10 / 15
R
=
W
T
p
fv
p
cv
w
v
,
(12)
where
p
cv
— is the probability of correct detection of the synchronization
code in the “Test” mode at the threshold value
ε
v
, and
p
fv
— is the
probability of false detection of the synchronization code in the message
symbols in the “Test” mode at
ε
v
. The value
R
should be as small as
possible.
Table 5 shows the values
R
at the selected value
ε
s
and at different
ε
v
and
w
v
.
Table 5
Values
R
in the “Test” mode
Values
R
at
p
r
= 0
.
1
,
n
= 16
,
b
= 145
and
ε
s
= 1
ε
v
w
v
= 1
w
v
= 2
w
v
= 3
w
v
= 4
w
v
= 5
0 6.13
∙
10
−
6
5.05
∙
10
−
10
4.158
∙
10
−
14
3.424
∙
10
−
18
2.819
∙
10
−
22
1 3.75
∙
10
−
5
1.89
∙
10
−
8
9.532
∙
10
−
12
4.803
∙
10
−
15
2.420
∙
10
−
18
2 0.000197 5.22
∙
10
−
7
1.383
∙
10
−
9
3.665
∙
10
−
12
9.708
∙
10
−
15
3
0.00085
9.71
∙
10
−
6
1.108
∙
10
−
7
1.265
∙
10
−
9
1.444
∙
10
−
11
4
0.00291
0.000114
4.441
∙
10
−
6
1.735
∙
10
−
7
6.780
∙
10
−
9
5
0.00785
0.000827
8.721
∙
10
−
5
9.192
∙
10
−
6
9.689
∙
10
−
7
6 0.016933
0.00385
0.000875
0.000199
4.524
∙
10
−
5
In Table 5, for example, the pairs
(
ε
v
, w
v
)
are selected for the
synchronization system in such a way that at the required value
R
T
the value
R
does not exceed the predetermined
R
T
(
R
≤
R
T
).
In this example, at the given acceptable probability value
R
T
= 10
−
6
,
R
=
{
5
.
22
∙
10
−
7
; 1
.
108
∙
10
−
7
; 1
.
735
∙
10
−
7
; 9
.
689
×
10
−
7
}
are selected for
the pair values
(
ε
v
, w
v
) =
{
(2
,
2)
,
(3
,
3)
,
(4
,
4)
,
(5
,
5)
}
, respectively.
The probability of outcoming from the states “Search” and “Test” in
the case of correct detection of the synchronization code is as follows:
p
tc
=
p
cs
(1
−
F
)
(1
−
q
w
s
)
(1
−
q
)
(
p
cv
)
w
v
,
(13)
where
q
= (1
−
p
cs
) (1
−
F
)
.
(14)
Table 6 shows the values
p
tc
for the chosen value
ε
s
and different
ε
v
and
w
v
.
The values
p
tc
=
{
0
.
454; 0
.
602; 0
.
681; 0
.
718
}
correspond to the selected
values
R
. It should be noted that while increasing the value of the pair
(
ε
v
, w
v
)
from (2, 2) to (3, 3) it increases
p
tc
(from 0.602 to 0.454) by 0.148,
but while increasing it from the value (3, 3) to (4, 4), it increases
p
tc
only
126 ISSN 0236-3933. HERALD of the BMSTU. Series Instrument Engineering. 2015. No. 2