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Wireless Algorithms. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A. … an oxymoron?. …as old as society. more recently?. Wireless Communication EE, Physics Maxwell Equations Simulation, Testing ‘Scaling Laws’. Network Algorithms - PowerPoint PPT PresentationTRANSCRIPT
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ETH Zurich – Distributed Computing Group Roger Wattenhofer 1ETH Zurich – Distributed Computing – www.disco.ethz.ch
Roger Wattenhofer
Wireless Algorithms
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… an oxymoron?
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…as old as society
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more recently?
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Wireless Communication
EE, PhysicsMaxwell EquationsSimulation, Testing‘Scaling Laws’
Network Algorithms
CS, Applied Math[Geometric] GraphsWorst-Case Analysis
Any-Case Analysis
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InterferenceRange
CS Models: e.g. Disk Model (Protocol Model)
ReceptionRange
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7
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EE Models: e.g. SINR Model (Physical Model)
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Signal-To-Interference-Plus-Noise Ratio (SINR) Formula
Minimum signal-to-interference
ratio
Power level of sender u Path-loss exponent
Noise
Distance betweentwo nodes
Received signal power from sender
Received signal power from all other nodes (=interference)
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Example: Protocol vs. Physical Model
1m
Assume a single frequency (and no fancy decoding techniques!)
Let =3, =3, and N=10nWTransmission powers: PB= -15 dBm and PA= 1 dBm
SINR of A at D:
SINR of B at C:
4m 2m
A B C D
Is spatial reuse possible? NO Protocol Model
YES With power control
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This works in practice!
… even with very simple hardware (sensor nodes)
Time for transmitting 20‘000 packets:
Speed-up is almost a factor 3
u1 u2 u3 u4 u5 u6
[Moscibroda, W, Weber, Hotnets 2006]
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The Capacity of a Wireless Network
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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…
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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.
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sender
receiver
Transport Capacity: Example
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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
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More capacities…
• The throughput capacity of an n node random network is
• There exist constants c and c‘ such that
• Transport capacity:– Per node transport 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
0]log
'Pr[lim
1]log
Pr[lim
feasible is
feasible is
nnWc
nnWc
n
n
)log
(nn
W
n1
nn log1
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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.
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Practical relevance?
• Efficient access to media, i.e. MAC layer!
• This (and related) problem is studied theoretically:
The Capacity of Wireless NetworksGupta, Kumar, 2000
[Toumpis, TWC’03]
[Li et al, MOBICOM’01]
[Gastpar et al, INFOCOM’02]
[Gamal et al, INFOCOM’04][Liu et al, INFOCOM’03]
[Bansal et al, INFOCOM’03]
[Yi et al, MOBIHOC’03]
[Mitra et al, IPSN’04]
[Arpacioglu et al, IPSN’04]
[Giridhar et al, JSAC’05]
[Barrenechea et al, IPSN’04][Grossglauser et al, INFOCOM’01]
[Kyasanur et al, MOBICOM’05][Kodialam et al, MOBICOM’05]
[Perevalov et al, INFOCOM’03]
[Dousse et al, INFOCOM’04]
[Zhang et al, INFOCOM’05]
etc…
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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…?
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‘Scaling Laws’
“Classic” Capacity Worst-Case Capacity
How much information can betransmitted in nice networks?
How much information can betransmitted in nasty networks?
How much information can betransmitted in any network?
Real Capacity
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Convergecast Capacity in Wireless Networks
• Data gathering & aggregation– Classic application of sensor networks– Sensor nodes periodically sense environment– Relevant information needs to be transmitted to sink
• Functional Capacity of Sensor Networks– Sink periodically wants to compute a function fn of sensor data– At what rate can this function be computed?
sink
,fn(2)fn
(1) ,fn(3)
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Convergecast Capacity in Wireless Networks
sink
x3=4x2=6
x1=7
x4=3
x5=1x6=4
x8=5
x9=2
x7=9
Example: simple round-robin scheme Each sensor reports its results directly to the root one after another
Simple Round-Robin Scheme: Sink can compute one
function per n rounds Achieves a rate of 1/n
fn(1)
fn(2)
fn(3)
fn(4)
t
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Convergecast Capacity in Wireless Networks
There are better schemes usingMulti-hop relayingIn-network processingSpatial ReusePipelining
fn(1)
fn(2)
fn(3)
fn(4)
t
sink
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Convergecast Capacity in Wireless Networks
At what rate can sensors transmit data to the sink?Scaling-laws how does rate decrease as n increases…?
(1/√n) (1/log n) (1)(1/n)
Answer depends on: Function to be computed Coding techniques Network topology …
Only perfectlycompressible functions(max, min, avg,…)
No fancy coding techniques
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Convergecast Capacity in Wireless Networks
27
Protocol Model
Physical Model (w/ power control)
Max. rate in arbitrary, worst-case deployment
(1/n)
The Price of Worst-Case Node Placement- Exponential in protocol model - Polylogarithmic in physical model
(almost no worst-case penalty!)
(1/log3 n)
Exponential gap between protocol and
physical model!
Max. rate in random, uniform deployment
(1/log n)
(1/log n)
Worst-Case Capacity
Networks
Model/Power
Best-Case Capacity
[Giridhar, Kumar, 2005][Moscibroda, W, 2006]
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Wireless Communication
EE, PhysicsMaxwell EquationsSimulation, Testing‘Scaling Laws’
Network Algorithms
CS, Applied Math[Geometric] GraphsWorst-Case Analysis
Any-Case Analysis
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Possible Application – Hotspots in WLAN
Traditionally: clients assigned to (more or less) closest access point far-terminal problem hotspots have less throughput
XY
Z
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Possible Application – Hotspots in WLAN
Potentially better: create hotspots with very high throughputEvery client outside a hotspot is served by one base station Better overall throughput – increase in capacity!
XY
Z
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Wireless Communication
EE, PhysicsMaxwell EquationsSimulation, Testing‘Scaling Laws’
Network Algorithms
CS, Applied Math[Geometric] GraphsWorst-Case Analysis
Any-Case Analysis
Wireless Algorithms
On the time-complexity of broadcast in multi-hop radio networks [Bar-
Yehuda, Goldreich, Itai , 1992]
Mobility increases the capacity of ad hoc wireless networks
[Grossglauser, Tse, 2002]
DistributedProtocols
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Wireless Communication 101
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Signal-To-Interference-Plus-Noise Ratio (SINR) Formula
Minimum signal-to-interference
ratio
Power level of sender u Path-loss exponent
Noise
Distance betweentwo nodes
Received signal power from sender
Received signal power from all other nodes (=interference)
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• 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.
Ratio β depends on receiver (hardware, software, parameters)
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Modulation and demodulation
synchronizationdecision
digitaldataanalog
demodulation
radiocarrier
analogbaseband
signal
101101001 radio receiver
digitalmodulation
digitaldata analog
modulation
radiocarrier
analogbaseband
signal
101101001 radio transmitter
Modulation in action:
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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
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Phase Shift Keying 101
f [Hz]
A [V]
R = A cos
I = A sin
*
A [V]
t [s]
amplitude domain frequency spectrum phase state diagram
I
R01
I
R
11
01
10
00
0000
0001
0011
1000
I
R
0010
BPSK (robust, satellites) QPSK QAM (large β)
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Signal-To-Interference-Plus-Noise Ratio (SINR) Formula
Minimum signal-to-interference
ratio
Power level of sender u Path-loss exponent
Noise
Distance betweentwo nodes
Received signal power from sender
Received signal power from all other nodes (=interference)
(BTW: dα has nothing to do with energy consumption)
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Path-loss-exponent α
distance
sender
receiving
interference
noise
Pr = PsGsGr ¸2
(4¼)2d2L
Pr = PsGsGr h2sh2
rd4
distance
rece
ived
pow
er
α = 2…
LOS NLOS
α = 4…6
15-25 dB drop
α ≥ Dimension2nd law of thermodyn.
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Wireless Propagation Depends on Frequency
1 Mm300 Hz
10 km30 kHz
100 m3 MHz
1 m300 MHz
10 mm30 GHz
100 m3 THz
1 m300 THz
visible lightVLF LF MF HF VHF UHF SHF EHF infrared UV
twisted pair coax
AM SW FM
regulated
ISM
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Path-loss-exponent α: Near-Field Effects
Pr = PsGsGr ¸2
(4¼)2d2Ld << 1?
1cm!!
… in other words, algorithmic papers should rule out near-field effects
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Real World Examples
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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)
reflection scattering diffractionshadowing
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• 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
Multipath
signal at sendersignal at receiver
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There’s much more…
MIMO
Analog Network Coding
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Advanced Algorithms?
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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
…followed by verification (1% false positives outdoors)
rx or alarm? tx ‘wave’ on freq f0 (FSK)
[Flury, W, 2010]
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Media Access: Theory and Practice
[Sommer, W, 2010]
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Ultrasound
(A different kind of communication)
[Sommer, W, 2010]
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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
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Summary
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ETH Zurich – Distributed Computing Group Roger Wattenhofer 52ETH Zurich – Distributed Computing – www.disco.ethz.ch
Roger Wattenhofer
Thank You!Questions & Comments?