Resource Allocation in OFDM Based Wireless Relay Networks ...

3.4 Joint Resource Allocation Scheme
formulated as
max
π,τ ,p A ,p R ,p B
s.t.
M
∑
K∑
m=1 k=1 j=1
K∑
( 1
π (k,j) τ m,(k,j)
2 C ( SNR A m,j
K∑
π (k,j) = 1, ∀j,
k=1
K∑
π (k,j) = 1, ∀k,
j=1
M∑
τ m,(k,j) = 1, ∀(k, j),
m=1
K∑
p A m,k≤ P Am ,∀m,
k=1
K∑
p R j ≤ P R ,
j=1
K∑
p B m,k≤ P Bm ,∀m,
k=1
p A m,k ≥ 0, p R j ≥ 0, p B m,k ≥ 0, ∀m, k, j,
) 1 +
2 C ( ) )
SNR B m,j (3.6)
where C(x) log 2 (1 + x), and τ = {τ m,(k,j) }, π = {π (k,j) }, p A = {p A m,k }, pB =
{p B m,k }, pR = {p R j } for all m = {1, ..., M}, k = {1, ..., K}, j = {1, ..., K}. The 1 2
factor appears due to the two time slots used for a complete transmission.
The first and the second constraints are originated from the the fact that
each sub-carrier in MAP can be coupled with one and only one sub-carrier in
BCP and vice verse. The third constraint ensures the exclusive allocation of the
sub-carrier pair (k, j) to the m-th user pair (A m , B m ) only. However more than
one sub-carrier pairs can be allocated to a particular MU pair. Other constraints
represent individual power constraint at each node.
3.4 Joint Resource Allocation Scheme
It is easily known that (3.6) is a mixed integer non-linear programming problem
[34], and we can solve the dual problem instead of the original problem [35]. The
dual problem associated with the primal problem (3.6) is defined as [13]
min
ν,λ,η
D(ν, λ, η) (3.7)
s.t. ν m ≥ 0, η m ≥ 0, ∀m, λ ≥ 0,
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