Minimum Interference Channel Assignment in Multi-Radio Wireless Mesh Networks

1. Minimum Interference Channel Assignment in Multi-Radio Wireless Mesh Networks Anand Prabhu Subramanian, Himanshu Gupta and Samir Das Stony Brook University, NY, USA anandps@cs.sunysb.edu

2. Capacity problem due to Wireless Interference Internet Wireless Mesh Network Objective: Reduce Interference anandps@cs.sunysb.edu

3. Our Approach How to reduce Interference? • Using different forms of diversities • Improve spatial reuse • Use Transmit Power Control • Use directional communication • Use multiple channels • Single Radio Approach • Multi-Radio Approach anandps@cs.sunysb.edu

4. Single Radio Approach 1 2 3 4 5 6 • Challenges: • Channel switching latency (in order of milliseconds) • Coordination between sender and receiver anandps@cs.sunysb.edu

5. Multi-Radio Approach 1 2 3 4 5 6 Challenge: Efficient channel assignment to links such that interference is minimized as much as possible Advantage: 1) No need to switch channels in “packet time scale.” 2) No need for synchronization between communicating nodes 3) Can work with commodity 802.11 Hardware anandps@cs.sunysb.edu

6. 1 2 3 4 5 6 Modeling Interference Network Graph: Conflict Graph: 1 - 2 2 - 3 1 - 4 Two-hop interference model 3 - 6 4 - 5 Models Interference between a pair of links Weighted Graph to model variable traffic and fractional interference 2 - 5 5 - 6 anandps@cs.sunysb.edu

7. 1 2 3 1 2 3 4 5 6 4 5 6 Channel Assignment Problem Conflict Graph: Network Graph: 1 - 2 2 - 3 1 - 4 K (=3) different channels 4 - 5 3 - 6 2 - 5 5 - 6 anandps@cs.sunysb.edu

8. 1 - 2 2 - 3 1 - 4 3 - 6 4 - 5 2 - 5 5 - 6 Max-K-Cut Problem 1 - 2 2 - 3 1 - 4 3 - 6 4 - 5 2 - 5 5 - 6 Maximize edges between nodes with different color Minimize edges between nodes with same color anandps@cs.sunysb.edu

9. 1 2 3 4 6 Channel Assignment Problem Max-K-Cut problem with Interface Constraint Interface Constraint 1 - 2 2 - 3 1 - 4 5 3 - 6 4 - 5 2 - 5 5 - 6 anandps@cs.sunysb.edu

10. 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 anandps@cs.sunysb.edu

11. Tabu Search Based Centralized Algorithm – Phase I 1 - 2 1 - 2 • Start from the random solution • In each iteration, generate certain number of neighboring solutions • Pick the solution with least interference • Repeat until no improvement for certain number of iterations 2 - 3 2 - 3 1 - 4 1 - 4 3 - 6 3 - 6 4 - 5 4 - 5 2 - 5 2 - 5 5 - 6 5 - 6 anandps@cs.sunysb.edu

12. Tabu Search Based Centralized Algorithm – Phase II • First phase could result in interface constraint violation in some nodes B C A D • 4 channels and 2 Interfaces • Violation at node D anandps@cs.sunysb.edu

13. Tabu Search Based Centralized Algorithm – Phase II • Merge 2 colors into 1 at node D B C A D 4 channels and 2 Interfaces anandps@cs.sunysb.edu

14. Tabu Search Based Centralized Algorithm – Phase II • Propagate color change to entire connected component B C A D 4 channels and 2 Interfaces anandps@cs.sunysb.edu

15. 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 anandps@cs.sunysb.edu

16. Lower Bound using SDP • Technique 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) anandps@cs.sunysb.edu

17. Performance with Random Graph 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. anandps@cs.sunysb.edu

18. 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. anandps@cs.sunysb.edu

19. 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). anandps@cs.sunysb.edu

20. MHz 2402 2407 2412 2417 2422 2427 2432 2437 2442 2447 2452 2457 2462 2467 2472 1 6 11 802.11b 2.4GHz 7 2 8 3 4 9 5 10 Channel Overlap Factor: Distance 0 1 2 3 4 5 Overlap 1 0.7272 0.2714 0.0375 0.0054 0 Non-Orthogonal Channels anandps@cs.sunysb.edu

21. Performance using Overlapping channels • Use of overlapped channels advantageous • Both Tabu and Greedy perform well with 11 channels compared to 3 channels anandps@cs.sunysb.edu

22. 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 anandps@cs.sunysb.edu

23. 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 anandps@cs.sunysb.edu