Due to the low utilization and scarcity of frequency spectrum in current spectrum allocation methodology, cognitive radio networks (CRNs) have been proposed as a promising method to solve the problem, of which spectrum sensing is an important technology to utilize the precious spectrum resources. In order to protect the primary user from being interfered, most of the related works focus only on the restriction of the missed detection probability, which may causes overprotection of the primary user. Thus the interference probability is defined and the interferenceaware sensing model is introduced in this paper. The interferenceaware sensing model takes the spatial conditions into consideration, and can further improve the network performance with good spectrum reuse opportunity. Meanwhile, as so many fading factors affect the spectrum channel, errors are inevitably exist in the reporting channel in cooperative sensing, which is improper to be ignored. Motivated by the above, in this paper, we study the throughput tradeoff for interferenceaware cognitive radio networks over imperfect reporting channel. For the cooperative spectrum sensing, the KoutofN fusion rule is used. By jointly optimizing the sensing time and the parameter K value, the maximum throughput can be achieved. Theoretical analysis is given to prove the feasibility of the optimization and computer simulations also shows that the maximum throughput can be achieved when the sensing time and the parameter of K value are both optimized.
1. Introduction
W
ith the rapid advances of wireless communication technology and the constraint of the current legacy commandandcontrol regulation, frequency spectrum is near its depletion
[1]
. However, it is known to all that the assigned spectrum is underutilized in spatial or temporal dimension. Therefore, the spectrum scarcity results from the fixed spectrum assignment policy rather than the physical scarcity of spectrum. In order to solve the problem of the spectrum scarcity, cognitive radio (CR) is proposed to hold the promise of a new frontier in wireless communications
[2]

[5]
. Since detecting the spectrum hole is an essential method to reuse the registered spectrum, the spectrum sensing function becomes one of the key technologies of the cognitive radio
[6]

[7]
.
Spectrum sensing, as a fundamental problem in CR, request the secondary user (SU) to efficiently and effectively detect the presence of the primary user (PU)
[8]

[10]
. Especially, in recent years, a hot technology come to people’s eyes called wideband spectrum sensing. The wideband spectrum sensing technology aims to find more spectral opportunities over wide frequency range and achieve higher opportunistic aggregate throughput in cognitive radio networks, thus can further improving the dynamic spectrum utilization
[11]

[12]
. However, due to many environmental factors such as low signaltonoise radio (SNR), multipath fading and shadowing, the sensing performance may be inherently limited, which makes the spectrum sensing problem more involved. In order to further improve the sensing performance, cooperative spectrum sensing (CSS) has been studied extensively
[13]

[17]
. In CSS, cooperative users (CUs) individually sense the channels and then send information to the secondary user, through proper fusion of the collected information, the SU will make the final decision. There are various cooperative sensing schemes to fuse the sensing information of the secondary users. The schemes can be classified into hard decision based fusion, soft decision based fusion
[9]
and data based fusion schemes
[13]
. In this paper, we consider hard decision fusion, such as KoutofN fusion rule
[14]
, as it requires the least communication overhead and is easy to implement.
However, most of the related works about cooperative spectrum sensing are based on the perfect reporting channel. In practice, the reporting channels in CSS also experience many environmental factors such as multipath fading and lognormal shadowing. This will typically deteriorate the transmission reliability of the sensing results reported from the CUs to the SU. Eventually, the performance of cooperative spectrum sensing will be degraded by the imperfect reporting channels. Sometimes the fading in reporting channel cannot be ignored
[18]
.
In order to analyze the performance of the spectrum sensing, two basic parameters of detection probability and false alarm probability are widely used and accepted by the world
[19]

[22]
. The higher the detection probability get, the better the PU can be protected from the interference of SU. Meanwhile, the lower the false alarm probability, the more chances the SU can have to reuse the registered channel. Thus, a fundamental tradeoff is appeared between the two probabilities. In order to improve the spectrum sensing performance, several system models aimed at optimizing the tradeoff are established and are widely accepted for spectrum sensing. Specifically,
[22]
designed a frame structure and holds the classical idea that a longer sensing time will get a higher detection probability as will as a lower false alarm probability. But within a fixed frame size, the longer sensing time will shorten the data transmission time of the secondary users. Thus, an optimal tradeoff of sensing and throughput is investigated in
[22]
. However,
[22]
ignores the influence made by the spatial environment. In fact, the distance between PU and SU may have an impact on the sensing performance. Based on this idea,
[23]
introduces a new concept named interferenceaware spectrum sensing that takes the distance between PU and SU into the consideration. It argues that even SU makes a missed detection, there still exists the case that SU does not interfere with PU due to the actual spatial distances between PU and SU. Finally, the sensing performance is well analyzed in this interferenceaware sensing model.
Motivated by the above considerations, in this paper we firstly introduce the interferenceaware spectrum sensing model. Then by using the KoutofN fusion rule as the basis, the issue of sensingthroughput tradeoff in interferenceaware cognitive radio networks over imperfect reporting channel is investigated. Finally, the optimization problem of the tradeoff is formulated and the achievable throughput is maximized by jointly optimizing the sensing time and the fusion parameter K along the distance between PU and SU. The analytical and numerical results obtained in this paper clearly show that the maximum throughput can be achieved when the sensing time and the parameter K value of CSS are both optimized.
2. System Model
 2.1 Network Model
As can be seen from
Fig.1
, we consider a cognitive radio network where a SU is looking for a chance to access the registered spectrum band. Around the SU, several cooperative users are performing the sensing process to help the SU for the final decision. Denote R as the radius of PU and the d as the distance between PU and SU. A synchronous system is assumed and a frame structure of periodic spectrum sensing is presented. In each sensing period T, we further divided the sensing period into two slots, the sensing slot and the transmission slot. During the sensing slot, each cooperative user performs its spectrum sensing individually, then report the sensing result to the SU, finally the SU determines the state of PU based on the spectrum sensing information of each CU.
System model of cognitive radio network (R: radius of PU; d: the distance between PU and SU)
Because of the complicated environment factors, the CUs make a mistake during spectrum sensing inevitably. If the PU is active while SU makes a missed detection, the SU will have the opportunity to use the frequency band. However, this behavior may bring interference to PU due to the distance d. Thus, the probability of interference is taken into consideration with the missed detection made by SU to further analyze the effects SU made to PU. The specific analysis of the probability of interference will be showed in the following part. The main work of this paper is to maximize the performance of spectrum sensing in interferenceaware cognitive radio networks over imperfect report channel.
 2.2 Sensing Model
For each CU, the energy detection scheme is proposed. Suppose
y_{i}
(
n
) represents the received signal of SU i during the sensing time, then the PU’s detection problem can be figured out as a binary hypothesis test between the following two hypotheses.
Where H
_{0}
and H
_{1}
denote that the PU is absent and present respectively.
x_{i}
(
n
) is the PU signal received at the CU i.
w
(
n
) is the background noise.
N_{i}
is the number of samples. Here we assume that the background noise is AWGN and the PU signal is a Gaussian signal.
In order to decide whether the PU is present, a test statistic is needed for the CU to calculate:
Based on the test statistic
Z_{i}
, by letting
θ_{i}
be the detection threshold, the CU then makes a binary decision regarding the presence of the primary user as follows:
As the CUs make individual sensing decision, let
τ_{i}
the sensing time,
f_{s}
the sampling frequency and
N_{i}
the number of samples (
N_{i}
=
τ_{i}
f_{s}
) of the CU i. If the number of samples
N_{i}
is adequately large (e.g.
N_{i}
⎕ 10), the distribution
f_{Z}
(
z
) of the test statistic Z can be approximated using the central limit theorem,
Where
P
is the average received power of the primary signal by SU and
σ
^{2}
is the AWGN variance.
Thus the probabilities of false alarm and missed detection for each CU can be defined and calculated as follows
[23]
:
 2.3 Cooperative Spectrum Sensing
CSS can address problems posed by low SNR, shadowing, and fading. In this paper, we consider the KoutofN decision fusion rule in CSS. Under the KoutofN fusion rule, each CU makes a binary decision based on its local observation and then forwards one bit of the decision
D_{i}
(1 standing for the presence of the PU, 0 for the absence of the PU) to the SU through the reporting channel. At the SU, all 1bit decisions are fused together according to logic rule
denote the inferences drawn by the SU after the decision fusion that the PU is active or not. It can be seen that the OR counting rule and the AND counting rule are the especial case of the KoutofN rule. The OR rule corresponds to the case of
K
=1 and the AND rule corresponds to the case of
K
=
N
.
We assume that, compared with the distance from any CU to the PU, the distance between any two CUs is small, so that the received signal at each CU experiences almost identical path loss. Also, the CUs are assumed to performing same performance. Thus this results in that the false alarm probability and the detection probability of each CU is independent of each other. Let
P_{f}
denote the false alarm probability,
P_{d}
denote the detection probability. Therefore, based on the Koutof N fusion rule, the final probability of false alarm and the final probability of detection after fusion are given as follows:
 2.4 Imperfect Reporting Channel
In practice, the reporting channels between the CUs and SU will also experience fading and shadowing. This will typically deteriorate the transmission reliability of the sensing results reported from the CUs to SU. For example, if a CU detects that the PU is present and then reports the sensing result to SU through a realistic fading channel, the SU will probability receive an error result that the PU is absent due to the complicated channel factors. Eventually, the performance of cooperative spectrum sensing will be degraded by the imperfect reporting channels.
In this paper, as all CUs transmit their binary sensing decision to SU, we assume that the reporting channel is a binary symmetric channel (BSC). Let
P_{e}
denote the error probability of signal transmission over the reporting channel. Then, the final probability of detection and the final probability of false alarm over the imperfect reporting channel can be given as
 2.5 Probability of Interference
As can be seen from
Fig. 1
, we consider the worst case in this paper that the primary receiver (PR) just lies in the intersection of the primary transmitter (PT) coverage boundary and the line connecting the PT and the SU. Whenever SU makes a missed detection, if SU lies within the radius of PT, then the SU does not have the access to the registered frequency band or it will cause interference to the PU without any doubt. Else if ST lies outside the radius of PT, we can figure out the PR’s received SNR
γ
by denoting
P_{P}
as the PU power received by PR and
P_{C}
as the power of secondary signals received by PR. Only when the cases occurs that the received SNR
γ
of PR is smaller than the desired SNR
γ_{t}
, rather than any missed detection, can we draw a conclusion that the PU is interfered by the SU. Thus the probability of interference can be defined and calculated as
[23]
Where M is the number of symbols in one packet during the reception.
3. Problem Formulation
In this section, in order to maximize the average throughput of cognitive radio networks, we jointly consider the problems of spectrum sensing parameter setting and CU assignment in cooperative spectrum sensing. The optimization problem is formulated under decision fusion rule.
There are two scenarios for which the secondary network can operate at the registered channel:
1. When the PU is absent and no false alarm is generated by SU. In this scenario, the achievable throughput of secondary networks is figured as
2. When the PU is present but is estimated to be absent by SU (missed detection). In this scenario, an interference that made by SU to PU is engendered inevitably. However, taking the spatial conditions into consideration, the influence of SU to PU also changes along with the variation of the distance between the PU and the SU. Thus, avoiding the overly protection, the achievable throughput of this scenario is expressed as
Let
P_{S}
be the power of secondary signals received by the SU and
N
_{0}
be the noise power. Then the throughput of the secondary network when the PU is absent and the PU is present can be respectively expressed as
C
_{0}
and
C
_{1}
, the corresponding formulas are written as follows:
Thus the average throughput of the cognitive radio network is given as
From (17) and (18) we can see that the achievable throughput is the function of sensing time
τ
, the detection probability
Q_{d}
and false alarm probability
Q_{f}
. By the constraint condition of the missed detection probability
Q_{MD}
is satisfied, we are able to determine a threshold
θ
with a certain K value and the sensing time
τ
.
Thus, by combining the formula (5), (6), (10) and (11), it is clearly that the optimal goal is the function of the parameter K value and sensing time
τ
. So, the main work in this paper is to maximize the achievable throughput by jointly optimizing the sensing time and the K value of the fusion rule in cooperative spectrum sensing over imperfect reporting channel.
Then the average achievable throughput of the cognitive radio network is reduced to
4. Performance Analysis
Lemma 1:
∀
d
, the maximum throughput is achieved with equality constraint in (21).
Proof:
For a given distance d, if a given sensing time
τ
and a K value is given, then let
θ
be the particular threshold that is certain to satisfy the constraint condition
Q_{MD}
(
K
,
τ
,
θ′
)
P_{I}
=
ε
, for any other threshold
θ′
that satisfy
θ
≤
θ
, we have
Q_{d}
(
K
,
τ
,
θ′
)
P_{I}
≥
Q_{d}
(
K
,
τ
,
θ
)
P_{I}
, thus
Q_{MD}
(
K
,
τ
,
θ′
)
P_{I}
≤
ε
which meets the condition in (21), however, from (13) and (14) we can deduce that
R
_{0}
(
K
,
τ
,
θ′
)≤
R
_{0}
(
K
,
τ
,
θ
) and that
R
_{1}
(
K
,
τ
,
θ′
)≤
R
_{1}
(
K
,
τ
,
θ
), so
R
(
K
,
τ
,
θ′
)≤
R
(
K
,
τ
,
θ
). This proves that the maximum throughput is achieved only with the equality constraint in (21).
Theorem 1:
under the interferenceaware condition with imperfect reporting channel that described in (20) and (21), for a given K, at any distances between PU and SU, there exists an optimal sensing time in the range of [0,T] which yields the maximum achievable throughput for the CRN.
Proof:
From lemma 1, we get the optimal condition that
Q_{MD}P_{I}
=
ε
. Meanwhile, because of the implicit constraint that 0 ≤
Q_{MD}
≤ 1, we divide
Q_{MD}
into the following two cases:
Case 1:
If
ε
/
P_{I}
<1, then the optimal value of
Q_{MD}
can be written as
Q_{MD}
=
ε
/
P_{I}
. According to (20), we have
For a fixed distance, we can get the differential equation from (22) that
From the above we can get that
Up to now, a conclusion can be reached that there exists an optimal sensing time to obtain the maximum achievable throughput within interval (0, T). Then exhaustive search is needed to help finding the optimal sensing time, by which the maximum achievable throughput can also be calculated.
Case 2:
If
ε
/
P_{I}
≥ 1, then the optimal value of
Q_{MD}
can be written as
Q_{MD}
= 1. According to (20), we have
We can see that it is a special case of (22). Thus we have
Obviously,
Thus, there is a maximum point of
R
(
τ
) within interval (0, T). Also, we can get the best sensing time by the exhaustive search, as well as the maximum achievable throughput.
Theorem 2:
under the interferenceaware condition with imperfect reporting channel that described in (20) and (21), for a given sensing time
τ
, at any distances between PU and SU, there exists an optimal K value which yields the maximum achievable throughput for the CRN.
Proof:
When the K is small, only less number of CUs can decide the existing of the PU, which raises the false alarm probability, while if the K is large to some degree, the probability of missed detection will be raised up, to some extent, may exceed the constraint condition. Especially when taking the imperfect reporting channel into consideration, the sensing information sending to the SU is not always true, so the analysis of cooperative spectrum sensing is more complex. Thus, an optimal K is existed for the maximum throughput of CRN.
There is no closedform solution for the optimal K in this optimization. However, since K is an integer, it is not computationally expensive to search the optimal K that maximizing the achievable throughput.
5. Performance Evaluation
In this section, computer simulation results are presented to evaluate the throughput tradeoff in interferenceaware cognitive radio networks over imperfect reporting channel. Koutof N fusion rule is used for final decision and each cooperative user is assumed to use the energy detector for local sensing. Simulations are carried out to find the optimal K value and sensing time
τ
at each distance between the PU and SU which achieve the maximum throughput while provide sufficient protection to the primary user simultaneously.
Let the radius of primary cell be 500m and the probability of activity PU be
P
(
H
_{1}
)=10.5. The error probability of the reporting channel is
P_{e}
=0.01. The number of CUs is
N
=10. The transmit power of PU and SU are respectively 30 dBm and 20 dBm, the noise variance is set to 100 dBm. The bandwidth of the PU is set to 30kHz, the sensing period
T
=100
ms
. The constraint for protection is
ε
= 0.05 and the desired SNR of the PU is
γ_{t}
= 8
dB
.
Fig. 2
describes the optimal K in the Koutof N fusion rule cooperative spectrum sensing at different distances. Based on the searching algorithm, the optimal problem can be solved and the optimal K values are achieved along the distance between the PU and the SU. From the figure we can see that there is no single K value that meets the optimal problem for all the distances, thus, an optimal K is needed to achieve the maximum throughput of the cognitive radio network.
Optimal K that maximize the achievable throughput
Fig. 3
indicates the optimal sensing time of the cooperative spectrum sensing at different distances. Based on the interferenceaware sensing frame model, the selection of sensing time should be taken into consideration also. A short sensing time may cause lower detection performance, then decrease the final CRN throughput. If the sensing time is longer to some extent, although the detection performance is higher, the transmission time is shorter, which can also decrease the final achievable throughput. Thus, an optimal sensing time is also exists for the maximum achievable throughput.
Optimal sensing time that maximize the achievable throughput
According to the pair of K value and the sensing time, then the special achievable throughput is calculated. Thus, if the optimal K value and optimal sensing time is gotten, the maximum throughput should be achieved. The numerical results will be provided to certify the conclusion in the following part.
Fig. 4
shows the maximum achievable throughput of optimal sensing time at each distance. The cases when the sensing time is fixed at
τ
=0.001
s
and
τ
=0.015
s
are compared in
Fig. 4
. As a common condition, the K value is optimized in the three cases along the distance between the PU and the SU. From
Fig. 4
we can see that when the SU is quite near to PU (e.g.
d
≤800
m
),
Q_{f}
is much too small that we should decrease the sensing time to get longer transmission time rather than further lessen
Q_{f}
; however, when the SU goes far away from the PU (e.g.
d
≥1580
m
), SU is almost interferencefree to PU, we should also try to reduce the sensing time in order to prolong the transmission time; when the distance lies between the two cases, as
Q_{f}
increases, longer sensing time should be taken when consider the overall throughput which both influenced by the false alarm probability and the transmission time. So, detailed theoretical analysis is needed so as to search for the optimal sensing time. Thus, we can draw a safe conclusion that the when compared to the fixed sensing time cases, the proposed algorithm can optimize the sensing time to maximum achievable throughput at each distance, for which the CRN performance can be further improved.
The achievable throughput of different sensing time
Fig. 5
shows the maximum achievable throughput of optimal K value at each distance. Also, the cases when K is fixed to 1 (OR fusion rule) and K fixed to 10 (AND fusion rule) are compared in
Fig. 5
. As a common condition, the sensing time
τ
is optimized in the three cases along the distance between the PU and the SU. From the figure, we can see clearly that for different K values, the achievable throughput is varies from each other. When the SU is close to the PU (
d
≤800
m
) or the distance is far from the PU (
d
≥1580
m
), due to the interferenceaware sensing model, the local sensing performance of each CU is more trustful, thus the main harmful influence is caused by the error in imperfect reporting channel, so the larger K value may raise the right decision probability of SU when comparing with the smaller K value, as a result, the achievable throughput is improved. However, in the distances among the range 800
m
≤
d
≤1580
m
, the sensing result by each CU’s local spectrum sensing and the harmful influence caused by the error in imperfect reporting channel should be considered simultaneously, then an optimal K is calculated to satisfy the special problem. As a result, the proposed algorithm which optimizing the K value can reach a maximum achievable throughput when compared the fixed K value cases.
The achievable throughput of different K values
Thus, in order to analyze the performance of cognitive radio networks, both the sensing time and the parameter K value of the KoutofN fusion rule should be taken into consideration. By jointly optimizing the sensing time and the K value, we will finally get the maximum achievable throughput in interferenceaware cognitive radio networks over imperfect reporting channel.
6. Conclusion
In this paper, we studied the issue of throughput tradeoff problem of cooperative spectrum sensing in interferenceaware cognitive radio networks over imperfect reporting channel. For the cooperative spectrum sensing, the KoutofN fusion rule is used. By jointly optimizing the sensing time and the K value, the maximum throughput can be achieved in interferenceaware cognitive radio networks over imperfect reporting channel. The theoretical analysis and computer simulation is also given to show the capability of improvement in CRN throughput.
Acknowledgements
This work was supported by the National Science Foundation of China under Grant No. 61172062 and No. 61301160, and in part by Jiangsu Province Natural Science Foundation of China under Grant No. BK2011116.
BIO
Changju Kan received his B.S. degree in communications engineering, from Institute of Communications Engineering, PLA University of Science and Technology, Nanjing, China, in 2011. He is currently pursuing his M.S. degree in communications and information system in Institute of Communications Engineering, PLA University of Science and Technology. His research interests are cognitive radio networks and green communication.
Qihui Wu received his B.S. degree in communications engineering, M.S. degree and Ph.D. degree in communications and information systems from Institute of Communications Engineering, Nanjing, China, in 1994, 1997 and 2000, respectively. From 2003 to 2005, he was a Postdoctoral Research Associate at Southeast University, Nanjing, China. From 2005 to 2007, he was an Associate Professor with the College of Communications Engineering, PLA University of Science and Technology, Nanjing, China, where he is currently a Professor and Ph.D. supervisor. From March 2011 to September 2011, he was an Advanced Visiting Scholar in Stevens Institute of Technology, Hoboken, USA.
His current research interests span the areas of wireless communications and signal processing, with emphasis on system design of software defined radio, cognitive radio, and spectrum management.
Fei Song received her B.S. degree in communications engineering, and her Ph.D. degree in communications and information system from Institute of Communications Engineering, PLA University of Science and Technology, Nanjing, China, in 2002 and 2007, respectively. She is currently a lecturer of PLA University of Science and Technology. Her current research interests are cognitive radio networks, MIMO and statistical signal processing.
Guoru Ding received his B.S. degree (with honors) in electrical engineering from Xidian University, Xi'an, China, in 2008. He is currently pursuing his Ph.D. degree in communications and information systems in College of Communications Engineering, PLA University of Science and Technology. His research interests include cognitive radio networks, machine learning, statistical signal processing, and big data analytics over wireless networks.
He currently serves as a TPC member of IEEE GLOBECOM 2014 and IEEE VTC 2014Fall and an invited reviewer for 10+ Journals, such as IEEE Signal Processing Magazine, IEEE Communications Magazine, IEEE Transactions on Communications, and IEEE Transactions on Wireless Communications, etc. He was a recipient of the Best Paper Award from IEEE WCSP 2009. He is a IEEE/ACM student member and was a voting member of IEEE 1900.7 White Space Radio Working Group.
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