Joint Power and Channel Minimization in Topology Control: A Cognitive Network Approach J ORGE M ORI A LEXANDER Y AKOBOVICH M ICHAEL S AHAI L EV F AYNSHTEYN.

Joint Power and Channel Joint Power and Channel Minimization in Topology Minimization in Topology Control: A Cognitive Network Control: A Cognitive Network ApproachApproach

JORGE MORIALEXANDER YAKOBOVICHMICHAEL SAHAILEV FAYNSHTEYN

Problem DefinitionProblem Definition

An ad-hoc wireless network topology faces two problems:

Power consumption◦Mobile devices have limited power supply

Overcrowded spectrum◦Too many devices try to use the same frequency simultaneously resulting in inteference

Previous WorkPrevious WorkInterference avoidance has led to

three viewpoints:Radio

◦Minimize channel interference at link-level

Topology◦Channel assignments made in an

already existing topology Network

◦A combination of channel assignment with routing

Previous WorkPrevious WorkTwo assumptions:

◦Power control◦Channel control

Power approaches:◦Bukhart, assigning weights to connections

that are equal to the number of radios the connection interferes with. Used with MMLIP, MAICPC and IMST algorithms.

◦Use of a radio interference function, in which the interference contribution of a radio is the maximum interference of all connections incident upon it. Used in MMMIP and LILT algorithms.

Previous Work Previous Work (Cont.) (Cont.)

Channel Control:• Connectivity of the network is fixed

and that two radios can only communicate if they share a common channel, of which there are fewer available than needed.

Researches’ ApproachResearches’ ApproachTheir work assume that radios regulate

both power and channel selection.

A two-phased, two cognitive element approach to:◦Power assignment◦Channel assignment

A game-theoretic model is used to analyze the behaviors of these elements.

MethodologyMethodologyA two-phased game model is used:

The first phase is a pure power control game where POWERCONTROL elements attempt to minimize their transmit power level and maintain network connectivity.

The output of the first phase is a power-efficient topology, which is fed into the second phase, where CHANNELCONTROL elements selfishly play the channel selection game.

Methodology Methodology (Cont.)(Cont.)

The POWERCONTROL elements utilize δ-Improvement Algorithm (DIA):

Methodology Methodology (Cont.)(Cont.)

LOCAL-RS - a localized version of the Random Sequential coloring algorithm:

Optimized Approach – Power Optimized Approach – Power ControlControlUse Minimum Spanning Tree (MST) algorithm to solve

Power Control problem: G = (V, E,W) denotes the input undirected stochastic

graph:◦ V - vertex set◦ E - edge set◦ matrix W - probability distribution of the edge weight in the

stochastic graph

Each node of the graph is a learning automaton

Resulting network is described by a triple < A, α, W >, where:◦ A = { A1, A2,..., Am } - set of the learning automata◦ α = { α 1, α 2,..., α m} - set of actions in which α i = { α i1, α

i2,..., α ij,..., α ir } defines the set of actions that can be taken by learning automata A i for each α ∈α i

◦ Weight w i j is the cost associated with edge e (i, j)

MST AlgorithmMST Algorithm

Optimized Approach – Optimized Approach – Channel ControlChannel ControlResulting network is described by the

pair < A, α >, where:◦A = {A1, A2, …, Am} denotes the set of

learning automata◦α = {α1, α2, …, αm} denotes the set of actions◦αi = {αi1, αi2, …, αir} defines the set of actions

that can be taken by learning automaton Ai, for each αi ∈ α

The set of colors with which each vertex vi can be colored from the set of actions can be taken by learning automaton Ai

Channel Control AlgorithmChannel Control Algorithm Step 1. Color selection phase

◦ For all learning automata do in parallel Each automaton Ai. Pick the colors that have not being selected yet Vertex Vi is colored with the color corresponding to the selected action The selected color is added to the list of colors (color-set) with which the graph may be

legally colored at this stage.

Step 2. Updating the dynamic threshold and action probabilities◦ If the cardinality of the color-set (in a legal coloring) created is less than or equal

to dynamic threshold Tk, then Threshold Tk is set to the cardinality of the color-set selected in this stage. All learning automata reward their actions and update action probably vectors using a LR-P

reinforcement scheme

◦ Otherwise Each learning automaton updates its probability vector by penalizing its chosen action.

Step 3. Stopping Condition◦ The process of selecting legal colorings of the graph and updating the action

probabilities are repeated until the product of the probability of choosing the colors of a legal coloring called PLC is greater than a certain threshold or the number of colorings exceeds a pre-specified threshold. The coloring which is chosen last before stopping the algorithm is the coloring with the smallest color-set among all proper colorings.

QUESTIONS?QUESTIONS?Thank you.