IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 6, JUNE 2010
1849
Spectrum Sensing with Active Cognitive Systems
S. H. Song, Member, IEEE, K. Hamdi, Student Member, IEEE, and K. B. Letaief, Fellow, IEEE
Abstract—Spectrum sensing is critical for cognitive systems
to locate spectrum holes. In the IEEE 802.22 proposal, short
quiet periods are arranged inside frames to perform a coarse
intra-frame sensing as a pre-alarm for fine inter-frame sensing.
However, the limited sample size of the quiet periods may not
guarantee a satisfying performance and an additional burden of
quiet-period synchronization is required. To improve the sensing
performance, we first propose a quiet-active sensing scheme
in which inactive customer-provided equipments (CPEs) will
sense the channels in both the quiet and active periods. To
avoid quiet-period synchronization, we further propose to utilize
(optimized) active sensing, in which the quiet periods are replaced
by ‘quiet samples’ in other domains, such as quiet sub-carriers
in OFDMA systems. By doing so, we not only save the need for
synchronization, but also achieve selection diversity by choosing
quiet sub-carriers based on channel conditions. The proposed
active sensing scheme is also promising for spectrum sharing
applications where both the cognitive and primary systems can
be active simultaneously.
Index Terms—Cognitive radio, spectrum sensing, feature detection.
I. I NTRODUCTION
I
N the IEEE 802.22 proposal [1], one short (much less than
one frame length) quiet period is arranged at the beginning
of each frame for intra-frame sensing [2]. Accordingly, intraframe sensing is performed when the cognitive system is quiet
and its performance depends on the signals received in the
quiet periods. Most of the works in spectrum sensing [3],
[4], [5], [6] and resource allocation [7], [8], [9] for cognitive
systems are based on this structure. However, such schemes
have two major problems. First, the limited sample size of
the quiet periods may not be able to provide a good sensing
performance. Second, the placement of the quiet periods
causes an additional burden of synchronization for the quiet
periods.
To improve the sensing performance, we first propose
a quiet-active sensing scheme, in which inactive customerprovided equipments (CPEs) will sense the channels in both
the quiet and active periods. Here, the active periods correspond to the time slots, in which the cognitive system is in
operation. It is easily recognized that quiet-active sensing can
obtain more information from the signals in the active periods
and thus achieve a better sensing performance than the quiet
sensing case. The arrangement of the inactive CPE for sensing
Manuscript received June 19, 2009; revised January 17, 2010; accepted
March 26, 2010. The associate editor coordinating the review of this letter
and approving it for publication was S. Wei.
This work was sponsored in part by the Hong Kong Research Grant Council
under Grant No. 610309.
The authors are with the Electronic and Computer Engineering Department, the Hong Kong University of Science and Technology (e-mail:
[email protected], [email protected], [email protected]).
Digital Object Identifier 10.1109/TWC.2010.06.090924
duty is justified as follows. As stated in the IEEE 802.22
proposal [1], we have 255 CPEs per base station (BS) per
TV channel and the probability that all CPEs are active is
small. In addition, quiet-active sensing can be performed by
some nodes in the cognitive system with only sensing duty.
To avoid the requirement of quiet-period synchronization,
we propose to replace the intra-frame sensing by active sensing
where no quiet periods are needed. This idea is motivated
by the following facts. First, although active sensing has
more uncertainty in its received signals, it has more signal
samples than quiet sensing. Second, the quiet periods represent
some (cognitive) clean samples in the time domain and such
clean samples can be obtained from other domains. For
example, we can obtain some quiet sub-carriers in Orthogonal
Frequency-Division Multiple Access (OFDMA) systems, and
the selection of such quiet sub-carriers can be optimized to
take advantage of frequency diversity. Thus, the optimized
active-sensing not only releases the need for synchronizing the
quiet periods but also achieves additional selection diversity
by choosing better sub-carriers.
In this paper, we will derive the feature detector [2] for
both the quiet-active and active sensing schemes. The sensing
performance of the quiet-active and active sensing schemes
will be evaluated and compared with quiet sensing to illustrate the advantage of the proposed schemes. We will also
investigate the effects of the signal-to-noise ratio (SNR) from
both the primary and cognitive systems on the sensing performance of different detectors. Furthermore, the performance
improvement of the optimized active-sensing over quiet-active
sensing, obtained by signal design in cognitive systems, will be
analyzed. Besides its application in the conventional cognitive
system, the proposed active sensing scheme is also promising
in the spectrum sharing system where the cognitive and
primary systems can be active at the same time.
The organization of this paper is as follows. In Section
II, we model the received signals at the sensing CPE under
different hypotheses. Based on the signal models, feature
detectors for quiet-active sensing is derived in Section III
whereby the probability of false alarm and probability of
detection are evaluated. In Section IV, we further analyze the
possibility of utilizing pure active sensing and investigate the
advantages of the optimized active sensing scheme over other
detectors. Numerical results are given in Section V and Section
VI concludes this paper.
II. S YSTEM M ODEL
In the IEEE 802.22 proposal, short quiet periods are arranged at the beginning of cognitive frames to perform intraframe sensing. The purpose of intra-frame sensing is to give
a pre-alarm about the presence of primary signals by making
c 2010 IEEE
1536-1276/10$25.00 ⃝
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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 6, JUNE 2010
Active periods
Quiet periods
rq
signal of the cognitive BS which is assumed to be Gaussian
distributed with s𝑐 ∼ 𝐶𝑁 (0, R𝑐 ). This Gaussian assumption
is justified by the facts that i.i.d. (independent and identically
distributed) signals from different users are transmitted on
different sub-carriers of an OFDMA frame [1]. The additive
Gaussian noise is assumed i.i.d. with n𝑞 ∼ 𝐶𝑁 (0, 𝜎𝑛2 I𝑁𝑞 ) and
n𝑎 ∼ 𝐶𝑁 (0, 𝜎𝑛2 I𝑁𝑎 ).
Under hypothesis 𝐻1 , the received signal can be expressed
as
ra
Inter-frame sensing
Intra-frame sensing
(a) Quiet sensing
(b) Quiet-Active sensing
Frame structures for various sensing schemes.
a decision about two hypotheses; namely, 𝐻0 : the primary
network is silent and 𝐻1 : the primary network is active. The
frame structures for both intra-frame and inter-frame sensing
are shown in part (a) of Fig. 1. We will utilize the 𝑁𝑞 ×1 vector
r𝑞 and 𝑁𝑎 × 1 vector r𝑎 to denote the received signals in the
quiet and active periods, respectively. Accordingly, the length
of one frame can be given by 𝑁 = 𝑁𝑞 + 𝑁𝑎 . In intra-frame
sensing, only signal r𝑞 is utilized to discriminate between two
hypotheses. However, the information in r𝑎 can certainly help
in sensing but so far has not been exploited. This is because
the working CPE can not receive signals from the cognitive BS
and perform sensing at the same time. Fortunately, as specified
in the IEEE 802.22 proposal, there are 255 CPEs per BS per
TV band. Thus, there should be many inactive CPEs, and it
is therefore possible to let inactive CPE perform sensing by
using both r𝑞 and r𝑎 . We shall refer to this as quiet-active
sensing whose frame structures are illustrated in part (b) of
Fig. 1.
For ease of illustration, we only consider the received signal
within one frame in the down link transmission and the results
can be easily extended to the case with multiple frames. Let
h𝑐 = [ℎ𝑐1 , .., ℎ𝑐𝐿 ]𝑇 denote the 𝐿-tap channel vector between
the cognitive BS and the sensing CPE where ℎ𝑐𝑙 represents
the 𝑙th tap. Under hypothesis 𝐻0 , the received signal r𝑞 and
r𝑎 can be expressed as
r𝑞0
r𝑎0
=
=
n𝑞 ,
H𝑐 s𝑐 + n𝑎
H𝑐 s𝑐 + H𝑎𝑝 s𝑎𝑝 + n𝑎
(2)
A. Feature detector
(c) Active sensing
Fig. 1.
H𝑞𝑝 s𝑞𝑝 + n𝑞 ,
=
III. Q UIET-ACTIVE S ENSING
Inter-frame sensing
Active sensing
=
where H𝑞𝑝 and H𝑎𝑝 denote the circulant channel matrices
between the primary system and the sensing CPE in the quiet
and active periods, respectively. The transmit signals from the
primary system are also assumed to be Gaussian distributed
[11], [12] with s𝑞𝑝 ∼ 𝐶𝑁 (0, R𝑞𝑝 ) and s𝑎𝑝 ∼ 𝐶𝑁 (0, R𝑎𝑝 ).
The Gaussian assumption is justified by the facts that OFDM
signals are transmitted in DVB-T systems with i.i.d. QPSK or
QAM signals on different sub-carriers [13].
Inter-frame sensing
Quiet-Active sensing
r𝑞1
r𝑎1
(1)
where H𝑐 = 𝐶𝑖𝑟(h𝑐 ) denotes a circulant channel matrix
generated from h𝑐 [10]. Here, s𝑐 represents the transmit
To derive the feature detector for quiet-active sensing, we
𝑇
define a new 𝑁 × 1 vector r = [r𝑞 r𝑎 ] , which collects
information from both the quiet and active periods. Under
hypothesis 𝐻0 , r is distributed as a zero-mean Gaussian vector
with covariance matrix
[
] [
]
r𝑞0 r†𝑞0 r𝑞0 r†𝑎0
0
Q𝑞0
Q0 = 𝐸
=
(3)
0
Q𝑎0
r𝑎0 r†𝑞0 r𝑎0 r†𝑎0
where Q𝑞0 and Q𝑎0 denote the covariance matrices for the
received signals in the quiet and active periods, respectively.
By definition, we can obtain
Q𝑞0 = 𝜎𝑛2 I𝑁𝑞
(4)
Q𝑎0 = 𝜎𝑛2 I𝑁𝑎 + H𝑐 R𝑐 H†𝑐 .
(5)
and
For hypothesis 𝐻1 , r is also distributed as a zero-mean
Gaussian vector where we can obtain the covariance matrices
for the quiet and active periods as
Q𝑞1 = H𝑞𝑝 R𝑞𝑝 H†𝑞𝑝 + 𝜎𝑛2 I𝑁𝑞
(6)
Q𝑎1 = H𝑎𝑝 R𝑎𝑝 H†𝑎𝑝 + 𝜎𝑛2 I𝑁𝑎 + H𝑐 R𝑐 H†𝑐 ,
(7)
and
respectively. In the above derivation, we have assumed that
s𝑞𝑝 and s𝑎𝑝 are independent of each other, which is only
taken so that the performance of quiet-active sensing can be
easily compared with that of quiet sensing. It follows that the
sufficient statistic for the likelihood detector can be given by
[14]
† −1
𝜂 = r† Q−1
0 r − r Q1 r
(8)
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 6, JUNE 2010
where the detector just checks which of the two covariance
structures the received signal is more close to. The decision
statistic can be further simplified as
(
)
( −1
)
−1
−1
†
𝜂 = r†𝑞 Q−1
𝑞0 − Q𝑞1 r𝑞 + r𝑎 Q𝑎0 − Q𝑎1 r𝑎
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C. Probability of detection
as
Under hypothesis 𝐻1 , we can rewrite the decision statistic
𝜂1 = x†1 (M1 − I) x1
(9)
where the second component represents the information collected from the active periods. Note that if there is no inactive
CPE, the quiet-active sensing scheme will revert to quiet
sensing.
where
†/2
(10)
where r0 denotes the received signal under hypothesis 𝐻0 . For
this purpose, we rewrite 𝜂0 as
𝜂0 = x†0 (I − M0 ) x0
(11)
where
r0 ∼ 𝐶𝑁 (0, I)
(12)
and
†/2
1/2
M0 = Q0 Q−1
1 Q0 .
(13)
Given that M0 can be decomposed as
M 0 = U† Λ 0 U
(14)
where Λ0 is a diagonal matrix and U† U = I, the decision
statistic can be expressed as
𝜂0 =
(1 − 𝜆0𝑖 )∣𝑦0𝑖 ∣
2
(15)
𝑖=1
where ∣𝑦0𝑖 ∣2 is distributed as a chi-squared variable with two
degrees of freedom and 𝜆0𝑖 is the 𝑖th diagonal entry of Λ0 . It
follows that the characteristic function of 𝜂0 can be expressed
as [15]
𝜓𝜂0 (𝑡) =
(𝑁
∏
)−1
(1 − 𝑗𝑡(1 − 𝜆0𝑖 ))
.
(16)
𝑖=1
As a result, given the decision threshold 𝜏 , we can obtain the
probability of false alarm as [16]
𝑃𝑓
𝑁
∑
(𝜆1𝑖 − 1)∣𝑦1𝑖 ∣2
(20)
𝑖=1
† −1
𝜂0 = r†0 Q−1
0 r0 − r0 Q1 r0
𝑁
∑
(19)
By following the same procedure, we can obtain
𝜂1 =
To determine the false alarm probability, we need to obtain
the pdf (probability density function) of the decision statistic
−1/2
1/2
M1 = Q1 Q−1
0 Q1 .
B. False alarm probability
x0 = Q0
(18)
= 𝑃 𝑟(𝜂0 > 𝜏 ∣ 𝐻0 )
∫
}
1 ∞1 {
1
+
ℑ 𝜓𝜂0 (𝑡)𝑒−𝑗𝑡𝜏 𝑑𝑡,
=
2 𝜋 0 𝑡
where ℑ(𝑥) denotes the imaginary part of 𝑥.
(17)
whose characteristic function can be determined and utilized
to obtain the probability of detection. By comparing (20) with
(15), we can observe that it is the eigenvalues of M0 and M1
that determine the false alarm probability and the probability
of detection.
D. Special case
To clearly illustrate the advantage of quiet-active sensing,
we consider here the special case with R𝑐 = 𝜎𝑐2 I𝑁𝑎 , R𝑞𝑝 =
𝜎𝑝2 I𝑁𝑞 , and R𝑎𝑝 = 𝜎𝑝2 I𝑁𝑎 . It should be noted that the i.i.d. case
is the worst scenario since the detector can not exploit any
correlation structure in the signals to differentiate them from
the i.i.d. noise. Thus, the following analysis can be regarded
as a bench mark for the performance of quiet-active sensing.
Recall that it is the eigenvalues of the matrices M0 and
M1 that determine the sensing performance. By substituting
the i.i.d. assumptions into (13) and (19), we can obtain the
concerned matrix structure as
[
]
D1 0
M0 = E†
E
0 D2
[
]
D3 0
E
(21)
M1 = E†
0 D4
where
[
E=
F𝑁 𝑞
0
0
F𝑁𝑎
]
,
(22)
and F denotes the unitary discrete Fourier transform matrix.
The four diagonal matrices can be given by
{
}
𝜎𝑛2
, 𝑖 = 1, ..., 𝑁𝑞
D1 = diag
𝜎𝑝2 ∣𝜙𝑖 ∣2 + 𝜎𝑛2
{
}
𝜎𝑐2 ∣𝜑𝑗 ∣2 + 𝜎𝑛2
D2 = diag
,
𝜎𝑝2 ∣𝜙𝑖 ∣2 + 𝜎𝑐2 ∣𝜑𝑗 ∣2 + 𝜎𝑛2
𝑖 = 𝑁𝑞 + 1, ..., 𝑁, 𝑗 = 1, ..., 𝑁𝑎
{
}
𝜎𝑝2 ∣𝜙𝑖 ∣2 + 𝜎𝑛2
D3 = diag
, 𝑖 = 1, ..., 𝑁𝑞
𝜎𝑛2
[
}
𝜎𝑝2 ∣𝜙𝑖 ∣2 + 𝜎𝑐2 ∣𝜑𝑗 ∣2 + 𝜎𝑛2
D4 = diag
,
𝜎𝑐2 ∣𝜑𝑗 ∣2 + 𝜎𝑛2
𝑖 = 𝑁𝑞 + 1, ..., 𝑁, 𝑗 = 1, ..., 𝑁𝑎
(23)
where ∣𝜙𝑖 ∣2 and ∣𝜑𝑗 ∣2 denote the eigenvalues of H𝑝 H†𝑝 and
H𝑐 H†𝑐 , respectively.
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It follows from (15) and (20) that the decision statistic under
two hypotheses 𝐻0 and 𝐻1 can be determined as
𝜂0
=
∼
𝜂𝑞0 + 𝜂𝑎0
𝑁𝑞
∑
𝑖=1
+
(24)
𝑁
∑
𝜂𝑎1
= 𝜂𝑞1 + 𝜂𝑎1
(25)
∼
+
𝑁
∑
𝑖=𝑁𝑞 +1
𝜎𝑝2 ∣𝜙𝑖 ∣2
𝜎𝑐2 ∣𝜑𝑖−𝑁𝑞 ∣2 +
𝜎𝑛2
𝜒2 (2)
respectively. Here, 𝜂𝑞0 and 𝜂𝑞1 are just the decision variables
for the quiet sensing scheme under two hypotheses. It is easily
recognized that the advantage of quiet-active sensing over
quiet sensing comes from the additional information provided
by 𝜂𝑎0 and 𝜂𝑎1 . With the decision statistics, we can then evaluate the performance of quiet-active sensing. In particular, for a
given false alarm requirement, we can determine the decision
threshold numerically by (17). Similarly, the probability of
detection can be obtained.
IV. ACTIVE S ENSING
A. Active sensing without quiet samples
To avoid quiet-periods synchronization, we can remove the
quiet periods and utilize pure active sensing. The motivation
for doing so comes from the fact that active sensing has more
signal samples for sensing. We show in part (c) of Fig. 1 the
new frame structures for active sensing where the quiet periods
are removed. Accordingly, we have two new hypotheses to
¯ 0 : the primary system is silent and
discriminate; namely, 𝐻
¯ 1 : both the primary
the cognitive system is in operation and 𝐻
and cognitive systems are active. Under these two hypotheses,
the 𝑁 × 1 received signal vector r can be expressed as
𝜎𝑝2 ∣𝜙𝑖 ∣2
𝜒2 (2),
𝜎𝑐2 ∣𝜑𝑖 ∣2 + 𝜎𝑛2
(30)
respectively. Note that we have 𝑁 samples for transmission in
the active sensing scheme which is 𝑁𝑞 more than that of the
quiet sensing scheme. Accordingly, we can make 𝑁𝑞 out of the
𝑁 samples ‘quiet’ to obtain some clean samples for sensing
purpose while maintaining the same transmission rate.
B. Active sensing with quiet samples
For ease of illustration, we consider here the OFDMA-based
cognitive system as specified in the IEEE 802.22 proposal
and this result can be extended to other signal models. In this
case, the transmit signal from the cognitive BS should have
the covariance structure
2
2
, ..., 𝜎𝑐𝑁
]F𝑁
R𝑐 = F†𝑁 diag[𝜎𝑐1
(31)
2
𝜎𝑐𝑖
where
represents the transmit power over the 𝑖th subcarrier and we have assumed that the data over different
sub-carriers are independent. Note that R𝑐 is not necessarily
of full rank, since the cognitive system may not utilize
all sub-carriers. If the power for the first 𝑁𝑞 sub-carriers,
2
𝜎𝑐𝑖
, 𝑖 = 1, ..., 𝑁𝑞 , are set to be zero, we can obtain two new
decision statistics as
𝜂0
∼
𝑁𝑞
∑
𝑖=1
𝜎𝑝2 ∣𝜙𝑖 ∣2
𝜒2 (2)
𝜎𝑝2 ∣𝜙𝑖 ∣2 + 𝜎𝑛2
𝑁
∑
+
𝑖=𝑁𝑞 +1
𝜎𝑝2 ∣𝜙𝑖 ∣2
2
2 ∣𝜑 ∣2 + 𝜎 2 𝜒 (2)
𝜎𝑝2 ∣𝜙𝑖 ∣2 + 𝜎𝑐𝑖
𝑖
𝑛
𝑁𝑞
𝜂1
∼
∑ 𝜎𝑝2 ∣𝜙𝑖 ∣2
𝑖=1
𝜎𝑛2
(32)
𝜒2 (2) +
𝑁
∑
𝜎𝑝2 ∣𝜙𝑖 ∣2
2
𝜎 ∣𝜑𝑖 ∣2 +
𝑖=𝑁𝑞 +1 𝑐𝑖
𝜎𝑛2
𝜒2 (2)
r0 = H𝑐 s𝑐 + n0
(26)
r1 = H𝑐 s𝑐 + H𝑝 s𝑝 + n1 ,
(27)
C. Optimized active-sensing
respectively.
By following the same procedure as that for the quiet-active
sensing case, we can obtain the feature detector as
† −1
𝜂𝑎 = r† Q−1
𝑎0 r − r Q𝑎1 r
(28)
where
Q𝑎1
𝜎𝑝2 ∣𝜙𝑖 ∣2
𝜒2 (2),
𝜎𝑝2 ∣𝜙𝑖 ∣2 + 𝜎𝑐2 ∣𝜑𝑖 ∣2 + 𝜎𝑛2
which resemble the decision statistics for quiet-active sensing.
This indicates that if we leave 𝑁𝑞 out of the 𝑁 sub-carriers
silent, we can obtain similar performance as that of quietactive sensing with 𝑁𝑞 quiet samples.
and
Q𝑎0
∼
𝑁
∑
𝑖=1
and
∑ 𝜎𝑝2 ∣𝜙𝑖 ∣2
𝜒2 (2)
2
𝜎
𝑛
𝑖=1
𝑁
∑
𝑖=1
𝜎𝑝2 ∣𝜙𝑖 ∣2
𝜒2 (2)
𝜎𝑝2 ∣𝜙𝑖 ∣2 + 𝜎𝑐2 ∣𝜑𝑖−𝑁𝑞 ∣2 + 𝜎𝑛2
𝑁𝑞
∼
𝜂𝑎0
𝜎𝑝2 ∣𝜙𝑖 ∣2
𝜒2 (2)
𝜎𝑝2 ∣𝜙𝑖 ∣2 + 𝜎𝑛2
𝑖=𝑁𝑞 +1
𝜂1
decision statistics for active sensing under two hypotheses can
be given by
= 𝜎𝑛2 I𝑁 + H𝑐 R𝑐 H†𝑐 ,
= H𝑝 R𝑝 H†𝑝 + 𝜎𝑛2 I𝑁 + H𝑐 R𝑐 H†𝑐 .
(29)
Note that the size of the covariance matrices has been changed
to match the received signal vector. With i.i.d. signals, the
The quiet periods in the time-domain are fixed but, with
active sensing, we can select such quiet sub-carriers in the
frequency domain. Thus, active sensing has a new freedom
in choosing the quiet sub-carriers (selection diversity). We
will refer to this scheme as the optimized active sensing. In
particular, we can adjust the decision statistic by resource
allocation over the sub-carriers in the cognitive systems. For
example, if we have a priori information about the multi-path
fading channel, we should not transmit signals in the 𝑁𝑞 subcarriers where the primary signals, if transmitted, are strong.
By doing so, we can obtain some clean samples that carry
more information about the primary system than the timedomain quiet samples. Thus, a better sensing performance can
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1
1
0.9
0.9
0.8
0.8
Probability of detection
Probability of detection
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 6, JUNE 2010
0.7
0.6
0.5
0.4
0.6
0.5
0.4
0.3
0.3
Quiet−Active Sensing
Active Sensing
Quiet Sensing
0.2
0.1
−10
0.7
−8
−6
−4
−2
0
2
Primary SNR (dB)
4
6
8
Quiet−Active Sensing
Active Sensing
Quiet Sensing
0.2
0.1
−10
10
Fig. 2. Performance comparison over multipath channels with high cognitive
SNR: 𝑁𝑞 = 10, 𝑁 = 100.
A. Effects of cognitive SNR
We first analyze the effects of cognitive SNR on sensing
performance with 𝑁𝑞 = 10 and 𝑁 = 100. For this purpose,
we compare the sensing performance under both high and
low cognitive SNR conditions with 𝜎𝑐2 /𝜎𝑛2 = 5𝑑𝐵 and −5𝑑𝐵
while the primary SNR changes from 𝜎𝑝2 /𝜎𝑛2 = −10𝑑𝐵 to
𝜎𝑝2 /𝜎𝑛2 = 10𝑑𝐵. Fig. 2 shows the performance comparison of
the concerned detectors with 𝜎𝑐2 /𝜎𝑛2 = 5𝑑𝐵 where the false
alarm probability is set to be 𝑃𝑓 = 0.1. The corresponding
results with 𝜎𝑐2 /𝜎𝑛2 = −5𝑑𝐵 are given in Fig. 3 where
the quiet-active sensing only slightly outperforms the active
scheme. This is because the cognitive SNR is very low such
that the performance of the quiet-active sensing is dominated
by the active periods. By comparing the results in Fig. 2
and Fig. 3, we observe that higher cognitive SNR will cause
a worse sensing performance, especially for active sensing,
indicating the necessity of placing quiet samples when the
cognitive SNR is high.
B. Effects of quiet-sample size
We now evaluate the effects of quiet-sample size on sensing
performance by changing the system setting to 𝑁𝑞 = 30 and
𝑁 = 100. The corresponding sensing performance under high
and low cognitive SNR circumstances is illustrated in Fig. 4
and Fig. 5, respectively. By comparing these results with those
in Fig. 2 and Fig. 3, we have the following two observations.
First, as the length of quiet samples increases, the performance
−4
−2
0
2
4
6
8
10
Fig. 3. Performance comparison over multipath channels with low cognitive
SNR: 𝑁𝑞 = 10, 𝑁 = 100.
1
0.9
0.8
Probability of detection
In this section, we will evaluate and compare the sensing
performance of the quiet, quiet-active and (optimized) active
sensing detectors over multipath channels with 4 i.i.d. paths.
−6
Primary SNR (dB)
be achieved. Note that both the quiet-active and active sensing
schemes process signals of size 𝑁 , which is larger than 𝑁𝑞 of
quiet sensing. Thus, the associated computational complexity
is higher.
V. N UMERICAL R ESULTS
−8
0.7
0.6
0.5
0.4
0.3
Quiet−Active Sensing
Active Sensing
Quiet Sensing
0.2
0.1
−10
−8
−6
−4
−2
0
2
Primary SNR (dB)
4
6
8
10
Fig. 4. Performance comparison over multipath channels with high cognitive
SNR: 𝑁𝑞 = 30, 𝑁 = 100.
of both quiet and quiet-active sensing are improved where the
advantages of the quiet-active scheme decrease. Second, the
performance of pure active sensing will be worse than that of
quiet sensing if more quiet samples are available in a high
cognitive SNR environment. It should be noted that the pure
active sensing scheme provides higher transmission rate.
C. Effects of frequency selectivity
In practice, it is easy for the cognitive system to obtain knowledge about the primary channels as H𝑝 H†𝑝 =
F†𝑁 diag[∣𝜙1 ∣2 , ..., ∣𝜙𝑁 ∣2 ]F𝑁 . Without loss of generality, we
assume that {∣𝜙𝑚 ∣2 } have been ordered with ∣𝜙1 ∣2 > ∣𝜙2 ∣2 >
, ..., > ∣𝜙𝑁 ∣2 . Thus, the power of the first 𝑁𝑞 sub-channels
in the cognitive system can be set to be zero, so that the
samples in sub-channels {∣𝜙𝑚 ∣2 } with 𝑚 = 1, ..., 𝑁𝑞 will
not be interfered with. By doing so, we have placed some
‘quiet samples’ in the frequency domain. The performance
1854
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 6, JUNE 2010
1
on the frame structure of the IEEE 802.22 proposal, we first
derived the quiet-active sensing scheme whose advantage over
quiet sensing comes from the additional information obtained
from the active periods. To further release the requirement of
quiet-period synchronization, the optimized active sensing was
proposed where quiet samples are placed in the frequency domain to achieve additional selection diversity. As a result, the
optimized active-sensing obtains better detection performance
than quiet-active sensing while at the same time saving the
need to synchronize the quiet periods. The proposed active
sensing scheme can also be applied to the spectrum sharing
system where the primary and cognitive systems work at the
same time.
0.9
Probability of detection
0.8
0.7
0.6
0.5
0.4
Quiet−Active Sensing
Active Sensing
Quiet Sensing
0.3
0.2
−10
−8
−6
−4
−2
0
2
4
6
8
10
Primary SNR (dB)
Fig. 5. Performance comparison over multipath channels with low cognitive
SNR: 𝑁𝑞 = 30, 𝑁 = 100.
1
0.9
Probability of detection
0.8
0.7
0.6
0.5
0.4
0.3
Quiet−Active Sensing
Optimized Active Sensing
Quiet−sensing
0.2
0.1
−10
−8
−6
−4
−2
0
2
Primary SNR (dB)
4
6
8
10
Fig. 6. Performance comparison of the quiet, quiet-active and optimized
active detectors with high cognitive SNR: 𝑁𝑞 = 10, 𝑁 = 100.
comparison is shown in Fig. 6 where the system parameters
are set to be the same as those of Fig. 2. It is observed
that optimized active sensing outperforms quiet-active sensing.
Note that such improvement is achieved without causing any
loss for the transmission rate of the cognitive systems, and at
the same time, the synchronization for the quiet periods is no
longer required.
VI. C ONCLUSION
In this paper, active sensing was proposed as an alternative
to intra-frame sensing in the IEEE 802.22 proposal. Based
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