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Energy Efficient Cooperative Wireless Communication and Networks
book

Energy Efficient Cooperative Wireless Communication and Networks

by Zhengguo Sheng, Chi Harold Liu
November 2014
Intermediate to advanced content levelIntermediate to advanced
221 pages
6h 17m
English
CRC Press
Content preview from Energy Efficient Cooperative Wireless Communication and Networks
Power Efficiency of Cooperative Transmission 77
where u>0,wehave
μ =
e
λπd
2
s,d
4
λπd
2
s,d
Γ
3
2
,
λπd
2
s,d
4
, (6.19)
which establishes the expectation of power ratio
E
[β]=
2e
λπd
2
s,d
4
K
λπd
2
s,d
Γ
3
2
,
λπd
2
s,d
4
, (6.20)
where
Γ(α, x)=
x
e
t
t
α1
dt is the incomplete gamma function.
Theorem 6.4 The average power ratio of DAF cooperation relative to direct
transmission for α =2is
1
2K
π
4ρ
< E[β] <
1
2K
π
4ρ
+1
. (6.21)
Proof Let ρ := πλd
2
s,d
/4. From the definition of the incomplete gamma
function, we have
g := e
ρ
Γ
3
2
=
ρ
t
1
2
e
ρt
dt . (6.22)
1. Upper bound:
g =
0
(ρ + s)
1
2
e
s
ds <
0
(ρ
1
2
+ s
1
2
)e
s
ds = ρ
1
2
3
2
.
(6.23)
2. Lower bound:
g>
0
t
1
2
e
t
dt
3
2
=
π
2
. (6.24)
Using the two
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Publisher Resources

ISBN: 9781482238211