Spectrum Sensing In Cognitive
Radio Networks
Spectrum Scarcity
•
Rapid
development in wireless communication
applications has increased the
demand on available wireless spectrum
•
Traditionally
the available spectrum is statically allocated by frequency
regulation bodies
•
However, spectrum occupancy measurements
shows the underutilization of
some licensed bands
Cognitive Radio Networks
•
Accordingly, dynamic spectrum allocation paradigms
emerged, called cognitive radio (CR) networks
•
Cognitive
Radio
(CR)
:
capable
of
sensing
operating
environment
and
dynamically
utilize
available
radio
resources
Cognitive Radio Networks
•
Two types of users:
▫
Primary users :
users of high priority or legacy
rights to use the spectrum.
▫
Secondary users :
users with lower priority, who
are not assigned a specific frequency band to operate
at.
•
Secondary users can only use the spectrum such
that they do not cause interference to primary
users
Cognitive Radio Networks
•
Three main functions to facilitate CR operation:
▫
Spectrum sensing
▫
Spectrum management and hand off
▫
Dynamic spectrum allocation and sharing
•
Spectrum sensing is a fundamental in CR
operation. Its performance decides the level of
interference with PUs and spectrum utilization
efficiency
•
The performance of a spectrum sensing techniques can be
evaluated using two metrics:
▫
Detection probability
: probability
that a CR correctly decides that the spectrum is busy,
when primary transmission is taking place
▫
False alarm probability
:
probability
that the CR makes a wrong decision that the spectrum
is occupied while it is actually
not
Note:
For the spectrum sensing algorithm to be efficient, it should satisfy both high spectral
utilization as well as minimal interference with primary users. In other words, the sensing
techniques needs to achieve high detection probability and a low false alarm probability, a
requirement that seems to be contradicting based on the above graph.
6
Spectrum Sensing
Techniques
Blind
no prior information is required
about the primary signal to be
detected
Energy based
spectrum
sensing
Spectrum
sensing based
on statistical
covariance
Eigenvalue
based sensing
Knowledge Based
information on primary signal needs to be
available a priori at the cognitive user end
Cyclostationary
feature detection
Coherent
detection/matched
filtering
1.Energy Based Sensing
•
Most common sensing technique with least
computational complexity
•
Secondary user decides whether or not there is primary
signal transmitted based on the energy of the received
signal x(t). Hence the detection statistics can be defined
as follows:
Where x(n) is the received signal and
N
s
is the number of
samples over which energy is computed
•
Let the received signal has the following hypothesis
•
H
0
represents the null hypothesis meaning that there is no primary signal and only
AWGN noise exists , H
1
describes the existence of a primary user’s signal in addition
to AWGN noise
•
The detection statistics
T
is compared with a threshold
λ
to know whether the primary
user’s signal exists or not. The primary user’s signal exists only if the detection
statistics
T
is larger than the threshold .
•
The probability of detection P
d
, at hypothesis H
1
,and the probability of false alarm P
f
,at hypothesis H
0
,can therefore be defined as follows:
P
d
= P
r
(T >
λ
 H
1
)=
P
f
= P
r
(T >
λ
 H
0
)=
1
.Energy Based Sensing
2. Spectrum Sensing Based On Statistical
Covariance
•
The received signal under H1 and H0 can be given by
:
•
Considering
L
samples, define the following vectors (Parameter
L is called
the smoothing factor
:
x(n)= [
x
(n)
x
(n

1)…
x
(n

L

1)]
T
s(n)= [
s
(n)
s
(n

1)…
s
(n

L

1)]
T
η
(n)= [
η
(n)
η
(n

1)…
η
(n

L

1)]
T
Hence, the statistical covariance matrices of the received signal can be defined
as:
It can be shown that
•
If the signal s(n) is not present R
s
=0. Hence, the off

diagonal
elements of R
x
are all zeros. If there is a signal and the signal
samples are correlated, Rs is not a diagonal matrix. Hence, some of
the off

diagonal elements of R
x
should be nonzero. Denote r
nm
as
the element of matrix R
x
at the n
th
row and m
th
column, and let
•
Then, if there is no signal,
T
1
/ T
2
= 1.
If the signal is present
, T
1
/ T
2
> 1.
Hence, ratio
T
1
/ T
2
can be used to detect the presence of the
signal.
2. Spectrum Sensing Based On Statistical
Covariance
•
In practice, the statistical covariance matrix can
only be calculated using a limited number of
available signal samples at the receiver. Hence,
we can compute the sample autocorrelations of
the received signal as
where
N
s
is the number of available samples
2. Spectrum Sensing Based On Statistical
Covariance
•
Statistical covariance matrix Rx can be
approximated by the sample covariance matrix
defined as
•
Based on the above sample covariance matrix we
can use the Covariance Absolute Value(CAV)
detection algorithm
2. Spectrum sensing based on statistical covariance
Covariance Absolute Value(CAV) Detection Algorithm
1.
Sample the received signal
2.
Choose a smoothing factor L and a threshold
γ
1
, where
γ
1
should
be chosen to meet the requirement for the probability of false
alarm
3.
Compute the autocorrelations of the received signal λ(
l
), l =
0
,
1
, .
. . ,
L
−
1
, and form the sample covariance matrix
4.
Compute
5.
Determine the presence of the signal based on
T
1
(N
s
), T
2
(N
s
),
and
threshold
γ
1
.
That is, if
T
1
(N
s
)/T
2
(N
s
) > γ
1
,
the signal exists;
otherwise, the signal does not exist.
Theoretical Analysis for the CAV Algorithm
•
The above proposed CAV algorithm is valid
based on the assumption that the transmitted
primary signal samples are correlated, i.e., R
s
is
not a diagonal matrix (Some of the off

diagonal
elements of R
s
should be
nonzeros
)
•
Obviously, if signal samples s(n) are
i.i.d
., then
in this case, the assumption is invalid,
and the algorithm cannot detect the presence of
the signal.
•
However, usually, the signal samples should be
correlated due to three reasons:
1.
The signal is oversampled
2.
The propagation channel has time dispersion;
3.
The original signal is correlated. In this case,
even if the channel is a flat

fading channel and
there is no oversampling, the received signal
samples are correlated.
Theoretical Analysis for the CAV Algorithm
Threshold Selection
•
As mentioned earlier, for a good detection algorithm, a high P
d
and low P
f
should be achieved. The choice of threshold γ is a
compromise between P
d
and P
f
•
Usually, the threshold is chosen such that a certain value of
false alarm probability P
f
is achieved
•
The threshold selection can be based on either theoretical
derivation or computer simulation:
1

If threshold selection based on computer simulation:
•
We first set a value for P
f
•
We find a threshold γ to meet the required P
f
: to do so we can
generate white Gaussian noises as the input (no signal) and adjust the
threshold to meet the P
f
requirement. Note that the threshold here is
related to the number of samples used for computing the sample
autocorrelations and the smoothing factor
L
2

If theoretical derivation is used:
We need to find the statistical distribution of
T
1
(N
s
)/T
2
(N
s
)
which is generally a
difficult task. In [1], using the central limit theorem, the distribution of this
random variable is approximated and the theoretical estimations for the two
probabilities P
d
, P
f
and the threshold associated with these probabilities are
derived as follows (equations (74)(76)(77) in [1]):
Threshold Selection
References
[1]
Yonghong
Zeng
and Ying

Chang Liang, “Spectrum

sensing
algorithms for cognitive radio based on statistical
covariances
”,
IEEE transactions on vehicular technology. Vol. 58. no. 4, pp.1804

1815, May 2009
[2] Z.
Quan
,
, S. Cui, and A. H. Sayed, "Optimal linear cooperation for
spectrum sensing in cognitive radio networks,"
IEEE Journal of
Selected Topics In Signal Processing
, vol.2, pp.23

40, 2008.
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