Transcript Lecture Search Algorithms - uni

HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Algorithms for Radio Networks
Winter Term 2005/2006
19 Oct 2005
1st Lecture
Christian Schindelhauer
[email protected]
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HEINZ NIXDORF INSTITUTE
Contents
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Introduction
– Cellular Networks
– Mobile Ad Hoc Networks (MANET)
– Wireless Sensor Networks (WSN)
General background
– Layers, Coding
– Congestion, Energy, and Dilation
Mobility in networks
– Mobility models
– Analyzing Mobility
Network Coding
Topology Control
The Call Problem in Cellular Networks
Location based Routing
Search Algorithms, WS 2004/05
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HEINZ NIXDORF INSTITUTE
Organization
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Lecture:
– Monday, 4pm - 6pm, F2.211
Exercise Class (Übung)
– Stefan Rührup
• Tuesday, 1pm - 2pm, F2.211
• Thursday, 1pm - 2pm, F1.110
Registration
– By StudInfo-System
– See web page:
• http://wwwcs.uni-paderborn.de/cs/ag-madh/WWW/Teaching/2005WS/AlgRadio/
– Go to
• http://studinfo.upb.de/cgi-bin/go?c=algradio_2005ws
Register for exercise classes as soon as possible!
Search Algorithms, WS 2004/05
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HEINZ NIXDORF INSTITUTE
Organization
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Material available at the web-site
– Slides of the lecture (PDF/PPT)
– Exercises
– Schedule
• with upcoming topics and examination dates
– Literature links
Web-site is ready on Oct 21 2005
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HEINZ NIXDORF INSTITUTE
Examinations
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Two types of exam
– Written exams (45 minutes)
• Four written exams
• Dates to be announced (lecture/web-site)
• No registration
• Each covers 1/4th of the lecture
• Participation voluntary
• The best two of the four exams produce half of the overall grade
– Oral exam (25 minutes)
• Participation mandatory
• Registration mandatory
• Passing the oral exam is necessary
• 23/24 Feb. 2006 or
• 27/28 Mar. 2006
• Registration before 8 Feb 2006
Search Algorithms, WS 2004/05
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HEINZ NIXDORF INSTITUTE
Chapter I
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Introduction to
Radio Networks
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HEINZ NIXDORF INSTITUTE
Types of Radio Networks
Cellular Networks
– base stations distributed over the field
– each base station covers a cell
– used for mobile phones
– WLAN can be seen as a special case
Mobile Ad Hoc Networks
– self-configuring network of mobile
nodes
– node serve as client and router
– no infrastructure necessary
Sensor Networks
– network of sensor devices with
controller and radio transceivers
– base station with more resources
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Zur Anzeige w ird der QuickTime™
Dekompressor „TIFF (Unkomprimiert)“
benötigt.
Zur Anzeige w ird der QuickTime™
Dekompressor „TIFF (Unkomprimiert)“
benötigt.
Search Algorithms, WS 2004/05
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HEINZ NIXDORF INSTITUTE
Physics of Electro-magnetic Waves
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Frequency f : number of oscilations per second
– unit of measurement : Hertz
– wave length : distance (in meters) between wave maxima
– The propagation speed of waves in vacuum is constant:
– speed of light c  3  108 m/s
Note that:
f = c
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HEINZ NIXDORF INSTITUTE
Amplitude Representation
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Amplitude representation of a sinus curve
– s(t) = A sin(2 f t + )
– A:
–f:
amplitude
frequency = 1/T
:
T:
phase shift
period
T
At

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HEINZ NIXDORF INSTITUTE
Fourier Transformation
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Fourier transformation of a periodic
function:
– Decomposition into sinus curves
 Dirichlet‘s conditions for a periodic function:
– f(x) = f(x+2)
– f(x) is continuous and monotone in finitely many intervals of (-,)
– If is non-coninuous in x0, then f(x0)=(f(x0-0)+f(x0+0))/2
 Theorem of Dirichlet:
– f(x) satisfies Dirichlet‘s conditions . Then the Fourier coefficients a0,a1,a2,…,b1,b2,… exist
such that:
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HEINZ NIXDORF INSTITUTE
Computation of Fourier coefficients
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Fourier coeffizients ai, bi can be computed as follows
– For k = 0,1,2,…
– For k = 1,2,3,…
Example: saw tooth curve
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HEINZ NIXDORF INSTITUTE
Frequency Bands
LF
EHF
Low Frequency MF
Medium Freq.
VHF
Very High Freq.
SHF
Super High Fr.
Extra High Frequency
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
HF
High Freq.
UHF Ultra High F.
UV
Ultra Violet
Search Algorithms, WS 2004/05
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HEINZ NIXDORF INSTITUTE
Radio Propagation
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Propagation on straight line
Signal strength is proportional to 1/d² in free space
– In practice can be modeled by 1/dc, for c up to 4 or 5
Energy consumption
– for transmitting a radio signal over distance d in empty space is d²
Basic properties
– Reflection
– Refraction (between media with slower speed of propagation)
– Interference
– Diffraction
– Attenuation in air (especially HV, VHF)
Search Algorithms, WS 2004/05
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HEINZ NIXDORF INSTITUTE
Radio Propagation
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
VLF, LF, MF
– follow the curvature of the globe (up zu 1000 kms in VLF)
– pass through buildings
HF, VHF
– absorbed by earth
– reflected by ionosphere in a height of 100-500 km
>100 MHz
– No passing through walls
– Good focus
> 8 GHz absorption by rain
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HEINZ NIXDORF INSTITUTE
Radio Propagation
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Multiple Path Fading
– Because of reflection, diffraction and diffusion the signal arrives on multiple
paths
– Phase shifts because of different path length causes interferences
Problems with mobile nodes
– Fast Fading
• Different transmission paths
• Different phase shifts
– Slow Fading
• Increasing or decreasing the distance between sender and receiver
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HEINZ NIXDORF INSTITUTE
Signal Interference Noise Ratio
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Receiving-power = Transmission-power  path-loss
– path loss ~ 1/rβ
– β  [2,5]
Signal to Interference + Noise Ratio = SINR
– S = receiving power from desired sender
– I = receiving power from interfering senders
– N = other interfering signals (e.g. noise)
Necessary for recognizing the signal:
S
SINR 
 Threshold
I N
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HEINZ NIXDORF INSTITUTE
Theory of Wireless Routing
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Search Algorithms, WS 2004/05
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HEINZ NIXDORF INSTITUTE
A Simple Physical Network Model
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Homogenous Network of
– n radio stations s1,..,sn on the plane
Radio transmission
– One frequency
– Adjustable transmission range
• Maximum range > maximum distance
of radio stations
• Inside the transmission area of sender:
clear signal or radio interference
• Outside: no signal
– Packets of unit length
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HEINZ NIXDORF INSTITUTE
(Omni-) Directed Antennae
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
directed communication
for sending and receiving
omni-directed communikation
classical radio communication
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HEINZ NIXDORF INSTITUTE
Path System and Link network
Path system
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Link network
l (e) = load of edge e = # paths(messages) through this link
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HEINZ NIXDORF INSTITUTE
Radio Interferences
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Links (edges) interfere, if simultaneous transmission
is not possible because radio signals interfere
Links are symmetric (because of acks)
Interference may be asymmetric
transmitted
message
acknowledgment
interference
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HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Thanks for your attention
End of 1st lecture
Next lecture:
Next exercise class:
Mo 26 Oct 2005, 4pm, F2.211
Tu 25 Oct 2005, 1.15 pm, F2.211 or
Th 27 Oct 2005, 1.15 pm, F1.110
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