Full Text - Journal of Theoretical and Applied Information Technology

Journal of Theoretical and Applied Information Technology
10 th June 2013. Vol. 52 No.1
© 2005 - 2013 JATIT & LLS. All rights reserved .
ISSN: 1992-8645 www.jatit.org E-ISSN: 1817-3195
n
⎞
+ ∑ ∫ ∫ ∫ϒdy3
dy
j
j=
3
⎟
Lj−2 Lj−1 L1
⎠
{ t < } = { t < LG g ù }
Pr 1 Pr ( , , )
2 1 i2
∞
2
{ 1
G gi2 g
i2 } 2
| |
= ∫ t < L ù = y p y dy
g
Pr ( , , ) | | ( )
0 i 2
2 2
{ , −1 L
−2 , } 2
| g |
ϒ= Pr | g | > | g | = y p ( y ) (14)
i j j i j j j
i,
j
6. CONCLUSIONS
In this paper we mainly studied the throughput of
multi- source relay wireless sensor network based
on cooperative diversity, a cooperative diversity
model of sensor network, which was multi-source
relay, was set up. Based on the model, the formulae
of throughput was derived. So the quantitative
calculation for the throughput performance of
multi-source relay sensor network under
cooperative diversity would provide us theoretical
judging rule for discussing farther the application of
technical proposal such as cooperative selection
scheme in the actual network environment of multihop
relay sensor network. On the other hand, it was
proved theoretically that throughput performance of
multi-source relay sensor network would be
improved by cooperative diversity.
According to the conclusions of throughput and
the simulation based on cooperative diversity, a
valuable judgment scale was given in the
application environment of multi-hop relay wireless
sensor network for balancing the relationship
between the throughput and network cost.
APPENDIX
Prove of theorem 1: for ∀i, ji , ≠ j, A
i
and A
j
are independent of each other. Combined with the
formula (9), we have:
⎧ ù
⎫
1
Pr{ t1 < 1} = Pr ⎨
< 1
2 ⎬
⎩log(1 + | g11 | ⋅PS
(
1))
⎭
⎧ ù
⎫
2
+ Pr ⎨
< 1
2 ⎬
⎩ log(1 + | g21 | ⋅PS
(
2
)) ⎭
⎧ ù
⎫
Pr < 1⎬
⎩log(1 | | ( )) ⎭
1
= ⎨
2
+ g11 ⋅PS1
⎧ ù
⎫
2
+ Pr ⎨
< 1
2 ⎬
⎩log(1 + | g21 | ⋅PS
(
2
)) ⎭
=
(17)
But
ù 1
⎧ e −1⎫
exp ⎨−
⎬
⎩ PS (
1)
⎭
+
(15)
(16)
ù 2
⎧ e −1⎫
exp ⎨−
⎬
⎩ PS (
2
) ⎭
=
∞ ⎧⎪
2
exp { ù
i
L( G, gi2, ù ) −1}
2
⎫⎪
∫ Pr ⎨| g
0
i1 | > | gi2
| = y⎬
⎪⎩
PS (
i
)
⎪⎭
p 2 ( y)
dy
| gi
2 |
(18)
∞
Pr | g |
0
1
> | g | ( )
2
=
| i 2 |
∫ i
L
i
y p y dy
g
2 2
= { } 2
(19)
∞ ∞
⎧ p
2 2( x | y) p 2 ( y)
dx dy if y <
⎪∫ 0 ∫
L
L | gi1| | gi2|
| gi
2 |
= ⎨
∞
⎪
p 2 ( y)
dy if y ≥
⎩ ∫
L
0 | gi
2 |
(20
)
in which
L( G, g , )
2 2
( g
2
PS G )
log 1 + | | ( ) + −ù
i i i
i2 ù =
2 2
⎛1 + | gi2
| PS (
i)
+ G ⎞
log ⎜
2 ⎟
1 + | gi2
| PS (
i)
⎝
exp ù
i
L( G, gi2, ù ) −1
L =
PS (
i
)
(21)
{ }
Combined with the conditional probability
density function, we easy to know that
{ }
y−x −y
Pr t < 1 = e dx dy + e dy
0
2
L
∫ ∫
∞
L
∞
L
−L
= 1− e + e
(22)
So we have
2
ipS C
i
throughput, m= n=
2
= ∑ ù
( Pr( t1 < 1) + Pr( t2
< 1) )
2
i=
1
i=
1
2 ù
ipS i
L
= ∑ × ( 1+ e − e − L
+
2
ù 1 ù 2
⎧ e −1⎫ ⎧ e −1⎫⎞
⎨ ⎬ exp ⎨ ⎬
PS (
1) PS (
2)
⎟
⎩ ⎭ ⎩ ⎭⎠
+ exp − + − ⎟
(23)
∫
⎠
L
,
8