A sum rate optimization for a wireless network has been considered in this problem. In this wireless network, each link will receive not only its desired signal but also interference from other links. Since the original optimization problem is not a convex optimization problem, we propose several methods to transform the original objective function into a concave form. Then, dual-based sub-gradient methods have been proposed to deal with each transformations. The simulation results show that our proposed algorithm can converge in an acceptable number of iterations. Besides, the comparison between each proposed methods is discussed via simulation.

1. Agenda Slide
Power control for
wireless interference Network
洪聖豐、蔡孝謙

2. Outline
01 02 03 04
Introduction System Model Flow Chart Performance

3. Introduction
01

4. Wireless network

5. Interference

6. Maximize summation of data rate

7. System
Model
02 Prove concave
Simple model
Complicate model

8. Prove concave
Power
Data rate
Optimization problem
SINR
𝑷 = [𝑷 𝟏, … , 𝑷 𝑵]
Gain
𝑮 =
𝑮 𝟏𝟏 ⋯ 𝑮 𝑵𝟏
⋮ ⋱ ⋮
𝑮 𝟏𝑵 ⋯ 𝑮 𝑵𝑵

9. Prove concave
Difference of convex -> non-concave[1]
Simple model
Assume that , data rate is approximated to
Define , the original objective function can be
transformed into
The log-sum-exp function is concave [2], so the transformed
object function is concave

10. The solution to the dual problem provides
an upper bound to the solution of the primal
(maximization) problem
Joseph-Louis Lagrange

11. How to solve
Primal problem is hard to solve, so we
need to turn it into dual problem
Primal problem
In dual problem, we can solve the
maximum P which lead us to get the
minimum of dual problem
Dual problem
After getting minimum value of dual
problem, we need to update Lagrange
multiplier to make dual gap lower
Update Lagrange multiplier

12. Simple model
Transformed optimization problem
Lagrange function

13. Simple model
Power allocation
Lagrange multiplier update function
where

14. Complicate model
No crash connection
Low throughput of any connection is not practical, so modify the objective
function as below

15. Complicate model
NO approximation
We assume previously so that the objective function is concave.
Now, we introduce two parameter to calculate the optimization problem
The Lower bound of the data rate can be expressed as
Transformed optimization problem

16. Complicate model
Power allocation
Lagrange function

17. Complicate model
where
Lagrange multiplier update function

18. Flow Chart
03

19. Simple model
 Initial parameters
 Update Pi
 Update λ
 Plot
Initial G, P, λ, Ϛ
Update λ and Ϛ by
Lagrange multiplier
update function
Update Pi by
power allocation
formula
Plot optimization
value vs iteration
index
Loop

20. Outer loop
Complicate model
 Initial parameters
 Update α,β
 Update Pi
 Update λ
 Plot
Initial
G, P, λ, Ϛ, μ
Update Pi by
power allocation
formula
Plot optimization
value vs iteration
index
Update α, β by
the newest SINR
Update λ, μ and
Ϛ by Lagrange
multiplier
update function
Inner loop

21. Performance
04

22. Parameter
Gain
Gij = Gji (symmetric matrix)
Gii >> Gji (good channel condition)
User_num = 20
P_max = 0.2
R_min = 0
LAGRANGIAN_INIT = 1
TOLERANCE = 10-5

23. Simple model
Iteration times: 14 Optimum value: 26.8780

24. Add throughput constraint(𝑹 𝒎𝒊𝒏)
Iteration times: 13 Optimum value: 26.8780

25. Complicate model
Iteration times: 13 Optimum value: 29.3375

26. Comparison

27. [1] G. Tychogiorgos, A. Gkelias and K. K. Leung, “Utility-Proportional Fairness in
Wireless Networks,” in IEEE PIMRC, 2012
[2] Q. Chen, G. Yu, R. Yin, and G. Y. Li, “Energy-Efficient User Association and
Resource Allocation for Multistream Carrier Aggregation,” IEEE Transactions on
Wireless Communications, vol. 65, no. 8, Aug. 2016
[3] G. Tychogiorgos, A. Gkelias and K. K. Leung, “Towards a Fair Non-convex
Resource Allocation in Wireless Networks,” in IEEE PIMRC, 2011
Reference