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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011
A Two-Level MAC Protocol Strategy for
Opportunistic Spectrum Access in
Cognitive Radio Networks
Qian Chen, Student Member, IEEE, Ying-Chang Liang, Fellow, IEEE, Mehul Motani, Member, IEEE,
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 is
proposed to optimize the system performance of the secondary
network and to adequately protect the operation of the primary
network. At the first level, secondary users (SUs) maintain a
sufficient detection probability to avoid interference with primary
users (PUs), and the spectrum sensing time is optimized to control
the total traffic rate of the secondary network allowed for random access when the channel is detected to be available. At the
second level, two MAC protocols called the slotted cognitive radio
ALOHA (CR-ALOHA) and cognitive-radio-based carrier-sensing
multiple access (CR-CSMA) are developed to deal with the packet
scheduling of the secondary network. We employ normalized
throughput and average packet delay as the network metrics and
derive closed-form expressions to evaluate the performance of the
secondary network for our proposed protocols. Moreover, we use
the interference and agility factors as the performance parameters
to measure the protection effects on the primary network. For
various frame lengths and numbers of SUs, the optimal performance of throughput and delay can be achieved at the same
spectrum sensing time, and there also exists a tradeoff between the
achievable performance of the secondary network and the effects
of protection on the primary network. Simulation results show
that the CR-CSMA protocol outperforms the slotted CR-ALOHA
protocol and that the PUs’ activities have an influence on the performance of SUs for both the slotted CR-ALOHA and CR-CSMA.
Index Terms—Cognitive radio networks,
CR-CSMA, opportunistic spectrum access.
CR-ALOHA,
Manuscript received July 27, 2010; revised December 23, 2010 and
March 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 the
Interactive and Digital Media Project Office, Media Development Authority
of Singapore, through the National Research Funding Grant NRF2007IDMIDM002-069 on Life Spaces. The review of this paper was coordinated by
Prof. J. Chun.
Q. Chen is with the Department of Electrical and Computer Engineering,
National University of Singapore, Singapore 118622, and also with the Institute
for Infocomm Research, A*STAR, Singapore 138632 (e-mail: qchen@i2r.
a-star.edu.sg).
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 and
Computer 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 online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TVT.2011.2141694
I. I NTRODUCTION
I
N conventional spectrum management, most of the spectrum bands are exclusively allocated to particular services,
which may potentially exhaust limited frequency resources as
wireless applications grow. In contrast to spectrum scarcity, the
utilization of the allocated spectrum bands is usually very low.
Measurement results have shown that only 2% of the allocated
spectrum is used, on the average, in the U.S. [1]. Furthermore,
although the allocated users are active, there still exists an
abundance 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 use
the spectrum bands that were originally assigned to primary
users (PUs).
One feasible approach is opportunistic spectrum access
(OSA), envisioned by the Defense Advanced Research Projects
Agency Next-Generation Communications (DARPA XG) Program [4], which allows SUs to utilize the unused channels
when PUs are detected to be inactive. This mechanism is
also called listening before transmission, where the listening
function is fulfilled by spectrum sensing at the physical (PHY)
layer, and the transmission function refers to packet scheduling
at the medium access control (MAC) layer. Obviously, the
introduction of spectrum sensing brings more challenges for
the 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 is
addressed is to coordinate the channel allocation or spectrum
reuse in some particular areas or locations (e.g., cellular-based
networks), whereas PUs’ states are considered static or slowly
varying in time. Other solutions, e.g., [8] and [9], address
the temporal OSA, where the unused time slots of PUs can
be accessed by SUs in real time. In [8], Liang et al. studied the performance tradeoff between sensing time and the
achieved throughput of SUs and demonstrated the existence
of an optimal spectrum sensing time that yields the maximum
achievable throughput for SUs under the constraint that PUs
are adequately protected. Although this policy can guarantee
the maximum throughput of a secondary link pair, it considers
only the point-to-point transmission model. In [9] and [10], a
MAC protocol based on the framework of partially observable
Markov decision processes (POMDPs) is developed to exploit
the optimal sensing and access strategy for CRNs. However, its
complexity exponentially grows with the number of channels,
0018-9545/$26.00 © 2011 IEEE
CHEN et al.: TWO-LEVEL MAC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRUM ACCESS IN CRNs
and the assumption that PUs’ usage statistics remain unchanged
simplifies the MAC protocol design. Moreover, SUs schedule
the packets and coordinate their access based on the following two different models: 1) the guaranteed-access model and
2) the random-access model. Most of the previous works, e.g.,
[11]–[19], applied the guaranteed-access model into CRNs by
using an exclusive common control channel (CCC) or central
coordinator to schedule SUs’ packets in a sequential manner. In
[13], each frame of the control channel is divided into the report
and the negotiation phases. In the report phase, two different
channel spectrum sensing policies were proposed to detect
the available subchannels and report the obtained information.
Then, in the negotiation phase, SUs exchange data following
the p-persistent carrier-sensing multiple access (CSMA) protocol to compete for the channel and get the permission to utilize
all the available subchannels in the next frame. In addition, the
authors considered only the perfect spectrum sensing case. In
fact, this CCC may not be always available in practice, and it
also easily suffers from the control channel saturation problem
[20]. To the best of our knowledge, fewer studies considered the
random-access model for packet scheduling under CRNs [21],
[22]. The difficulty is that, in a CR environment, SUs not only
compete for the channel with other SUs but need to vacate the
channel to avoid interference to PUs as well. Huang et al. [21]
proposed the following three random-access schemes with different sensing, transmission, and backoff mechanisms for SUs:
1) virtual transmit if busy (VX); 2) VAC; and 3) keep sensing if
busy (KS). Considering the scenario of one PU band and
one SU, the authors investigated the capacity of SUs and
derived closed-form expressions of performance metrics for
each scheme. However, because they assume that the PUs’
packet arrival process and spectrum sensing performed at SUs
are independent of each other, the spectrum sensing technique
is unhelpful in increasing the SUs’ access opportunities. Therefore, the relevant achievable performance is pessimistic.
In this paper, we consider the MAC protocol design problem
for CRNs based on the random-access model and the imperfect
spectrum sensing assumption, where all the SUs share a single
transmission channel with PUs, and no additional CCC is
needed. To protect the operation of the primary network and
optimize the system performance of the secondary network, we
propose a two-level OSA strategy here. The first level performs
spectrum sensing, which is arranged at the beginning of each
MAC frame before data transmission. Limited by the interference constraint from PUs, SUs must maintain their detection
probabilities at a target threshold. Furthermore, because an
SU’s packet transmission probability depends on its detection
and false-alarm probabilities, the actual traffic rate can be
controlled by adjusting the spectrum sensing time. The second
level 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 slotted
cognitive radio ALOHA (CR-ALOHA) and cognitive-radiobased carrier-sensing multiple access (CR-CSMA) to deal with
the packet scheduling of SUs under a CR environment. These
two protocols can easily be implemented, and closed-form expressions of our network metrics can also be derived to compare
with each other. Moreover, due to the property of discrete
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Fig. 1. System model of a CRN.
channel access time, we design an appropriate frame structure
to support our proposed two-level OSA strategy and develop
a framework to evaluate the performance of the secondary
network for each protocol in terms of normalized throughput
and average packet delay. To measure the protection effects
on the primary network, we define the interference factor as
the outage probability that SUs would interfere with PUs in an
arbitrary frame and also define the agility factor as the ability
that SUs can rapidly vacate the channel once PUs have become
active. Thus, we study the tradeoff between the achievable performance of the secondary network and the protection effects
on the primary network and accordingly design the optimal
frame length. Conversely, we also consider the effects of the
spectrum utilization of the primary network on the performance
of the secondary network.
This paper is organized as follows. Section II introduces
the system model and our proposed access strategy for CRNs.
In Sections III and IV, we propose the slotted CR-ALOHA
and CR-CSMA and analyze their performances, respectively.
The evaluation results, performance-protection tradeoffs, and
effects of PUs’ activities are shown in Section V. Finally,
conclusions are drawn in Section VI.
II. S YSTEM M ODEL
A. System Model
The system model considered in this paper is shown in
Fig. 1. The primary network consists of one primary transmitter
(denoted by Pt ) and several primary receivers (denoted by
Pr ’s), where Pt can broadcast signals to Pr ’s over a single channel using the licensed spectrum band. The secondary network
consists 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 sensing), and are self organized into a wireless local area network
(WLAN). Each Ui can directly communicate with other SUs
or secondary access points (SAPs); thus, the synchronization
problem can be solved by the coordination function of SAPs
when Ui dynamically joins the secondary network. In addition,
the primary and the secondary networks operate independent
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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 PUs
and SUs.
According to OSA, SUs can use Pt ’s channel only when Pt is
detected to be inactive. Once Pt has woken up, Ui ’s must vacate
the channel within a certain duration, i.e., Tv s. Therefore, Ui ’s
are forced to suspend their access and periodically detect the
Pt ’s states within Tv . This policy results in the discrete channel
access time under a CRN in contrast to the continuous access
time under conventional networks. To support OSA, a relevant
frame structure is designed, as shown in Fig. 2. Each frame
with the length Tf (Tf ≤ Tv ) consists of a duration of Ts for
spectrum sensing and Td for data transmission. Ts is arranged at
the beginning of each frame, and Td can accommodate up to M
transmission periods (TPs) that are indexed by j, j = 1 · · · M .
The advantage of this small data piece structure is that more
than one SU can compete for channel access in the same frame
duration, which reduces the waiting (or response) time and
transmission failure cost of each SU and, furthermore, improves
the system performance of the whole secondary network. In
addition, we assume that all packets have the same size; thus,
each TP consists of a fixed packet transmission time T and
a 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 in
a CR environment are usually unknown to each other, and
the PUs’ information (e.g., modulation technique and location)
seems to be a “black box” for SUs. Obviously, if SUs are
located outside the carrier-sensing range (CSR) of PUs, it is
impossible for them to know the PUs’ ON/OFF states only by
the carrier sense technique. Thus, we must consider using the
spectrum sensing technique to perform PU detection at each
SU in every frame. In general, the following three techniques
are widely used: 1) matched filter; 2) energy detection; and
3) cyclostationary feature detection. In this paper, we adopt
the energy detection technique [8], [25] due to its simplicity.
An energy detector computes the power (denoted by Yi ) of
the received signal from Pt at Ui and compares Yi with a
predetermined threshold . If Yi ≥ , Pt is deemed to be active,
and vice versa. Let t be the spectrum sensing time, fs be the
sampling frequency, and γ be the received signal-to-noise ratio
(SNR) from Pt at Ui . Considering the complex-valued phaseshift keying (PSK) signal and circularly symmetric complex
Gaussian (CSCG) noise case, the detection probability Pd for
each SU is approximately given by [8]
tfs
Pd (t) = Q
−γ−1
(1)
σu2
2γ + 1
where σu2 is the variance of the received Gaussian noise, and
Q(·) is the complementary
√ function
∞ of a standard Gaussian
variable, i.e., Q(x) = (1/ 2π) x exp(−s2 /2)ds. To protect
the operation of the primary network, the overall detection
probability that all the SUs know the existence of Pt when
Pt is active is given by PdN , which should be set larger than
a threshold based on the application requirement.
Assume that Ui ’s are located outside Pt ’s CSR; thus, the
primary network would not affect the secondary network. However, Ui can still interfere with the receiving of neighboring
Pr ’s that are located within Ui ’s CSR. Therefore, to protect
the primary network, Ui ’s detection probability Pd should not
be less than a certain threshold. Then, the corresponding falsealarm probability Pf is given by
Pf (t) = Q
2γ + 1Q−1 (Pd ) + tfs γ .
(2)
Based on (1) and (2), we see that Pf is a monotonically
decreasing function of t for fixed Pd and γ. The spectrum
sensing 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 characterized as follows.
Wellens et al. [26] introduced time-frequency models of
spectrum use for various applications. First, because the exponential distribution can provide a good approximation for
the packet service time [27], we assume that the run and
burst lengths of aggregated arrivals in the primary network
follow exponential distributions with the parameters λr and λb ,
respectively. Moreover, in the secondary network, each Ui is
assumed to be an independent Poisson source with an average
packet generation rate of λi packets per TP; thus, the lengths of
packet-generating intervals follow the exponential distribution
with mean 1/λi . Suppose that all the λi ’s are equal to λ; then,
the total traffic rate is G = N λ.
Second, a positive acknowledgment scheme is adopted. If a
packet is successfully transmitted, Ui will receive a positive
acknowledgment. Otherwise, after a time-out period, it knows
this failure and uniformly chooses a time to retransmit within a
fixed back-off window of size [0, 2X̄]. Let Ta be the length of
an acknowledgment packet; then, the time-out period is given
by T + Ta + 2Tp . At any instant, each Ui has at most one
packet that waits for transmission, regardless of whether it is
newly generated or backlogged. Moreover, we consider that the
channel error problem has been solved by an error correction
mechanism 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 total
frame length is given by f = β + M (1 + α).
CHEN et al.: TWO-LEVEL MAC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRUM ACCESS IN CRNs
D. Spectrum Access Scheme
To protect the operation of the primary network and optimize
the system performance of the secondary network, we propose
a two-level OSA strategy as follows.
At the first level, spectrum sensing is periodically executed
by Ui to detect Pt ’s activity before its packet transmission.
Using energy detection, Pd is set according to the protection
requirement. If Pt is detected to be active, Ui will be blocked
for transmission in the current frame; otherwise, it will attempt
to transmit. Thus, the packet transmission probability for each
Ui is determined by both Pd and Pf . Furthermore, because Pf
is monotonically decreasing with t for a given Pd , the actual
traffic rate of SUs is eventually determined by t. Therefore, we
can choose an appropriate t to achieve better performance of
the secondary network.
The second level aims at the packet scheduling of SUs, which
is similar to the function of conventional MAC protocols. In this
paper, the slotted CR-ALOHA and CR-CSMA are proposed to
solve the channel access contention problem. The details will
be given in the following sections.
E. PUs’ Activities and Performance Parameters
We use H0 and H1 to denote the events that Pt is inactive and
active, respectively, during the spectrum sensing duration and
use PH0 and PH1 to denote the occurrence probabilities of H0
and H1 , respectively. To compute their values, we directly map
the active and inactive states of Pt to the operation and repair
states of a one-unit system [28], where “one unit” means that
the system is collectively viewed and the failure of any component should be interpreted as the failure of the whole system.
Thus, in reliability analysis, interval reliability is defined as the
probability that, at a specified time, the system operates and
will continue to operate for at least a given interval, and serving
reliability is defined as the probability that either the system
operates at a specified time, or if it is not operating, it will
be repaired within a given interval. Considering that both the
run and burst lengths of Pt follow the exponential distributions,
we have
PH0 = λb e−λr β /(λr + λb )
PH1 = 1 − PH0 .
(3)
Obviously, PH0 and PH1 are related to the length of spectrum
sensing duration β.
Based on our proposed spectrum access scheme, we know
that Ui sends only when it detects that Pt is inactive, which may
result in incorrect sensing cases of false alarm and missed detection. Although the sensing result is correct, there still exists
the possibility (denoted by H2 ) that this result is inconsistent
with the fact that, when Pt keeps inactive during β, later on, it
wakes up during the data transmission time Td of the current
frame. Let PH3 be the probability that Pt is inactive during the
whole frame; thus, we have
PH3 = λb e−λr f /(λr + λb ).
(4)
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Then, the probability of H2 (which is denoted by PH2 ) is
given by
PH2 = PH0 − PH3 .
(5)
Obviously, the secondary network interferes with the primary
network in the following two aspects: 1) missed detection under
H1 and 2) transmission under H2 . Note that the case Pt is active
at the beginning of the spectrum sensing duration but later
on turns to be inactive before the end of the sensing duration
exists. However, the corresponding occurrence probability is
negligible; thus, we can ignore this case and focus only on
cases H1 and H2 . To measure these effects, we define a new
parameter, i.e., interference factor (denoted by IF ), which is
the outage probability that SUs would interfere with PUs in an
arbitrary frame, and use subscripts 1 and 2 to distinguish the
aforementioned two cases. First, we consider the case of missed
detection under H1 . Based on (1) and (3), we have
(6)
IF1 = 1 − PdN PH1 .
For the second case of transmission under H2 , based on (2)
and (5), we have
(7)
IF2 = 1 − PfN PH2 .
Combining (6) and (7) yields
IF = IF1 + IF2 .
(8)
Based on (8), we see that, for fixed Pd and N , IF depends
only on Pf and f . Moreover, because Pf is a monotonically
decreasing function of t, IF is a monotonically increasing
function of t and is also a monotonically increasing function
of f .
In addition, we consider another parameter called the agility
factor (which is denoted by AF ), which refers to the Ui ’s ability
to rapidly vacate the channel once Pt has turned active from
an inactive state. Based on our designed frame structure, we
define that AF = Tf /Tv , which varies in (Ts /Tv , 1] due to the
condition of Ts < Tf ≤ Tv . By definition, the smaller the value
of AF is, the quicker the channel is vacated, and vice versa.
Obviously, AF is related to the configuration of the frame
length. Therefore, we take this parameter into account to design
the optimal frame length.
III. S LOTTED CR-ALOHA AND I TS P ERFORMANCE
A. Slotted CR-ALOHA
The slotted CR-ALOHA is developed from the conventional
slotted ALOHA, which differs in the discrete channel access
time and the constraint of protecting the primary network. We
assume that, for each frame, the data transmission duration l is
slotted, and the slot size is equal to the TP length of 1 + α. As
shown in Fig. 3, the slotted CR-ALOHA operates as follows.
1) If Ui detects that the channel is available in the current
frame, any packet that arrives in the M th slot of the
previous frame or the spectrum sensing duration of this
frame will be transmitted in the first slot; otherwise, if
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Fig. 3. Operation scheme of the slotted CR-ALOHA. The box with solid lines
indicates the inactive Pt case, and the box with dash lines indicates the active
case.
a packet arrives in the jth slot (j = M ), it will start to
transmit at the beginning of the (j + 1)th slot.
2) If the channel is unavailable, any packet arrival within this
frame up to the (M − 1)th slot will be blocked to the end
of this frame and then uniformly retransmit within a backoff window, as mentioned in Section II-C.
3) The current transmission is successful when there is only
one packet that was transmitted; otherwise, a collision
occurs, and the packets involved will be retransmitted
after corresponding separate random delays to avoid continuously repeated conflicts.
4) Any arrival in the M th slot of one frame will be processed
in the next frame.
For the conventional slotted ALOHA, the normalized
throughput S, defined as the fraction of time that can successfully transmit SUs’ packets, is given by S = Ge−G , and the
maximum S is equal to 0.368 when G = 1. However, in a CR
environment, Pt ’s activities will definitely degrade S, which
will be shown as follows.
B. Throughput Analysis
Based on the operation scheme of the slotted CR-ALOHA, a
packet that can successfully be transmitted by Ui must satisfy
the following three conditions if the capture effect is ignored:
1) Ui can access the channel in the current frame; 2) no collision
occurs between Pt ’s transmission and Ui ’s transmission; and
3) no collision occurs between Ui and any other SU’s packets.
Let Ci , i = 1, 2, 3, denote the aforementioned conditions. Obviously, C2 and C3 are independent of each other, conditioned
on C1 .
First, we consider C1 . For H0 , Ui can access the channel
with a probability of 1 − Pf , because no false alarm occurs.
Moreover, if Ui cannot detect Pt ’s activeness under H1 , Ui can
still access with a probability of 1 − Pd . Let V0 and V1 be the
probabilities of both cases, respectively; then, we have
V0 = 1 − Pf , H0
Pr{C1 } =
(9)
V1 = 1 − Pd , H1 .
Based on (2) and (9), we see that V1 is constant and V0 is
monotonically increasing with t; thus, we have
2γ + 1Q−1 (Pd ) + tfs γ .
(10)
V0 (t) = 1 − Q
For notational simplicity, we use V0 or V0 (t) as the intermediate variable for analyzing the performance in the remainder
part.
Because Ui ’s independently detect Pt , the number of SUs
that can access the channel in one frame (which is denoted
by n) follows a binomial distribution, whose occurring probability is given by
N
Pr{n SUs can access} =
(Pr{C1 })n (1 − Pr{C1 })N −n
n
N n
N −n
, H0
n V0 (1 − V0 )
= N
n
N −n
V
(1
−
V
)
, H1
1
1
n
0 ≤ n ≤ N.
(11)
Accordingly, we use G(n) to denote the actual traffic rate
that corresponds to n SUs; thus, we have G(n) = nλ, with the
probability given by (11).
Then, we consider C2 . Because we have assumed that Ui ’s
are located outside Pt ’s CSR, Pt ’s transmission has no influence on Ui ’s transmission, but Ui can still interfere with Pr ’s
reception. In this case, the transmission by SUs under H1 is not
encouraged, and the achieved performance should be ignored.
Therefore, we have
1, H0
Pr{C2 } =
(12)
0, H1 .
Last, C3 occurs if and only if no other SU’s packet waits at
the beginning of the current slot. In particular, when a packet
transmits 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 would
overlap) lasts from the M th slot of the prior frame to the end
of the spectrum sensing duration in this frame. Based on the
condition that n SUs satisfy C1 , we obtain
Pr{C3 } =
1 + α + β −(n−1)λ(1+α+β)
e
l+β
+
l − (1 + α) −(n−1)λ(1+α)
·e
. (13)
l+β
Let C denote the event that a packet is successfully transmitted by Ui . Combining the results in (11)–(13), we have
Pr{C|n SUs can access}
= Pr{C2 C3 |H0 }PH0 + Pr{C2 C3 |H1 }PH1
(14)
where the second term is equal to zero due to Pr{C2 |H1 } = 0
given by (12). Then, we use S(n, t) to denote the achieved
throughput that corresponds to n SUs and spectrum sensing
time t, and the average achievable S(t) is given by
S(t) =E {S(n, t)}
N
G(n) Pr{C|n SUs can access} Pr{n SUs can access}
=
n=0
N −1 λ e−λr β
b
=N λV0 1−V0 +V0 e−λ(1+α)
λ
r + λ
b
(1 + α + β) 1 − e−(N −1)λV0 β
· 1−
l+β
N −1
N λV0 1 − V0 + V0 e−λ(1+α)
λb e−λr β
≈
λr + λb
(15)
CHEN et al.: TWO-LEVEL MAC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRUM ACCESS IN CRNs
where E is the expectation operator, and the last equation holds
for small λ and β. Therefore, the optimization problem of S can
be expressed as
max
S(t)
s.t.
V0 ∈ dom V0 = {V0 |0 < V0 ≤ 1 − Pf,min }
V0
(16)
where dom V0 is obtained from (2) and (10) as t varies in its
domain [0, Ts ].
Let Smax denote the maximum S(t) and V0∗ denote the
optimal V0 for Smax . Solving (16), the extremum of S is
achieved 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 α
and λ are relatively small. If 1/G ∈ dom V0 , V0∗ = 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 V0∗ = 1 − Pf,min . Using (10), the optimal
sensing time t for Smax , which is denoted by t∗ , is given by
⎧
2
√
⎨ f 1γ 2 Q−1 (1 − 1/G) − 2γ + 1Q−1 (Pd )
s
∗
t =
1/G ∈ dom V0 (17)
⎩
Ts , otherwise.
Moreover, combining (10) and (15), for large N and small α,
we have
∗
Smax = N λV0 (t∗ )λb e−(N −1)λV0 (t
≈ λb G∗ e−G
∗
∗
−λr β
)−λr β
/(λr + λb )
/(λr + λb )
Proof: Although the number of arrivals that were generated by SUs follows a Poisson distribution, the arriving instants
of these packets would still be uniformly distributed over the
time axis. Therefore, the average pretransmission delay ω can
be calculated as follows: 1) If the packet arrives in the M th
slot of one frame, the probability density function (pdf) of
the arrival instant is given by f (x) = 1/(1 + α), and thus, the
average pretransmission time for this case (denoted by ω1 )
consists of the residual time of the current frame and the spec1+α
trum sensing duration of the next frame, i.e., ω1 = 0 (1 +
α − x)f (x)dx + β = (1 + α)/2 + β; 2) if the packet arrives
in the spectrum sensing duration, the pdf of the arrival instant
β
is f (x) = 1/β, and we have ω2 = 0 (β − x)f (x)dx = β/2;
and 3) if a packet arrives in the jth slot (j = M ), we have
1+α
ω3 = 0 (1 + α − x)f (x)dx = (1 + α)/2.
Based the aforementioned analysis, ω is given by
ω=
=
βω2
(l − 1 − α)ω3
(1 + α)ω1
+
+
l+β
l+β
l+β
β 2 + 2β(1 + α) + l(1 + α)
.
2(l + β)
R 1 = tb + δ =
where G = N λV0 (t ) is the optimal traffic rate adjusted by
our proposed two-level OSA strategy. Compared to the conventional slotted ALOHA, we note that Smax under the slotted
CR-ALOHA decreases by a fraction PH0 due to the existence
of Pt .
C. Delay Analysis
In this section, we analyze the average packet delay D for
the slotted CR-ALOHA, which refers to the average interval
from the instant that a packet is originally generated until
the instant that it is successfully transmitted. We make the
following assumption.
Assumption 2: The packet-processing time is negligible, including the sum check and acknowledgment generation time.
Let R0 and R1 be the average duration between two consecutive transmissions of the same packet due to collision and
being blocked, respectively. According to Assumptions 1 and 2,
we have
(19)
where ω is the average length of the pretransmission delay,
which refers to the interval from the instant that the SU attempts
to transmit until the instant that it senses that the channel is idle
for transmission.
Theorem 1: If a packet can be transmitted, its average pretransmission delay ω is given by ω = β 2 + 2β(1 + α) + l(1 +
α)/2(l + β), and limα,β→0 ω = 1/2.
(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 of
the average blocking time tb and the average retransmission
delay δ. It is easily derived that tb = (l + β)/2; thus, we have
(18)
∗
R0 = 1 + 2α + a + δ + ω
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l+β
+ δ.
2
(21)
Therefore, the average number of collisions is given by
G(n)/S(n, t) − 1, and the average number of being blocked
is (G − G(n))φ/S(n, t), where φ = δ/R1 denotes the fraction
of the unblocked time during R1 . Therefore, the average packet
delay D(t) is expressed as
G(n)
[G−G(n)] φ
−1 R0 +
R1 +1+α+ω
D(t) = E
S(n, t)
S(n, t)
N
−λ(1+α)
e
(R0 − φR1 ) 1 − V0 + V0 eλ(1+α)
=
PH0
N +1
−2λ(1+α)
e
φR1 1−V0 +V0 eλ(1+α)
+
−(α+a+δ)
V0 PH0
≈ eλr β (λr + λb ) [R0 + (1/V0 − 1)δ]
N −1 λb − (α + a + δ)
× 1 − V0 + V0 eλ(1+α)
(22)
where the last equation holds due to e−λ(1+α) ≈ [1 − V0 +
V0 eλ(1+α) ]−1 . Similarly, the optimization problem of D can be
written as
min
D(t)
s.t.
V0 ∈ dom V0 .
V0
(23)
Let Dmin denote the minimum D(t) and V0
denote the
optimal V0 for Dmin . Because D(t) as given in (22) is
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differentiable, the extremum of D is obtained as dD(t)/dV0 =
0. When G ≥ 4(1 − R0 /δ), we obtain
V0 =
G+
2
G2
− 4G(1 − R0 /δ)
Δ
= V 0.
(24)
(V0 ) < 0,
If V 0 ∈ dom V0 , we have V0
= V 0 , because D−
and D+ (V0 ) > 0. Otherwise, if V 0 > 1 − Pf,min , D(t) is a
monotonically decreasing function of V0 . Therefore, Dmin is
achieved at V0
= 1 − Pf,min .
Then, the corresponding optimal sensing time t for Dmin
(denoted by t
) is eventually given by
−1
2
√
1
−1
t
= fs γ 2 Q (1−V 0 )− 2γ +1Q (Pd ) , V 0 ∈ dom V0
Ts , otherwise.
(25)
Based on (22) and (25), for large N and small α and λ,
we have
Dmin = eG +λr β (λr +λb ) [R0 +(G/G
−1)δ] /λb −(α+a+δ)
(26)
where G
= N λV0 (t
) is the corresponding optimal traffic rate
for 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 know
that V 0 < 1/G due to R0 > δ; furthermore, we have t
≤ t∗ .
In other words, Smax and Dmin cannot simultaneously be
achieved, and there exists a range defined as R(t) = {t|t
≤ t ≤
t∗ }, within which increasing S will result in the increasing of
D, and vice versa.
In fact, the back-off window size is chosen as a large value
to avoid continuous collisions, i.e., δ is much greater than
1 + 2α + a + ω; thus, we have R0 /δ ≈ 1 and V 0 ≈ 1/G. Furthermore, we note that t
= t∗ and R(t) converges to a point.
IV. C OGNITIVE -R ADIO -BASED C ARRIER -S ENSING
M ULTIPLE ACCESS AND I TS P ERFORMANCE
A. CR-CSMA Protocol
In the previous section, we assume that the data transmission
duration l of each frame is divided into slots of length TP. Now,
in CR-CSMA, we assume that l is divided into minislots of
length σ, which is called the slot time (ST) in the IEEE 802.11
distributed coordination function (DCF). The concepts of slot
and minislot are different due to the differences of the operation
schemes. CR-CSMA requires that each packet starts to transmit
at the beginning of the following ST. To improve the utilization
of the channel access time, we assume that one slot or TP
is equal to the integral number (denoted by m) of minislots,
i.e., 1 + α = mσ. Moreover, because the carrier-sensing time
is relatively short compared to the spectrum sensing time, we
neglect it in the following analysis. As shown in Fig. 4, the
details 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 indicates
the inactive Pt case, and the box with dash lines indicates the active case.
or the spectrum sensing duration of this frame will be
transmitted in the first slot; otherwise, if it arrives in the
jth slot (j = M ), the following conditions hold.
• If the channel is idle, it will be transmitted at the
beginning of the next ST.
• If the channel is busy, Ui keeps sensing until the
channel again becomes idle (i.e., the end of the
current transmission) and then attempts to transmit.
2) If Ui detects that Pt is active, any arrival within the
current frame up to the (M − 1)th slot will be blocked
to the end of this frame, and then, Ui chooses a uniformly
distributed back-off time to retransmit.
3) The current transmission will be successful if there are
no other packets transmitting during this TP; otherwise,
it fails and will be retransmitted after a random delay to
avoid continuously repeated conflicts.
4) Any attempt during the M th slot of one frame must wait
to be processed in the next frame.
The difference between the slotted CR-ALOHA and
CR-CSMA is obvious: SUs transmit only from the beginning
of a slot under the slotted CR-ALOHA, and thus, they need
not sense the channel. However, under CR-CSMA, SUs become
more aggressive to transmit, because they keep sensing until the
channel becomes idle.
B. Throughput Analysis
We define idle period (IP) as the duration within which the
channel is available but no packet is transmitted or waits to
be transmitted, busy period (BP) as the duration occupied by
Ui ’s, and useful period (UP) as the successful transmission time
within one BP. According to the CR-CSMA scheme, BP always
starts from the instant when an arrival comes in an IP. If any
other packet arrives during the current transmission, this BP
continues; otherwise, it terminates at the end of the current
transmission, 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 was
successfully transmitted must satisfy the three conditions of
Ci ’s. Based on the renewal theory, the normalized throughput
S(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 that
was generated within a duration τ . Then, it is easily verified
that Z(τ ) = 1 − V0 + V0 e−λτ ≈ e−λV0 τ . Moreover, we use
CHEN et al.: TWO-LEVEL MAC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRUM ACCESS IN CRNs
Y to denote the length of an arbitrary IP, and the cumulative
distribution function (cdf) of Y is given by
FY (y) = 1 − Pr{Y > y} = 1 − Z N (y) = 1 − e−GV0 y . (28)
Furthermore, the mean value of I is given by
∞
ydFY (y) ≈
I=
1
.
GV0
(29)
0
Second, we consider the total number of packets (denoted by
K) that were transmitted in one BP. Let z be the probability that
no SUs transmit in one TP; thus, we have
z = Z N (1 + α)
N
= 1 − V0 + V0 e−λ(1+α)
≈ e−GV0 (1+α) .
(30)
Therefore, the probability that the next TP belongs to the
current BP is given by 1 − z. In particular, when a BP processes
in the last slot of one frame, it continues only when there exists
any packet that waits at the end of the current transmission.
If the next frame is available, the waiting packets will be
processed in the first slot of the next frame. Conversely, if the
next frame is unavailable, the waiting packets will be blocked
for transmission or insist to proceed but interfere with Pt ’s
transmission. In the second case, once the channel has again
become available, the packets that accumulate at the end of
the last unavailable frame will be processed in the first slot of
this frame. However, we see that BP continues with the same
probability of 1 − z, regardless of which case occurs, i.e., BP
can jump over the unavailable frames and, without interruption,
proceeds in the available frames. Therefore, K is geometrically
distributed with mean 1/z, and
Pr{K = k} = z(1 − z)k−1 ,
k = 1, 2, . . . .
(31)
Now, we use B j and U j , j = 0, 1, . . . , M , to distinguish the
expected lengths of BP and UP, beginning within the jth slot
of one frame, respectively. Then, their values are calculated as
follows.
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 the
current slot, and this process continues, unless BP terminates.
However, due to the frame length limitation, at most M TPs
can be accommodated in one frame, and any larger than M th
TP will be processed in the next available frames. In addition,
B0 =
U0 =
β(1 − z)M
1+α
β
+
+
z
1 − (1 − z)M
2
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the (iM + 1)th TP, i = 1, 2, . . . must wait an extra spectrum
sensing time β to detect the channel states.
Obviously, the first TP is successfully transmitted only when
no other packets wait at the end of β. Similarly, the next TP is
successful if and only if one packet waits at the beginning of this
transmission. For the (iM + 1)th case, successful transmission
must satisfy the following two conditions: 1) There must exist
a packet that waits at the end of the previous TP such that the
current BP can continue, and 2) only one packet accumulates at
the beginning of the current TP, i.e., no collision would occur.
Lemma 1: For j = 0, the average length of a BP and a UP
are 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 the
following ST, which produces a false-busy period (FP) with
a length of (x − β)/σσ − (x − β), referring to the unused
idle time slots in this BP. If no other packets accumulate at the
end of this FP, it will successfully be transmitted. In particular,
when K > M − j, the (M − j + 1)th TP will proceed in the
next available frame, which results in a FP of j(1 + α) − (x −
β)/σσ, lasting from the end of the (M − j)th TP to the end of
the frame.
Lemma 2: For 0 < j < M , the average length of a BP and
UP are given by (34) and (35), shown at the bottom of the next
page, 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 will
proceed in the next available frame.
Lemma 3: For j = M , the average length of a BP and UP are
given 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 at
the bottom of the next page, respectively, where θ = β/f is the
fraction of spectrum sensing duration per frame.
Proof: Because the packet arrival process is random,
we have
B=
β
1+α
1+α
B0 +
B1 + · · · +
BM
l+β
l+β
l+β
(40)
U=
β
1+α
1+α
U0 +
U1 + · · · +
UM.
l+β
l+β
l+β
(41)
(32)
GV0 (1 + α)e−GV0 (1+α) 1
(1 − z)M
1 − e−GV0 β
GV0 (1 + α + β)e−GV0 (1+α+β) (1 − z)M
+
−
1
−
+
M
−GV
(1+α)
0
GV0 β
z
1 − (1 − z)
1 − (1 − z)M
1−e
1 − e−GV0 (1+α)
(33)
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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 the
expression of S(t) for CR-CSMA. Note that the closed-form
expression of t∗ for S(t) cannot easily be obtained, but we can
find its value by a numerical method.
In addition, if α, β, and σ are relatively small and M is large
enough, we see that
S(t) ≈
PH0 (1 + GV0 ) GV0 λb e−GV0 −λr β (1 + GV0 )
.
=
eGV0 + 1/GV0
(GV0 + e−GV0 )(λr + λb )
(42)
recalculate the value of R0 . Thus, the pretransmission time ω is
derived as follows.
1) If a packet arrives in the spectrum sensing duration, its
average waiting time is β/2.
2) If a packet arrives in the jth TP (j = 1, . . . , M − 1) of
one frame when the channel is idle, its average waiting
time is σ/2; otherwise, when the channel is busy, its
average waiting time equates to (1 + α)/2.
3) If a packet arrives in the M th TP of one frame, its average
waiting time is (1 + α)/2 + β.
Therefore, we obtain
C. Delay Analysis
Similar to the analysis for the slotted CR-ALOHA in
Section III-C, we determine the average packet delay D for
CR-CSMA. Due to the different operation schemes, we must
ω=
β 2 + 2β(1 + α) + (1 + α)2 + (l − 1 − α) σI+(1+α)B
B+I
2(l + β)
β(1 − z)M −j σ (1 + α − σ)(1 − z)M −j
1+α
+
+ +
z
1 − (1 − z)M 2
2
−GV0 σ
−GV0 (1+α)
1
GV0 (1 + α)e
(1 − z)M −j
1−e
GV0 (1 + α + β)e−GV0 (1+α+β)
+
−
1
−
Uj =
+
GV0 σ
z
1 − (1 − z)M
1 − e−GV0 (1+α)
1 − e−GV0 (1+α)
(1 − z)M −j
×
− PH0 (1 − z)M −j + PH0 (1 − z)M −j
1 − (1 − z)M
1
1
−GV0 (1+α+β)
−GV0 (2+2α+β)
e
−
2
+
2α
+
β
+
1 + α + β + GV
GV0 e
0
×
(1 + α) 1 − e−GV0 (1+α)
Bj =
β
1+α
1+α
+
+
M
z
1 − (1 − z)
2
−GV0 β
−GV0 (1+α)
e
1−e
V0 PH0
GV0 (1 + α)e−GV0 (1+α) 1
1
+
−
=
GV0 (1 + α)
z
1 − (1 − z)M
1 − e−GV0 (1+α)
1
GV0 (1 + α + β)e−GV0 (1+α+β)
+
− PH0
−GV
(1+α)
0
1 − (1 − z)M
1−e
BM =
UM
.
(43)
(34)
(35)
(36)
(37)
β
β(1 − z)M
1+α
σ 2β + (1 + α − σ) 1 − (1 − z)M
+θ
+
+
(38)
B=
+ (1 − θ)
z
2
1 − (1 − z)M
2
2M z
θ(1 − z)M
GV0 (1 + α)e−GV0 (1+α) 1
(1 − θ)(1 − z)
GV0 (1 + α + β)e−GV0 (1+α+β)
−
1
−
U=
−
+
M
−GV
(1+α)
0
z
1 − (1 − z)
Mz
1−e
1 − e−GV0 (1+α)
θ(1 − z)M
PH1 + PH0 (1 − z)M
×
+
(1
−
θ)
1 − (1 − z)M
Mz
θ (l − 1 − α)(1 − e−GV0 σ ) 1 − e−GV0 β + e−GV0 β 1 − e−GV0 (1+α) V0 PH0
+
+
β
GV0 σ
GV0
1
1
−GV0 (1+α+β)
−GV0 (2+2α+β)
−
2
+
2α
+
β
+
1 + α + β + GV
e
GV0 e
1 − z − (1 − z)M
0
+ PH0
(39)
z
1 − e−GV0 (1+α)
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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 theexpected
rate
N traffic
N
n
in any available frame is given by
n=1 n nλV0 (1 −
V0 )N −n = GV0 , D(t) for CR-CSMA can be derived as
GV0
(G − GV0 )φ
D(t) =
− 1 R0 +
R1 + 1 + α + ω (44)
S(t)
S(t)
where S(t) corresponds to the normalized throughput of
CR-CSMA given by (27). Therefore, we can obtain the theoretical value of t
by a numerical method.
V. S IMULATION R ESULTS
We develop an event-driven network simulator to evaluate the
performance of our proposed CR-ALOHA and CR-CSMA. The
simulator is written in MATLAB, closely following all the details of the protocols for each SU, as described in Sections III-A
and IV-A. Suppose that the bandwidth of the channel and the
sampling frequency fs are both chosen as 6 MHz. To protect
the primary network, Ui ’s are required to vacate the channel
within 100 ms, i.e., Tv = 100 ms. We assume that, for the worst
case, the received SNR γ from Pt at Ui is given by −13 dB
and the overall detection probability is larger than 0.9. These
configurations consist with the sensing requirement of wireless
microphones in the IEEE 802.22 Draft Standard [29].
Fig. 5. S versus t for the slotted CR-ALOHA.
A. Performance of the Slotted CR-ALOHA
We design the frame structure for SUs as follows. The packet
size is 2000 b, the channel bit rate is 1 Mb/s, and the propagation delay is ignored; thus, the length of TP is standardized to
2 ms. The maximum spectrum sensing duration Ts equates
to one TP length of 2 ms (i.e., β = 1), which ensures that
Pf is small enough as the actual sensing time t goes to Ts
according to (2). Moreover, we assume that Td consists of
49 TPs; therefore, the total frame length Tf is 100 ms, and f =
50. Note that the constraint Tf ≤ Tv is satisfied here. Suppose
that the traffic rate λ of each Ui is given by 0.02 and the
parameters λr and λb used to simulate that Pt ’s traffic are given
by 0.01 and 0.99, respectively. Thus, we obtain PH0 = 0.98 and
PH1 = 0.02 by (3), i.e., the average occupancy by the primary
network is 2% in our interested frequency band [1].
Next, we validate the accuracy of the analytical results derived in Section III. In Figs. 5 and 6, we plot the curves of
normalized throughput S and average packet delay D versus
the spectrum sensing time t for different numbers of SUs N ,
respectively. In these figures, it is clearly shown that the simulation results (dashed line) perfectly match with the theoretical
results (solid line). Here, theoretical S and D are obtained by
(15) and (22), respectively.
Then, we consider the effects of spectrum sensing time t on
the achievable normalized throughput S and average delay D.
As shown in Fig. 5, for N = 25 and 50 as G ≤ 1, S monotonically increases with t, and the corresponding Smax is achieved
at t = Ts . For N = 100 as G > 1 and 1/G ∈ dom V0 , S first
monotonically increases with t until t = t∗ , which is attained by
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 ∈ dom V0 , D initially decreases with
t until t = t
, which is attained by (25), and then, D later
monotonically increases with t. The curvilinear trend of D is
similar to S, which means that D’s decrease corresponds with
S’s increase, and vice versa. This phenomenon can be explained
by the fact that the longer the sensing time t, the larger
the packet transmission probability V0 . When G ≤ 1, a larger
V0 increases the transmission opportunity and achieves better
performance. However, when G > 1, a larger V0 aggravates
the system burden and results in more collisions such that the
performance degrades. We also observe that Smax and Dmin
are achieved at the same t, which validates the conclusion that
t∗ = t
and R(t) converges at a point in Section III-D.
Last, we plot Smax and Dmin versus the number of SUs N in
Figs. 7 and 8, respectively. The simulation results (dashed line)
closely match with the theoretical results (solid line) obtained
by (18) and (26). Then, we compare the performance of the
slotted CR-ALOHA under the optimal t (t = t∗ or t
) and
maximum t (t = Ts ). Here, the optimal t is obtained by our
proposed two-level OSA strategy, and the maximum t means
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Fig. 7. Smax versus N for the optimal t and maximum t (slotted
CR-ALOHA).
Fig. 8. Dmin versus N for the optimal t and maximum t (slotted
CR-ALOHA).
Fig. 9. S versus t for CR-CSMA.
Fig. 10. D versus t for CR-CSMA.
B. Performance of CR-CSMA
that Ui sends its packets without traffic control, unless it has
detected Pt to be active, which is used by several existing
protocols. As shown in Fig. 7, Smax keeps the same value
for both cases and increases with N until N = 50. However,
when N > 50, the former case can still maintain a stable large
value, but in the latter case, Smax dramatically degrades as N
increases. Moreover, for both cases shown in Fig. 8, we see that
Dmin monotonically increases with N . However, Dmin for the
optimal t keeps linearly increasing rather than exponentially increasing compared with the maximum t case. This phenomenon
vigorously validates the dominance of our proposed two-level
OSA strategy. Note that there exists a small gap between the
simulation results and the theoretical results for the maximum t.
The reason is that, in this case, the collisions increase with the
increase of number N , which eventually results in the back-off
and retransmission at SUs. Thus, the actual input traffic rate
for each SU will be less than its theoretical value of λ under
the assumption of Poisson distribution. Therefore, Dmin of the
simulation results is accordingly smaller than the theoretical
results, as shown in Fig. 8.
In a similar way, we evaluate the performance of CR-CSMA
analyzed in Section IV. We set each ST to 20 μs, as configured
in the IEEE 802.11 DCF. As shown in Figs. 9 and 10, the
simulation results (dashed line) perfectly match with the theoretical 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. However, as N = 100, we see that the maximum S and minimum D
are attained at the same point within domain t. This condition
validates that the optimal performance of CR-CSMA can be
achieved at the same t, i.e., t∗ = t
.
Furthermore, Smax and Dmin versus the number of SUs
N for the optimal t and maximum t are plotted in Figs. 11
and 12, respectively. Simulation results (dashed line) perfectly
match with the theoretical results (solid line) obtained by the
numerical method. Obviously, when N ≤ 50, both the optimal t
and maximum t can achieve the same performance due to
t∗ = t
= Ts . However, if N continues to increase, Smax in
the former case still maintains a stable large value, and the
corresponding Dmin also keeps linearly increasing, which
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primary network. Based on the definition of interference factor
given 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 changes
from 2 to 50. As shown in Figs. 13 and 14, the normalized
throughput S monotonically increases, and the average delay D monotonically decreases with IF for both the slotted
CR-ALOHA and CR-CSMA, which shows that the performance improvement of the secondary network results in more
interference on the primary network. In other words, we can
sacrifice the performance of the primary network to improve the
performance of the secondary network or restrain SUs’ transmissions to protect more PUs, because they exist in the same
spectrum band. Therefore, we conclude that the achievable
performance of secondary network depends on the interference
requirement of protecting the primary network.
Fig. 11. Smax versus N for the optimal t and maximum t (CR-CSMA).
D. Tradeoff Between Performance and Agility
According to the definition of agility factor, we know that a
smaller value of AF leads to more rapidly vacating the channel
to PUs but degrades the performance of SUs as well. Similar
to the tradeoff between performance and interference, there
also exists a tradeoff between performance and agility, which
is shown in Figs. 15 and 16 for the slotted CR-ALOHA and
CR-CSMA, respectively. We observe that Smax monotonically
increases and Dmin monotonically decreases with AF , and
meanwhile, the optimal performance is achieved at AF = 1
for different numbers of N . Therefore, we conclude that the
achievable performance of the secondary network depends on
the agility requirement of protecting the primary network.
E. Optimal Frame Length
Fig. 12. Dmin versus N for the optimal t and maximum t (CR-CSMA).
outperforms the latter case. This phenomenon is similar to the
slotted CR-ALOHA.
Then, we compare the performance between the slotted
CR-ALOHA and CR-CSMA. Based on Figs. 5, 6, 9, and 10,
given the same t, CR-CSMA always performs better than the
slotted CR-ALOHA for both S and D. Moreover, given the
same N , the performance of Smax and Dmin for CR-CSMA is
much better than the slotted CR-ALOHA, as shown in Figs. 8,
9, 11, and 12. This performance advantage is because the packets of the secondary network can more efficiently be scheduled
into the channel and accordingly wait less time for transmission
under the scheduling operation of CR-CSMA compared with
the slotted CR-ALOHA.
Moreover, compared to the performance of normalized
throughput under the slotted CR-ALOHA and CR-CSMA with
the performance under the VX scheme [21], we can easily see
that the values of Smax in Figs. 7 and 11 are much greater than
in [21], which shows the advantages of our proposed protocols.
C. Tradeoff Between Performance and Interference
We study the tradeoff between the performance achieved by
the secondary network and the resulting interference on the
Now, we take into account the influence of the total frame
length f . Based on the aforementioned analysis, we know
that parameters IF and AF are both monotonically increasing
functions of f . Therefore, a longer frame length f achieves
higher Smax and lower Dmin for both the slotted CR-ALOHA
and 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 the
frame is very short, and 2) for a longer frame length, more SUs
are allowed to compete for channel access rather than being
blocked, which increases the transmission opportunities and
finally improves the system performance.
Moreover, we know that the performance of the secondary
network depends on both IF and AF . In fact, these two parameters are usually predefined by the application requirement.
In our simulation, Tv is set at 100 ms; therefore, the optimal
frame length that satisfies the requirement of AF (denoted by
fAF ) should be chosen as fAF = 50. On the other hand, if
the primary network requires that IF ≤ 0.2, we can calculate
that the optimal frame length that satisfies the IF requirement
(denoted by fIF ) is given by fIF = 23. Considering both
effects of interference and agility, the optimal f should be
chosen as the minimum value of fIF and fAF , i.e., f = 23.
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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 contains
only one TP, i.e., f = 2, the Smax for N = 25 is greater than
for N = 50 or N = 100, as shown in Fig. 13. This case is
because 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 frame
length 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
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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 is
really poor. Thus, we design the frame structure that one frame
duration contains M TPs, as mentioned in Section II-A.
In addition, when N ≥ 50, the curves of Smax in Figs. 13–16
are very close to each other. Furthermore, the performance
curves sharply vary at the beginning of increasing f , but later
on, they more gently change, and the performance finally
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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 5, JUNE 2011
approaches a stable value, regardless of f ’s increase. This
phenomenon is due to the maximum achievable performance
constraints of the slotted CR-ALOHA or CR-CSMA.
F. Effects of the PUs’ Activities
According to Section II-E, we know that PUs’ activities are
related to their traffic parameters λr and λb . To consider the
effects of the spectrum utilization of the primary network on the
performance of the secondary network, we change the values
of λr and λb to ensure that PH0 (the probability that Pt is
detected to be inactive in one frame) varies in the range [0.1, 1].
Intuitively, given a smaller PH0 , Ui ’s would more possibly be
blocked for transmission. Conversely, given a larger PH0 , Ui ’s
obtain more opportunities to compete for the channel, and the
performance would be improved.
Thus, we plot the Smax and Dmin versus PH0 for the slotted
CR-ALOHA and CR-CSMA in Figs. 17 and 18, respectively.
We see that Smax linearly increases and Dmin monotonically decreases with the increase of PH0 for both the slotted
CR-ALOHA and CR-CSMA. This phenomenon validates the
fact that Pt ’s activities, indeed, have an influence on the performances of SUs and the spectrum utilization of the primary
network determines the maximum achievable performance of
the secondary network. Moreover, in the beginning of the
range PH0 , because Pt frequently occupies the current channel,
the performance of Ui ’s is really disappointing, regardless of
whether N is equal to 25, 50, or 100, as shown in Figs. 17
and 18. In this case, to achieve better performance, SUs must
consider shifting to another channel with a higher PH0 . In fact,
how we can choose a good channel is another key technique for
CRNs, and we will consider it as our future work.
(k − 1)/M N (1 − z3 )z3N −1 /(1 − z), respectively, where
z1 = Z(β − x), z2 = Z(1 + α), and z3 = Z(1 + α + β). By
removing the conditions of k and x, B 0 and U 0 are given by
1
B0 =
β
β ∞ k−1
β −x+k(1+α)+
β z(1−z)k−1 dx
M
0 k=1
(45)
1
U0 =
β
β ∞ k−1
N (1−z2 )z2N −1
N −1
z1 +
k−1−
1−z
M
0 k=1
k−1 N (1−z3 )z3N −1
+
z(1−z)k−1 dx
M
1−z
(46)
respectively.
∞
is easily verified that
− z)k−1 = 1,
k=1 z(1
∞
It
∞
k−1
= 1/z,
and
k=1 kz(1 − z)
k=1 (k + j −
1)/M z(1 − z)k−1 = (1 − z)M −i /[1 − (1 − z)M ]; therefore,
(32) and (33) in Lemma 1 hold.
A PPENDIX B
P ROOF OF L EMMA 2
In a similar way, we obtain B j and U j , j = 1, . . . ,
M − 1, as
1
Bj =
1+α
VI. C ONCLUSION
In this paper, we have proposed a two-level OSA strategy and
developed two random-access MAC protocols called the slotted CR-ALOHA and CR-CSMA for CRNs. A suitable frame
structure has been designed, and closed-form expressions
of network metrics, i.e., normalized throughput and average
packet delay, have been derived, respectively. For various frame
lengths and numbers of SUs, the optimal performance of SUs
can be achieved at the same spectrum sensing time, and the
maximum achievable performance of the secondary network
is affected by the spectrum utilization of the primary network.
Moreover, using the interference and agility factors, we have
shown that there exists a tradeoff between the achieved performance of the secondary network and the effects of protection
on the primary network; therefore, the optimal frame length can
accordingly be designed.
A PPENDIX A
P ROOF OF L EMMA 1
In this case, because the BP starts at time x during β and it
consists of exact k TPs, the length of this BP and the UP are
given by B0 |k,x = β − x + k(1 + α) + (k − 1)/M β and
U0 |k,x = z1N −1 +(k−1−(k−1)/M)N (1−z2 )z2N −1/(1−z) +
!
∞ x−β
σ−(x−β)+k(1+α)
σ
β+j(1+α)
β+(j−1)(1+α) k=1
k+j −1
β z(1 − z)k−1
+
M
∞
+
k=M −j+1
! x−β
j(1+α)−
σ z(1−z)k−1 dx
σ
(47)
1
Ij =
1+α
β+j(1+α)
∞ k+j −1
N −1
z4 + k−1−
M
β+(j−1)(1+α) k=1
N (1−z2 )z2N −1
×
z(1−z)k−1
1−z
+
∞
k=M −j+1
+
k+j −1
N (1 − z3 )z3N −1
−PH0
M
1−z
PH0 N (1−z5 )z5N −1
z(1−z)k−1 dx
1−z
(48)
CHEN et al.: TWO-LEVEL MAC PROTOCOL STRATEGY FOR OPPORTUNISTIC SPECTRUM ACCESS IN CRNs
respectively, where the variables z4 and z5 are given
by z4 = Z((x − β)/σσ − (x − β)) and z5 = Z(β + (j +
1)(1 + α) − (x − β)/σσ).
β+i(1+α)
N −1
dx =
Moreover, we note that
β+(j−1)(1+α) z4
β+i(1+α)
(1 + α)(1 − e−GV0 σ )/(GV0 σ) and
β+(j−1)(1+α) N (1 −
z5 )z5N −1 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), it
follows that Lemma 2 is proved.
A PPENDIX C
P ROOF OF L EMMA 3
The proof process is similar to Lemmas 1 and 2. In this case,
we obtain B M and U M
BM
1
=
1+α
β+l
β+l−(1+α)
∞
"
β + l − x + k(1 + α)
k=1
#
k+M −1
+
β z(1−z)k−1 dx
M
(49)
UM
1
=
1+α
β+l
β+l−(1+α)
∞
z6N −1 V0 + (N − 1)
k=1
× (1 − z6 )z6N −2 (1 − V0 )
k+M −1
× PH0 + k−
M
N (1 − z2 )z2N −1
1−z
k+M −1
+
− PH0
M
N (1 − z3 )z3N −1
×
1−z
·
× z(1 − z)k−1 dx.
(50)
respectively, where z6 = Z(l − x + β). Solving (49) and (50),
we see that (36) and (37) are verified.
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Qian Chen (S’09) received the B.Eng. and M.Eng.
degrees in computer science and engineering from
Xi’an Jiao Tong University, Xi’an, China, in 2003
and 2006, respectively. He is currently working
toward the Ph.D. degree with the Department of
Electrical and Computer Engineering, National University of Singapore, Singapore.
He is currently a Research Fellow with the
Institute for Infocomm Research, A∗ STAR,
Singapore. His research interests include cognitive
radio networks, mobile ad hoc and sensor networks,
and medium-access-control (MAC) layer protocols.
Ying-Chang Liang (F’11) received the Ph.D. degree in electrical engineering from Jilin University,
Changchun, China, in 1993.
From December 2002 to December 2003, he was
a Visiting Scholar with the Department of Electrical
Engineering, Stanford University, Stanford, CA. He
is currently a Principal Scientist with the Institute for
Infocomm Research, A∗ STAR, Singapore, and holds
a joint appointment with Nanyang Technological
University, Singapore. His research interests include
cognitive radio, dynamic spectrum access, reconfigurable signal processing for broadband communications, space–time wireless
communications, wireless networking, information theory, and statistical signal
processing.
Dr. Liang is currently an Associate Editor for the IEEE T RANSACTIONS
ON V EHICULAR T ECHNOLOGY . He was an Associate Editor for the IEEE
T RANSACTIONS ON W IRELESS C OMMUNICATIONS from 2002 to 2005 and
the Lead Guest Editor of the IEEE J OURNAL ON S ELECTED A REAS IN
C OMMUNICATIONS—Special Issue on Cognitive Radio: Theory and Applications and Special Issue on Advances in Cognitive Radio Networking and
Communications. He is the Lead Guest Editor of the EURASIP Journal on
Advances in Signal Processing Special Issue on Advanced Signal Processing
for Cognitive Radio and a Guest Editor of the Elsevier Computer Networks
Journal Special Issue on Cognitive Wireless Networks. He received the Best
Paper Award at the IEEE Vehicular Technology Conference–Fall, in 1999
and the IEEE International Symposium Personal, Indoor, and Mobile Radio
Communications in 2005 and from the EURASIP Journal on Wireless Communications and Networking in 2010. He also received the Institute of Engineers
Singapore Prestigious Engineering Achievement Award in 2007.
Mehul Motani (M’98) received the B.S. degree from
Cooper Union, New York, NY, the M.S. degree from
Syracuse University, Syracuse, NY, and the Ph.D.
degree from Cornell University, Ithaca, NY, all in
electrical and computer engineering.
He is currently a Visiting Fellow with Princeton
University, Princeton, NJ, and an Associate Professor with the Electrical and Computer Engineering Department, National University of Singapore,
Singapore. Previously, he was a Research Scientist
with the Institute for Infocomm Research, Singapore,
for three years and a Systems Engineer with Lockheed Martin, Syracuse, for
over four years. His research interests are in the area of wireless networks.
Recently, he has been working on research problems which sit at the boundary
of information theory, communications, and networking, including the design
of wireless ad hoc and sensor network systems.
Dr. Motani received the Intel Foundation Fellowship for work related to
his Ph.D. research, which focused on information theory and coding for code
division multiple access systems. He has served on the organizing committees of ISIT, WiNC, and ICCS, and the technical program committees of
MobiCom, Infocom, ICNP, SECON, and several other conferences. He participates actively in the IEEE and the Association for Computing Machinery and
has served as the secretary of the IEEE Information Theory Society Board of
Governors. He is currently an Associate Editor for the IEEE T RANSACTIONS
ON I NFORMATION T HEORY and an Editor for the IEEE T RANSACTIONS ON
C OMMUNICATIONS.
Wai-Choong (Lawrence) Wong (SM’93) received
the B.Sc. (first-class honors) and Ph.D. degrees in electronic and electrical engineering from
Loughborough University, Loughborough, U.K.
From November 2002 to November 2006, he was
the Executive Director of the Institute for Infocomm
Research, A∗ STAR, Singapore. From 1980 to 1983,
he was a Member of Technical Staff with AT&T
Bell Laboratories, Crawford Hill, NJ. He is currently a Professor with the Department of Electrical
and Computer Engineering, National University of
Singapore (NUS), Singapore, where he is also the Deputy Director (Strategic
Development) with the Interactive and Digital Media Institute. Since joining
NUS in 1983, he has served in various positions at the department, faculty, and
university levels, e.g., the Head of the Department of Electrical and Computer
Engineering from January 2008 to October 2009, the Director of the NUS
Computer Centre from July 2000 to November 2002, and the Director of
the Centre for Instructional Technology from January 1998 to June 2000.
He is a coauthor of the book Source-Matched Mobile Communications. His
research interests include wireless networks and systems, multimedia networks,
and source-matched transmission techniques, for which he has more than
200 publications and is the holder of four patents.
Dr. Wong received the 1989 IEEE Marconi Premium Award, the 1989 NUS
Teaching Award, the 2000 IEEE Millennium Award, the 2000 e-nnovator
Award, Open Category, and the Best Paper Award at the 2006 IEEE International Conference on Multimedia and Expo.