 20, 2011. This work was supported in part by theInteractive and Digital Media Project Office, Media Development Authorityof Singapore, through the National Research Funding Grant NRF2007IDM-IDM002-069 on Life Spaces. The review of this paper was coordinated byProf. J. Chun.
Q. Chen is with the Department of Electrical and Computer Engineering,National University of Singapore, Singapore 118622, and also with the Institutefor Infocomm Research, A*STAR, Singapore 138632 (e-mail: [email protected]).
Y.-C. Liang is with the Institute for Infocomm Research, A*STAR,Singapore 138632 (e-mail: [email protected]).
M. Motani and W.-C. Wong are with the Department of Electrical andComputer Engineering, National University of Singapore, Singapore 118622(e-mail: [email protected]; [email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TVT.2011.2141694
I. INTRODUCTION
IN conventional spectrum management, most of the spec-trum bands are exclusively allocated to particular services,
which may potentially exhaust limited frequency resources aswireless applications grow. In contrast to spectrum scarcity, theutilization of the allocated spectrum bands is usually very low.Measurement results have shown that only 2% of the allocatedspectrum is used, on the average, in the U.S. [1]. Furthermore,although the allocated users are active, there still exists anabundance of spectrum access opportunities at the slot level.This condition motivates the development of cognitive radio(CR) [2], [3], where secondary users (SUs) are allowed to usethe spectrum bands that were originally assigned to primaryusers (PUs).
One feasible approach is opportunistic spectrum access(OSA), envisioned by the Defense Advanced Research ProjectsAgency Next-Generation Communications (DARPA XG) Pro-gram [4], which allows SUs to utilize the unused channelswhen PUs are detected to be inactive. This mechanism isalso called listening before transmission, where the listeningfunction is fulfilled by spectrum sensing at the physical (PHY)layer, and the transmission function refers to packet schedulingat the medium access control (MAC) layer. Obviously, theintroduction of spectrum sensing brings more challenges forthe MAC protocol design under cognitive radio network (CRN)compared with conventional networks. Several existing works[5]–[7] focus on the spatial OSA, and the main issue that isaddressed is to coordinate the channel allocation or spectrumreuse in some particular areas or locations (e.g., cellular-basednetworks), whereas PUs’ states are considered static or slowlyvarying in time. Other solutions, e.g., [8] and [9], addressthe temporal OSA, where the unused time slots of PUs canbe accessed by SUs in real time. In [8], Liang et al. stud-ied the performance tradeoff between sensing time and theachieved throughput of SUs and demonstrated the existenceof an optimal spectrum sensing time that yields the maximumachievable throughput for SUs under the constraint that PUsare adequately protected. Although this policy can guaranteethe maximum throughput of a secondary link pair, it considersonly the point-to-point transmission model. In [9] and [10], aMAC protocol based on the framework of partially observableMarkov decision processes (POMDPs) is developed to exploitthe optimal sensing and access strategy for CRNs. However, itscomplexity exponentially grows with the number of channels,
CHEN et al.: TWO-LEVEL MAC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRUM ACCESS IN CRNs 2165
and the assumption that PUs’ usage statistics remain unchangedsimplifies the MAC protocol design. Moreover, SUs schedulethe packets and coordinate their access based on the follow-ing two different models: 1) the guaranteed-access model and2) the random-access model. Most of the previous works, e.g.,[11]–[19], applied the guaranteed-access model into CRNs byusing an exclusive common control channel (CCC) or centralcoordinator to schedule SUs’ packets in a sequential manner. In[13], each frame of the control channel is divided into the reportand the negotiation phases. In the report phase, two differentchannel spectrum sensing policies were proposed to detectthe available subchannels and report the obtained information.Then, in the negotiation phase, SUs exchange data followingthe p-persistent carrier-sensing multiple access (CSMA) proto-col to compete for the channel and get the permission to utilizeall the available subchannels in the next frame. In addition, theauthors considered only the perfect spectrum sensing case. Infact, this CCC may not be always available in practice, and italso easily suffers from the control channel saturation problem[20]. To the best of our knowledge, fewer studies considered therandom-access model for packet scheduling under CRNs [21],[22]. The difficulty is that, in a CR environment, SUs not onlycompete for the channel with other SUs but need to vacate thechannel to avoid interference to PUs as well. Huang et al. [21]proposed the following three random-access schemes with dif-ferent sensing, transmission, and backoff mechanisms for SUs:1) virtual transmit if busy (VX); 2) VAC; and 3) keep sensing ifbusy (KS). Considering the scenario of one PU band andone SU, the authors investigated the capacity of SUs andderived closed-form expressions of performance metrics foreach scheme. However, because they assume that the PUs’packet arrival process and spectrum sensing performed at SUsare independent of each other, the spectrum sensing techniqueis unhelpful in increasing the SUs’ access opportunities. There-fore, the relevant achievable performance is pessimistic.
In this paper, we consider the MAC protocol design problemfor CRNs based on the random-access model and the imperfectspectrum sensing assumption, where all the SUs share a singletransmission channel with PUs, and no additional CCC isneeded. To protect the operation of the primary network andoptimize the system performance of the secondary network, wepropose a two-level OSA strategy here. The first level performsspectrum sensing, which is arranged at the beginning of eachMAC frame before data transmission. Limited by the interfer-ence constraint from PUs, SUs must maintain their detectionprobabilities at a target threshold. Furthermore, because anSU’s packet transmission probability depends on its detectionand false-alarm probabilities, the actual traffic rate can becontrolled by adjusting the spectrum sensing time. The secondlevel is similar to the function of conventional MAC protocols.Based on the slotted ALOHA and CSMA (e.g., [23] and [24]),respectively, we develop two MAC protocols called the slottedcognitive radio ALOHA (CR-ALOHA) and cognitive-radio-based carrier-sensing multiple access (CR-CSMA) to deal withthe packet scheduling of SUs under a CR environment. Thesetwo protocols can easily be implemented, and closed-form ex-pressions of our network metrics can also be derived to comparewith each other. Moreover, due to the property of discrete
Fig. 1. System model of a CRN.
channel access time, we design an appropriate frame structureto support our proposed two-level OSA strategy and developa framework to evaluate the performance of the secondarynetwork for each protocol in terms of normalized throughputand average packet delay. To measure the protection effectson the primary network, we define the interference factor asthe outage probability that SUs would interfere with PUs in anarbitrary frame and also define the agility factor as the abilitythat SUs can rapidly vacate the channel once PUs have becomeactive. Thus, we study the tradeoff between the achievable per-formance of the secondary network and the protection effectson the primary network and accordingly design the optimalframe length. Conversely, we also consider the effects of thespectrum utilization of the primary network on the performanceof the secondary network.
This paper is organized as follows. Section II introducesthe system model and our proposed access strategy for CRNs.In Sections III and IV, we propose the slotted CR-ALOHAand CR-CSMA and analyze their performances, respectively.The evaluation results, performance-protection tradeoffs, andeffects of PUs’ activities are shown in Section V. Finally,conclusions are drawn in Section VI.
II. SYSTEM MODEL
A. System Model
The system model considered in this paper is shown inFig. 1. The primary network consists of one primary transmitter(denoted by Pt) and several primary receivers (denoted byPr’s), where Pt can broadcast signals to Pr’s over a single chan-nel using the licensed spectrum band. The secondary networkconsists of N number of fixed or mobile SUs (denoted by Ui,i = 1, . . . , N ), which are located within Pt’s coverage range(the range that Pt can be detected at Ui’s by spectrum sens-ing), and are self organized into a wireless local area network(WLAN). Each Ui can directly communicate with other SUsor secondary access points (SAPs); thus, the synchronizationproblem can be solved by the coordination function of SAPswhen Ui dynamically joins the secondary network. In addition,the primary and the secondary networks operate independent
2166 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011
Fig. 2. MAC frame structure of our proposed two-level OSA strategy.
of each other, and there is no message exchange between PUsand SUs.
According to OSA, SUs can use Pt’s channel only when Pt isdetected to be inactive. Once Pt has woken up, Ui’s must vacatethe channel within a certain duration, i.e., Tv s. Therefore, Ui’sare forced to suspend their access and periodically detect thePt’s states within Tv . This policy results in the discrete channelaccess time under a CRN in contrast to the continuous accesstime under conventional networks. To support OSA, a relevantframe structure is designed, as shown in Fig. 2. Each framewith the length Tf (Tf ≤ Tv) consists of a duration of Ts forspectrum sensing and Td for data transmission. Ts is arranged atthe beginning of each frame, and Td can accommodate up to Mtransmission periods (TPs) that are indexed by j, j = 1 · · ·M .The advantage of this small data piece structure is that morethan one SU can compete for channel access in the same frameduration, which reduces the waiting (or response) time andtransmission failure cost of each SU and, furthermore, improvesthe system performance of the whole secondary network. Inaddition, we assume that all packets have the same size; thus,each TP consists of a fixed packet transmission time T anda propagation delay Tp. Therefore, we have Tf = Ts + Td =Ts + M(T + Tp).
B. Spectrum Sensing Methods
Compared with the traditional networks, PUs and SUs ina CR environment are usually unknown to each other, andthe PUs’ information (e.g., modulation technique and location)seems to be a “black box” for SUs. Obviously, if SUs arelocated outside the carrier-sensing range (CSR) of PUs, it isimpossible for them to know the PUs’ ON/OFF states only bythe carrier sense technique. Thus, we must consider using thespectrum sensing technique to perform PU detection at eachSU in every frame. In general, the following three techniquesare widely used: 1) matched filter; 2) energy detection; and3) cyclostationary feature detection. In this paper, we adoptthe energy detection technique [8], [25] due to its simplicity.An energy detector computes the power (denoted by Yi) ofthe received signal from Pt at Ui and compares Yi with apredetermined threshold ε. If Yi ≥ ε, Pt is deemed to be active,and vice versa. Let t be the spectrum sensing time, fs be thesampling frequency, and γ be the received signal-to-noise ratio(SNR) from Pt at Ui. Considering the complex-valued phase-shift keying (PSK) signal and circularly symmetric complexGaussian (CSCG) noise case, the detection probability Pd foreach SU is approximately given by [8]
Pd(t) = Q((
ε
σ2u
− γ − 1)√
tfs
2γ + 1
)(1)
where σ2u is the variance of the received Gaussian noise, and
Q(·) is the complementary function of a standard Gaussianvariable, i.e., Q(x) = (1/
√2π)
∫∞x exp(−s2/2)ds. To protect
the operation of the primary network, the overall detectionprobability that all the SUs know the existence of Pt whenPt is active is given by PN
d , which should be set larger thana threshold based on the application requirement.
Assume that Ui’s are located outside Pt’s CSR; thus, theprimary network would not affect the secondary network. How-ever, Ui can still interfere with the receiving of neighboringPr’s that are located within Ui’s CSR. Therefore, to protectthe primary network, Ui’s detection probability Pd should notbe less than a certain threshold. Then, the corresponding false-alarm probability Pf is given by
Pf (t) = Q(√
2γ + 1Q−1(Pd) +√
tfsγ)
. (2)
Based on (1) and (2), we see that Pf is a monotonicallydecreasing function of t for fixed Pd and γ. The spectrumsensing time t varies in the domain of dom t = {t|0 < t ≤Ts}, whereas the minimum Pf (which is denoted by Pf,min)is attained at t = Ts.
C. Traffic Model and Assumptions
The traffic model and its underlying assumptions are charac-terized as follows.
Wellens et al. [26] introduced time-frequency models ofspectrum use for various applications. First, because the ex-ponential distribution can provide a good approximation forthe packet service time [27], we assume that the run andburst lengths of aggregated arrivals in the primary networkfollow exponential distributions with the parameters λr and λb,respectively. Moreover, in the secondary network, each Ui isassumed to be an independent Poisson source with an averagepacket generation rate of λi packets per TP; thus, the lengths ofpacket-generating intervals follow the exponential distributionwith mean 1/λi. Suppose that all the λi’s are equal to λ; then,the total traffic rate is G = Nλ.
Second, a positive acknowledgment scheme is adopted. If apacket is successfully transmitted, Ui will receive a positiveacknowledgment. Otherwise, after a time-out period, it knowsthis failure and uniformly chooses a time to retransmit within afixed back-off window of size [0, 2X̄]. Let Ta be the length ofan acknowledgment packet; then, the time-out period is givenby T + Ta + 2Tp. At any instant, each Ui has at most onepacket that waits for transmission, regardless of whether it isnewly generated or backlogged. Moreover, we consider that thechannel error problem has been solved by an error correctionmechanism that is performed at the PHY layer.
Last, we make the following assumption.Assumption 1: Suppose that all packets that were sent by
SUs are of constant length, which assumed to be T = 1;then, we normalize that α = Tp/T , β = Ts/T , a = Ta/T , l =Td/T , f = Tf/T , and δ = X̄/T , respectively.
Therefore, the length of TP is equal to 1 + α, and the totalframe length is given by f = β + M(1 + α).
CHEN et al.: TWO-LEVEL MAC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRUM ACCESS IN CRNs 2167
D. Spectrum Access Scheme
To protect the operation of the primary network and optimizethe system performance of the secondary network, we proposea two-level OSA strategy as follows.
At the first level, spectrum sensing is periodically executedby Ui to detect Pt’s activity before its packet transmission.Using energy detection, Pd is set according to the protectionrequirement. If Pt is detected to be active, Ui will be blockedfor transmission in the current frame; otherwise, it will attemptto transmit. Thus, the packet transmission probability for eachUi is determined by both Pd and Pf . Furthermore, because Pf
is monotonically decreasing with t for a given Pd, the actualtraffic rate of SUs is eventually determined by t. Therefore, wecan choose an appropriate t to achieve better performance ofthe secondary network.
The second level aims at the packet scheduling of SUs, whichis similar to the function of conventional MAC protocols. In thispaper, the slotted CR-ALOHA and CR-CSMA are proposed tosolve the channel access contention problem. The details willbe given in the following sections.
E. PUs’ Activities and Performance Parameters
We use H0 and H1 to denote the events that Pt is inactive andactive, respectively, during the spectrum sensing duration anduse PH0 and PH1 to denote the occurrence probabilities of H0
and H1, respectively. To compute their values, we directly mapthe active and inactive states of Pt to the operation and repairstates of a one-unit system [28], where “one unit” means thatthe system is collectively viewed and the failure of any compo-nent should be interpreted as the failure of the whole system.Thus, in reliability analysis, interval reliability is defined as theprobability that, at a specified time, the system operates andwill continue to operate for at least a given interval, and servingreliability is defined as the probability that either the systemoperates at a specified time, or if it is not operating, it willbe repaired within a given interval. Considering that both therun and burst lengths of Pt follow the exponential distributions,we have
{PH0 = λbe
−λrβ/(λr + λb)PH1 = 1 − PH0 .
(3)
Obviously, PH0 and PH1 are related to the length of spectrumsensing duration β.
Based on our proposed spectrum access scheme, we knowthat Ui sends only when it detects that Pt is inactive, which mayresult in incorrect sensing cases of false alarm and missed de-tection. Although the sensing result is correct, there still existsthe possibility (denoted by H2) that this result is inconsistentwith the fact that, when Pt keeps inactive during β, later on, itwakes up during the data transmission time Td of the currentframe. Let PH3 be the probability that Pt is inactive during thewhole frame; thus, we have
PH3 = λbe−λrf/(λr + λb). (4)
Then, the probability of H2 (which is denoted by PH2) isgiven by
PH2 = PH0 − PH3 . (5)
Obviously, the secondary network interferes with the primarynetwork in the following two aspects: 1) missed detection underH1 and 2) transmission under H2. Note that the case Pt is activeat the beginning of the spectrum sensing duration but lateron turns to be inactive before the end of the sensing durationexists. However, the corresponding occurrence probability isnegligible; thus, we can ignore this case and focus only oncases H1 and H2. To measure these effects, we define a newparameter, i.e., interference factor (denoted by IF ), which isthe outage probability that SUs would interfere with PUs in anarbitrary frame, and use subscripts 1 and 2 to distinguish theaforementioned two cases. First, we consider the case of misseddetection under H1. Based on (1) and (3), we have
IF1 =(1 − PN
d
)PH1 . (6)
For the second case of transmission under H2, based on (2)and (5), we have
IF2 =(1 − PN
f
)PH2 . (7)
Combining (6) and (7) yields
IF = IF1 + IF2. (8)
Based on (8), we see that, for fixed Pd and N , IF dependsonly on Pf and f . Moreover, because Pf is a monotonicallydecreasing function of t, IF is a monotonically increasingfunction of t and is also a monotonically increasing functionof f .
In addition, we consider another parameter called the agilityfactor (which is denoted by AF ), which refers to the Ui’s abilityto rapidly vacate the channel once Pt has turned active froman inactive state. Based on our designed frame structure, wedefine that AF = Tf/Tv , which varies in (Ts/Tv, 1] due to thecondition of Ts < Tf ≤ Tv . By definition, the smaller the valueof AF is, the quicker the channel is vacated, and vice versa.Obviously, AF is related to the configuration of the framelength. Therefore, we take this parameter into account to designthe optimal frame length.
III. SLOTTED CR-ALOHA AND ITS PERFORMANCE
A. Slotted CR-ALOHA
The slotted CR-ALOHA is developed from the conventionalslotted ALOHA, which differs in the discrete channel accesstime and the constraint of protecting the primary network. Weassume that, for each frame, the data transmission duration l isslotted, and the slot size is equal to the TP length of 1 + α. Asshown in Fig. 3, the slotted CR-ALOHA operates as follows.
1) If Ui detects that the channel is available in the currentframe, any packet that arrives in the M th slot of theprevious frame or the spectrum sensing duration of thisframe will be transmitted in the first slot; otherwise, if
2168 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011
Fig. 3. Operation scheme of the slotted CR-ALOHA. The box with solid linesindicates the inactive Pt case, and the box with dash lines indicates the activecase.
a packet arrives in the jth slot (j �= M), it will start totransmit at the beginning of the (j + 1)th slot.
2) If the channel is unavailable, any packet arrival within thisframe up to the (M − 1)th slot will be blocked to the endof this frame and then uniformly retransmit within a back-off window, as mentioned in Section II-C.
3) The current transmission is successful when there is onlyone packet that was transmitted; otherwise, a collisionoccurs, and the packets involved will be retransmittedafter corresponding separate random delays to avoid con-tinuously repeated conflicts.
4) Any arrival in the M th slot of one frame will be processedin the next frame.
For the conventional slotted ALOHA, the normalizedthroughput S, defined as the fraction of time that can success-fully transmit SUs’ packets, is given by S = Ge−G, and themaximum S is equal to 0.368 when G = 1. However, in a CRenvironment, Pt’s activities will definitely degrade S, whichwill be shown as follows.
B. Throughput Analysis
Based on the operation scheme of the slotted CR-ALOHA, apacket that can successfully be transmitted by Ui must satisfythe following three conditions if the capture effect is ignored:1) Ui can access the channel in the current frame; 2) no collisionoccurs between Pt’s transmission and Ui’s transmission; and3) no collision occurs between Ui and any other SU’s packets.Let Ci, i = 1, 2, 3, denote the aforementioned conditions. Ob-viously, C2 and C3 are independent of each other, conditionedon C1.
First, we consider C1. For H0, Ui can access the channelwith a probability of 1 − Pf , because no false alarm occurs.Moreover, if Ui cannot detect Pt’s activeness under H1, Ui canstill access with a probability of 1 − Pd. Let V0 and V1 be theprobabilities of both cases, respectively; then, we have
Pr{C1} ={
V0 = 1 − Pf , H0
V1 = 1 − Pd, H1.(9)
Based on (2) and (9), we see that V1 is constant and V0 ismonotonically increasing with t; thus, we have
V0(t) = 1 −Q(√
2γ + 1Q−1(Pd) +√
tfsγ)
. (10)
For notational simplicity, we use V0 or V0(t) as the interme-diate variable for analyzing the performance in the remainderpart.
Because Ui’s independently detect Pt, the number of SUsthat can access the channel in one frame (which is denoted
by n) follows a binomial distribution, whose occurring prob-ability is given by
Pr{n SUs can access} =(
N
n
)(Pr{C1})n (1 − Pr{C1})N−n
={(
Nn
)V n
0 (1 − V0)N−n, H0(Nn
)V n
1 (1 − V1)N−n, H1
0 ≤ n ≤ N. (11)
Accordingly, we use G(n) to denote the actual traffic ratethat corresponds to n SUs; thus, we have G(n) = nλ, with theprobability given by (11).
Then, we consider C2. Because we have assumed that Ui’sare located outside Pt’s CSR, Pt’s transmission has no influ-ence on Ui’s transmission, but Ui can still interfere with Pr’sreception. In this case, the transmission by SUs under H1 is notencouraged, and the achieved performance should be ignored.Therefore, we have
Pr{C2} ={
1, H0
0, H1.(12)
Last, C3 occurs if and only if no other SU’s packet waits atthe beginning of the current slot. In particular, when a packettransmits in the first slot of this frame, its “vulnerable” period(defined as the time slots during which, if other packet sends,the ongoing transmission and the current transmission wouldoverlap) lasts from the M th slot of the prior frame to the endof the spectrum sensing duration in this frame. Based on thecondition that n SUs satisfy C1, we obtain
Pr{C3} =1 + α + β
l + βe−(n−1)λ(1+α+β)
+l − (1 + α)
l + β· e−(n−1)λ(1+α). (13)
Let C denote the event that a packet is successfully transmit-ted by Ui. Combining the results in (11)–(13), we have
Pr{C|n SUs can access}= Pr{C2C3|H0}PH0 + Pr{C2C3|H1}PH1 (14)
where the second term is equal to zero due to Pr{C2|H1} = 0given by (12). Then, we use S(n, t) to denote the achievedthroughput that corresponds to n SUs and spectrum sensingtime t, and the average achievable S(t) is given by
S(t)=E {S(n, t)}
=N∑
n=0
G(n) Pr{C|n SUs can access}Pr{n SUs can access}
=NλV0
[1−V0+V0e
−λ(1+α)]N−1 λbe
−λrβ
λr + λb
·{
1 −(1 + α + β)
[1 − e−(N−1)λV0β
]l + β
}
≈NλV0
[1 − V0 + V0e
−λ(1+α)]N−1
λbe−λrβ
λr + λb(15)
CHEN et al.: TWO-LEVEL MAC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRUM ACCESS IN CRNs 2169
where E is the expectation operator, and the last equation holdsfor small λ and β. Therefore, the optimization problem of S canbe expressed as
maxV0
S(t)
s.t. V0 ∈ domV0 = {V0|0 < V0 ≤ 1 − Pf,min} (16)
where domV0 is obtained from (2) and (10) as t varies in itsdomain [0, Ts].
Let Smax denote the maximum S(t) and V ∗0 denote the
optimal V0 for Smax. Solving (16), the extremum of S isachieved as dS/dV0 = 0; thus, we obtain that V0 = (1/N [1 −e−λ(1+α)]) ≈ 1/G due to e−λ(1+α) = 1 − λ(1 + α) when αand λ are relatively small. If 1/G ∈ domV0, V ∗
0 = 1/G, be-cause S ′
−(V0) > 0 and S ′+(V0) < 0. Otherwise, if 1/G > 1 −
Pf,min, S is a monotonically increasing function of V0; thus,Smax is obtained at V ∗
0 = 1 − Pf,min. Using (10), the optimalsensing time t for Smax, which is denoted by t∗, is given by
t∗ =
⎧⎨⎩
1fsγ2
[Q−1(1 − 1/G) −
√2γ + 1Q−1(Pd)
]21/G ∈ domV0
Ts, otherwise.
(17)
Moreover, combining (10) and (15), for large N and small α,we have
Smax =NλV0(t∗)λbe−(N−1)λV0(t
∗)−λrβ/(λr + λb)
≈λbG∗e−G∗−λrβ/(λr + λb) (18)
where G∗ = NλV0(t∗) is the optimal traffic rate adjusted byour proposed two-level OSA strategy. Compared to the con-ventional slotted ALOHA, we note that Smax under the slottedCR-ALOHA decreases by a fraction PH0 due to the existenceof Pt.
C. Delay Analysis
In this section, we analyze the average packet delay D forthe slotted CR-ALOHA, which refers to the average intervalfrom the instant that a packet is originally generated untilthe instant that it is successfully transmitted. We make thefollowing assumption.
Assumption 2: The packet-processing time is negligible, in-cluding the sum check and acknowledgment generation time.
Let R0 and R1 be the average duration between two con-secutive transmissions of the same packet due to collision andbeing blocked, respectively. According to Assumptions 1 and 2,we have
R0 = 1 + 2α + a + δ + ω (19)
where ω is the average length of the pretransmission delay,which refers to the interval from the instant that the SU attemptsto transmit until the instant that it senses that the channel is idlefor transmission.
Theorem 1: If a packet can be transmitted, its average pre-transmission delay ω is given by ω = β2 + 2β(1 + α) + l(1 +α)/2(l + β), and limα,β→0 ω = 1/2.
Proof: Although the number of arrivals that were gener-ated by SUs follows a Poisson distribution, the arriving instantsof these packets would still be uniformly distributed over thetime axis. Therefore, the average pretransmission delay ω canbe calculated as follows: 1) If the packet arrives in the M thslot of one frame, the probability density function (pdf) ofthe arrival instant is given by f(x) = 1/(1 + α), and thus, theaverage pretransmission time for this case (denoted by ω1)consists of the residual time of the current frame and the spec-trum sensing duration of the next frame, i.e., ω1 =
∫ 1+α
0 (1 +α − x)f(x)dx + β = (1 + α)/2 + β; 2) if the packet arrivesin the spectrum sensing duration, the pdf of the arrival instantis f(x) = 1/β, and we have ω2 =
∫ β
0 (β − x)f(x)dx = β/2;and 3) if a packet arrives in the jth slot (j �= M), we haveω3 =
∫ 1+α
0 (1 + α − x)f(x)dx = (1 + α)/2.Based the aforementioned analysis, ω is given by
ω =(1 + α)ω1
l + β+
βω2
l + β+
(l − 1 − α)ω3
l + β
=β2 + 2β(1 + α) + l(1 + α)
2(l + β). (20)
Furthermore, as α and β go to zero, we have limα,β→0 ω =1/2. �
Now, we consider R1. Due to blocking, R1 consists ofthe average blocking time tb and the average retransmissiondelay δ. It is easily derived that tb = (l + β)/2; thus, we have
R1 = tb + δ =l + β
2+ δ. (21)
Therefore, the average number of collisions is given byG(n)/S(n, t) − 1, and the average number of being blockedis (G − G(n))φ/S(n, t), where φ = δ/R1 denotes the fractionof the unblocked time during R1. Therefore, the average packetdelay D(t) is expressed as
D(t) =E{[
G(n)S(n, t)
−1]
R0+[G−G(n)] φ
S(n, t)R1
}+1+α+ω
=e−λ(1+α)(R0 − φR1)
[1 − V0 + V0e
λ(1+α)]N
PH0
+e−2λ(1+α)φR1
[1−V0+V0e
λ(1+α)]N+1
V0PH0
−(α+a+δ)
≈ eλrβ(λr + λb) [R0 + (1/V0 − 1)δ]
×[1 − V0 + V0e
λ(1+α)]N−1 /
λb − (α + a + δ)
(22)
where the last equation holds due to e−λ(1+α) ≈ [1 − V0 +V0e
λ(1+α)]−1. Similarly, the optimization problem of D can bewritten as
minV0
D(t)
s.t. V0 ∈ domV0. (23)
Let Dmin denote the minimum D(t) and V ′0 denote the
optimal V0 for Dmin. Because D(t) as given in (22) is
2170 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011
differentiable, the extremum of D is obtained as dD(t)/dV0 =0. When G ≥ 4(1 − R0/δ), we obtain
V0 =2
G +√
G2 − 4G(1 − R0/δ)Δ= V 0. (24)
If V 0 ∈ domV0, we have V ′0 = V 0, because D′
−(V0) < 0,and D′
+(V0) > 0. Otherwise, if V 0 > 1 − Pf,min, D(t) is amonotonically decreasing function of V0. Therefore, Dmin isachieved at V ′
0 = 1 − Pf,min.Then, the corresponding optimal sensing time t for Dmin
(denoted by t′) is eventually given by
t′={
1fsγ2
[Q−1(1−V 0)−
√2γ+1Q−1(Pd)
]2, V 0∈domV0
Ts, otherwise.(25)
Based on (22) and (25), for large N and small α and λ,we have
where G′ = NλV0(t′) is the corresponding optimal traffic ratefor Dmin.
D. Optimal Sensing Time t
In (17) and (25), we have derived the optimal t for Smax
and Dmin, respectively. Moreover, based on (24), we knowthat V 0 < 1/G due to R0 > δ; furthermore, we have t′ ≤ t∗.In other words, Smax and Dmin cannot simultaneously beachieved, and there exists a range defined as R(t) = {t|t′ ≤ t ≤t∗}, within which increasing S will result in the increasing ofD, and vice versa.
In fact, the back-off window size is chosen as a large valueto avoid continuous collisions, i.e., δ is much greater than1 + 2α + a + ω; thus, we have R0/δ ≈ 1 and V 0 ≈ 1/G. Fur-thermore, we note that t′ = t∗ and R(t) converges to a point.
IV. COGNITIVE-RADIO-BASED CARRIER-SENSING
MULTIPLE ACCESS AND ITS PERFORMANCE
A. CR-CSMA Protocol
In the previous section, we assume that the data transmissionduration l of each frame is divided into slots of length TP. Now,in CR-CSMA, we assume that l is divided into minislots oflength σ, which is called the slot time (ST) in the IEEE 802.11distributed coordination function (DCF). The concepts of slotand minislot are different due to the differences of the operationschemes. CR-CSMA requires that each packet starts to transmitat the beginning of the following ST. To improve the utilizationof the channel access time, we assume that one slot or TPis equal to the integral number (denoted by m) of minislots,i.e., 1 + α = mσ. Moreover, because the carrier-sensing timeis relatively short compared to the spectrum sensing time, weneglect it in the following analysis. As shown in Fig. 4, thedetails of CR-CSMA are described as follows.
1) If Ui detects that Pt is inactive during the current frame,any arrival during the M th slot of the previous frame
Fig. 4. Operation scheme of CR-CSMA. The box with solid lines indicatesthe inactive Pt case, and the box with dash lines indicates the active case.
or the spectrum sensing duration of this frame will betransmitted in the first slot; otherwise, if it arrives in thejth slot (j �= M), the following conditions hold.
• If the channel is idle, it will be transmitted at thebeginning of the next ST.
• If the channel is busy, Ui keeps sensing until thechannel again becomes idle (i.e., the end of thecurrent transmission) and then attempts to transmit.
2) If Ui detects that Pt is active, any arrival within thecurrent frame up to the (M − 1)th slot will be blockedto the end of this frame, and then, Ui chooses a uniformlydistributed back-off time to retransmit.
3) The current transmission will be successful if there areno other packets transmitting during this TP; otherwise,it fails and will be retransmitted after a random delay toavoid continuously repeated conflicts.
4) Any attempt during the M th slot of one frame must waitto be processed in the next frame.
The difference between the slotted CR-ALOHA andCR-CSMA is obvious: SUs transmit only from the beginningof a slot under the slotted CR-ALOHA, and thus, they neednot sense the channel. However, under CR-CSMA, SUs becomemore aggressive to transmit, because they keep sensing until thechannel becomes idle.
B. Throughput Analysis
We define idle period (IP) as the duration within which thechannel is available but no packet is transmitted or waits tobe transmitted, busy period (BP) as the duration occupied byUi’s, and useful period (UP) as the successful transmission timewithin one BP. According to the CR-CSMA scheme, BP alwaysstarts from the instant when an arrival comes in an IP. If anyother packet arrives during the current transmission, this BPcontinues; otherwise, it terminates at the end of the currenttransmission, and a new IP immediately follows. Obviously,IP and BP alternately distribute themselves over the time axis,except when there are unavailable frames.
Based on Section III-B, we know that a packet that wassuccessfully transmitted must satisfy the three conditions ofCi’s. Based on the renewal theory, the normalized throughputS(t) for CR-CSMA is obtained as
S(t) = PH0 ·U
B + I(27)
where I , B, and U are the expected lengths of IP, BP, and UP,respectively. Then, we compute them as follows.
First, let Z(τ) be the probability that Ui has no packet thatwas generated within a duration τ . Then, it is easily verifiedthat Z(τ) = 1 − V0 + V0e
−λτ ≈ e−λV0τ . Moreover, we use
CHEN et al.: TWO-LEVEL MAC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRUM ACCESS IN CRNs 2171
Y to denote the length of an arbitrary IP, and the cumulativedistribution function (cdf) of Y is given by
FY (y)=1 − Pr{Y > y}=1 − ZN (y)=1 − e−GV0y. (28)
Furthermore, the mean value of I is given by
I =
∞∫0
ydFY (y) ≈ 1GV0
. (29)
Second, we consider the total number of packets (denoted byK) that were transmitted in one BP. Let z be the probability thatno SUs transmit in one TP; thus, we have
z =ZN (1 + α)
=[1 − V0 + V0e
−λ(1+α)]N
≈ e−GV0(1+α). (30)
Therefore, the probability that the next TP belongs to thecurrent BP is given by 1 − z. In particular, when a BP processesin the last slot of one frame, it continues only when there existsany packet that waits at the end of the current transmission.If the next frame is available, the waiting packets will beprocessed in the first slot of the next frame. Conversely, if thenext frame is unavailable, the waiting packets will be blockedfor transmission or insist to proceed but interfere with Pt’stransmission. In the second case, once the channel has againbecome available, the packets that accumulate at the end ofthe last unavailable frame will be processed in the first slot ofthis frame. However, we see that BP continues with the sameprobability of 1 − z, regardless of which case occurs, i.e., BPcan jump over the unavailable frames and, without interruption,proceeds in the available frames. Therefore, K is geometricallydistributed with mean 1/z, and
Pr{K = k} = z(1 − z)k−1, k = 1, 2, . . . . (31)
Now, we use Bj and U j , j = 0, 1, . . . ,M , to distinguish theexpected lengths of BP and UP, beginning within the jth slotof one frame, respectively. Then, their values are calculated asfollows.
1) BP starts in the spectrum sensing duration j = 0.When a packet arrives at time x within the spectrum sensing
duration β, it will be transmitted in the first slot of this frame.The next slot transmits only if any packet waits at the end of thecurrent slot, and this process continues, unless BP terminates.However, due to the frame length limitation, at most M TPscan be accommodated in one frame, and any larger than M thTP will be processed in the next available frames. In addition,
the (iM + 1)th TP, i = 1, 2, . . . must wait an extra spectrumsensing time β to detect the channel states.
Obviously, the first TP is successfully transmitted only whenno other packets wait at the end of β. Similarly, the next TP issuccessful if and only if one packet waits at the beginning of thistransmission. For the (iM + 1)th case, successful transmissionmust satisfy the following two conditions: 1) There must exista packet that waits at the end of the previous TP such that thecurrent BP can continue, and 2) only one packet accumulates atthe beginning of the current TP, i.e., no collision would occur.
Lemma 1: For j = 0, the average length of a BP and a UPare given by (32) and (33), shown at the bottom of the page,respectively.
Proof: See Appendix A. �2) BP starts in the jth slot of one frame, j = 1, . . . , M − 1.Suppose that the first packet arrives during the jth slot of
one frame. Then, it starts to transmit at the beginning of thefollowing ST, which produces a false-busy period (FP) witha length of �(x − β)/σ σ − (x − β), referring to the unusedidle time slots in this BP. If no other packets accumulate at theend of this FP, it will successfully be transmitted. In particular,when K > M − j, the (M − j + 1)th TP will proceed in thenext available frame, which results in a FP of j(1 + α) − �(x −β)/σ σ, lasting from the end of the (M − j)th TP to the end ofthe frame.
Lemma 2: For 0 < j < M , the average length of a BP andUP are given by (34) and (35), shown at the bottom of the nextpage, respectively.
Proof: See Appendix B. �3) BP starts in the M th slot of one frame.In this case, the interval from the arrival of the first packet to
the end of the current frame is a FP. Moreover, the first TP willproceed in the next available frame.
Lemma 3: For j = M , the average length of a BP and UP aregiven by (36) and (37), shown at the bottom of the next page,respectively.
Proof: See Appendix C. �Theorem 2: Based on the CR-CSMA scheme, the average
length of a BP and a UP are given by (38) and (39), shown atthe bottom of the next page, respectively, where θ = β/f is thefraction of spectrum sensing duration per frame.
Proof: Because the packet arrival process is random,we have
B =β
l + βB0 +
1 + α
l + βB1 + · · · + 1 + α
l + βBM (40)
U =β
l + βU0 +
1 + α
l + βU1 + · · · + 1 + α
l + βUM . (41)
B0 =1 + α
z+
β(1 − z)M
1 − (1 − z)M+
β
2(32)
U0 =1 − e−GV0β
GV0β+
GV0(1 + α)e−GV0(1+α)
1 − e−GV0(1+α)
[1z− 1 − (1 − z)M
1 − (1 − z)M
]+
GV0(1 + α + β)e−GV0(1+α+β)
1 − e−GV0(1+α)
(1 − z)M
1 − (1 − z)M
(33)
2172 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011
Substituting the equations from Lemmas 1–3 into (40) and(41), we see that (38) and (39) hold. �
Last, substituting (29), (38), and (39) into (27), we obtain theexpression of S(t) for CR-CSMA. Note that the closed-formexpression of t∗ for S(t) cannot easily be obtained, but we canfind its value by a numerical method.
In addition, if α, β, and σ are relatively small and M is largeenough, we see that
S(t)≈ PH0(1 + GV0)eGV0 + 1/GV0
=GV0λbe
−GV0−λrβ(1 + GV0)(GV0 + e−GV0)(λr + λb)
. (42)
C. Delay Analysis
Similar to the analysis for the slotted CR-ALOHA inSection III-C, we determine the average packet delay D forCR-CSMA. Due to the different operation schemes, we must
recalculate the value of R0. Thus, the pretransmission time ω isderived as follows.
1) If a packet arrives in the spectrum sensing duration, itsaverage waiting time is β/2.
2) If a packet arrives in the jth TP (j = 1, . . . , M − 1) ofone frame when the channel is idle, its average waitingtime is σ/2; otherwise, when the channel is busy, itsaverage waiting time equates to (1 + α)/2.
3) If a packet arrives in the M th TP of one frame, its averagewaiting time is (1 + α)/2 + β.
CHEN et al.: TWO-LEVEL MAC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRUM ACCESS IN CRNs 2173
Obviously, the value of ω in (43) is less than the value in (20).Substituting (43) into (19), we can obtain the corresponding R0
for CR-CSMA.According to Little’s law, because the expected traffic rate
in any available frame is given by∑N
n=1
(Nn
)nλV n
0 (1 −V0)N−n = GV0, D(t) for CR-CSMA can be derived as
D(t)=[GV0
S(t)− 1
]R0 +
(G − GV0)φS(t)
R1 + 1 + α + ω (44)
where S(t) corresponds to the normalized throughput ofCR-CSMA given by (27). Therefore, we can obtain the theo-retical value of t′ by a numerical method.
V. SIMULATION RESULTS
We develop an event-driven network simulator to evaluate theperformance of our proposed CR-ALOHA and CR-CSMA. Thesimulator is written in MATLAB, closely following all the de-tails of the protocols for each SU, as described in Sections III-Aand IV-A. Suppose that the bandwidth of the channel and thesampling frequency fs are both chosen as 6 MHz. To protectthe primary network, Ui’s are required to vacate the channelwithin 100 ms, i.e., Tv = 100 ms. We assume that, for the worstcase, the received SNR γ from Pt at Ui is given by −13 dBand the overall detection probability is larger than 0.9. Theseconfigurations consist with the sensing requirement of wirelessmicrophones in the IEEE 802.22 Draft Standard [29].
A. Performance of the Slotted CR-ALOHA
We design the frame structure for SUs as follows. The packetsize is 2000 b, the channel bit rate is 1 Mb/s, and the propaga-tion delay is ignored; thus, the length of TP is standardized to2 ms. The maximum spectrum sensing duration Ts equatesto one TP length of 2 ms (i.e., β = 1), which ensures thatPf is small enough as the actual sensing time t goes to Ts
according to (2). Moreover, we assume that Td consists of49 TPs; therefore, the total frame length Tf is 100 ms, and f =50. Note that the constraint Tf ≤ Tv is satisfied here. Supposethat the traffic rate λ of each Ui is given by 0.02 and theparameters λr and λb used to simulate that Pt’s traffic are givenby 0.01 and 0.99, respectively. Thus, we obtain PH0 = 0.98 andPH1 = 0.02 by (3), i.e., the average occupancy by the primarynetwork is 2% in our interested frequency band [1].
Next, we validate the accuracy of the analytical results de-rived in Section III. In Figs. 5 and 6, we plot the curves ofnormalized throughput S and average packet delay D versusthe spectrum sensing time t for different numbers of SUs N ,respectively. In these figures, it is clearly shown that the simu-lation results (dashed line) perfectly match with the theoreticalresults (solid line). Here, theoretical S and D are obtained by(15) and (22), respectively.
Then, we consider the effects of spectrum sensing time t onthe achievable normalized throughput S and average delay D.As shown in Fig. 5, for N = 25 and 50 as G ≤ 1, S monoton-ically increases with t, and the corresponding Smax is achievedat t = Ts. For N = 100 as G > 1 and 1/G ∈ domV0, S firstmonotonically increases with t until t = t∗, which is attained by
Fig. 5. S versus t for the slotted CR-ALOHA.
Fig. 6. D versus t for the slotted CR-ALOHA.
(17), and then, further increase of t will decrease S. Moreover,in Fig. 6, for N = 25 and 50, D monotonically decreases with t.For N = 100 and 1/G ∈ domV0, D initially decreases witht until t = t′, which is attained by (25), and then, D latermonotonically increases with t. The curvilinear trend of D issimilar to S, which means that D’s decrease corresponds withS’s increase, and vice versa. This phenomenon can be explainedby the fact that the longer the sensing time t, the largerthe packet transmission probability V0. When G ≤ 1, a largerV0 increases the transmission opportunity and achieves betterperformance. However, when G > 1, a larger V0 aggravatesthe system burden and results in more collisions such that theperformance degrades. We also observe that Smax and Dmin
are achieved at the same t, which validates the conclusion thatt∗ = t′ and R(t) converges at a point in Section III-D.
Last, we plot Smax and Dmin versus the number of SUs N inFigs. 7 and 8, respectively. The simulation results (dashed line)closely match with the theoretical results (solid line) obtainedby (18) and (26). Then, we compare the performance of theslotted CR-ALOHA under the optimal t (t = t∗ or t′) andmaximum t (t = Ts). Here, the optimal t is obtained by ourproposed two-level OSA strategy, and the maximum t means
2174 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011
Fig. 7. Smax versus N for the optimal t and maximum t (slottedCR-ALOHA).
Fig. 8. Dmin versus N for the optimal t and maximum t (slottedCR-ALOHA).
that Ui sends its packets without traffic control, unless it hasdetected Pt to be active, which is used by several existingprotocols. As shown in Fig. 7, Smax keeps the same valuefor both cases and increases with N until N = 50. However,when N > 50, the former case can still maintain a stable largevalue, but in the latter case, Smax dramatically degrades as Nincreases. Moreover, for both cases shown in Fig. 8, we see thatDmin monotonically increases with N . However, Dmin for theoptimal t keeps linearly increasing rather than exponentially in-creasing compared with the maximum t case. This phenomenonvigorously validates the dominance of our proposed two-levelOSA strategy. Note that there exists a small gap between thesimulation results and the theoretical results for the maximum t.The reason is that, in this case, the collisions increase with theincrease of number N , which eventually results in the back-offand retransmission at SUs. Thus, the actual input traffic ratefor each SU will be less than its theoretical value of λ underthe assumption of Poisson distribution. Therefore, Dmin of thesimulation results is accordingly smaller than the theoreticalresults, as shown in Fig. 8.
Fig. 9. S versus t for CR-CSMA.
Fig. 10. D versus t for CR-CSMA.
B. Performance of CR-CSMA
In a similar way, we evaluate the performance of CR-CSMAanalyzed in Section IV. We set each ST to 20 μs, as configuredin the IEEE 802.11 DCF. As shown in Figs. 9 and 10, thesimulation results (dashed line) perfectly match with the the-oretical results, which are obtained by (27) and (44). Moreover,in the cases of N = 25 and 50, S monotonically increases,and D monotonically decreases with t in its domain. How-ever, as N = 100, we see that the maximum S and minimum Dare attained at the same point within domain t. This conditionvalidates that the optimal performance of CR-CSMA can beachieved at the same t, i.e., t∗ = t′.
Furthermore, Smax and Dmin versus the number of SUsN for the optimal t and maximum t are plotted in Figs. 11and 12, respectively. Simulation results (dashed line) perfectlymatch with the theoretical results (solid line) obtained by thenumerical method. Obviously, when N ≤ 50, both the optimal tand maximum t can achieve the same performance due tot∗ = t′ = Ts. However, if N continues to increase, Smax inthe former case still maintains a stable large value, and thecorresponding Dmin also keeps linearly increasing, which
CHEN et al.: TWO-LEVEL MAC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRUM ACCESS IN CRNs 2175
Fig. 11. Smax versus N for the optimal t and maximum t (CR-CSMA).
Fig. 12. Dmin versus N for the optimal t and maximum t (CR-CSMA).
outperforms the latter case. This phenomenon is similar to theslotted CR-ALOHA.
Then, we compare the performance between the slottedCR-ALOHA and CR-CSMA. Based on Figs. 5, 6, 9, and 10,given the same t, CR-CSMA always performs better than theslotted CR-ALOHA for both S and D. Moreover, given thesame N , the performance of Smax and Dmin for CR-CSMA ismuch better than the slotted CR-ALOHA, as shown in Figs. 8,9, 11, and 12. This performance advantage is because the pack-ets of the secondary network can more efficiently be scheduledinto the channel and accordingly wait less time for transmissionunder the scheduling operation of CR-CSMA compared withthe slotted CR-ALOHA.
Moreover, compared to the performance of normalizedthroughput under the slotted CR-ALOHA and CR-CSMA withthe performance under the VX scheme [21], we can easily seethat the values of Smax in Figs. 7 and 11 are much greater thanin [21], which shows the advantages of our proposed protocols.
C. Tradeoff Between Performance and Interference
We study the tradeoff between the performance achieved bythe secondary network and the resulting interference on the
primary network. Based on the definition of interference factorgiven in (8), we know that IF increases with t or f . Moreover,if the optimal t has been adopted, IF only depends on f ,and its value varies in the range of [0, 0.382] as f changesfrom 2 to 50. As shown in Figs. 13 and 14, the normalizedthroughput S monotonically increases, and the average de-lay D monotonically decreases with IF for both the slottedCR-ALOHA and CR-CSMA, which shows that the perfor-mance improvement of the secondary network results in moreinterference on the primary network. In other words, we cansacrifice the performance of the primary network to improve theperformance of the secondary network or restrain SUs’ trans-missions to protect more PUs, because they exist in the samespectrum band. Therefore, we conclude that the achievableperformance of secondary network depends on the interferencerequirement of protecting the primary network.
D. Tradeoff Between Performance and Agility
According to the definition of agility factor, we know that asmaller value of AF leads to more rapidly vacating the channelto PUs but degrades the performance of SUs as well. Similarto the tradeoff between performance and interference, therealso exists a tradeoff between performance and agility, whichis shown in Figs. 15 and 16 for the slotted CR-ALOHA andCR-CSMA, respectively. We observe that Smax monotonicallyincreases and Dmin monotonically decreases with AF , andmeanwhile, the optimal performance is achieved at AF = 1for different numbers of N . Therefore, we conclude that theachievable performance of the secondary network depends onthe agility requirement of protecting the primary network.
E. Optimal Frame Length
Now, we take into account the influence of the total framelength f . Based on the aforementioned analysis, we knowthat parameters IF and AF are both monotonically increasingfunctions of f . Therefore, a longer frame length f achieveshigher Smax and lower Dmin for both the slotted CR-ALOHAand CR-CSMA, which has been validated in Figs. 13–16.This case can be explained by the following two reasons:1) Periodic spectrum sensing takes up data transmission time,which reduces the channel utilization, particularly when theframe is very short, and 2) for a longer frame length, more SUsare allowed to compete for channel access rather than beingblocked, which increases the transmission opportunities andfinally improves the system performance.
Moreover, we know that the performance of the secondarynetwork depends on both IF and AF . In fact, these two param-eters are usually predefined by the application requirement.In our simulation, Tv is set at 100 ms; therefore, the optimalframe length that satisfies the requirement of AF (denoted byfAF ) should be chosen as fAF = 50. On the other hand, ifthe primary network requires that IF ≤ 0.2, we can calculatethat the optimal frame length that satisfies the IF requirement(denoted by fIF ) is given by fIF = 23. Considering botheffects of interference and agility, the optimal f should bechosen as the minimum value of fIF and fAF , i.e., f = 23.
2176 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011
Fig. 13. Tradeoff between performance and interference for the slotted CR-ALOHA.
Fig. 14. Tradeoff between performance and interference for CR-CSMA.
Fig. 15. Tradeoff between performance and agility for the slotted CR-ALOHA.
In particular, we observe that, when each frame containsonly one TP, i.e., f = 2, the Smax for N = 25 is greater thanfor N = 50 or N = 100, as shown in Fig. 13. This case isbecause the item in the right side of (15) cannot be neglected
when l = β = 1. Thus, the value of optimal t∗ obtained from(17) is inaccurate for this special case. However, as the framelength f increases, the curve of S(t) in (15) becomes concave,and t∗, indeed, can achieve the maximum S. Moreover, this
CHEN et al.: TWO-LEVEL MAC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRUM ACCESS IN CRNs 2177
Fig. 16. Tradeoff between performance and agility for CR-CSMA.
Fig. 17. Effects of PH0 on the slotted CR-ALOHA.
Fig. 18. Effects of PH0 on CR-CSMA.
phenomenon proves the fact that, for f = 2 (short frame length)and larger N (heavy traffic rate), the system performance isreally poor. Thus, we design the frame structure that one frameduration contains M TPs, as mentioned in Section II-A.
In addition, when N ≥ 50, the curves of Smax in Figs. 13–16are very close to each other. Furthermore, the performancecurves sharply vary at the beginning of increasing f , but lateron, they more gently change, and the performance finally
2178 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011
approaches a stable value, regardless of f ’s increase. Thisphenomenon is due to the maximum achievable performanceconstraints of the slotted CR-ALOHA or CR-CSMA.
F. Effects of the PUs’ Activities
According to Section II-E, we know that PUs’ activities arerelated to their traffic parameters λr and λb. To consider theeffects of the spectrum utilization of the primary network on theperformance of the secondary network, we change the valuesof λr and λb to ensure that PH0 (the probability that Pt isdetected to be inactive in one frame) varies in the range [0.1, 1].Intuitively, given a smaller PH0 , Ui’s would more possibly beblocked for transmission. Conversely, given a larger PH0 , Ui’sobtain more opportunities to compete for the channel, and theperformance would be improved.
Thus, we plot the Smax and Dmin versus PH0 for the slottedCR-ALOHA and CR-CSMA in Figs. 17 and 18, respectively.We see that Smax linearly increases and Dmin monotoni-cally decreases with the increase of PH0 for both the slottedCR-ALOHA and CR-CSMA. This phenomenon validates thefact that Pt’s activities, indeed, have an influence on the per-formances of SUs and the spectrum utilization of the primarynetwork determines the maximum achievable performance ofthe secondary network. Moreover, in the beginning of therange PH0 , because Pt frequently occupies the current channel,the performance of Ui’s is really disappointing, regardless ofwhether N is equal to 25, 50, or 100, as shown in Figs. 17and 18. In this case, to achieve better performance, SUs mustconsider shifting to another channel with a higher PH0 . In fact,how we can choose a good channel is another key technique forCRNs, and we will consider it as our future work.
VI. CONCLUSION
In this paper, we have proposed a two-level OSA strategy anddeveloped two random-access MAC protocols called the slot-ted CR-ALOHA and CR-CSMA for CRNs. A suitable framestructure has been designed, and closed-form expressionsof network metrics, i.e., normalized throughput and averagepacket delay, have been derived, respectively. For various framelengths and numbers of SUs, the optimal performance of SUscan be achieved at the same spectrum sensing time, and themaximum achievable performance of the secondary networkis affected by the spectrum utilization of the primary network.Moreover, using the interference and agility factors, we haveshown that there exists a tradeoff between the achieved perfor-mance of the secondary network and the effects of protectionon the primary network; therefore, the optimal frame length canaccordingly be designed.
APPENDIX APROOF OF LEMMA 1
In this case, because the BP starts at time x during β and itconsists of exact k TPs, the length of this BP and the UP aregiven by B0|k,x = β − x + k(1 + α) + �(k − 1)/M�β andU0|k,x =zN−1
1 +(k−1−�(k−1)/M�)N(1−z2)zN−12 /(1−z) +
�(k − 1)/M�N(1 − z3)zN−13 /(1 − z), respectively, where
z1 = Z(β − x), z2 = Z(1 + α), and z3 = Z(1 + α + β). Byremoving the conditions of k and x, B0 and U0 are given by
In a similar way, we obtain Bj and U j , j = 1, . . . ,M − 1, as
Bj =1
1+α
β+j(1+α)∫β+(j−1)(1+α)
∞∑k=1
[⌈x−β
σ
⌉σ−(x−β)+k(1+α)
+⌊
k+j−1M
⌋β
]z(1 − z)k−1
+∞∑
k=M−j+1
[j(1+α)−
⌈x−β
σ
⌉σ
]z(1−z)k−1dx
(47)
Ij =1
1+α
β+j(1+α)∫β+(j−1)(1+α)
∞∑k=1
[zN−14 +
(k−1−
⌊k+j−1
M
⌋)
×N(1−z2)zN−12
1−z
]z(1−z)k−1
+∞∑
k=M−j+1
[(⌊k+j−1
M
⌋−PH0
)N(1 − z3)zN−1
3
1 − z
+PH0N(1−z5)zN−1
5
1−z
]z(1−z)k−1dx
(48)
CHEN et al.: TWO-LEVEL MAC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRUM ACCESS IN CRNs 2179
respectively, where the variables z4 and z5 are givenby z4 = Z(�(x − β)/σ σ − (x − β)) and z5 = Z(β + (j +1)(1 + α) − �(x − β)/σ σ).
Moreover, we note that∫ β+i(1+α)
β+(j−1)(1+α) zN−14 dx =
(1 + α)(1 − e−GV0σ)/(GV0σ) and∫ β+i(1+α)
β+(j−1)(1+α) N(1 −z5)zN−1
5 dx ≈ [1 + α + β + 1/(GV0)]e−GV0(1+α+β) − [2 +2α + β + 1/(GV0)]e−GV0(2+2α+β). Based on (47) and (48), itfollows that Lemma 2 is proved.
APPENDIX CPROOF OF LEMMA 3
The proof process is similar to Lemmas 1 and 2. In this case,we obtain BM and UM
BM =1
1 + α
β+l∫β+l−(1+α)
∞∑k=1
[β + l − x + k(1 + α)
+⌊
k+M−1M
⌋β
]z(1−z)k−1dx
(49)
UM =1
1 + α
β+l∫β+l−(1+α)
∞∑k=1
{[zN−16 V0 + (N − 1)
× (1 − z6)zN−26 (1 − V0)
]× PH0 +
(k−
⌊k+M−1
M
⌋)
· N(1 − z2)zN−12
1 − z
+(⌊
k + M − 1M
⌋− PH0
)
× N(1 − z3)zN−13
1 − z
}
× z(1 − z)k−1dx. (50)
respectively, where z6 = Z(l − x + β). Solving (49) and (50),we see that (36) and (37) are verified.
REFERENCES
[1] U.S. Fed. Commun. Comm., Spectrum Policy Task Force Report,Nov. 2002. [Online]. Available: www.fcc.gov/sptf/reports.html
[2] J. Mitola, “Cognitive radio: An integrated agent architecture for software-defined radio,” Ph.D. dissertation, Roy. Inst. Technol. (KTH), Stockholm,Sweden, 2000.
[3] S. Haykin, “Cognitive radio: Brain-empowered wireless communica-tions,” IEEE J. Sel. Areas Commun., vol. 23, no. 2, pp. 201–220,Feb. 2005.
[4] DARPA: The next generation (XG) program. [Online]. Available: http://www.darpa.mil/ato/programs/xg/index.htm
[5] H. Zheng and C. Peng, “Collaboration and fairness in opportunisticspectrum access,” in Proc. IEEE ICC, Seoul, Korea, May 2005, vol. 5,pp. 3132–3136.
[6] S. Sankaranarayanan, P. Papadimitratos, A. Mishra, and S. Hershey, “Abandwidth sharing approach to improve licensed spectrum utilization,” inProc. IEEE DySPAN, Baltimore, MD, Nov. 2005, pp. 279–288.
[7] R. Urgaonkar and M. J. Neely, “Opportunistic scheduling with reliabilityguarantees in cognitive radio networks,” IEEE Trans. Mobile Comput.,vol. 8, no. 6, pp. 766–777, Jun. 2009.
[8] Y.-C. Liang, Y. Zeng, E. Peh, and A. T. Hoang, “Sensing-throughputtradeoff for cognitive radio networks,” IEEE Trans. Wireless Commun.,vol. 7, no. 4, pp. 1326–1337, Mar. 2008.
[9] Q. Zhao, L. Tong, A. Swami, and Y. Chen, “Decentralized cognitiveMAC for opportunistic spectrum access in ad hoc networks: A POMDPframework,” IEEE J. Sel. Areas Commun., vol. 25, no. 3, pp. 589–600,Apr. 2007.
[10] Q. Zhao, L. Tong, and A. Swami, “Decentralized cognitive MAC fordynamic spectrum access,” in Proc. IEEE DySPAN, Baltimore, MD,Nov. 2005, pp. 224–232.
[11] S. Krishnamurthy, M. Thoppian, S. Venkatesan, and R. Prakash, “Control-channel-based MAC-layer configuration, routing and situation awarenessfor cognitive radio networks,” in Proc. IEEE MILCOM, Atlantic City, NJ,Oct. 2005, vol. 1, pp. 445–460.
[12] M. Thoppian, S. Venkatesan, and R. Prakash, “CSMA-based MAC pro-tocol for cognitive radio networks,” in Proc. IEEE WoWMoM, Helsinki,Finland, 2007, pp. 1–8.
[13] H. Su and X. Zhang, “Cross-layer-based opportunistic MAC protocols forQoS provisionings over cognitive radio wireless networks,” IEEE J. Sel.Areas Commun., vol. 26, no. 1, pp. 118–129, Jan. 2008.
[14] L. Le and E. Hossain, “OSA-MAC: A MAC protocol for opportunisticspectrum access in cognitive radio networks,” in Proc. IEEE WCNC,Las Vegas, NV, Mar. 2008, pp. 1426–1430.
[15] J. Jia, Q. Zhang, and X. Shen, “HC-MAC: A hardware-constrained cog-nitive MAC for efficient spectrum management,” IEEE J. Sel. AreasCommun., vol. 26, no. 1, pp. 106–117, Jan. 2008.
[16] X. Zhang and H. Su, “CREAM-MAC: Cognitive radio-enabled mul-tichannel MAC protocol over dynamic spectrum access networks,”IEEE J. Sel. Topics Signal Process., vol. 5, no. 1, pp. 110–123,Feb. 2011.
[17] H. A. B. Salameh, M. M. Krunz, and O. Younis, “MAC protocol foropportunistic cognitive radio networks with soft guarantees,” IEEE Trans.Mobile Comput., vol. 8, no. 10, pp. 1339–1352, Oct. 2009.
[18] M. Timmers, S. Pollin, A. Dejonghe, L. V. Perre, and F. Catthoor,“A distributed multichannel MAC protocol for multihop cognitive ra-dio networks,” IEEE Trans. Veh. Technol., vol. 59, no. 1, pp. 446–459,Aug. 2009.
[19] B. Hamdaoui and K. G. Shin, “OS-MAC: An efficient MAC protocol forspectrum-agile wireless networks,” IEEE Trans. Mobile Comput., vol. 7,no. 8, pp. 915–930, Aug. 2008.
[20] N. Choi, M. Patel, and S. Venkatesan, “A full-duplex multichannelMAC protocol for multihop cognitive radio networks,” in Proc. IEEECROWNCOM, Mykonos Island, Greece, Jun. 2006, pp. 1–5.
[21] S. Huang, X. Liu, and Z. Ding, “Opportunistic spectrum access in cogni-tive radio networks,” in Proc. IEEE INFOCOM, Phoenix, AZ, Apr. 2008,pp. 1427–1435.
[22] S. Huang, X. Liu, and Z. Ding, “Optimal transmission strategies for dy-namic spectrum access in cognitive radio networks,” IEEE Trans. MobileComput., vol. 8, no. 12, pp. 1636–1648, Dec. 2009.
[23] Y.-J. Choi, S. Park, and S. Bahk, “Multichannel random access inOFDMA wireless networks,” IEEE J. Sel. Areas Commun., vol. 24, no. 3,pp. 603–613, Mar. 2006.
[24] L. Kleinrock and F. Tobagi, “Packet switching in radio channels—Part I:Carrier sense multiple-access modes and their throughput-delay charac-teristics,” IEEE Trans. Commun., vol. COM-23, no. 12, pp. 1400–1416,Dec. 1975.
[25] Q. Chen, F. Gao, A. Nallanathan, and Y. Xin, “Improved cooperative spec-trum sensing in cognitive radio,” in Proc. IEEE VTC—Spring, Singapore,May 2008, pp. 1418–1422.
[26] M. Wellens, J. Riihijärvi, and P. Mähönen, “Empirical time- andfrequency-domain models of spectrum use,” Phys. Commun.—SpecialIssue on Cognitive Radio: Algorithms and System Design, vol. 2, no. 1/2,pp. 10–32, Mar.–Jun. 2009.
[27] H. Zhai, Y. Kwon, and Y. Fang, “Performance analysis of IEEE 802.11MAC protocols in wireless LANs,” Wireless Commun. Mobile Comput.,vol. 4, no. 8, pp. 917–931, Nov. 2004.
[28] R. E. Barlow and L. C. Hunter, “Reliability analysis of a one-unit system,”Oper. Res., vol. 9, no. 2, pp. 200–208, Mar./Apr. 1961.
[29] Fed. Commun. Comm., Revision of Parts 2 and 15 of the CommissionsRules to Permit Unlicensed National Information Infrastructure (U-NII)Devices in the 5-GHz Band, FCC Std. 802.22, 2003.
2180 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011
Qian Chen (S’09) received the B.Eng. and M.Eng.degrees in computer science and engineering fromXi’an Jiao Tong University, Xi’an, China, in 2003and 2006, respectively. He is currently workingtoward the Ph.D. degree with the Department ofElectrical and Computer Engineering, National Uni-versity of Singapore, Singapore.
He is currently a Research Fellow with theInstitute for Infocomm Research, A∗STAR,Singapore. His research interests include cognitiveradio networks, mobile ad hoc and sensor networks,
and medium-access-control (MAC) layer protocols.
Ying-Chang Liang (F’11) received the Ph.D. de-gree in electrical engineering from Jilin University,Changchun, China, in 1993.
From December 2002 to December 2003, he wasa Visiting Scholar with the Department of ElectricalEngineering, Stanford University, Stanford, CA. Heis currently a Principal Scientist with the Institute forInfocomm Research, A∗STAR, Singapore, and holdsa joint appointment with Nanyang TechnologicalUniversity, Singapore. His research interests includecognitive radio, dynamic spectrum access, reconfig-
urable signal processing for broadband communications, space–time wirelesscommunications, wireless networking, information theory, and statistical signalprocessing.
Dr. Liang is currently an Associate Editor for the IEEE TRANSACTIONS
ON VEHICULAR TECHNOLOGY. He was an Associate Editor for the IEEETRANSACTIONS ON WIRELESS COMMUNICATIONS from 2002 to 2005 andthe Lead Guest Editor of the IEEE JOURNAL ON SELECTED AREAS IN
COMMUNICATIONS—Special Issue on Cognitive Radio: Theory and Appli-cations and Special Issue on Advances in Cognitive Radio Networking andCommunications. He is the Lead Guest Editor of the EURASIP Journal onAdvances in Signal Processing Special Issue on Advanced Signal Processingfor Cognitive Radio and a Guest Editor of the Elsevier Computer NetworksJournal Special Issue on Cognitive Wireless Networks. He received the BestPaper Award at the IEEE Vehicular Technology Conference–Fall, in 1999and the IEEE International Symposium Personal, Indoor, and Mobile RadioCommunications in 2005 and from the EURASIP Journal on Wireless Commu-nications and Networking in 2010. He also received the Institute of EngineersSingapore Prestigious Engineering Achievement Award in 2007.
Mehul Motani (M’98) received the B.S. degree fromCooper Union, New York, NY, the M.S. degree fromSyracuse University, Syracuse, NY, and the Ph.D.degree from Cornell University, Ithaca, NY, all inelectrical and computer engineering.
He is currently a Visiting Fellow with PrincetonUniversity, Princeton, NJ, and an Associate Pro-fessor with the Electrical and Computer Engineer-ing Department, National University of Singapore,Singapore. Previously, he was a Research Scientistwith the Institute for Infocomm Research, Singapore,
for three years and a Systems Engineer with Lockheed Martin, Syracuse, forover four years. His research interests are in the area of wireless networks.Recently, he has been working on research problems which sit at the boundaryof information theory, communications, and networking, including the designof wireless ad hoc and sensor network systems.
Dr. Motani received the Intel Foundation Fellowship for work related tohis Ph.D. research, which focused on information theory and coding for codedivision multiple access systems. He has served on the organizing commit-tees of ISIT, WiNC, and ICCS, and the technical program committees ofMobiCom, Infocom, ICNP, SECON, and several other conferences. He partic-ipates actively in the IEEE and the Association for Computing Machinery andhas served as the secretary of the IEEE Information Theory Society Board ofGovernors. He is currently an Associate Editor for the IEEE TRANSACTIONS
ON INFORMATION THEORY and an Editor for the IEEE TRANSACTIONS ON
COMMUNICATIONS.
Wai-Choong (Lawrence) Wong (SM’93) receivedthe B.Sc. (first-class honors) and Ph.D. de-grees in electronic and electrical engineering fromLoughborough University, Loughborough, U.K.
From November 2002 to November 2006, he wasthe Executive Director of the Institute for InfocommResearch, A∗STAR, Singapore. From 1980 to 1983,he was a Member of Technical Staff with AT&TBell Laboratories, Crawford Hill, NJ. He is cur-rently a Professor with the Department of Electricaland Computer Engineering, National University of
Singapore (NUS), Singapore, where he is also the Deputy Director (StrategicDevelopment) with the Interactive and Digital Media Institute. Since joiningNUS in 1983, he has served in various positions at the department, faculty, anduniversity levels, e.g., the Head of the Department of Electrical and ComputerEngineering from January 2008 to October 2009, the Director of the NUSComputer Centre from July 2000 to November 2002, and the Director ofthe Centre for Instructional Technology from January 1998 to June 2000.He is a coauthor of the book Source-Matched Mobile Communications. Hisresearch interests include wireless networks and systems, multimedia networks,and source-matched transmission techniques, for which he has more than200 publications and is the holder of four patents.
Dr. Wong received the 1989 IEEE Marconi Premium Award, the 1989 NUSTeaching Award, the 2000 IEEE Millennium Award, the 2000 e-nnovatorAward, Open Category, and the Best Paper Award at the 2006 IEEE Interna-tional Conference on Multimedia and Expo.
