Energy Detection Sensing of Unknown Signals
over Fading Channels
V.Meghana
V.Sabitha
Dept. of Electronics and Communications Engineering
Vaagdevi College of Engineering,
Warangal, INDIA
email:meghanaveeramalla123@gmail.com
Dept. of Electronics and Communications Engineering
Vaagdevi College of Engineering,
Warangal, INDIA
e-mail:sabithavem@gmail.com
Abstract- Energy detection is the most popular spectrum sensing
method in cognitive radio. This paper focuses on energy detection
based spectrum sensing because of its low complexity. As it does
not require proper knowledge of channel gains, and estimations
of other parameters it is also considered as a low cost option.
Different other spectrum sensing methods like matched filter
detection, cyclostationary feature detection etc. need to know the
prior information i.e. frequency, phase, modulation scheme etc.
about the primary signal whereas energy detection does not and
it is also simpler to implement. In this paper, we compare the
ROC (Receiver Operating Characteristics), complementary ROC
curves and probability of detection versus SNR (Signal-to-Noise
Ratio) curves for AWGN, log-normal, Hoyt (or Nakagami-q),
Rayleigh, Rician (or Nakagami-n), Nakagami-m, and Weibull
channels with and without considering diversity techniques. Both
the results are compared and it showed that energy detection
based spectrum sensing technique over various fading channel
considering diversity case has better performance than for no
diversity case.
Keywords—
Cognitive Radio (CR), Spectrum Sensing, Energy
Detection, Detection Probability.
I.
Introduction
Detecting unknown signals is a critical topic in wireless
communications and has attracted for years the attention of
both Academia and Industry. The detection is typically
realized in the form of spectrum sensing with energy detection
(ED) constituting the most simple and popular method. The
operating principle of ED is based on the deployment of a
radiometer, which is a non-coherent detection device that
measures the energy level of a received signal waveform over
an observation time window. The obtained measure is
subsequently compared with a pre-defined energy threshold
which determines accordingly whether an unknown signal is
present or not [1]–[3].
Detection of unknown signals over a flat bandlimited Gaussian noise channel was firstly addressed by H.
Urkowitz in [4]. There, he comprehensively derived analytic
expressions for the corresponding probability of detection, Pd,
and probability of false alarm, P fa, performance metrics. These
measures are generally based on the statistical assumption that
the decision statistics follow the central chi-square and the
non-central chi-square distribution, respectively. A few
decades later, this problem was revisited by Kostylev [5] who
considered quasi deterministic signals operating in fading
conditions.
Thanks to its low implementation complexity and no
requirements for prior knowledge of the signal, the ED
method has been widely associated with applications in
RADAR systems while it has been also shown to be
particularly useful in emerging wireless technologies such as
ultra-wideband communications and cognitive radio [6], [7].
In the former, the energy detector is exploited for borrowing
an idle channel from authorized users, whereas in the latter it
identifies the presence or absence of a deterministic signal and
decides whether a primary licensed user is in active or idle
state, respectively. According to the corresponding decision,
the secondary unlicensed user either remains silent, or
proceeds in utilizing the unoccupied band until the primary
user becomes again active [1], [8]. This opportunistic method
has been shown to increase substantially the utilization of the
already allocated radio spectrum, offering a considerable
mitigation of the currently extensive spectrum scarcity [9]–
[15].
Several studies have been devoted to the analysis of
the performance of energy detection-based spectrum sensing
for different communication and fading scenarios.
Specifically, the authors in [16] derived closed-form
expressions for the average probability of detection over
Rayleigh, Rice and Nakagamim fading channels for both
single-channel and multi-channel scenarios. Similarly, the ED
performance in the case of equal gain combining over
Nakagami-m multipath fading has been reported by [17]
whereas the performance in collaborative spectrum sensing
and in relay-based cognitive radio networks has been
investigated by [18]–[21]. A semi-analytic method for
analyzing the performance of energy detection of unknown
deterministic signals was reported in [20] and is based on the
moment-generating function (MGF) method.
This method was utilized in the case of maximalratio combining (MRC) in the presence of Rayleigh, Rice and
Nakagami-m fading in [19] as well as for the useful case of
correlated Rayleigh and Rician fading channels in [18].
Finally, the detection of unknown signals in low signal-tonoise-ratio (SNR) over K distributed (K), generalized K (KG)
and the flexible η−μ and κ−μ generalized fading channels have
been analyzed in [20]–[21]. In this paper, probability of
detection (pd) probability of false alarm (pf) and probability of
missed detection (Pm=1-Pd) are the key measurement metrics
that analyze the performance of an energy detector. The
performance of an energy detector is illustrated by probability
of detection versus SNR curves and the complementary
receiving operating characteristics (CROC) curves which is a
plot of versus or versus.
The rest of the paper is organized as follows. In Section II,
energy detection and channel model is described and we
briefly describe the probabilities of detection and of false
alarm over additive white Gaussian noise (AWGN) channel,
shadowing and fading channels. Our simulation results and
discussions are presented in Section III. Finally we conclude
in Section IV.
II.
SYSTEM MODEL
Energy detection is a non coherent detection method that is
used to detect the licensed User signal. [6]. It is a simple
method in which prior knowledge of primary or licensed user
signal is not required, it is one of popular and easiest sensing
technique of non-cooperative sensing in cognitive radio
networks [7]-[8]. If the noise power is known, then energy
LDPC Code detector is good choice [9]. Mathematical model
for Energy detection is given by the following two hypotheses
H 0 and H1 :
Pf 
, λ 2 
Q
(2)



Pd
2γ , λ 
(3)
whereis the Rician factor. The average Pd in the case
of a Rician channel, Pd , Ric is then obtained by substituting (11)
in (6). The resulting expression can be solved for = 1 to yield
P
d , Ric | u 1
2 Kγ
Q
, λ (K  1)
K1γ
(4)
K  1 γ
For = 0, this expression reduces to the Rayleigh expression
with = 1 [18].
ii.
Nakagami-m fading Channel
If the signal amplitude follows a Nakagami-m distribution,
then PDF of follows a gamma PDF given by [17]
H 0 : (primary user absent)
y(n) = u(n) n = 1, 2, . . . ,N
H1 : (primary user present)
y(n) = s(n) + u(n) n = 1, 2, . . . ,N
Where u (n) is noise and s (n) is the primary
user signal.
In energy detection, the received signal is first pre-filtered
by an ideal band pass filter which has bandwidth , and the
output of this filter is then squared and integrated over a time
interval to produce the test statistic. The test statistic Y is
compared with a predefined threshold value [10]. The
probabilities of false alarm (Pf) and detection (Pd) can be
evaluated as Pr (Y  λ / H0 ) and Pr (Y  λ / H1 ) respectively
to yield [11]
m
(1)
fγ
(γ ) 
m
γ
Where
γ m −1
mγ
exp −
γ
(m)
(5)
;γ ≥ 0
is the Nakagami parameter. The average Pd in the
case of Nakagami- fading channel P
can be evaluated
d , Nak
by substituting (13) in (6):
Figure 1: Block diagram of an energy detection
Figure 1 shows the block diagram of an energy detector. The
band pass filter selects the specific band of frequency to which
user wants to sense. After the band pass filter there is a
squaring device which is used to measure the received energy.
The energy which is found by squaring device is then passed
through integrator which determines the observation interval
T. Now the output of integrator is compared with a value
called threshold and if the values are above the threshold, it
will consider that primary user is present otherwise absent.
A. Energy detection and False alarm Probabilities
The probability of detection and probability of false alarm in
non faded, that is, AWGN channel and faded environments are
studied in this section.
i.
Over AWGN Channel
λn
u −1
P
d , Nak
 α G1  β ∑
n 1
α
2
2n |
2(m γ )
ɺ
m
1
m −1
(m)2
β  (m)
λγ
F1 m; n  1;
2γ
(6)
m
(7)
γ
m
exp −
m γ
2m −1 (m− 1) | γ
mλ
ɺ exp −

G1  m
m
(
2(m
)
(m
γ
)
γ
)
γ
λ
2
(8)
m
1

m
m −1
L
γ mγ
mn
m− 2
∑
n0
mγ
m −1
λγ
−
2(m  γ )
(9)
L
−
n
distributed random variable with parameters ( / , ) [23].Thus is
also a Weibull distributed random variable with
V
V ,  aγ  − 2 where a 
1
parameters
The PDF

of
2(m  γ )
and with (a γ )
obtain an alternative expression for Pd , Ray when setting m=1 in
2
V

with /2
as [24]
(γ )
V
2(a γ )
(V/ 2 −1)
exp
−
γ
V/2
(15)
aγ
2
Where γ is the average SNR given as
Weibull Fading Channel
In theWeibull fading model, the channel fading coefficient h
can be expressed as a function of the Gaussian in-phase and
quadrature elements of the multipath components [19, 20]
h  (X  jY)
2
V
fγ (γ ) 
(16) and this expression is numerically equivalent to the
one obtained in (10)
Where j 
If = | +
1 
can then be derived from (13) by replacing
−V
Where Ln (⋅) is the Laguerre polynomial of degree . We can
iii.

2
λγ
2 /V
(10)
E
γ EZ2
N
s
 S 2/V1

2
E
s
(16)
V N01
01
2
Here, E(Z) the second moment of which can be obtained
from the generalized expression for moments as [21]
E  Z n   S n /V
−1 Let be the magnitude of h, that is, = |h|.
| is a Rayleigh distributed random variable, the
1  nV 
(17)
Weibull distributed random variable can be obtained by
Where is a positive integer and Γ(.) is the Gamma function. The
average Pd in the case of a Weibull channel can be
transforming and using (17) as
Z  R 2 /V
(11)
obtained analytically by substituting (12) in (6).
From (18), the PDF of Z can be given as
III.
rV −1 exp −
r
S
S
(12)
with S  E (ZV ) and (.) denoting the
expectation.is the
Weibull fading parameter expressing how severe the fading
can be ( > 0) andis the average
fading power. As
increases, the effect of fading decreases, while for the special
case of= 2, the Weibull PDF of reduces to the Rayleigh
PDF. For= 1 the Weibull PDF ofreduces to the well
known negative exponential PDF
The corresponding CDF of can be expressed as [21]
rV
S
FZ (r)  1 − exp −
(13)
In Weibull fading the instantaneous signal-to-noise ratio at a
cognitive radio is given by [20]
An extensive set of simulations have been conducted in
MATLAB using the
system model as described in the
previous section. The emphasis is to analyze the performance
of energy based spectrum sensing techniques in different
fading channel. The result is conducted on the basis of
probability of false alarm and probability of detection under
different SNR in different channels.
1
o detectio
f n
V
robabi
P lity
f z (r) 
SIMULATION RESULTS AND
DISCUSSIONS:
V
0.8
0.6
Awgn Simulation SNR=5db
Awgn Theory SNR=5db
Awgn SimulationSNR=10db
Awgn Theory SNR=10db
Awgn Simulation SNR=15db
Awgn Theory SNR=15db
0.4
0.2
γ Z2
E
s
N
(14)
01
0
0
It may be noted that the th power of a Weibull distributed
random variable with parameters ( , ) is another Weibull
0.2
0.4
0.6
Probability of false alarm
0.8
1
li
P r o b a b i t y o f d e t e c ti o n
1
0.8
0.6
weibull theory 5dB
weibull simulation 5dB
weibull theory 10dB
weibull simulation 10dB
weibull theory 15dB
weibull simulation 15dB
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.1
Simulation SNR=5db
Theoretical SNR=5db
0.4
0
0
Simulation SNR=10db
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
Fig.3. probability of detection under Rayleigh fading for
different SNRs and (m=5).
1
0.8
0.6
Rician Simulation SNR=15db
Rician Theory SNR=15db
Rician Simulation SNR=10db
Rician Theory SNR=10db
Rician Simulation SNR=5db
Rician Theory SNR=5db
0.4
0.2
0
0
0.1 0.2 0.3 0.4 0.5
0.6 0.7 0.8 0.9
1
Probability of false alarm
Fig.4. probability of detection under Rician for different SNRs
and (m=5).
nakagami theory 5dB
nakagami simulation 5dB
nakagami theory 10dB
nakagami simulation 10dB
nakagami theory 15dB
nakagami simulation 15dB
0.9
0.8
0.7
0.2
0.3
0.4
0.5
0.6 0.7
probability of false alarm
0.8
0.9
1
By observing the graphs from Fig.2-Fig.6, it is clear that
detection probability is less in weibull fading when compared
to AWGN, Rician and Rayleigh fading. Fig.6 illustrate
complementary receiver-operating characteristics (ROC)
curves Pm vs Pf for m = 5 of weibull over AWGN channel.
Therefore Weibull distribution is an adequate model for
accounting the multipath fading effect. This performance
indicates that, spectrum utilization is less when fading is
considered.
IV.
1
0.1
Fig.6. probability of detection under Weibull for different
SNRs and (m=5).
Theoretical SNR=10db
Simulation SNR=15db
Theoretical SNR=15db
0.2
Probability of false alarm
P r o b a b i l i ty o f d e te c ti o n
1
0.2
0
0
probability of detection
Fig.5. probability of detection under nakagami for different
SNRs and (m=5)
probability of detection
Fig.2. probability of detection under AWGN for different
SNRs and (m=5).
Fig.2 to Fig.6 are shows the Receiver Operating
Characteristic (ROC) curves for different fading channels like
AWGN, Rayleigh , Rician and weibull fading scenarios. From
Fig.4, we can tell that the weibull fading performance
degrades significantly when it uses energy detector under
fading conditions for different SNRs.
Conclusion
This work analyzed the performance of energy detection
over different fading channels. A novel analytic expression
was derived for the average probability of detection and was
shown that the overall performance of the detector is largely
affected by the value of the involved parameters. This is
evident by the fact that even slight variations of the fading
parameter results to substantial variation of the corresponding
probability of detection. As a result, the offered results are
useful in quantifying the effect of fading in energy detection
spectrum sensing which can contribute towards improved and
energy efficient cognitive radio wireless communication
deployments.
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0.6
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