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Cellular Operators in a Shared Spectrum

Sivan Altinakar

Supervisors:Tinaz Ekim-AsiciMárk Félegyházi

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Summary

Introduction Modeling Game Theory Program Simulations Results Further Research Conclusion

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Introduction

In a given network with non-cooperative operators on a shared frequency band:

we are interested in optimizing the interference from the point of view of the network, by setting each base station's transmission power.

Modeling

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Modeling

Cellular Network

components• operators• base stations (BS)• threshold distance of interference

our approach• shared frequency band• notion of Interference (related to SINR)• finite number of power settings

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Definitions

Signal-to-Interference-plus-Noise-Ratio:

Interference from one Base Station:

Interference from whole Network

ws,B,A

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ModelingFirst Attempt: edge-deletion

Mutual Disturbance

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ModelingFirst Attempt: edge-deletion

B

DA

CDifficult to interpret

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ModelingSecond Attempt: node-deletion

Base Station A

A1

A2

A3

B1

B2

B3

Base Station B

Interference

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ModelingSecond Attempt: node-deletion

Threshold = 6059

59

59

59

5959

59

59

59

61

59

• pairwise threshold• NP-complete

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Modeling

Early results in first version (IMax):

quality of a "uniform setting" ( infinite ) response by "chunks" ( when decreasing

)

"almost" equivalent solutions ( N0=0 )

effect of changing one base station's setting coverage constraint & inactive base stations

introduce second version (SMax)

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Modeling

A

B

C

XNetwork

Final Model

ws,X,C

ws,X,A

ws,B,Aws,C,A

ws,A,C

ws,A,B

ws,X,B

Individual Interference of B over A (w/ setting s)

noise factor of B (w/ setting s)

Interference over A (w/ setting s)

SUM

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Modeling

Interference over A

Game Theory

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Definition strategic-form game

• player base station

• strategy power level

• utility function (based on Interference )

Nash equilibrium (=stable strategy profile)

price of anarchy

Game Theory

simultaneous sequential gamechoice of a strategy

No need of an objective

function

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Game Theory

Utility functions used (for a base station A ):

simulations

related to the SINR of a

virtual user very close to

the base station

(BA)

(BWFS)

(BPON)

Program

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Program Initialization:

• network• upper-bound constraint (if defined)• initial strategy profile (=power setting)

• objective function• choice of the next base stations• utility function

Result:• the final strategy profile reached (result of the game)• the best strategy profile encountered (result of the heuristic)

Procedure:While a stopping criteria is not met, perform the steps

1. choose a base station2. choose a strategy for this base station3. update the best strategy profile encountered (if necessary)

change of strategy

= MOVE

simultaneously:• play game• run optimization

heuristic

}

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Program

Stopping criteria:• Nash equilibria• max # of iterations without move• max # of iterations

Additional fine-tuning capabilities:• limited range of strategies• tabu list

Choice of the next base station:• RAN RandomSearch• SEQ SequenceSearch• GTS GlobalTabuSearch• DTS DistributedTabuSearch

Simulations &Results

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Simulations

It's time for a demo…?

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Program

Software & Hardware• Java 1.5• Dell with 600MHz Intel Pentium III and 128 MB RAM• Matlab

Implementation: 3 types of classes• model representation

model parameters base stations, operators, network,…

• algorithms brute force search game tabu search

• interfaces SharedSpectrumSolver MultipleRunLauncher SSS

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SimulationsEnvironment parameters

• N = 0.0001• = 4• dthresh = 10 km

Network parameters• = ∞• set of power levels = {6.25, 12.5, 25, 50, 100}

Experiment variables• objective function (IMin, SMax)• utility function (Base, BWFS, BPON, )• initial setting (PMin, PMax, PRan)• range (free, 1-step)• tabu list length (no list, 1, 3, 5, 7)• procedure (RAN, SEQ, GTS, DTS)

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ResultsNE at the end of the procedure:

• RAN: 99%• SEQ: 100%• GTS: 30-90%• DTS: 65-90%

Observations:• better with structured network• decrease of efficiency with a limited range• iterations average between 10 and 60• unusual behavior with particular utility functions

Reached Nash equilibria:• usually 1 point: PMax• for too high: PMaxMin solution(s)• for limited range: extra Nash equilibria (!)• starting from PMin: difficulties, range effect

Tabu list length (free range, PRan) no effect on RAN longer=better (-> SEQ) Random network:

GTS useless for {0,1,3} and DTS for {0,1} w/ list: DTS better than GTS

Random Pyramidal

RAN 32 31

SEQ 20 20

GTS 23 18

DTS 50 44

Example3 utility functions with

• = 0.2

• tabu = 5

• range = free

• initial s. = PRan

= ∞

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Results

Objective function value

IMin: optimum is PMax

Nash eq. for almost all utility functions the game always stabilizes at the optimum Price of Anarchy = 1

SMax: optimum is PMaxMin

Nash equ. for no utilitiy good solutions are rare and purely accidental on

the way to PMAX Price of Anarchy not relevant

Further Research

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Further Research

open questions

effect of <∞

new utility functions

simultaneous strategy choice

edge- and node-deletion

Conclusion

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Conclusion

Optimization of the quality of the transmissions in a wireless communication system.

We designed several models, defined a game and build a program for running simulations.

We observed that:• usually our utility functions have a unique Nash equilibrium at the

maximum power setting• the utility functions match perfectly the objective of IMin, but

absolutely not SMax• other variables such as tabu list length and the range of available

strategies influence a game or an algorithm.

Further research could be conducted on the proposed open questions, the influence of and new utility functions. This could be done theoretically and by using the developed simulator.

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References

Félegyházi and HubauxWireless Operators in a Shared Spectrum(2005)

Halldórsson, Halpern, Li and MirrokniOn Spectrum Sharing Games(2004)

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Thank you for your Attention!