Docstoc

Lecture Search Algorithms

Document Sample
Lecture Search Algorithms Powered By Docstoc
					                                   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
                   schindel@upb.de




                                                                  1
                                              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        2
                                                                            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         3
                                                          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




                                                     Search Algorithms, WS 2004/05        4
                                                                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        5
                 HEINZ NIXDORF INSTITUTE
Chapter I             University of Paderborn
                     Algorithms and Complexity
                      Christian Schindelhauer




Introduction to
 Radio Networks


            Search Algorithms, WS 2004/05        6
                                                                 HEINZ NIXDORF INSTITUTE
Types of Radio Networks                                                  University of Paderborn
                                                                        Algorithms and Complexity
                                                                         Christian Schindelhauer



Cellular Networks
  – base stations distributed over the field     Zur Anze ige wird der Qu ickTime™
                                               Dekompre ssor „TIFF (Unkomprimie rt)“

  – each base station covers a cell                            benötigt.




  – 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            Zur Anzeige wird der QuickTime™
                                               Dekompre ssor „TIFF (Unkomprimiert)“

  – base station with more resources
                                                              benötigt.




                                                        Search Algorithms, WS 2004/05               7
                                                            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



                                                       Search Algorithms, WS 2004/05        8
                                                       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:   amplitude           :    phase shift
   –f:    frequency = 1/T     T:    period



                                             T

                               At
                      




                                                  Search Algorithms, WS 2004/05        9
                                                                              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:




                                                                         Search Algorithms, WS 2004/05        10
                                                               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




                                                          Search Algorithms, WS 2004/05        11
                                                    HEINZ NIXDORF INSTITUTE
Frequency Bands                                          University of Paderborn
                                                        Algorithms and Complexity
                                                         Christian Schindelhauer




 LF    Low Frequency MF        Medium Freq.   HF  High Freq.
       VHF              Very High Freq.       UHF Ultra High F.
       SHF              Super High Fr.
 EHF   Extra High Frequency                   UV      Ultra Violet
                                               Search Algorithms, WS 2004/05        12
                                                                  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        13
                                                                 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




                                                           Search Algorithms, WS 2004/05        14
                                                                   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




                                                              Search Algorithms, WS 2004/05        15
                                                         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



                                                    Search Algorithms, WS 2004/05        16
                                  HEINZ NIXDORF INSTITUTE
                                       University of Paderborn
Theory of Wireless Routing            Algorithms and Complexity
                                       Christian Schindelhauer




                             Search Algorithms, WS 2004/05        17
                                                       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




                                                  Search Algorithms, WS 2004/05        18
                                          HEINZ NIXDORF INSTITUTE
                                               University of Paderborn

         (Omni-) Directed Antennae            Algorithms and Complexity
                                               Christian Schindelhauer




  directed communication
    for sending and receiving




omni-directed communikation

  classical radio communication




                                     Search Algorithms, WS 2004/05        19
                                                     HEINZ NIXDORF INSTITUTE
Path System and Link network                              University of Paderborn
                                                         Algorithms and Complexity
                                                          Christian Schindelhauer




Path system                                            Link network




 l (e) = load of edge e = # paths(messages) through this link




                                                Search Algorithms, WS 2004/05        20
                                                              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




   acknowledgment                                   transmitted
                                                      message

                                interference




                                                         Search Algorithms, WS 2004/05        21
                                          HEINZ NIXDORF INSTITUTE
                                              University of Paderborn
                                             Algorithms and Complexity
                                              Christian Schindelhauer




Thanks for your attention
End of 1st lecture
Next lecture:          Mo 26 Oct 2005, 4pm, F2.211
Next exercise class:
                       Tu 25 Oct 2005, 1.15 pm, F2.211 or
                       Th 27 Oct 2005, 1.15 pm, F1.110




                                                                         22

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:4
posted:9/27/2012
language:English
pages:22