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

2 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.

3 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

4 Preliminary Game Theory Non-cooperativeCooperative Single StageRepeated Strategic-formExtensive-form Perfect InformationImperfect Information

5 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

6 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

7 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)

8 Algorithm I Channel array: 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.

9 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).

10 Simulation Results Converging to the NE Number of Devices: 20 Number of Radios per device :4 Number of Channels: 11 Sliding averaging Node 1 Node 6

11 Simulation Results Converging to the NE Node 12 Average Convergence time: 76.5 time units σ: time units Average Data Rate/device =.55 channel/device

12 Simulation Results Flat Data Rate per Device Device Data Rate per Radio /Device

13 Simulation Results Effect of Averaging (α) on Convergence Time Number of Devices: 20 Number of Radios/Device: 4 Number of Channels: 11 Number of Devices: 20 Number of Radios/Device: 2 Number of Channels: 11

14 Simulation Results Effect of Number of Devices on Convergence Time Number of Radios/Device: 3 Number of Channels: 11 α =.9 [errors for 22 and 44 nodes] Number of Radios/Device: 4 Number of Channels: 11 α =.9

15 Simulation Results Effect of Number of Radios on Convergence Time Number of Devices: 20 Number of Channels: 11 α =.9 5 x 20=100=9 x 11+1

16 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 Channel Device #

17 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 some cooperative game. We cannot apply the Algorithm I to the problem because we cannot impose any stopping condition 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 with sequential (Algorithm II) and without sequential deciding (Algorithm III). 2) Defining our requirements More 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 of Fairness issue. Fairness? We simply expect better data rate for nodes with fewer neighbours We have based our work on the total data rate of the network, while not allowing zero data rate.

18 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.

19 Simulation Results * Algorithm IV * Algorithm III * Algorithm II 15 random Topology 10 x 10 field Collision radius: 4 15 devices 4 radio/device Performs the best in 80% of topologies

20 Simulation Results 15 random Topology 10 x 10 field Collision radius: 6 15 devices 4 radio/device * Algorithm IV * Algorithm III * Algorithm II Performs the best in all topologies

21 Simulation Results Effect of Collision Radius The 6 th Topology (the worst in slide 23) 15 devices 4 radio/device 11 channels * Algorithm IV * Algorithm III * Algorithm II

22 Simulation Results Effect of Collision Radius The 3 th Topology (the worst in slide 23) 15 devices 4 radio/device 11 channels * Algorithm IV * Algorithm III * Algorithm II

23 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

24 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”.

25 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 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.