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Sabita MaharjanSimula Research LaboratoryUniversity of Oslo
Sept. 2011
A Demo PresentationWang et. Al, Evolutionary Cooperative Spectrum Sensing Game: How to Collaborate?, IEEE Transactions on Communications, March 2010
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Spectrum sensing in cognitive radio networks
Equilibrium Analysis
This talk presents an evolutionary game framework as an effective approach to enforce cooperation
Evolutionary game Model
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Secondary users can coexist with primary users by sharing the spectrum not being used by primary users
Occupied
Vacant
Primary Base Station
Secondary Base Station
Primary Spectrum
Secondary usersCognitive Radio Network
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Spectrum holes are detected for the data transmission of SUs
The PUs are prevented from excessive interference
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Probability of false alarmIt is the probability that the channel is declared
as occupied although it is vacant
Probability of miss detectionIt is the probability of not detecting the channel when it is occupied
Probability
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It avoids hidden terminal problem
No signal
Shadowed node
Primary receiver
Primary transmitter
Cooperative nodes
Secondary base station
CSS mitigates multipath fading & shadowing by spatial diversity
SU1
SU2
SU3
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The secondary users may belong to different authorities
There may not be a central authority
They try to take advantage of free riding as far as possible
All users are selfish
All users do not aim for the greater good of the system
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The secondary users are assumed to be located far from primary transmitter and are clustered
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Throughput of sensing users
Throughput of non-sensing users
Throughput of non-sensing users
Throughput of sensing users
> If J:[1, K-1]
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Cooperation is desired but users are non-cooperative
How to enforce cooperation?
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Game theory has been used extensively to study competition and cooperation in various fields
Economics
Ecology
Computer Networks
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The throughput obtained by the secondary users depends on
1. their own decisions 2. the decisions of other SUs
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PlayersA set of strategiesA set of payoff for each player
Components of the spectrum sensing game
Players Secondary users
Strategies A = {Contribute, Deny}
Payoff Throughput obtained
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Players in the game (SUs) have the uncertainty about the best strategy to take
In an evolutionary game, players learn during the strategic interactions by taking out of equilibrium behavior
With learning, the players approach a robust equilibrium called evolutionarily stable strategy
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The probability of false alarm of each contributing user is
Signal to noise ratio
Target probability of detection
Number of users contributing in sensing
Number of samples sensed
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The payoff of a contributor is
Probability that the channel is vacant
Duration of transmission
Probability that no false alarm is generated
Data rate of user sj
Probability of false alarm for cooperative sensing
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The payoff of a denier is
The payoffs can be rewritten as
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The average utility of a contributor is
The average utility of a denier is
Probability of contributing in cooperative sensing
Mixed strategy equilibrium is obtained by solving
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As number of secondary users increases, each user will think that others will perform sensing
Optimal contributing probability x*
Increase in sensing duration increases the cost of sensing
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For small sensing duration, increase in sensing duration increases the throughput
Further increase in sensing duration decreases the throughput
Average throughput per user at optimal probability of contributing
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A distributed learning algorithm is necessary
A distributed learning algorithm that gradually converges to the ESS is required
The ESS can be obtained by solving the average utility equations
However, it requires the knowledge of utility function as well as exchange of private information and strategies adopted by the other users
This results in a lot of communication overhead
Secondary users may not have complete information about others’ utilities
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Start with an arbitrary probability and converge to the ESS using iterative procedure
Probability of contribution at slot (m+1)T
Average utility for pure strategy “contribute”
Average utility for mixed strategy
Probability of contribution at slot mT
Speed adjustment parameter
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In case of homogeneous user sensing game, all users converge to a mixed strategy (ESS)
Behavior dynamics of a K user sensing game
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Behavior dynamics of a heterogeneous 3 user sensing game
User 1, SNR =-14 dB
User 2, SNR =-10 dB
User 3, SNR =-10 dB
The users with higher SNR will converge to ”contribute” while the ones with lower SNR converge to ”deny”
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In case of full cooperation, no user can utilize the sub-channels when sensing is undergoing
Comparison of full cooperation and ESS
When there are less secondary users, almost all of them tend to contribute
As the number of users increases, more users can take free rides
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Questions?
In summary, cooperation was enforced among non-cooperative secondary using evolutionary game theory
Homogeneous users converge to the same strategy
The equilibrium strategies differ for heterogeneous users
The proposed game has a better performance than the fully cooperative scenario