The Power of Non-Uniform Wireless Power

1. The Power of • Non-Uniform Wireless Power Magnus M. Halldorsson Reykjavik University Stephan Holzer ETH Zürich Pradipta Mitra Reykjavik University Roger Wattenhofer ETH Zürich Presentedby Klaus-Tycho Förster Slides by Stephan Holzer and Roger Wattenhofer ETH Zürich ETH Zurich – Distributed Computing Group TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAA

2. Wireless Communication

3. Wireless Communication EE, Physics Maxwell Equations Simulation, Testing ‘Scaling Laws’ Network Algorithms CS, Applied Math [Geometric] Graphs Worst-Case Analysis Any-Case Analysis

4. CS Models: e.g. Disk Model (Protocol Model) ReceptionRange InterferenceRange

6. EE Models: e.g. SINR Model (Physical Model)

8. Signal-To-Interference-Plus-Noise Ratio (SINR) Formula Received signal power from sender Power level of sender u Path-loss exponent Minimum signal-to-interference ratio Noise Distance between two nodes Received signal power from all other nodes (=interference)

9. The Capacityof a Network(Howmanyconcurrentwirelesstransmissionscanyouhave)

10. … is a well-studied problem in Wireless Communication The Capacity of Wireless Networks Gupta, Kumar, 2000 [Arpacioglu et al, IPSN’04] [Giridhar et al, JSAC’05] [Barrenechea et al, IPSN’04] [Grossglauser et al, INFOCOM’01] [Liu et al, INFOCOM’03] [Gamal et al, INFOCOM’04] [Toumpis, TWC’03] [Kyasanur et al, MOBICOM’05] [Kodialam et al, MOBICOM’05] [Gastpar et al, INFOCOM’02] [Zhang et al, INFOCOM’05] [Mitra et al, IPSN’04] [Li et al, MOBICOM’01] [Dousse et al, INFOCOM’04] [Bansal et al, INFOCOM’03] etc… [Yi et al, MOBIHOC’03] [Perevalov et al, INFOCOM’03]

11. The Capacityof a Network(Howmanyconcurrentwirelesstransmissionscanyouhave) • Power control helps: arbitrarily better than uniform power (worst case) • Arbitrary power: O(1)-Approximation Complex optimization problem • Simpler ways?

12. Oblivious Power This Paper • Power only depends on length of link • Mean power has “star status” O( + )-approximation [SODA’11] [ESA’09] Essentially: O( ) vs. (usually: small constant)

13. Old Definitions v w • Affectance • SINR-condition is now just • p-power: assigns power to link l

14. New Crucial Definitions • Length-ordered version of symmetric affectance: • Interferencemeasure:

15. Structural Property Let be a p-power power-assignment and be an arbitrary power-assignment, then * *= for non-weak links

16. Yields -approximation for capacity. Analysis uses Algorithm Links increase by length For i=1 to n do If then

17. Applications Connectivity: given a set of nodes, connect them in an interference aware manner. Strongly connected in + time slots using mean power. Centralized and distributed algorithms any p-power

18. Applications Distributed Scheduling: schedule a given set of links in a minimal number of time slots. There is randomized distributed + -approximation to scheduling using mean-power. any p-power

19. Applications Spectrum Sharing Auctions: channels, users, each user has valuation of each subset of channels. Find: allocation of users to channels such that each channel is assigned a feasible set and the social welfare is maximized. -approximation

20. Summary capacity max. SINR-model Length- oblivious power -approximation 3 (out of >5) applications

21. Thanks!