Resource Allocation in OFDM Based Wireless Relay Networks ...

4.3 Cooperative Non-Orthogonal Transmission
received at DN over sub-carrier pair (k, j) is
y DN
(k,j) =
N∑ √
g n,j w n,j h n,k pk s k +
n=1
N∑
g n,j w n,j z n,k + z d ,
where z d represents the additive noise at DN with the variance σ 2 d .
n=1
The SNR received over sub-carrier pair (k, j) is given by [58]
SNR (k,j) =
(∣ ∣∣ ∑ N
n=1 g n,jw n,j h n,k
∣ ∣∣
) 2
pk
∑ N
n=1 |w n,jg n,j | 2 σ 2 r + σ 2 d
. (4.2)
To assist the mathematical formulation, we introduce a binary variable π (k,j) ∈ {0, 1}
for the sub-carrier pairing, such that π (k,j) = 1 if the k-th sub-carrier of the first hop
is paired with the j-th sub-carrier of the second hop, and π (k,j) = 0 otherwise.
The overall system throughput can then be expressed as
C = 1 2
K∑ K∑
π (k,j) log 2 (1 + SNR (k,j) ). (4.3)
k=1 j=1
Since each sub-carrier in the first hop can be coupled with one and only one
sub-carrier in the second hop and vice verse, the sub-carrier pairing constraint can
be expressed as
K∑
K∑
π (k,j) ∈ {0, 1}, ∀k, j, π (k,j) = 1, ∀j, π (k,j) = 1, ∀k. (4.4)
k=1 j=1 n=1
k=1
j=1
Further, The power constraints are defined as
K∑ K∑ N∑
π (k,j) |w n,j | 2 (p k |h n,k | 2 + σr) 2 ≤ P R , (4.5)
K∑
p k ≤ P S . (4.6)
Our aim is to jointly optimize the power allocation at source node, the
beamforming coefficients at each relay node, and the sub-carrier pairing at relay
nodes such that the overall system throughput is maximized under the power
constraints at the source and relay nodes.
k=1
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