International Core Journal of Engineering 2020-26 | Page 162
and i-1 are found to be PU (i.e. q i 1 and q i 1 1 ). If E i+1 is
below the threshold, it is detected that the PU does not exist.
Otherwise, continue to perform additional checks on E i-2 and
E i+2 accordingly.
Step4: The 5IED algorithm validates the existence of an
energy value not exceeding the threshold in five continuous
sensing time slots (i.e. i 2, i 1, i , i 1, i 2 ), detects the
non-existent PU q i 0 in the current time period i. The PU
channel is in an "idle" state (H 0 hypothesis that SU receives
signals that include only channel noise).
Y
Y Input E
E i ! O
i 2
E i 1 , E i 1 , E i 2
Input E i
P f
N
E i 2 ! O
Y
q i 1
p x 111 x
T B 3
T B
p 11110 p 11111
, p 1111 x
T B
T B 4
p x 010 x
(6)
,
2
T B
.
CED
P f
T B 3
T B
CED
P f
2 P
CED
f
P d
CED
T B 3
T B
CED
P d
P
CED
f
P d
CED
u
Similarly, 5IED P d can be estimated at (8).
P d
P E i ! O H 1 P E i O H 1 > p x 10 xx P E i 1 ! O H 1 p x 00 xx P E i 1 ! O H 0 @
P E i ! O H 1 u * u ª p x 100 x P
¬
E
i 1
! O H 0 p x 101 x P E i 1 ! O H 1 º ¼
Ĺ
P E i 1 O H 0 p x 101 x P E i 1 O H 1 @ u ª p 0101
Ĺ > p x x100
100 x
¬ 0 x P E i 2 ! O H 0
(8)
ĺ
P E i ! O H 0 P E i ! O H 0 ª ¬ p x 11 xx P E i 1 O H 1 p x 01 xx P E i 1 O H 1 º ¼
P E i ! O H 1 u # u ª ¬ p x 111 x P E i 1 O H 0 p x 110 x P E i 1 O H 0 º ¼
ĸ
p x 011 x p x 010 x
T B
,
,
ª T B 4 P CED 1 P CED º u ª 2 P CED 2 P CED P CED º .
»
d
« ¬ T B d T B f » ¼ « ¬ T B f f
¼
A. Theoretical Performance of 5IED
We consider the PU signaling model in previous section 3,
where B and T are known. And then, use the PU signal of the
5IED to detect P f .
º ª
ķ ª ¬ p x x110
110 x P E i 1 ! O H 0 p x 111 x P E i 1 ! O H 1 ¼ u ¬ p 0 0111 x P E i 2 O H 0
p x 01 xx
1
T B
ª T B 4 1 P CED 1 P CED º 2 T B 3 P CED P CED P CED u
f d (7)
d
« ¬ T B f T B f » ¼
T B
q i 0
ķ
p x 110 x
T B
T B 3
p x 111 x p x 110 x
, p x 11 xx
Because each energy detection item is a separate CED issue
through (5), (6) P f can be rewritten as following:
Fig. 1. 5IED algorithm flow
P f
p x 011 x
2
We can deduce the sequence probability value in (6) by
assuming the average value of the known "idle" slot of T - B.
Among them, only one sequence includes a "busy" time slot
(i.e. ^ q i 2 1, q i 1 1, q i 1, q i 1 1, q i 2 1 ` ), which is "busy"
occurs only at the beginning and end of the time period in
which the idle slot occurs. All other T – B – 1 sequences are
"idle" slots.
It can be noted that the 5IED algorithm introduces the
maximum processing delay of the sensing slot. In order to
detect the change of PU state better, the sensing time slot can
be decreased. Therefore, the delay introduced by 5IED
becomes trifling, but the computational workload increases.
The system model of the 5IED detection method is shown in
Fig.1.
N
p 01110 p 01111
Where subscript x indicates that all values may be detected
xę{0,1}.
Step5: Otherwise, if the PU signal can be found in each of
these five intervals (i.e. q i 2 i 2 1 ), PU is considered to be
present. That is, the PU channel is in a "busy" state (H 1
assuming that the signals received by the SU include channel
PU signals and noise).
N
p 0111 x
p 1101 x P E i 2 ! O H 1 º ¼ ĺ u > p 1101 x P E i 2 ! O H 1 P E i 2 ! O H 0 @ .
Where (*) is p x 10 xx P E i 1 O H 1 p x 00 xx P E i 1 O H 0
for B ≥ 5, as shown in (6), the probability of five items with
signals present in the middle is given by:
(5)
p 1111 x P E i 2 O H 0 º ¼ ĸ u ª p 1111 x P E i 2 O H 0 P E i 2 O H 1 º .
¬
¼
Where (#) is p x 11 xx P E i 1 ! O H 1 p x 01 xx E i 1 ! O H 0 as
well as H 0 and H 1 are defined in part 2. Where B ≥ 5 and T-B ≥
4, can export the following expression to indicate the
probability that five consecutive items in the intermediate
signal are missing, expressed in (5) as p q i 2 , q i 1 , q i , q i 1 , q i 2 :
p 0101 x p 01010 p 01011
p x 100 x p x 001 x
p x 00 xx p x 001 x p x 000 x
1
B
2
B
,
,
p x 10 xx
p x 101 x
B 3
B
,
B 3
p x 101 x p x 100 x
p x 111 x
p 1101 x
B 4
B
B
,
,
p 11011 p 11010
(9)
2
B
.
Analogously, with the expressions in (9), we can rewrite
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