Resource Allocation in OFDM Based Wireless Relay Networks ...

4.4 Optimization under Orthogonal Transmission
where
X n =
( N
∑
i=1,i≠n
a i,k p k b i,j q i,j
a i,k p k + b i,j q i,j
+ 1
)
. (4.39)
The detailed derivation steps are given in the Appendix A. Now for the obtained
value of ¯q j , we can easily find ¯p k (which is the optimal power at the source node for
the obtained ¯q j ) through gradient descent method. Then the optimal values p ∗ k and
q ∗ j are obtained from alternate optimization over ¯p k and ¯q j .
(ii) Subcarrier Pairing Algorithm
Now it only remains to find the solution of sub-carrier pairing. Let S be a K × K
sub-carrier pairing matrix whose (k, j)-th entry is ∆ (k,j) . The optimum paring could
be obtained from the Hungarian method, for a lower complexity we find a suboptimal
pairing strategy similar to the previous section. In the first step, we choose the
maximum valued entry in S, whose index is denoted by (ˆk, ĵ). Then, remove the
ˆk-th row and the ĵ-th column from S. This process is repeated until we get the
complete optimum pairing set ˆπ.
Resource Optimization with Relay Selection
The resource optimization under orthogonal transmission enhances the system
performance. However, the number of time slots required for a complete transmission
increase with increasing the relay stations. Following the work in [56], we propose
a relay selection scheme where a single best relay station is selected and a complete
transmission between the source and destination takes only two time slots.
For the n-th relay station, we find the optimization
C n = max
p k ,q n,j
K
∑
K∑
k=1 j=1
s.t. (4.4),
(
1
π (k,j)
2 log 2 1 + a )
n,kp k b n,j q n,j
a n,k p k + b n,j q n,j
K∑
p k ≤ P,
k=1
K∑
q n,j ≤ Q n .
j=1
(4.40)
75