Resource Allocation in OFDM Based Wireless Relay Networks ...

4.5 Simulations
40
30
20
Sum−ρ
Sum−P ObjSub
JPC
OPNC
10
0
0 100 200 300 400 500
Number of iterations
1.5
1
0.5
0
FP
GD
FP−GD
5 10 15 20 25
Number of iterations
Figure 4.3: Convergence.
best performance over all schemes while SPC gives very near performance to JPC.
The convergence of the proposed algorithms is shown in Fig. 4.3. The maximum
power per transmission are taken as P S = 10, and P R = 15. Fig. 4.3 (a) shows the
convergence of the sub-gradient for JPC and OPNC algorithms. The abbreviations
Sum-P, Sum-ρ and ObjSub denote the total power allocated at source node (i.e.,
∑ K
k=1 ˆp k), power allocated at relay nodes (i.e., ∑ K
j=1 ˆρ j), and the value of objective
function at ˆp k and ˆρ j , respectively. We see that the convergence is attained at
290 iterations. Further, at convergence both the power constraints P S and P R are
satisfied, i.e., Sum-P and Sum-ρ converges to the P S and P R , respectively. Figure
4.3 (b) shows the convergence of per-sub-carrier pair power allocation algorithm,
discussed in section 4.3.1. In the figure, FP and GD denote the fixed point algorithm
and gradient descent algorithm, respectively, where FP-GD shows the convergence of
alternate optimization over p k and ρ j . It can be seen that the fixed point algorithm
converges very fast only after few iterations, i.e., in 5 iterations, while the alternate
optimization over p k and ρ j takes 12 iterations to converge. The gradient descent
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