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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 Ns is the number of
samples over which energy is computed
1.Energy Based Sensing
• Let the received signal has the following hypothesis
• H0 represents the null hypothesis meaning that there is no primary signal and only
AWGN noise exists , H1 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 Pd , at hypothesis H1 ,and the probability of false alarm Pf
,at hypothesis H0 ,can therefore be defined as follows:
Pd = Pr(T > λ | H1)=
Pf = Pr(T > λ| H0)=
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
2. Spectrum Sensing Based On Statistical
Covariance
• If the signal s(n) is not present Rs=0. Hence, the off-diagonal
elements of Rx 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 Rx should be nonzero. Denote rnm as
the element of matrix Rx at the nth row and mth column, and let
• Then, if there is no signal, T1 / T2 = 1. If the signal is present, T1 / T2
> 1. Hence, ratio T1 / T2 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 Ns 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
Covariance Absolute Value(CAV) Detection Algorithm
1.
2.
3.
4.
5.
Sample the received signal
Choose a smoothing factor L and a threshold γ1, where γ1 should
be chosen to meet the requirement for the probability of false
alarm
Compute the autocorrelations of the received signal λ(l), l = 0, 1, .
. . , L − 1, and form the sample covariance matrix
Compute
Determine the presence of the signal based on T1 (Ns), T2(Ns), and
threshold γ1. That is, if T1(Ns)/T2(Ns) > γ1, 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., Rs is
not a diagonal matrix (Some of the off-diagonal
elements of Rs 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.
Theoretical Analysis for the CAV Algorithm
• 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.
Threshold Selection
•As mentioned earlier, for a good detection algorithm, a high Pd
and low Pf should be achieved. The choice of threshold γ is a
compromise between Pd and Pf
•Usually, the threshold is chosen such that a certain value of
false alarm probability Pf 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 Pf
• We find a threshold γ to meet the required Pf : to do so we can
generate white Gaussian noises as the input (no signal) and adjust the
threshold to meet the Pf requirement. Note that the threshold here is
related to the number of samples used for computing the sample
autocorrelations and the smoothing factor L
Threshold Selection
2- If theoretical derivation is used:
We need to find the statistical distribution of T1(Ns)/T2(Ns) 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 Pd , Pf and the threshold associated with these probabilities are
derived as follows (equations (74)(76)(77) in [1]):
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.18041815, 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.