1. Vaggelis G. Douros George C. Polyzos Stavros Toumpis
A Bargaining Approach to Power Control in Networks of Autonomous Wireless Entities
Vaggelis G. Douros
George C. Polyzos
Stavros Toumpis
ACM MOBIWAC Oct. 2010, Bodrum, Turkey
4/5/2019

2. Some couples may not communicate efficiently 
Motivation (1)
Deadline is today!
This is urgent!
The food is delicious
Fantastic shirt!
Some couples may not communicate efficiently 

3. Motivation (2) N couples of friends discuss in the same cafeteria
Each couple aims at achieving a (different) “minimum quality of discussion”
Discussions of other couples may prevent an efficient communication
N pairs of wireless nodes (e.g., BSs-MNs, APs-Clients) transmit their data sharing the same wireless medium
Each pair aims at achieving a (different) (SINR) target
Interference among wireless devices may prevent an efficient communication
Competition for resources among multiple players, where the influence from each player is different ≡ Weighted Congestion Game

4. Fundamentals of SINR-Based Power Control (1)
Power control is a standard radio resource management method for interference mitigation
Analogy: A person that increases/ reduces his level of voice
The Simplified Foschini-Miljanic Formula (FM) [F&M, TVT ’93], [Bambos, IEEE Pers. Comm. ’98]:
(+) fully distributed algorithm
no need for cooperation among the nodes to apply FM
At steady state, for each node i: Pi(k+1)=Pi(k)
each node i has either achieved its SINR target γi or it is below its target and transmits with Pmax

5. Fundamentals of SINR-Based Power Control (2)
The problem: Even in small topologies, there are cases that it is impossible for all wireless nodes to achieve their SINR targets
One solution: One/ many nodes need to “power off”.
E.g. Trunc(ated) Power Control [Zander, TVT ’92]
“N-1” links apply a power control algorithm
the one that is furthest from its SINR target powers off
(-) Unfair for this node – no opportunity to achieve its target
More importantly, how to oblige an autonomous entity to power off?

6. The Bargaining Foschini-Miljanic Scheme (BFM)
A heuristic approach that aims at maximizing the number of links that have achieved their targets
Should be at most “N-1”≡ “(N-1)-feasible” solution
Bargaining as an incentive tool for negotiations among unsatisfied nodes (those that are below their SINR targets)
BFM works on top of FM, starting from its steady state
Links that have achieved their targets apply FM
Unsatisfied links negotiate in pairs. Each one uses part of its budget to make an offer to the other
“I offer you X credits if you reduce your power Y %”
These virtual credits may be used for future networking functions [Blazevic et al., IEEE Comm. Mag. ’01]

7. Fundamentals of BFM (1) How to choose who makes an offer?
How to choose to whom it offers?
Choose randomly one among the set of unsatisfied nodes
(-) This demands an external entity
A distributed approach: Each unsatisfied link decides independently whether it is a “Seller” or a “Buyer” and broadcasts its status to the network
Which is the desired percentage reduction Pred?
The minimum needed to achieve its target in the next round (but if, e.g., the node is distant this may be impossible)

8. Fundamentals of BFM (2)
Tx1 computes the reward R12 that is willing to offer to Tx2
If Tx2 accepts its offer, then Tx1 updates its power according to the FM scheme and achieves its target
If Tx2 rejects its offer, then Tx1 voluntarily reduces a bit its current transmission power (0<c<1)
Otherwise, all nodes may stay at the same state

9. Fundamentals of BFM (3)
Tx2 computes through the reward R21 that would have given if Tx2 had asked for the same Pred
If R21 ≤ R12,Tx2 accepts the offer and transmits at Pred*P2(k)
If R21 > R12,Tx2 rejects the offer and updates its power using the FM algorithm
Can you show us an example to see how this works?
Just raise your hand during the questions ;-)

10. On the Number of “(N-1)-feasible” Solutions
Number of “(N-1)-feasible” solutions after the application of both BFM and Trunc FM for different scenarios
Similar Performance with Trunc FM
But Trunc FM is not suitable for autonomous nodes and it is unfair

11. On the Long Term Fairness of BFM (1)
Application of BFM for the same set of nodes for transmission rounds
The budget at the start of the (m+1)th round is the one at the end of the mth round
For every period of 100 transmission rounds, we count how many times Tx5 and Tx6 (the only unsatisfied nodes in this particular example) do not achieve their targets

12. On the Long Term Fairness of BFM (2)
There is an average ratio 3:2 per period
(+) This ratio represents well every transmission period
(+) All nodes get the opportunity to transmit their data
(-) In Trunc FM, the weakest node always powers off
(+) This ratio is independent of the initial budget of the nodes
Due to the dynamically adjusting mechanism that nodes follow when they either make or evaluate an offer

13. “The Meat”
BFM: A heuristic approach for joint power control and bargaining that aims at maximizing the number of satisfied entities, in cases that it is impossible for all of them to achieve their SINR targets
(+) distributed implementation
(+) efficient – finds out a large number of solutions
(+) fair – statistical rotation of unsatisfied nodes
Ongoing Work: To cast this problem as a weighted congestion game and apply findings from recent works of the algorithmic game theory

14.  Teşekkür ederim  Vaggelis G. Douros Mobile Multimedia Laboratory
Department of Informatics
Athens University of Economics and Business

15. BACKUP

16. Performance Evaluation of FM
Even in small topologies, where few entities coexist, there are many cases where at least one node cannot achieve its SINR target

17. Topology

18. FM: SINR Evolution

19. Trunc FM: SINR Evolution

20. Trunc FM: Power Evolution

21. BFM: SINR Evolution

22. BFM: Power Evolution

23. Simulation Parameters (1)
Value
# Links of each Topology
4, 7, 10
# Scenarios per Topology
50000
Max # Iterations per Algorithm
1000
Simulation Terrain
A square of size 100
Transmitters (Tx) Distribution
Uniform
Receivers (Rx) Distribution
Rx is placed randomly in the interior of a circle of radius 5 from its associated Tx
Path Loss Model
G= f(d-4), d: distance between Tx and Rx

24. Simulation Parameters (2)
Value
Mobility Model
Quasi-static model
Noise
10-6
Pmax
5.0
SINR Targets (in dB)
[11,15]
Initial Transmission Powers
Randomly selected at (0, Pmax]
Parameter c (Voluntarily Power Reduction)
0.9
Initial Budget B
Randomly value at [100, 200]