
Delay Analysis of Cooperative Transmission 53
(2) When
S
1
=0
The linear network only prefers cooperative transmission from the source to
the destination, either using AF or DAF as shown in Figure 5.2(b). We can
derive the optimal
C
AF
i,j
=
2
ρ ln
1+
γ(2τ/H)
−α
+f(γ(τ/H)
−α
,γ(τ/H)
−α
)
1+ρ
to achieve the minimum delay; the error probability for each cooperative link
is
CT
i,j
=
2
H
. The minimum ETE delay by using only AF is
D
AF
min
≥
H(ρL − ln(2/H))
ρ ln
1+
γ(2τ/H)
−α
+f(γ(τ/H)
−α
,γ(τ/H)
−α
)
1+ρ
. (5.26)
For DAF, the minimum ETE delay is
D
DAF
min
≥
⎧
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎩
H(ρL − ln (2/H))
ρ ln
1+
2γ(2τ/H)
−α
1+ρ
, if b>I,
H(ρL − ln (2/H))
ρ ln
1+
γ(2τ/H)
−α
+γ(τ/H)
−α
1+ρ
, if b ≤ I,
(5.27)
where