dynamic coalitions and cooperation in cognitive network communications

Dynamic Coalitions and Cooperation in CognitiveNetwork Communications

Zaheer Khan, Janne Lehtomaki, Marian Codreanu and HeliNiva-Puupera

Centre for Wireless Communications (CWC)Joint work with

Luiz DaSilva (Trinity College Dublin, Ireland)

Cognac ProjectJan 11, 2010

Zaheer Khan, Janne Lehtomaki, Marian Codreanu and Heli Niva-Puupera Centre for Wireless Communications (CWC) Joint work with Luiz DaSilva (Trinity College Dublin, Ireland)

Dynamic Coalitions and Cooperation in Cognitive Network Communications

Outline

Background and motivation.

Coalition formation preliminaries.

Coalition formation in cognitive networks: An example

Dynamics of coalition formation.

Markov chain based modeling of a coalition game.

Questions/Comments.



Background

Interactions between devices give rise to networks....

Networks between.....

Cognitive communicating devices.

Cognition:a) An intelligent terminal device who can learn about availablefrequency spectrum by employing spectrum sensing techniques.b) The device is able to self-organize appropriate communicationand networking functions through re-configurablecommunication/network processor(s).



Motivation

The next generation of wireless networks will increasingly rely ondistributed and self-configuring architectures.

The desire to ”to develop automated ways for deploying andmaintaining wireless infrastructure with minimal humaninteraction.”

Cooperation among autonomous network nodes is a likely approachfor the efficient use of network resources.

To seek suitable game theoretical tools that allow to analyze andstudy the behavior and interactions of the nodes in futurecommunication networks.



Why Coalitions?Is Selfishness that Good?

Imagine youre riding in a car that becomes stuck in a snowdrift.

You and a fellow passenger share the same interest: you both wantthe snowdrift to be removed. But whos going to get out and shovel?

It might seem fair just to get out and shovel the snow together inother words, to cooperate.

But what if the other passenger just sits there and refuses to help?

If the cost of shoveling is low compared to the benefit of getting outof the drift, it will be in your interest to shovel by yourself. Sure, theother passenger is a freeloader who shares the benefit un deservedly,but so what?

Table: Snow drift Game

(a) Commune Dilemma

A/B C D

C b-c/2, b-c/2 b-c,b

D b,b-c 0,0



Why Coalitions?

Games in which”in which two or more players can make coalitions and obtainprizes and penalties.”



Why Coalitions?To Motivate the Participants

In traditional network protocol design, it is generally assumed thatdevices cooperate to correctly execute the intended protocol.

This cooperation assumption is based on the fact that the devicesare controlled by the same authority.

In emerging self-organizing networks this basic assumption might nothold.

In self-organizing networks, a potentially selfish participant cantamper with the networking protocols of its device to exploit thenetwork at the expense of other participants.

This behavior may lead to the collapse of service provisioning in thenetwork.

Motivate the participants to cooperate.



Example:Cooperative spectrum sensing with trust issues

Trust issues arise in cooperative sensing.

Sensing a frequency band, consumes energy and time which mayalternatively be diverted to data transmissions.

Hence users have incentives to either not sense at all or to sense fora shorter duration then stipulated.

Motivate users to perform cooperative sensing.



Why Coalitions?To Aim to Achieve Gains

Cognitive users perform the task of sensing the spectrum to detectthe primary user presence.

For performing the task of spectrum sensing, the cognitive usersobtain reward in terms of transmission opportunities.

A single CR sensing decision may be unreliable, due to, for example,fading.

Co-operation among cognitive users has been recently shown toincrease the reliability of spectrum sensing and hence increase thereward in terms of interference free transmission opportunity.

Example: Perform sensing via cooperation



Coalition Formation: Challenges and Solutions

Implementing cooperation in large scale communication networksfaces several challenges such asa) Adequate modeling,b) Efficiency,c) Complexity,d) and fairness.

Coalition game theory provides useful tools to decide which group ofplayers will cooperate with each other to efficiently achieve theirgoals.



Coalition Formation Preliminaries

N denote the set of players (CRs) playing the coalition game,N = {1, 2, ..., n}.A coalition, S, is defined as a subset of N, S ⊆ N.

An individual non-cooperating player is called a singleton coalition and theset N is called the grand coalition, where all players cooperate.

The most common form of a coalition game is the characteristic functionform.

In the characteristic function form (CFF) of coalition games, utilitiesachieved by the players in a coalition are unaffected by those outside it.

The quantity v(S) in the CFF game is a real number associated with eachsubset of N, S ⊆ N, which may be considered as the worth of a coalitionwhen its members group together as a unit.

Similarly, the quantity vi,i∈S(S) in the CFF game is a real number for eachplayer i , i ∈ S, which represents the payoff obtained by player i fromcoalition S.

Transferable and non-transferable payoff coalition games



Coalition Formation: General Approach

Most coalition formation models use a two-period structure.

Players must first decide whether or not to join a coalition.

In a second step, both the coalition and the remaining deviceschoose their behavior non-cooperatively.

A coalition is stable if no device has an incentive to leave.



Coalition Formation in Wireless NetworksSimplistic Approaches

The study of coalition formation in wireless networks has previouslyfocused on cohesive games.

Cohesive games: Where the value of the grand coalition formed by theset of all users N is at least as large as the sum of the values of anypartition of N.

Cohesive games are easy to analyze and solve.

In general it is also assumed that there is no cost to the coalitionformation process.

In such coalition games, coalition structure generation is trivial becausethe wireless nodes always benefit by forming the grand coalition.

Many coalition game models of wireless node cooperation are notcohesive:1) In wireless networks there is some cost to the coalition formationprocess itself.2) Due to the fact that in the grand coalition there is no resource reuse.



Cognitive Coalition Formation: An ExampleSystem Setup

The system setup used includes a primary user transmitter and adistributed CR network of n active CRs.

The CRs are uniformly and independently distributed in a circle withradius Rs and centered at the coordinates (β,0).

The BS (primary user) is at coordinates (0,0) as shown in the figurebelow

BS

RS

β

CR

CR

Figure: Topology of cognitive radio network.



System Setup (contd)

We assume that n cognitive radios make primary user detectionobservations in the frequency band they are monitoring.

We assume that energy detection is employed for channel sensing by theCRs.

In order to detect the primary user, each CR can either sense the spectrumon its own (non-cooperative strategy) or it can perform cooperativesensing by forming coalitions with the other CRs (cooperative strategy).

For cooperative case: OR fusion rule to combine the individual sensing CRdecisions.

OR rule is a simple decision rule: If any one CR detects the primary userthen the final decision detects the primary user.

The received primary user’s signal-to-noise ratio (SNR) at CR i isrepresented by γi and σ2 represents noise variance.



System Setup (contd)

We assume the complex-valued PSK primary user signal and circularsymmetric complex Gaussian (CSCG) noise case.

For CSCG noise case the probability of false alarm of CR i for a chosendetection threshold λi is given by

Pf ,i (λi ) = Q

((λi

σ2− 1)

√N

)(1)

where Q(.) is the tail probability of the standard normal distribution andN represent the number of samples and is given as N = τ fs , where τ isthe sensing duration and fs is the sampling frequency.

For a chosen threshold λi , the probability of detection of CR i is given by

Pd,i (λi ) = Q

((λi

σ2− γi − 1)

√N

2γi + 1

)(2)



Cognitive Coalition Formation: An ExampleValue Function

Throughput equations:

R0 = PH0(1−Ts

Tp)(1− Pf ,i )Ci (3)

when primary user absent.

R1 = PH1(1−Ts

Tp)(1− Pd,i )Ci (4)

when primary user present.

Value of a coalition: v(S) = gain − cost

Gain can be in terms of detection of primary users.

Cost can be in terms of false alarm.



Value FunctionPrimary User Perspective

From the primary user perspective set a target detection probabilityand CRs cooperate to minimize the false alarm.

The individual CR’s targeted probability of detection in a coalitionusing OR fusion rule is given by

Pd,i = 1− (1− Pd)1|S| (5)

where | S | is the number of CRs in a coalition. The probability offalse alarm of each CR i for the targeted Pd,i is given by

Pf ,i = Q

(√2γi + 1)Q−1(Pd,i ) +

√Nγi

)∗ (6)

∗derived from (1) and (2).



Value FunctionCognitive Radio User Perspective

From the CR perspective set a minimum false alarm target andcooperate to maximize the detection probability. For a chosenthreshold λi , the probability of detection of CR i is given by

Pd,i (λi ) = Q

((

1√2λi + 1

Q−1(Pf ,i )−√

Nγi

)∗ (7)

∗derived from (1) and (2)



Dynamics of Coalition Formation

Establishing cooperation in a wireless network is a dynamic process

Proposed game theoretic coalition formation models must addressthree important questions:1) How are the coalitions formed?; 2) How do players arrive atequilibrium?; and 3) What is the long term behavior of the coalitionformation process?



Proposed Dynamic Coalition Formation ModelFor large N coalitional interaction becomes an issue, leading to acombinatorial explosion.

Participating in coalition formation incurs cost in terms of energyconsumption or delay due to coalitional negotiations.

Self-interested CRs participate in coalition formation only if theirvalue function is below certain threshold value.

Figure: One round of coalition formation model.



Markov Chain based Modeling of the Coalition GameA time evolving sequence of steps is followed by the CRs to reachself-organizing stable spectrum sensing coalition structures (network2 partitions).We model coalition structures as a sequence of random variablesdescribing the state of the CR network, and the transitionmechanism between coalition structures is modeled as a Markovchain.

G1

G2 G4 G6

G3 G5 G7

G8 G9

[

∅|{

{1}, {2}, {3}}]

[

∅|{

{1, 2}, {3}}] [

∅|{

{1, 3}, {2}}] [

∅|{

{2, 3}, {1}}]

[{

{1, 2, 3}}

|∅][

∅|{

{1, 2, 3}}]

Initial state

[{

{1, 2}}

|{

{3}}] [{

{1, 3}}

|{

{2}}] [{

{2, 3}}

|{

{1}}]

1

Figure: A three CR Markov chain representation.



Benefits of Markov Modeling

Using standard theory of absorbing Markov chains one can calculatethe mean time µ and its variance σ2 for the dynamic coalition gamestarting from the initial state of all singleton coalitions to reachstable network structure.

We propose a technique to reduce the time taken by the CRs toform a stable coalition.



Stability of Formed Coalitions

Once coalitions are formed then the stability of the cooperativenetwork is a major concern.

Grand coalition feasible or not?

Internal and External stability : Internal stability means that nolink has an incentive to leave its coalition to become a singleton(individual non-cooperative link), i.e., vi,i∈S1(S1) ≥ v({i}), ∀i ∈ S1,

external stability means that no other coalition has an incentive tojoin coalition S1, i.e., v(S2) > v(S1 ∪ S2)− v(S1), ∀S2 ⊆ S1

c ,where S1

c represents the complement of S1.



Time to Convergence

An absorbing Markov chain in canonical form :

P =

(I OR Q

),

where I is an identity matrix, O is a matrix with all zero entries, R isthe matrix of transition probabilities from transient to absorbingstates and Q is the matrix of transition probabilities between thetransient states.

The matrix F = (I − Q)−1 is called the fundamental matrix for P.

Using F , one can calculate the mean time µ and its variance σ2 forthe game before the coalition game process converges to theabsorbing state:

µ = F τ, σ2 = (2F − I )µ− µsq, (8)



Result

0 5 10 15 20 25 3010

−2

10−1

Number of SUs (N)

Ave

rage

mis

sing

pro

babi

lity

per

SU

Centralized SolutionNon coperative CRs are selfishCRs are partially altruistic

Figure: Average missing probability per secondary user.



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dynamic coalitions and cooperation in cognitive network communications

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