Resource Allocation in OFDM Based Wireless Relay Networks ...

5.3 Problem Statement
The constraint on the end-to-end performance can be written as
where R is the rate requirement.
min
n
C n ≥ R,
5.3 Problem Statement
From previous discussion, the consumed powers over sub-hop n from DF n and AF n
are p n = ∑ K
k=1 p n,k and q n = ∑ K
k=1 q n,k, respectively. Assume that the total battery
energies of DF n and AF n are E DF
n
is given by
T net = min
( E
DF
1
p 1
and En
AF , respectively. Then the network lifetime
, . . . , EDF N
p N
, EAF 1
q 1
)
, . . . , EAF N
. (5.4)
q N
Our aim is to maximize the network lifetime by jointly optimizing the powers at
each node such that a minimum end-to-end rate requirement is fulfilled. To make
the discussion complete, we also assume that DF n and AF n have maximum power
constraints as P n and Q n , respectively, due to the linearity of the power amplifiers.
The optimization problem is finally formulated as
max T net (5.5)
p n,k ,q n,k
{ K
}
∑
K∑
s.t. min r n,k ≥ R, p n,k ≤ P n , ∀n
n
k=1
K∑
q n,k ≤ Q n ,
k=1
∀n
k=1
p n,k ≥ 0, q n,k ≥ 0, ∀n, k.
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