1 Multi-radio Channel Allocation algorithms based on game theory analysis Shirin Saeedi Bidokhti Supervised by Mark Felegyhazi Prof. Hubaux Feb. 2006.

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Multi-radio Channel Allocation algorithms based on game theory analysis

Shirin Saeedi Bidokhti

Supervised by Mark Felegyhazi Prof. Hubaux

Feb. 2006

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Introduction

In the year 2003, within a workshop on the practical issues of cognitive radio networks,

FCC started to look forward to improvement of access to radio spectrum through better

use of time, space, frequency, etc. as the potential capabilities of cognitive radios.

So Cognitive radio has received significant interest as a technology that could improve

performance and efficiency of spectrum usage. And as a result channel allocation for

has brought the topic back to the research field.

Cognitive radio is an enhancement on the traditional concept wherein the radio is aware

of its environment and its capabilities, is able to independently alter its physical layer

behaviour, and is capable of some complex adaptation strategies. As a result the

need for game theory in the analysis of such networks is inevitable.

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Outline

Preliminary Game Theory A Review on “M. Felegyhazi, M. Cagalj, J.P. Hubaux, “Multi-

radio channel allocation in competitive radio networks”” Assumptions Steps Algorithms Simulation Results Conclusion References

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Preliminary Game Theory

Non-cooperative Cooperative

Single Stage Repeated

Strategic-form Extensive-form

Perfect Information Imperfect Information

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A review on M. Felegyhazi, M. Cagalj, J.P. Hubaux, “Multi-radio channel allocation in competitive radio networks”

A game theoretic analysis of fixed channel allocation strategies of devices using multiple radios is presented in this paper.

N users each having k < |C| number of radios as the game players.(C as the set of available channels)

Strategy of user i defined by Utility function has been defined as the total rate in the system and as a result in

the form of

Assumptions: 1) A single stage game 2) All Transmitters in the same collision domain

Theorems I & II: Existence of the Pareto-optimal NEs - special conditions on the channel

)()( ,, c

Cc Cc c

cicii KR

K

KRsU

},...,{ ,1, Ciii KKS

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Assumptions

Critical Assumptions in the paper Perfect information assumed A sequentially implemented algorithm A single collision domain assumption

Assumptions in our work Each user only knows about the channels it has some radio on . All the users are deciding simultaneously about changing the channels Multiple collision domains

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Steps

Algorithm I (single collision domain, not perfect information, not sequential, non-cooperative game)

Algorithm II (Multiple collision domain, perfect information, sequential decisions, non-cooperative game)

Algorithm III (Multiple collision domain, perfect information, not sequential decisions, non-cooperative game)

Algorithm IV (Multiple collision domain, perfect information, sequential decisions, cooperative game)

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Algorithm I

1 2

1

553

3 43 2 3

Channel array:

1 2 11

1 2 11

• Imperfect information through channels the node is using• Nodes decide simultaneously• Nodes try to reach a flat situation (among their radios)• Nodes move radios which are receiving smaller data rate.

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Algorithm I (Cont.)When to stop? A difference of max 1 on channels a node is using Its average data rate within that range

How to decide to move a radio? Move the radios with less than expected value of data rate (m) with

probability of (channel(j)-m)/channel(j).

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Simulation ResultsConverging to the NE Number of Devices: 20 Number of Radios per device :4 Number of Channels: 11 Sliding averaging

Node 1 Node 6

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Simulation ResultsConverging to the NE

Node 12

Average Convergence time: 76.5 time unitsσ: 74.27 time unitsAverage Data Rate/device =.55 channel/device

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Simulation ResultsFlat Data Rate per Device

Device

Dat

a R

ate

per

Rad

io /D

evic

e

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Simulation ResultsEffect of Averaging (α) on Convergence Time

Number of Devices: 20Number of Radios/Device: 4Number of Channels: 11

Number of Devices: 20Number of Radios/Device: 2Number of Channels: 11

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Simulation ResultsEffect of Number of Devices on Convergence Time

Number of Radios/Device: 3Number of Channels: 11α = .9[errors for 22 and 44 nodes]

Number of Radios/Device: 4Number of Channels: 11α = .9

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Simulation ResultsEffect of Number of Radios on Convergence Time

Number of Devices: 20Number of Channels: 11α = .9

5 x 20=100=9 x 11+1

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On Multiple Collision Domains Nodes are only aware of the nodes in their collision domain. It can happen that among the many possible equally valued channels for a node, one can be

better for a node out of its collision domain. Flat channel allocation is not generally the solution.

Example.

..

. ..

1

2

34

5• • • •

• • • • • • • • • • • • • •

• • • •

ChannelDevice #

1

2

34

5

1 2 3 4 5 6

2

3 4

11

2 2

2 2

3

3

3

3 3

3 3

33

4

4

4

3 3

3 3

3 3

3 3

2

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On Multiple Collision Domains

How To Deal with the problem?

1) The case of selfish devices.If fulfilling the requirements, we are happy, else we have to deal with the problem with somecooperative game.We cannot apply the Algorithm I to the problem because we cannot impose any stoppingcondition because we know neither about the NEs nor about the Pareto-optimal states.A possible case to check is the non-cooperative game with perfect information both withsequential (Algorithm II) and without sequential deciding (Algorithm III).

2) Defining our requirementsMore data rate? How to choose the best in the case of having more than one Pareto-Optimal

state?Maybe the best average on the devices’ data rate. However, this doesn’t include any kind ofFairness issue.Fairness? We simply expect better data rate for nodes with fewer neighboursWe have based our work on the total data rate of the network, while not allowing zero data rate .

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On Multiple Collision Domains (Cont.)

3) Proposing an algorithm The algorithm we propose is a kind of cooperative game.

Idea: Having more than one radio on one channel but guaranteeing the channel to be dedicated

privately to that specific device with a probability. This can in a sense provide a little more fair

situation for the Nodes. After dedicating the first channels to each device, The rest of radios shall

be put on the remaining channels.

We assume sequential deciding with perfect information and let nodes listen to all the available

channels and decide which one to choose.

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Simulation Results

* Algorithm IV* Algorithm III* Algorithm II

15 random Topology10 x 10 fieldCollision radius: 415 devices4 radio/device

Perf

orm

s th

e be

st in

80%

of

topo

logi

es

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Simulation Results

15 random Topology10 x 10 fieldCollision radius: 615 devices4 radio/device

* Algorithm IV* Algorithm III* Algorithm II

Perf

orm

s th

e be

st in

all

topo

logi

es

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Simulation ResultsEffect of Collision Radius

The 6th Topology (the worst in slide 23)15 devices4 radio/device11 channels

* Algorithm IV* Algorithm III* Algorithm II

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Simulation ResultsEffect of Collision Radius

The 3th Topology (the worst in slide 23)15 devices4 radio/device11 channels

* Algorithm IV* Algorithm III* Algorithm II

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Conclusion Algorithm II

Perfect information Sequential deciding Small convergence time Inferior results

Algorithm III Perfect information Simultaneous decisions Noticeable but reasonable results Depending on topology and collision radius, superior with probability less than 20%

Algorithm IV Perfect information Sequential decisions No convergence time needed Superior results most often Possible use of extra radios in some scenarios

Same results for single collision problem

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Future Work

Possible modifications on the algorithm IV. Study on the fairness provided by the algorithm using the Jain’s

fairness index. Connection to the paper “M. Cagalj, J.P. Hubaux, “Resource Allocation

in Competitive Wireless Networks”.

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References

M. Felegyhazi, M. Cagalj, J.P. Hubaux, “Multi-radio channel allocation in competitive radio networks”, submitted in IBC2006

J. O. Neel, J. H. Reed, R.P. Gilles, “Convergence of Cognitive Radio Networks”, WCNC 2004.

N. Nie, C. Comaniciu, “Adaptive Channel Allocation Spectrum Etiquette for Cognitive Radio Networks”, ACM MONET.

M. J. Osborne, A. Rubinstein, A Course in Game Theory, MIT Press 1997.