Aerospace and Electronic Systems Magazine May 2018 - 25
Ivanov et al.
h=
p − Pn
,
2E p
(7)
where Ep is the energy of the transmitted signal, p is the received
signal sample when the transmitter is close to the receiver and Pn
is the noise (power measured when there is no signal in the band).
Since we concentrate on the spectrum sensing method itself and
its ability to discover weak signals, we generalize the transmitted
signal and do not transmit any specific information by it. Therefore,
there is no need to make any discrimination between the information
and pilot signals. The transmitter uses the same signals with the same
cyclic characteristics, modulation, and output power. Thus, it is not
needed to create a transmission cycle of pilot and information signals,
we simply aim to recognize the presence of a particular type of signal.
Based on this, we can build an estimator very similar to the one proposed in [39]. A part of the samples k gathered during the sensing period is divided into ten chunks (which contain Mk elements) and thus,
by performing the estimation 10 times, the vector for h is formed. By
generalizing (6) from [39], as suggested in [40], we get
hk = hk −1 +
M k −1
k =0
2M k
pk
.
(8)
The minimum and maximum values of h in the vector are taken
as boundaries of the integral. All of the gathered samples (including those used for estimation) are used in the calculation of the
CAF, so they are fully utilized.
ENERGY DETECTION-BASED SPECTRUM SENSING
The energy detector is a simple and often applied detection technique for spectrum sensing. It is based on comparing the average
of the squared of the received energy samples y(k) during the sensing period ts, to a decision threshold λ [41]. The test statistic Λ is
defined as:
Λ=
1
M
M
y (n)
2
,
(9)
n =1
where M = fs ts is the number of the observed samples and fs is the
sampling rate.
If the received energy is greater than the threshold, the detector decides in favor of H1, otherwise, H0 will be chosen. The hypothesis H0 is true when the received sample y(n) is comprised of
only noise w(n), while the alternative will be chosen if both the PU
signal s(n) (multiplied by the channel coefficient h(n)) and noise
are detected.
then H 0
w ( n ) ,
y (n) =
h ( n ) s ( n ) + w ( n ) , then H1.
(10)
The noise is AWGN with a zero mean and a variance of σ w2
while the signal's distribution is generalized with zero mean and
variance σ s2. Because we use a large number of samples, we can
define the variance in the same way as it is done in [28]. Following
these definitions, the authors in [28] have derived the expressions
for the probability of miss-detection in various fading channels.
MAY - JUNE 2018
Because of our conclusion that the channel has Rayleigh distribution, we choose the respective expression
2
1
erfc (α ) − e a e 2 aα erfc ( a + α ) ,
2
M σ w2 − λ
1
;
,
α=
a=
2M γ
2 M σ w2
′ =
Pmd
(11)
where the SNR is γ = h 2σ s2 σ w2 .
The probability of false alarm is
Pfa
M w2
1
erfc
2
2
2M w
.
(12)
In [28] the noise uncertainty ρ is represented by a uniform disP
tribution in the limits of n , ρ Pn , where Pn is the nominal noise
ρ
power (in our case, the average power when no signal is present in
the band). The uncertainty (in the premise where the experiment is
performed) is estimated to be 1.6 (2 dB) by empirically defining
the SNR wall as is described in [25]. The probability density function (PDF) of ρ is
P
1
, x ∈ n , ρ Pn
gσ 2 ( x ) = ρ Pn − ( Pn ρ )
ρ
w
0,
otherwise.
(13)
′ and Pfa′ over the limits of the function,
By integrating the Pmd
as is done in the article [28], the effect of the noise uncertainty is
accounted for.
ρ Pn
Pmd = Pn Pm′d gσ 2 ( x ) dx
w
ρ
(14)
ρ Pn
Pfa = Pn Pfa′ gσ 2 ( x ) dx.
w
ρ
As for the decision threshold λ, the authors in [28] propose a
double-bounded threshold in order for a specific target probability
to be achieved for both the probability of miss-detection and the
probability of false alarm, at the same time. The lower bound is
defined by the threshold λ *f which guarantees that the false alarm
probability will be below the required value (denoted by Pfa).
2
erfc −1 2 Pfa + 1 M σ w2 .
N
(
λ *f =
)
(15)
*
The upper bound is defined by the threshold λmd
, which guarantees that the miss-detection probability will be below the requirement (the required value is denoted by Pmd ):
λ
*
md
1
2 π u −π 4 b
= 1 −
M 2a 1 − π u
(
( (
)
b = 4 Pmd a − 2 a − u 2 a 2 Pmd − 1
IEEE A&E SYSTEMS MAGAZINE
)
2
Mσ w
)
π + π u − 2 u = ae a erfc ( a ) .
2
(16)
25
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