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

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

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

Spectrum holes are detected for the data transmission of SUs

The PUs are prevented from excessive interference

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

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

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

The secondary users are assumed to be located far from primary transmitter and are clustered

Throughput of sensing users

Throughput of non-sensing users

Throughput of non-sensing users

Throughput of sensing users

> If J:[1, K-1]

Cooperation is desired but users are non-cooperative

How to enforce cooperation?

Game theory has been used extensively to study competition and cooperation in various fields

Economics

Ecology

Computer Networks

The throughput obtained by the secondary users depends on

1. their own decisions 2. the decisions of other SUs

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

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

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

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

The payoff of a denier is

The payoffs can be rewritten as

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

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

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

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

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

In case of homogeneous user sensing game, all users converge to a mixed strategy (ESS)

Behavior dynamics of a K user sensing game

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”

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

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