Resource Allocation in OFDM Based Wireless Relay Networks ...

2.6 Summary
2.4
2.2
2
1.8
Rate (bits/s/Hz)
1.6
1.4
1.2
Dual Solution (D(ν,λ)/K)
1
JntSol
SubOpt
0.8
JSP−(with matching)
0.6
EP−ECarr
EP−RndCarr
0.4
2 3 4 5 6 7 8 9 10
N
Figure 2.7: Throughput versus the number of relays for M = 6.
conditions.
• For a sub-carrier pair, the optimal throughput is obtained from the optimal
power allocation. A sub-carrier pair is assigned to a user which has the
maximum optimal throughput among all other candidates.
• A profit matrix is obtained for the assigned sub-carrier pairs. The optimal
pairing is then obtained from the Hungarian method.
The dual problem is solved from the sub-gradient algorithm and a near optimal
solution is obtained. In order to reduce the computational complexity, we also
presented a suboptimal algorithm which separates the joint optimization into three
steps such that: 1) The sub-carrier assignment is obtained under equal power
distribution at each node. 2) The allocated sub-carriers are then paired in such a way
that the sub-carrier with highest channel gain over the first hop is paired with the
sub-carrier of best gain at the second hop. 3) For the obtained sub-carrier allocation
and the pairing, the optimal power is obtained from the waterfilling. The suboptimal
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