Resource Allocation in OFDM Based Wireless Relay Networks ...

4.3 Cooperative Non-Orthogonal Transmission
Subcarrier Pairing under Fixed Power Allocation
We define a K × K matrix Γ, where the (k, j)-th entry is
)
[Γ] (k,j) = 1 N∑
(1
2 log 2 p k |h n,k | 2 ρ j |g n,j | 2
+
p k |h n,k | 2 σr 2 + ρ j |g n,j | 2 σd 2 + .
σ2 rσd
2
n=1
Our aim is to maximize the overall throughput such that a particular sub-carrier
at hop-1 is paired with one and only one sub-carrier over hop-2. The different steps
of algorithm are
1: Choose the optimal pairing (k ∗ , j ∗ ) such that
(k ∗ , j ∗ ) = max([Γ] (k,j) ), ∀(k, j),
where [Γ] (k,j) denote the (k, j)-th entry in Γ,
2: Remove the k ∗ -th row and j ∗ -th column from Γ.
3: Repeat step-1 and step-2 until we get the complete optimum pairing set π ∗ .
Power Refinement Under Fixed Pairing
To obtain a more close performance to the joint resource allocation scheme, we
re-compute the power allocation for the obtained sub-carrier pairing in step 2.
Assume that the sub-carrier k is paired with the sub-carrier m(k), where m is the
mapping function. The problem in (4.18) becomes
where
D (µ, λ) = max
p,ρ
K∑
( )
1
2 log 2 (1 + SNR k ) − µp k − λρ j + µP S + λP R , (4.27)
k=1
SNR k =
N∑
n=1
a n,k p k b n,m(k) ρ m(k)
a n,k p k + b n,j ρ m(k) + 1 . (4.28)
The problem (4.27) can be decomposed into K sub-problems, each being similar to
(4.19), and the solution for per sub-carrier problem follows the same steps in (4.19)
to (4.23). Finally, the dual variables can be found from sub-gradient method.
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