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
(11)
C
m n
i
throughput
pS p
i j
i= 1 j=
1 n
= ∑∑ ù
In which, the probability, which the source (or
relay) node sent information was p .
5. THROUGHPUT ANALYSIS
Now we analyse the throughput of multi-source
sink relay sensor network.
Throughput of sensor network when m= n = 1
There is only a source (or relay) node S 1
and a
target (or relay) node R
1
, i = j = 1 , so it is a
situation of unicast and non-cooperation diversity.
Because the probability density function of gain
2
| g
ij
| is p 2 ( x ) = e − x , and in here i = j = 1 , so
| g |
ij
from the formula (9) and (11), we have:
C = ù = =
p Pr{ t < 1}
throughput, m n 1 1 S1
1
⎧ ù
⎫
1
= ù
1
p S
Pr ⎨
< 1
1
2 ⎬
⎩log(1 + | g11 | ⋅PS
(
1))
⎭
ù 1
⎧e
−1
2
⎫
+∞
− x
= ù
1
pS
Pr ⎨ < | g
1
11
| ⎬ = 1
1
1
1
⎩PS
(
1)
ù pS
∫ e e dx
ù −
⎭
P( S1
)
ù 1
⎧ e −1⎫
= ù
1
pS
exp ⎨−
⎬
(12)
1
⎩ PS (
1)
⎭
From(12), if the source (or relay ) node S 1
sent the information to R
1
with the nonzero
probability p
S 1
and the rate ù 1
, C
throughput, m= n=
1
reached the maximum. Hence, when the level of
node power and the possibility of sending
information are to achieve a dynamic balance, the
throughput was maximum.
Throughput of sensor network when m = 2 ,
n = 2
There were two source (or relay) nodes and
target (or relay) nodes, respectively, and the
network was based on the cooperative diversity
model, radio strategy and decoding technology
mentioned above in this paper. Because the Joint
2
probability density function16 of gain | g
i1
| and
2
| g | ( i = 1, 2) was
i2
S i
and the conditional probability density function was
y x
p ( x| y)
= e − , ( i = 1, 2) . We have the
2 2
| gi1| | gi2|
theorem 1.
Theorem 1 Based on the cooperative diversity
model, radio strategy and decoding technology
mentioned above, the parameters were described as
2
following: the path index was | g
ij
| , the
2
cooperation index was G , the power of source
node was PS ( i
) , the rate of sending information
was ù
i
, i, j = 1, 2 . Then the throughput of sensor
network was:
2
i S
C
throughput, m= n= 2
= ∑
i
(
i=
1 2
ù
p
L
× 1+ e − e − L
+
ù 1 ù 2
⎧ ⎫ ⎧ ⎫⎞
e −1 e −1
+ exp ⎨− ⎬+ exp ⎨− ⎬ PS ( ) PS ( ) ⎟
In which
⎩ 1 ⎭ ⎩ 2 ⎭⎠
{ ù L G g ù − }
exp
i
( ,
i2, ) 1
L =
,and
PS ( )
L( G, g , )
i
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)
The proof of thoerem 1 see appendix.
⎝
⎠
(13)
Obviously, it included the throughput under the
condition of non-cooperation relay in the formula
(23), this emphasizes the fact that the throughput
could be improved by cooperative diversity. For the
common m and n , similar to the mark mentioned
above, we have
L( G, gi2, g
i3, ù ) ,…, L( G, gi2, gi3,..., g
ij
, , ù )
and L1,..., L
j−2
,thereby, we have the following
corollary.
Corollary: For the other m and n , Under the
condition of theorem 1, the calculation formula of
throughput of multi-hop relay sensor network based
on cooperative diversity technology was
C
throughput
=
⎛ ⎧ 1⎫⎪
⎜ + − + − ⎬+
⎝
⎪⎩
( ) ⎪⎭
m
n
ù j
ù
i
L −L
⎪ e −
∑ pS
1 e e exp ⎨
i
i= 1 n ⎜ ∑
j=
1 PSj
−x
p| | , | |( xy , ) = e e
2 2
gi1 gi2
−y
, ( i = 1, 2) ,
7