MAC Protocol for Cognitive Radio Networks

1
Course Report
Student: Le Thanh Tan (LETT25047901)
Instructor: Prof. Le Bao Long
Semester: Winter 2011
Report Topic: MAC Protocol for Cognitive Radio Networks
I. INTRODUCTION
Emerging broadband wireless applications have been demanding unprecedented increase in radio spec-
trum resources. As a result, we have been facing a serious spectrum shortage problem. However, several
recent measurements reveal very low spectrum utilization in most useful frequency bands [1]. To resolve
this spectrum shortage problem, the Federal Communications Commission (FCC) has opened licensed
bands for unlicensed users’ access. This important change in spectrum regulation has resulted in growing
research interests on dynamic spectrum sharing and cognitive radio in both industry and academia. In
particular, IEEE has established an IEEE 802.22 workgroup to build the standards of WRAN based on
CR techniques [1].
Hierarchical spectrum sharing between primary networks and secondary networks is one of the most
popular dynamic spectrum sharing paradigms. For this spectrum sharing paradigm, primary users typically
have strictly higher priority than secondary users in accessing the underlying spectrum. Therefore, a
proper spectrum sensing mechanism is needed so that secondary users can search for and exploit available
spectrum holes (i.e., available frequency bands) [2]. There are several challenging technical issues related to
this spectrum discovery and exploitation problem. On one hand, secondary users should spend sufficiently
long time for spectrum sensing so that they do not interfere with active primary users. On the other hand,
secondary users should efficiently exploit spectrum holes to transmit their data by using an appropriate
spectrum sharing mechanism. Even though these aspects are tightly coupled with each other, they are not
treated thoroughly in the existing literature.
There is a rich literature on spectrum sensing for cognitive radio networks (e.g., see [3] and references
therein). Classical sensing based on, for example, energy detection techniques or advanced cooperative
sensing strategies [4] where multiple secondary users collaborate with another to improve the sensing
performance have been investigated in the literature. In [2], optimization of sensing and throughput tradeoff
under a detection probability constraint was investigated. It was shown that the detection constraint is met
with equality at optimality. However, this optimization tradeoff was only investigated for a simple scenario
with one pair of secondary users. There are also a large number of papers considering MAC protocol
design and analysis for cognitive radio networks [5]-[10]. However, these existing works either assumed
perfect spectrum sensing or did not explicitly model the sensing imperfection in their design and analysis.
In this paper, we make a further bold step in designing, analyzing, and optimizing a MAC protocol
for cognitive radio networks considering sensing performance captured in detection and false alarm
probabilities. Specifically, the contributions of this paper can be summarized as follows: i) we design
a distributed synchronized MAC protocol for cognitive radio networks incorporating spectrum sensing
operation; ii) we analyze saturation throughput of the proposed MAC protocols; iii) we perform the
throughput maximization of the proposed MAC protocol against its key parameters, namely sensing time
and contention window; iv) we present numerical results to illustrate performance of the proposed MAC
protocol and the throughput gain due to the optimal protocol configuration.

TEL352 Reading Course - Final Report
Fig. 1. Typical spectrum sharing model.
The remaining of this paper is organized as follows. Section II describes a system model and the
design of a synchronized MAC protocol. Throughput analysis and optimization are provided in Section
III. Section IV demonstrates numerical results followed by concluding remarks in Section V.
II. SYSTEM MODEL AND MAC PROTOCOL DESIGN
A. System Model
We consider a network setting where N pairs of secondary users opportunistically exploit one particular
radio channel (i.e., a frequency band) for their data transmission, which belongs a primary network.
Extension to a more general case with multiple channels will be discussed later. We assume that each pair
of secondary users can overhear transmissions from other pairs of secondary users (i.e., it is a collocated
network). It is further assumed that transmission from each individual pair of secondary users affects
one different primary receiver. Note that it is straightforward to extend this assumption to the scenario
where each pair of secondary users affects more than one primary receiver and/or each primary receiver
is affected by more than one pair of secondary users. The network setting under investigation is shown
in Fig. 1. In the following, we will refer to pair i of secondary users as secondary link i or flow i
interchangeably.
B. Spectrum Sensing
We assume that secondary links rely on a distributed synchronized MAC protocol to share the spectrum
when it is available. Specifically, time is divided into fixed-size cycles and it is assumed that secondary links
can perfectly synchronize with each other (i.e., there is no synchronization error) [8], [11]. It is assumed
that each secondary link performs spectrum sensing at the beginning of each cycle and only proceeds to
contend with others to capture the channel if the sensing outcome indicates an available channel (i.e., it
is not being used by nearby primary users). Detailed MAC protocol design will be elaborated in the next
subsection.
Let H0 and H1 denote the events that a particular primary user is idle and active, respectively (i.e., the
underlying channel is available and busy, respectively). In addition, let Pi
(H0) and Pi
(H1) = 1−Pi
(H0)
be the probabilities that secondary link i sees an idle and busy channel, respectively. We assume that
secondary users employ an energy detection scheme and let fs be the sampling frequency used in the
sensing period whose length is τ for all secondary links. There are two important performance measures,
which are used to quantify the sensing performance, namely detection and false alarm probabilities. In
particular, detection event occurs when a secondary link successfully senses a busy channel and false
2

…
One cycle
SensingSYN Backoff
DATA ACK DATA ACK
Backoff
time
Fig. 2. Timing diagram of the proposed MAC protocol.
alarm represents the situation when a spectrum sensor returns a busy state for an idle channel (i.e., a
transmission opportunity is overlooked).
Assume that transmission signals from primary users are complex-valued PSK signals while the noise
at the secondary links is independent and identically distributed circularly symmetric complex Gaussian
CN (0, N0) [2]. Then, the detection and false alarm probability for secondary link i can be calculated as
[2]
Pi
d εi
, τ = Q
εi
N0
− γi
− 1
τfs
2γi + 1
, (1)
Pi
f εi
, τ = Q
εi
N0
− 1 τfs
= Q 2γi + 1Q−1
Pi
d εi
, τ + τfsγi
, (2)
where εi
is the detection threshold for an energy detector, γi
is the signal-to-noise ratio (SNR) of the
PU’s signal at the secondary link, fs is the sampling frequency, N0 is the noise power, τ is the sensing
interval, and Q (.) is defined as Q (x) = 1/
√
2π ∞
x exp (−t2
/2) dt. These probabilities will be used in
throughput analysis in the next section.
C. MAC Protocol Design
We describe our proposed synchronized MAC for dynamic spectrum sharing among secondary flows
in this subsection. We assume that each fixed-size cycle of length Tcycle is divided into 3 phases, namely
sensing phase, synchronization phase, and data transmission phase. During the sensing phase of length τ,
all secondary users perform spectrum sensing on the underlying channel. Then, only secondary links whose
sensing results indicate an available channel proceed to the next phase (they will be called active secondary
users/links in the following). In the synchronization phase, active secondary users broadcast beacon signals
for synchronization purposes. Finally, active secondary users perform contention and transmit data in the
data transmission phase. The timing diagram of one particular cycle is illustrated in Fig. 2.
We assume that the length of each cycle is sufficiently large such that secondary links can transmit
several packets during the data transmission phase. Indeed, the current 802.22 standard specifies the
spectrum evacuation time upon the return of primary users is 2 seconds, which is a relatively large
interval. Therefore, our assumption would be valid for most practical cognitive systems. During the data
transmission phase, we assume that active secondary links perform a standard contention technique to
capture the channel similar to that employed by the CSMA/CA protocol. For simplicity, we assume a
fixed contention window equal to W is used for random backoff. Extension to the case where exponential
backoff [12] is employed will be discussed later.
Specifically, each active secondary link starts the contention by choosing a random backoff time
uniformly distributed in the range [0, W − 1] and starts decrementing its backoff time counter while
carrier sensing transmissions from other secondary links. Let σ denote a mini-slot interval, each of which
corresponds one unit of the backoff time counter. Upon hearing a transmission from any secondary
link, each secondary link will “freeze” its backoff time counter and reactivate when the channel sensed
3

idle again. Otherwise, if the backoff time counter reaches zero, the underlying secondary link wins
the contention and transmits one data packet to its intended receiver. The transmitter then waits for an
acknowledgment (ACK) from the receiver to indicate a successful reception of the packet. Standard small
intervals, namely DIFS and SIFS, are used before backoff time decrements and ACK packet transmission
as described in [12].
D. Throughput Maximization
Given the sensing model and proposed MAC protocol, we are interested in finding its optimal con-
figuration to achieve the maximum throughput subject to protection constraints for primary receivers.
Specifically, let NT (τ, W) be the normalized total throughput, which is a function of sensing time τ and
contention window W. Suppose that each primary receiver requires that detection probability achieved by
its conflicting primary link i to be at least P
i
d. Then, the throughput maximization problem can be stated
as follows:
max
τ,W
NT (τ, W)
s.t. Pi
d (εi
, τ) ≥ ¯Pi
d, i = 1, 2, · · · , N
0 < τ ≤ Tcycle, 0 < W ≤ Wmax,
(3)
where Wmax is the maximum contention window and recall that Tcycle is the cycle interval. In fact, optimal
sensing τ would allocate sufficient time to protect primary receivers and optimal contention window would
balance between reducing collisions among active secondary links and protocol overhead.
III. THROUGHPUT ANALYSIS AND OPTIMIZATION
We perform saturation throughput analysis and solve the optimization problem (3) in this section.
Throughput analysis for the cognitive radio setting under investigation is more involved compared to
standard MAC protocol throughput analysis (e.g., see [11], [12]) because the number of active secondary
links participating in contention in each cycle varies depending on the sensing outcomes. Suppose that all
secondary links have same packet length. Let Pr (n = n0) and T (τ, φ |n = n0 ) be the probability that n0
secondary links participating in contention and the conditional normalized throughput when n0 secondary
links join the channel contention, respectively. Then, the normalized throughput can be calculated as
NT =
N
n0=1
T (τ, W |n = n0 ) Pr (n = n0), (4)
where recall that N is the number of secondary links, τ is the sensing time, W is the contention window.
In the following, we show how to calculate Pr (n = n0) and T (τ, φ |n = n0 ).
A. Calculation of Pr (n = n0)
It is noted that only secondary links whose sensing outcomes in the sensing phase indicate an available
channel proceed to contention in the data transmission phase. There are two scenarios for which this can
happen for a particular secondary link i:
• The primary user is not active and no false alarm is generated by the underlying secondary link.
• The primary user is active and secondary link i mis-detects its presence.
Therefore, secondary link i joins contention in the data transmission phase with probability
Pi
idle = 1 − Pi
f εi
, τ Pi
(H0) + Pi
m εi
, τ Pi
(H1) , (5)
where Pi
m (εi
, τ) = 1 − Pi
d (εi
, τ) is the mis-detection probability. Otherwise, it will be silent for the
whole cycle and waits until the next cycle. This occurs with probability Pi
busy = 1 − Pi
idle. We assume
that interference of active primary users to secondary users is negligible; therefore, a transmission from
4

any secondary link only fails when it collides with transmissions from other secondary links. Now, let
Sk denote one particular subset of all secondary links having exactly n0 secondary links. There are
Cn0
N = N!
n0!(N−n0)!
such sets Sk. The probability of the event that n0 secondary links join contention in the
data transmission phase can be calculated as
Pr (n = n0) =
C
n0
N
k=1 i∈Sk
Pi
idle
j∈SSk
Pj
busy, (6)
where S denotes the set of all N secondary links, and SSk is the set of remaining N − n0 secondary
links. If all secondary links have the same SNRp and the same probabilities Pi
(H0) and Pi
(H1), then
we have Pi
idle = Pidle and Pi
busy = Pbusy = 1 − Pidle for all i. In this case, (6) becomes
Pr (n = n0) = Cn0
N (Pidle)n0
(1 − Pidle)N−n0
, (7)
where all terms in the sum of (6) become the same.
B. Calculation of Conditional Throughput
The conditional throughput can be calculated by using the standard technique developed by Bianchi
in [12] where we approximately assume a fixed transmission probability φ in a generic slot time. It was
shown in [12] that for a fixed contention window W, we have φ = 2/ (W + 1). Suppose there are n0
secondary links participating in contention in the third phase, the probability of the event that at least one
secondary link transmits is data packet can be written as
Pt = 1 − (1 − φ)n0
. (8)
However, the probability that a transmission occurring on the channel is successful given there is at least
one secondary link transmitting can be written as
Ps =
n0φ(1 − φ)n0−1
Pt
. (9)
The average duration of a generic slot time can be calculated as
¯Tsd = (1 − Pt) Te + PtPsTs + Pt (1 − Ps) Tc, (10)
where Te = σ, Ts and Tc represent the duration of an empty slot, the average time the channel is sensed
busy due to a successful transmission, and the average time the channel is sensed busy due to a collision,
respectively. These quantities can be calculated as [12]



Ts = T1
s = H + PS + SIFS + 2 ∗ PD+ACK+DIFS
Tc = T1
c = H + PS + DIFS + PD
H = HPHY + HMAC
, (11)
where HPHY and HMAC are the packet headers for physical and MAC layers, PS is the packet size, which
is assumed to be fixed in this paper, PD is the propagation delay, SIFS is the length of a short interframe
space, DIFS is the length of a distributed interframe space, ACK is the length of an acknowledgment.
Based on these quantities, we can express the conditional normalized throughput as follows:
T (τ, φ |n = n0 ) =
Tcycle − τ
¯Tsd
PsPtPS
Tcycle
, (12)
where ⌊.⌋ denotes the floor function and recall that Tcycle is the duration of a cycle. Note that
Tcycle−τ
¯Tsd
denotes the average number of generic slot times in one particular cycle excluding the sensing phase.
Here, we omit the length of the synchronization phase, which is assumed to be negligible.
5

C. Optimal Sensing and MAC Protocol Design
Now, we turn to solve the throughput maximization problem formulated in (3). Note that we can
calculate the normalized throughput given by (4) by using Pr (n = n0) calculated from (6) and the
conditional throughput calculated from (12). It can be observed that the detection probability Pi
d (εi
, τ)
in the primary protection constraints Pi
d (εi
, τ) ≥ ¯Pi
d depends on both detection threshold εi
and the
optimization variable τ.
We can show that by optimizing the normalized throughput over τ and W while fixing detection
thresholds εi
= εi
0 where Pi
d (εi
0, τ) = ¯Pi
d, i = 1, 2, · · · , N, we can achieve almost the maximum
throughput gain. The intuition behind this can be interpreted as follows. If we choose εi
< εi
0 for a
given τ, then both Pi
d (εi
, τ) and Pi
f (εi
, τ) increase compared to the case εi
= εi
0. As a result, Pi
idle
given in (5) decreases. Moreover, it can be verified that the decrease in Pi
idle will lead to the shift of the
probability distribution Pr (n = n0) to the left. Specifically, Pr (n = n0) given in (6) increases for small
n0 and decreases for large n0 when Pi
idle decreases. Fortunately, with appropriate choice of contention
window W the conditional throughput T (τ, W |n = n0 ) given in (12) is quite flat for different n0 (i.e., it
only decreases slightly when n0 increases). Therefore, the normalized throughput given by (4) is almost
a constant when we choose εi
< εi
0.
In the following, we will optimize the normalized throughput over τ and W while choosing detection
thresholds such that Pi
d (εi
0, τ) = ¯Pi
d, i = 1, 2, · · · , N. From these equality constraints and (2) we have
Pi
f = Q αi
+ τfsγi
(13)
where αi
=
√
2γi + 1Q−1 ¯Pi
d . Hence, the optimization problem (3) becomes independent of all detection
thresholds εi
, i = 1, 2, · · · , N. Unfortunately, this optimization problem is still a mixed integer program
(note that W takes integer values), which is difficult to solve. In fact, it can be verified even if we allow W
to be a real number, the resulting optimization problem is still not convex because the objective function
is not concave [13]. Therefore, standard convex optimization techniques cannot be employed to find the
optimal solution for the optimization problem under investigation.
Therefore, we have to rely on numerical optimization [14] to find the optimal configuration for the
proposed MAC protocol. Specifically, for a given contention window W we can find the corresponding
optimal sensing time τ as follows:
max
0<τ≤Tcycle
NT(τ, W) =
N
n0=1
T (τ, W |n = n0 )Pr (n = n0). (14)
This optimization problem is not convex because its objective function is not concave in general.
However, there exists an optimal solution τ∗
for this problem because the objective function is bounded
from above (because Pr (n = n0) < 1 and conditional throughput are all bounded) and its objective
function increases in small τ and decreases in large τ. This second property is formally stated in the
following proposition.
Proposition 1: The objective function NT(τ) of (14) satisfies the following properties
lim
τ→Tcycle
∂NT
∂τ
< 0, lim
τ→0
∂NT
∂τ
= +∞. (15)
Proof: Let us start the proof by defining the following quantities: ϕj
:= −
αj+
√
τfsγj
2
2
and cn0 :=
6

PsPtPS
Tcycle
. Taking the derivative of NT versus τ, we have
∂NT
∂τ
=
N
n0
cn0
CN
n0
k=1


−1
Tsd
i∈Sk
Pi
idle
j∈SSk
Pj
busy+
Tcycle−τ
Tsd
fs
8πτ
×



i∈Sk
γi
exp (ϕi
) Pi
(H0)
l∈Ski
Pl
idle
j∈SSk
Pj
busy
−
j∈SSk
γj
exp (ϕj
) Pj
(H0)
l∈SSkj
Pl
busy
i∈Sk
Pi
idle






. (16)
From this we have
lim
τ→Tcycle
∂NT
∂τ
=
N
n0
cn0
CN
n0
k=1
−1
Tsd i∈Sk
Pi
idle
j∈SSk
Pj
busy < 0. (17)
Now, let us define the following quantity
Kτ:=
N
n0
cn0
CN
n0
k=1



i∈Sk
γi
exp (ϕi
)Pi
(H0)
l∈Ski
Pl
idle
j∈SSk
Pj
busy−
j∈SSk
γj
exp (ϕj
)Pj
(H0)
l∈SSkj
Pl
busy
i∈Sk
Pi
idle


. (18)
Then, it can be verified that Kτ > 0. Therefore, we have
lim
τ→0
∂NT
∂τ
= +∞. (19)
Hence, we have completed the proof.
In summary, one can find the globally optimal (W∗
, τ∗
) by finding optimal τ for each W in its feasible
range [1, Wmax]. The procedure to find (W∗
, τ∗
) can be described in the following algorithm.
Algorithm 1 OPTIMIZATION OF COGNITIVE MAC PROTOCOL
1: For each W ∈ [1, Wmax], find the optimal τ according to (14), i.e.,
τ(W) = argmax
0<τ≤Tcycle
NT(τ, W) (20)
2: The globally optimal (W∗
, τ∗
) can then be found as
(W∗
, τ∗
) = argmax
W,τ(W)
NT(τ(W), W). (21)
Numerical studies reveal that this algorithm has quite low computation time for practical values of
Wmax and Tcycle.
Remark 1: The above analysis and optimization can be extended to the case where exponential backoff
with minimum contention window Wmin and maximum backoff stage m is employed. However, transmission
probability φ needs to be found as a fixed point solution of two equations [12], which is used to calculate
conditional throughput in Section III.B. In this case, Wmin and τ will be optimization variables.
Remark 2: We can extend the presented MAC protocol design to the case where there are multiple
channels. To exploit spectrum holes in this case, we assume that there is one control channel which
belongs to the secondary network (i.e., it is always available) and M data channels whose states (i.e.,
idle or busy) change over time. We further assume that each secondary user has two transceivers one
which is always tuned to the control channel while the remaining one may be switched to different data
channels. We can design a multi-channel synchronized MAC protocol for this setting as follows. Each
cycle is still divided into 3 phases as before. However, in the sensing phase each secondary link needs to
7

8 16 32 64 128 256 512 1,000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Contention window (W)
Throughput(NT)
Throughput vs contention window
N = 2
N = 5
N = 10
N = 15
N = 20
Fig. 3. Normalized throughput versus contention window W for τ = 1ms and different N.
0 0.5 1 1.5 2 2.5 3 3.5
x 10
−3
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
Sensing time (τ)
Throughput(NT)
Throughput vs sensing time
N = 30
N = 20
N = 2
N = 5
N = 10
Fig. 4. Normalized throughput versus the sensing time τ for W = 32 and different N.
sequentially perform spectrum sensing on all data channels. Therefore, by the end of the first phase each
secondary link i has a list of available channel Ci.
In the data transmission phase, active secondary links who find at least one available channel contend
on the control channel to choose a data channel for their transmissions. Again, contention is performed by
using the CSMA-based random backoff mechanism and secondary links winning the contention exchange
RTS/CTS which contains information about one chosen data channel for data transmission as well as
the packet length to be transmitted (for other secondary users to update their network allocation vector
(NAV)). Note that because all secondary users have one transceiver tuned to the control channel, they
always know which channels are being used by other secondary users. Due to the space constraint,
analysis and optimization of this multi-channel MAC protocol are not pursued further in this paper.
IV. NUMERICAL RESULTS
We present numerical results to illustrate throughput performance of the proposed cognitive MAC
protocol. We take key parameters for the MAC protocol from Table II in [12]. Other parameters are chosen
as follows: cycle time is Tcycle = 100ms; mini-slot (i.e., generic empty slot time) is σ = 20µs; sampling
frequency for spectrum sensing is fs = 6MHz; bandwidth of PUs’ QPSK signals is 6MHz. The signal-
to-noise ratio of PU signals at secondary links SNRi
p are chosen randomly in the range [−15, −20]dB.
The target detection probability for secondary links and the probabilities Pi
(H0) are chosen randomly in
the intervals [0.7, 0.9] and [0.7, 0.8], respectively.
In Fig. 3, we show normalized throughput NT versus contention window W for different values of
N when the sensing time is fixed at τ = 1ms for one particular realization of system parameters. The
maximum throughput on each curve is indicated by a star symbol. This figure indicates that the maximum
throughput is achieved at larger W for larger N. This is expected because larger contention window
can alleviate collisions among active secondary for larger number of secondary links. It is interesting to
8

0
0.5
1
1.5
x 10
−3
0
0.02
0.04
0.06
0
0.2
0.4
0.6
0.8
1
Sensing time (τ)
Throughput vs transmission probability and sensing time
Transmission
probability (φ)
Throughput(NT)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
NT opt (0.0003, 0.0125) = 0.8542
Fig. 5. Normalized throughput versus sensing time τ and transmission probability φ for N = 15.
0
2
4
6
8
x 10
−4
0
0.02
0.04
0.06
0
0.2
0.4
0.6
0.8
1
Sensing time (τ)
Throughput vs transmission probability and sensing time
Transmission
probability (φ)
Throughput(NT)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
NT opt (0.0002, 0.0091) = 0.8546
Fig. 6. Normalized throughput versus sensing time τ and transmission probability φ for N = 20.
observe that the maximum throughput can be larger than 0.8 although Pi
(H0) are chosen in the range
[0.7, 0.8]. This is due to a multiuser gain because secondary links are in conflict with difference primary
receivers.
In Fig. 4 we present the normalized throughput NT versus sensing time τ for a fixed contention window
W = 32 and different number of secondary links N. Again, the maximum throughput is indicated by a
star symbol on each curve. This figure confirms the fact that the normalized throughput NT increases
when τ is small and decreases with large τ as being proved in Proposition 2. In addition, the normalized
throughput NT is not a concave function of τ for large N. Moreover, for a fixed contention window
optimal sensing time indeed decreases with the number of secondary links N. Finally, the multi-user
diversity gain can also be observed in this figure.
To illustrate the joint effect of contention window W and sensing time τ, we show the normalized
throughput NT versus τ and transmission probability φ for N = 15 and N = 20 in Fig. 5 and Fig. 6,
respectively. Recall that the transmission probability can be calculated from contention window W as
φ = 2/(W + 1). We show the globally optimal parameters (φ∗
, τ∗
) which maximize the normalized
throughput NT of the proposed cognitive MAC protocol by a star symbol in these two figures. These
figures reveal that the performance gain due to optimal configuration of the proposed MAC protocol
is very significant. Specifically, while the normalized throughput NT tends to be less sensitive to the
transmission probability φ, therefore the contention window W, it decreases significantly when the sensing
time τ is deviated from the optimal value τ∗
. Therefore, the proposed optimization approach would be
9

very useful in achieving the largest throughput performance for the secondary network.
V. CONCLUSION
In this paper, we have designed, analyzed, and optimized a MAC protocol for cognitive radio networks
that explicitly take into account spectrum sensing performance. Specifically, we have derived the normal-
ized throughput of the proposed MAC protocol as a function of sensing time, contention window and
other system parameters. Then, we have showed how to choose detection thresholds for energy spectrum
sensors, sensing time, and contention window to maximize the normalized throughput subject to protection
constraints for primary receivers. In addition, we have presented numerical results to confirm important
theoretical findings in the paper and show the significant performance gain achieved by the optimal
configuration for proposed MAC protocol. Finally, several potential extensions including consideration of
exponential backoff and multi-channel scenario have been discussed.
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