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1. Wireless Algorithms TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

2. … an oxymoron?

3. …as old as society

4. more recently?

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

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

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

10. 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)

11. Example: Protocol vs. Physical Model Assume a single frequency (and no fancy decoding techniques!) Let =3, =3, and N=10nW Transmission powers: PB= -15 dBm and PA= 1 dBm SINR of A at D: SINR of B at C: C D B A 4m 1m 2m NO Protocol Model Is spatial reuse possible? YES With power control

12. This works in practice! … even with very simple hardware (sensor nodes) u1 u2 u3 u4 u5 u6 Time for transmitting 20‘000 packets: Speed-up is almost a factor 3 [Moscibroda, W, Weber, Hotnets 2006]

13. The Capacity of a Wireless Network

14. Measures for Capacity Throughput capacity • Number of packets successfully delivered per time • Dependent on the traffic pattern • E.g.: What is the maximum achievable rate, over all protocols, for a random node distribution and a random destination for each source? Transport capacity • A network transports one bit-meter when one bit has been transported a distance of one meter. • What is the maximum achievable rate, over all node locations, and all traffic patterns, and all protocols? Convergecast capacity • How long does it take to get information from all nodes to a sink Many more…

15. Transport Capacity • n nodes are arbitrarily located in a unit disk. • We adopt the protocol model with R=2, that is a transmission is successful if and only if the sender is at least a factor 2 closer than any interfering transmitter. In other words, each node transmits with the same power, and transmissions are in synchronized slots. • Quiz: What configuration and traffic pattern will yield the highest transport capacity? • Idea: Distribute n/2 senders uniformly in the unit disk. Place the n/2 receivers just close enough to senders so as to satisfy the threshold.

16. sender receiver Transport Capacity: Example

17. Transport Capacity: Understanding the example • Sender-receiver distance is £(1/√n). Assuming channel bandwidth W [bits], transport capacity is £(W√n) [bit-meter], or per node: £(W/√n) [bit-meter] • Can we do better by placing the source-destination pairs more carefully? No,having a sender-receiver pair at distance dinhibits another receiver within distance upto 2d from the sender. In other words, it killsan area of £(d2). • We want to maximize n transmissions with distances d1, d2, …, dn given that the total area is less than a unit disk. This is maximized if all di = £(1/√n). So the example was asymptotically optimal. • BTW, a fun open geometry problem: Given k circles with total area 1, can you always fit them in a circle with total area 2? d

18. More capacities… • The throughput capacity of an n node random network is • There exist constants c and c‘ such that • Transport capacity: • Per nodetransport capacity decreases with • Maximized when nodes transmit to neighbors • Throughput capacity: • For random networks, decreases with • Near-optimal when nodes transmit to neighbors • In one sentence: local communication is better

19. Even more capacities… • Similar claims hold in the physical (SINR) model as well… • There are literally thousands of results on capacity, e.g. • on random destinations • on power-law traffic patterns • communication through relays • communication in mobile networks • channel broken into subchannels • etc.

20. Practical relevance? • Efficient access to media, i.e. MAC layer! • This (and related) problem is studied theoretically: 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]

21. Network Topology? • All these capacity studies make very strong assumptions on node deployment, topologies • randomly, uniformly distributed nodes • nodes placed on a grid • etc. What if a network looks differently…?

22. ‘Scaling Laws’ Real Capacity How much information can be transmitted in any network? Worst-Case Capacity “Classic” Capacity How much information can be transmitted in nasty networks? How much information can be transmitted in nice networks?

23. Convergecast Capacity in Wireless Networks • Data gathering & aggregation • Classic applicationofsensornetworks • Sensor nodesperiodically sense environment • Relevant informationneedstobetransmittedtosink • FunctionalCapacityof Sensor Networks • Sink periodicallywantstocompute a functionfnofsensordata • Atwhatratecanthisfunctionbecomputed? (1) (2) (3) ,fn fn ,fn sink

24. Convergecast Capacity in Wireless Networks Example: simple round-robin scheme  Each sensor reports its results directly to the root one after another sink • Simple Round-Robin Scheme: • Sink can compute one • function per n rounds •  Achieves arate of 1/n x1=7 x3=4 x2=6 x4=3 (3) (2) (1) (4) fn fn fn fn x8=5 x7=9 t x5=1 x6=4 x9=2

25. Convergecast Capacity in Wireless Networks There are better schemes using Multi-hop relaying In-network processing Spatial Reuse Pipelining sink (1) (2) (3) (4) fn fn fn fn t

26. Convergecast Capacity in Wireless Networks At what ratecan sensors transmit data to the sink? Scaling-laws  how does rate decrease as n increases…? (1) (1/log n) (1/n) (1/√n) Only perfectly compressible functions (max, min, avg,…) Answer depends on: Function to be computed Coding techniques Network topology … No fancy coding techniques

27. Convergecast Capacity in Wireless Networks [Moscibroda, W, 2006] [Giridhar, Kumar, 2005] Worst-Case Capacity Best-Case Capacity Max. rate in random, uniform deployment Max. rate in arbitrary, worst-case deployment Networks Model/Power (1/n) (1/log n) Protocol Model Physical Model (w/ power control) (1/log n) (1/log3n) • The Price of Worst-Case Node Placement • Exponential in protocol model • Polylogarithmic in physical model • (almost no worst-case penalty!) Exponential gap between protocol and physical model!

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

29. Possible Application – Hotspots in WLAN Traditionally: clients assigned to (more or less) closest access point  far-terminal problem  hotspots have less throughput Y X Z

30. Possible Application – Hotspots in WLAN Potentially better: create hotspots with very high throughput Every client outside a hotspot is served by one base station  Better overall throughput – increase in capacity! Y X Z

31. Wireless Communication EE, Physics Maxwell Equations Simulation, Testing ‘Scaling Laws’ Network Algorithms CS, Applied Math [Geometric] Graphs Worst-Case Analysis Any-Case Analysis Wireless Algorithms DistributedProtocols Mobility increases the capacity of ad hoc wireless networks [Grossglauser, Tse, 2002] On the time-complexity of broadcast in multi-hop radio networks [Bar-Yehuda, Goldreich, Itai , 1992]

32. Wireless Communication 101

33. 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)

34. Simple solutions have β > 10 But β < 1 is possible (thanks to forward error correction) Algorithmically speaking, the exact value of β does not really matter, thanks to SINR robustness [Halldorsson, W, 2009] and [Fanghänel, Kesselheim, Räcke, Vöcking, 2009] Model not only robust with regard to β, but also with regard to other constant factor disturbances, for instance, wind, constant antenna gain, etc. Concretely: If we adapt model by factor Á, results will change at most by factor Á2. Ratioβdepends on receiver (hardware, software, parameters)

35. Modulation and demodulation analog baseband signal digital data digital modulation analog modulation radio transmitter 101101001 radio carrier analog baseband signal digital data analog demodulation synchronization decision radio receiver 101101001 radio carrier Modulation in action:

36. Digital modulation • Modulation of digital signals known as Shift Keying • Amplitude Shift Keying (ASK): • very simple • low bandwidth requirements • very susceptible to interference • Frequency Shift Keying (FSK): • needs larger bandwidth • Phase Shift Keying (PSK): • more complex • robust against interference 1 0 1 t 1 0 1 t 1 0 1 t

37. I R 1 0 I 11 10 R 0010 I 0001 0011 00 01 0000 R 1000 Phase Shift Keying 101 A [V] I = A sin  A [V] t [s]  R = A cos  * f [Hz] amplitude domain frequency spectrum phase state diagram BPSK (robust, satellites) QPSK QAM (large β)

38. 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) (BTW: dα has nothing to do with energy consumption)

39. Path-loss-exponent α α = 2… 15-25 dB drop sender received power α = 4…6 receiving LOS NLOS distance interference distance noise α≥ Dimension 2nd law of thermodyn.

40. Wireless Propagation Depends on Frequency regulated 1 Mm 300 Hz 10 km 30 kHz 100 m 3 MHz 1 m 300 MHz 10 mm 30 GHz 100 m 3 THz 1 m 300 THz VLF LF MF HF VHF UHF SHF EHF infrared UV visible light twisted pair coax ISM AM SW FM

41. Path-loss-exponent α: Near-Field Effects d << 1? 1cm!! … in other words, algorithmic papers should rule out near-field effects

42. Real World Examples

43. Attenuation by objects • Shadowing (3-30 dB): • textile (3 dB) • concrete walls (13-20 dB) • floors (20-30 dB) • reflection at large obstacles • scattering at small obstacles • diffraction at edges • fading (frequency dependent) shadowing reflection scattering diffraction

44. Multipath • Signal can take many different paths between sender and receiver due to reflection, scattering, diffraction • Time dispersion: signal is dispersed over time • Interference with “neighbor” symbols: Inter Symbol Interference (ISI) • The signal reaches a receiver directly and phase shifted. Distorted signal depending on the phases of the different parts signal at sender signal at receiver

45. There’s much more… Analog Network Coding MIMO

46. Advanced Algorithms?

47. Quiz: How to Build a Multi-Hop Alarm System Problem: More than 1 node may sense problem at the same time. Potentially we have a massive interference problem! root 1 hop 2 hops 3 hops rx or alarm? tx ‘wave’ on freq f0 (FSK) …followed by verification (1% false positives outdoors) [Flury, W, 2010]

48. Media Access: Theory and Practice [Sommer, W, 2010]

49. Ultrasound (A different kind of communication) [Sommer, W, 2010]

50. Ultra-Wideband (UWB) • An example of a new physical paradigm. • Discard the usual dedicated frequency band paradigm. • Instead share a large spectrum (about 1-10 GHz). • Modulation: Often pulse-based systems. Use extremely short duration pulses (sub-nanosecond) instead of continuous waves to transmit information. Depending on application 1M-2G pulses/second PPM PAM OOK