
182 Appendix
per hop using non-interference subtraction transmission is
D
NON
=
ρL − ln
ph
ρ ln
1+
p
(1+ρ)(N
0
+
∞
i=1
(iK+1)
−α
p+
∞
i=1
(iK−1)
−α
p)
and the minimum delay per hop using interference subtraction is
D
IS
=
ρL − ln
ph
ρ ln
1+
p
(1+ρ)(N
0
+
∞
i=1
(iK+1)
−α
p)
.
Assuming the system is in an interference-limited region, in which white
noise power
N
0
p, the delay performance gain is
g =
D
IS
D
NON
=
ln
1+
1
(1+ρ)(
∞
i=1
(iK+1)
−α
+
∞
i=1
(iK−1)
−α
)
ln
1+
1
(1+ρ)(
∞
i=1
(iK+1)
−α
)
. (A.2)
A.4.1 Numerator of
g
g
NUM
=ln
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
1+
1
(1 + ρ)
∞
i=1
(iK +1)
−α
T
1
+
∞
i=1
(iK − 1)
−α
T
2
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
.
We can obtain the bounds for T
1
and T
2
as follows:
∞
i=1
(iK + i)
−α
< T
1
<
∞
i=1
(iK)
−α
⇒ (1 + K)