Cognitive radio has been recently considered a promising technology to improve spectrum utilization by enabling secondary access to licensed bands that are not used by primary users temporarily or spatially. A prerequisite to this secondary access is the lack of interference to the primary system. This requirement makes spectrum sensing a key process for cognitive radio. In this study, we consider amplify and forward (AF)based cooperative spectrum sensing for cognitive radio networks where multiple relay nodes are utilized to amplify and forward the primary user signal for better spectrum sensing, and maximum ratio combining is used for fusion detection by a cognitive coordinator. Further, the detection probability and the bit error rate of AFbased cooperative spectrum sensing are analyzed in fading multiple cognitive relay channels. The simulation results show that the AFbased cooperative spectrum sensing scheme outperforms the conventional scheme.
I. INTRODUCTION
In wireless communication, spectrum utilization plays a vital role. A spectrum is shared by a licensed user (primary user [PU]); however, most of the time the spectrum remains underutilized, particularly in the case of a television (TV) band.
Cognitive radio provides an excellent solution to this spectrum scarcity problem by utilizing the underutilized bands, in which unlicensed users (secondary users [SUs]) access and utilize the spectrum when the PU is not present. The key features of a cognitive transceiver are radio environment awareness and spectrum intelligence
[1]
. Intelligence can be achieved by learning the spectrum environment and adapting the transmission parameters. For instance, SU attempts to detect the activities of PU, and if there are no PU activities, then SU gets access to the spectrum such that dynamic spectrum access can be achieved
[2

5]
.
However, realization of the cognitive radio requires a strong guarantee of no interference to the licensed user. This motivates research on spectrum sensing and related technologies. At present, local spectrum sensing does not meet the requirement of reliable detection of the PU because of its limitations in the fading environment
[6]
.
Therefore, cooperative spectrum sensing is introduced as a key to reduce the probability of interference to legacy systems
[7]
. Traditionally, three methods are used for performing spectrum sensing
[8]
: energy detection (noncoherent detection through received energy), matched filter (coherent detection through maximization of signaltonoise ratio [SNR]), and cyclostationary feature detection (exploitation of the inherent periodicity of the primary signal). Among them, the energy detector is the most popular method. To improve the spectrum sensing accuracy, cooperative sensing makes use of the information exchange among SUs.
In
[9]
, a twouser cooperative model is compared with noncooperative systems. Detection probability is increased while the sensing time is decreased by 35%, which is important for longterm sensing. Further, Atapattu et al.
[10]
evaluated the performance of the energy detector in a Rayleigh fading channel and demonstrated a reduction of both the detection probability and the falsealarm probability.
In this study, we consider amplify and forward (AF)based cooperative spectrum sensing in a cognitive radio network where multiple relay nodes are utilized to amplify and forward the primary user signal for better spectrum sensing, and maximal ratio combining is used for fusion detection by a cognitive coordinator. We also analyze the probability of detection and the bit error rate (BER) of the AFbased cooperative spectrum sensing. The simulation results show that the AFbased cooperative spectrum scheme outperforms the conventional scheme.
The rest of this paper is organized as follows: In Section II, we describe the proposed system model. In Section III, we analyze the detection probability and the BER of AFbased cooperative spectrum sensing. In Section IV, we present the simulation and numerical results. Finally, we draw conclusions in Section V.
II. SYSTEM MODEL
 A. Channel Model
A wireless network is assumed to cooperate over an independent and not necessarily identically distributed Rayleigh fading channel. Let
h_{pucc}
be the fading for the PU → CC link; the magnitude of
h_{pucc}
is calculated using the probability density function (pdf) as follows
[11]
:
where
E
(
h_{pucc}
)
^{2}
) = 1 and
E
(.) denotes the expectation.
Additive white Gaussian noise, denoted by
w_{pu}
at node PU, is assumed to be a circulatory symmetric complex Gaussian random variable with a zero mean and variance
N_{0}
such that we have
w_{pu}
~
CN
(0,
N_{0}
).
 B. AFbased Cooperative Spectrum Sensing
In AFbased cooperative spectrum sensing, relays receive information from the PU, and then amplify and forward this information to the cognitive coordinator by using the AF relay protocol. The relay nodes amplify both information and noise. The cognitive coordinator (fusion center) uses the energy detector method to decide the presence or absence of the PU by comparing with the detection threshold value.
Let us consider the model illustrated in
Fig. 1
; it has
n
cognitive relays, i.e., (
r
_{1}
,
r
_{2}
,
r
_{3}
, …
r
_{n}
), where all the relay nodes listen to the PU when the PU starts using the spectrum. Instead of taking the decision about the presence or absence of the PU, the relays just amplify and forward the PU’s signal to the cognitive coordinator. In order to avoid the interchannel interference, communication between relays and the cognitive coordinator should be orthogonal. For example, the cognitive coordinator may use time division multiple access (TDMA) to receive a signal from the PU and cognitive relays.
The cognitive coordinator combines all signals using maximal ratio combining (MRC), compares the output of the energy detector with the threshold value, and decides on the presence or absence of the PU. In the next subsection, single and multiple cognitive relays are discussed.
 1) Single Cognitive Relay Communication
Single cognitive relay communication consists of the PU, a cognitive relay node, and a cognitive coordinator. The signal received by the cognitive relay
y_{pur}
=
θxh_{pur}
+
w_{r}
where
θ
shows the PU action,
θ
= 1 PU present or
θ
= 0 PU absent;
x
denotes the transmitted signal from the PU.
h_{pur}
denotes the channel gain between the PU and the cognitive relay, and
w_{r}
represents the noise at the cognitive relay and has a transmission power of
E_{c}
. The amplification factor
α_{r}
denotes the power transmitted for the PU, as follows:
Cooperative network with cognitive relays.
Now, the received power at the cognitive coordinator is
For the energy detector, we use the signal squaring method. The detector at the cognitive coordinator uses a binary hypothesis such that we have
The output of the signal squaring method
Y
is used for solving the pdf of
y
as follows
[6]
:
where Γ(.) denotes the gamma function,
I_{n}
(.) represents the
n
^{th}
order modified Bessel function of the first type, and
u
=
TW
, where
T
and
W
are chosen to restrict
u
to an integer value. The total endtoend SNR, denoted by
γ
is calculated as follows
[12]
:
where
denote the SNR of the link from the PU to the relay node, and from the relay node to the cognitive coordinator, respectively.
 2) Multiple Cognitive Relay Communication
In multiple cognitive relay communication, there are n cognitive relay nodes, the PU, and the cognitive coordinator, as shown in
Fig. 1
.
All the cognitive relay nodes receive the signal from the PU through an independent fading channel.
The amplification factor is calculated as
Each cognitive relay node amplifies the signal and forwards it to the cognitive coordinator. All cognitive relay nodes are orthogonal to each other and forward information to the cognitive coordinator. Further, such an orthogonal channel can be realized by TDMA. The MRC ratio is used at the cognitive coordinator.
The SNR of γ is calculated as follows:
where
γ_{puri}
and
γ_{ricc}
represent the SNR from the PU to the relay nodes, and from the relay nodes to the cognitive coordinator, respectively.
However, the transmission between the PU and the cognitive coordinator can also take place by a direct link. The SNR of the cognitive coordinator and the single relay can be calculated as follows:
Further, the total SNR of the cognitive coordinator and the multiple relays can be calculated as follows:
III. PERFORMANCE ANALYSIS
In this section, we analyze the performance of AFbased cooperative spectrum sensing in terms of the average detection probability and the BER. To this end, we assume that the energy detection is used at the cognitive coordinator to make a decision regarding whether the PU is active or not, on the basis of the output of the energy detector,
Y
. The probability of detection (
p_{d}
) and the probability of a false alarm (
p_{f}
) are evaluated by using
P
(
Y
>
λ
/
H
_{1}
) and
P
(
Y
>
λ
/
H
_{0}
) , respectively. They further can be evaluated as follows
[6]
:
where
Q_{U}
(.,.) denotes the generalized Marcum Qfunction and Γ(.,.) represents the upper incomplete gamma function, which is defined by the integral form
and Γ(
a
,0) = Γ(
a
).
 A. Average Detection Probability over a Fading Channel
The probability of a false alarm is independent of γ; thus, the probability of a false alarm over a fading channel can be calculated using Eq. (11). On the other hand, the probability of detection is a function of γ. Thus, the average probability of detection can be calculated by averaging Eq. (12) over the fading channel such that we have
where
f_{Y}
(
γ
) denotes the pdf of the SNR under fading.
For measuring
f_{YAF}
(
γ
), we calculate the cumulative distribution function (CDF) and the pdf of
γ_{min}
. Thus, CDF can be calculated as follows:
For calculating pdf, we take a derivative of Eq. (14), and we have
The pdf of
γ_{AF}
is an independent channel and can be expressed as follows
[13]
:
An alternative representation of the generalized Marcum Qfunction can be expressed as follows
[11]
:
By substituting (16) and (17) in Eq. (13), we can calculate the average probability as follows:
This is the upper bound expression of AFbased cooperative spectrum sensing for average probability detection. When there is no relay cooperation, the average probability of detection for a direct link can be expressed as follows:
In the next section, we describe the BER analysis.
 B. Bit Error Rate Analysis
As the probability of detection increases, the BER at the cognitive coordinator decreases. The BER is calculated with MRC in a Rayleigh fading channel. The instantaneous equivalent endtoend SNR is given in Eq. (5). The most vital feature of a cooperative relay is CDF. The CDF of the ith relay can be expressed as follows:
F
(
γ
) denotes the outage probability evaluated at threshold γ; therefore, under the independent channel assumption of the joint CDF, we can express
F
(
γ
) as follows:
where
F
(
γ_{i}
) denotes the CDF of the ith path.
The conditional bit error probability for different modulation schemes can be formulated as follows
[11]
:
where
Q
(.) denotes the Gaussian Qfunction and
c
represents the constant determined by the modulation scheme. For example,
c
= 2 in the case of binary phase shift keying. Therefore, the average BER (ABER) is defined as follows:
where
p
(
γ
) denotes the joint pdf of the instantaneous SNR for the sequence
γ_{i}
, and
i
= 1, …,
M
.
Under the independent channel assumption and by using Eq. (21), we can express the joint pdf in terms of the joint CDF as follows:
By substituting (22) in (23), we can express the ABER as follows:
IV. SIMULATION AND NUMERICAL RESULTS
In this section, we describe the simulation of the AFbased cooperative spectrum sensing scheme for the probability of detection and BER. The Rayleigh fading channel and MRC are simulated in MATLAB for calculating the probability of detection and the BER. We have simulated the receiver operating characteristic (ROC) for the detection of the probability of AFbased cooperative spectrum sensing with different values of the amplification factor.
From
Fig. 2
, it can be observed that the detection probability increases with an increase in the amplification.
Figs. 3
and
4
depict the BER analysis with SNR for direct (noncooperative) and cooperative links with different amplification factors. The BER decreases with an increase in the amplification factor. Further, with an increase in the amplification factor, the probability of detection increases.
In the BER analysis, it can be observed from the figures that the BER decreases with an increase in the amplification factor. However, keeping in view the tradeoff between the amplification factor and the power, the amplification factor should not be very high.
Receiver operating characteristic curve of amplify and forwardcooperative spectrum sensing with different values of amplification factor(AF), α.
Bit error rate of noncooperative link and amplify and forwardrelay when amplification factor (AF) is 2.
Bit error rate of noncooperative link and amplify and forwardrelay when amplification factor (AF) is 3.
V. CONCLUSION
In this study, the performance of AFbased cooperative spectrum sensing was investigated in terms of the detection probability and the BER. It was observed that the cooperative relay played a vital role in improving the performance of the detection of the PU in an environment with the most interference; this directly affected the BER, which was an important factor for the sensing and transmission.
Acknowledgements
This work was supported by a National ResearchFoundation of Korea (NRF) grant funded by the Koreangovernment (NRF2013R1A2A2A05004535 and NRF2012R1A1A2038831).
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