June 21, 2007 anandps@cs.sunysb.edu Minimum Interference Channel Assignment in Multi-Radio Wireless...

June 21, 2007 anandps@cs.sunysb.edu

Minimum Interference Channel Assignment in Multi-Radio Wireless Mesh Networks

Anand Prabhu Subramanian, Himanshu Gupta and Samir Das

Stony Brook University, NY, USA

June 21, 2007 anandps@cs.sunysb.edu

Wireless Mesh Network

Internet

Capacity problem due to

Wireless Interference

Objective: Reduce Interference

June 21, 2007 anandps@cs.sunysb.edu

Using different forms of diversities Improve spatial reuse

Use Transmit Power Control Use directional communication

Use multiple channels Single Radio Approach Multi-Radio Approach

How to reduce Interference?

Our Approach

June 21, 2007 anandps@cs.sunysb.edu

Single Radio Approach

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Challenges:

1) Channel switching latency (in order of milliseconds)2) Coordination between sender and receiver

June 21, 2007 anandps@cs.sunysb.edu

Multi-Radio Approach

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Advantage:

1) No need to switch channels in “packet time scale.”2) No need for synchronization between communicating nodes3) Can work with commodity 802.11 Hardware

Challenge:

Efficient channel assignment to links such that interference is minimized as much as possible

June 21, 2007 anandps@cs.sunysb.edu

Modeling Interference

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Network Graph:

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Conflict Graph:

Models Interference between a pair of links

Two-hop interference model

Weighted Graph to model variabletraffic and fractional interference

June 21, 2007 anandps@cs.sunysb.edu

Channel Assignment Problem

Network Graph:

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K (=3) different channels

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Conflict Graph:

June 21, 2007 anandps@cs.sunysb.edu

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Max-K-Cut Problem

Maximize edges between nodes with different color

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Minimize edges between nodes with same color

June 21, 2007 anandps@cs.sunysb.edu

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Interface Constraint

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Channel Assignment Problem

Max-K-Cut problem with Interface Constraint

June 21, 2007 anandps@cs.sunysb.edu

Our Contribution

Design efficient heuristic algorithms (Upper bound on interference) Tabu search based centralized algorithm Distributed greedy algorithm

Establish lower bound on interference using Semi-definite Programming (SDP)

Show the bounds are close by simulation

June 21, 2007 anandps@cs.sunysb.edu

Tabu Search Based Centralized Algorithm – Phase I

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Start from the random solutionIn each iteration, generate certain number of neighboring solutionsPick the solution with least interferenceRepeat until no improvement for certain number of iterations

June 21, 2007 anandps@cs.sunysb.edu

First phase could result in interface constraint violation in some nodes

Tabu Search Based Centralized Algorithm – Phase II

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4 channels and 2 Interfaces Violation at node D

June 21, 2007 anandps@cs.sunysb.edu

Merge 2 colors into 1 at node D

Tabu Search Based Centralized Algorithm – Phase II

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4 channels and 2 Interfaces

June 21, 2007 anandps@cs.sunysb.edu

Propagate color change to entire connected component

Tabu Search Based Centralized Algorithm – Phase II

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4 channels and 2 Interfaces

June 21, 2007 anandps@cs.sunysb.edu

Greedy Heuristic Takes the interface constraint right from the start

Initially, color all the nodes in the conflict graph with same color

In each iteration choose the node-color pair that minimizes interference (not violating the interface constraint) the most and change the color

Repeat untill interference decrease monotonically

Can be distributed/localized as interference is local

June 21, 2007 anandps@cs.sunysb.edu

Lower Bound using SDPTechnique to optimize a linear function of a

symmetric positive semi-definite matrix subject to linear constraints

Max-K-cut has a good approximate solution using SDP

Add interface constraint to get a lower bound for the channel assignment problem

Can be solved in polynomial time (theoretically)Public domain solvers to solve SDP (DSDP 5.0)

June 21, 2007 anandps@cs.sunysb.edu

Performance with Random Graph

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Number of radio interfaces per node

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Random CLICA-SCE Dist. Greedy Tabu Based SDP

Fractional no. of monochromatic edges in conflict graph (edges outside the cut)

Random disk graphs. Dense - average node degree 10. Interference range = 2 x Transmission range 802.11 interference model (with RTS/CTS) 12 channels.

June 21, 2007 anandps@cs.sunysb.edu

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Number of radio interfaces per node

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Random CLICA-SCE Dist. Greedy Tabu Based SDP

Performance with Random Graph

Fractional no. of monochromatic edges in conflict graph (edges outside the cut)

Random disk graphs. Sparse – barely connected Interference range = 2 x Transmission range 802.11 interference model (with RTS/CTS) 12 channels.

June 21, 2007 anandps@cs.sunysb.edu

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Number of radio interfaces per node

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Random CLICA-SCE Dist. Greedy Tabu Based SDP

Performance with Random Graph

Fractional no. of monochromatic edges in conflict graph (edges outside the cut)

Little improvement beyond a certain no. of interfaces. Saturation reached with smaller no. of interfaces for sparser networks Tabu is generally better than greedy except with for small no. of interfaces (the merging technique is inefficient).

June 21, 2007 anandps@cs.sunysb.edu

Non-Orthogonal Channels

Channel Overlap Factor:

0.2714

2

00.00540.03750.72721Overlap

54310Distance

2402 2407 2412 2417 2422 2427 2432 2437 2442 2447 2452 2457 2462 2467 2472 MHz

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802.11b2.4GHz

June 21, 2007 anandps@cs.sunysb.edu

Performance using Overlapping channels

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Number of radio interfaces per node

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Tabu-11 Channels Dist. Greedy-11 Channels

Tabu-3 Channels Dist. Greedy-3 Channels

Single Channel

Use of overlapped channels advantageous

Both Tabu and Greedy perform well with 11 channels compared to 3 channels

June 21, 2007 anandps@cs.sunysb.edu

Practicalities

Can implement algorithms centrally. Not a problem for managed networks. Collect average load information periodically

from links.

Conflict graph is an input to the problem. How to determine?

Use Standard models (Protocol, Physical…) Based on measurements

June 21, 2007 anandps@cs.sunysb.edu

Summary

Formulated the channel assignment problem to minimize interference

Two efficient algorithms for channel assignment in multi-radio mesh networks

Lower bounding techniques using SDP

Future work: Approximation algorithms, Joint routing