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University of FreiburgComputer Networks and Telematics
Prof. Christian Schindelhauer
Wireless SensorNetworks
4th Lecture07.11.2006
Christian [email protected]
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-2
Amplitude Representation
Amplitude representation of a sinus curveâ s(t) = A sin(2Ď f t + Ď)
â A: amplitude Ď: phase shiftâ f : frequency = 1/T T: period
At
Ď
T
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-3
Fourier Transformation
Fourier transformation of a periodicfunction:
â Decomposition into sinus curves
Dirichletâs conditions for a periodic function:
â f(x) = f(x+2Ď)â f(x) is continuous and monotone in finitely many intervals of (-Ď,Ď)
â If is non-coninuous in x0, then f(x0)=(f(x0-0)+f(x0+0))/2 Theorem of Dirichlet:
â f(x) satisfies Dirichletâs conditions . Then the Fourier coefficients a0,a1,a2,âŚ,b1,b2,âŚexist such that:
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-4
Computation of Fouriercoefficients
Fourier coeffizients ai, bi can be computed as followsâ For k = 0,1,2,âŚ
â For k = 1,2,3,âŚ
Example: saw tooth curve
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-5
Fourier-Analysis
Thoerem of Fourier for period T=1/f:â The coefficients c, an, bn can be computed as follows
The square of the sum of the k-th terms is proportional to the energy inthis frequency
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-6
Frequency Bands
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
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-7
Radio Propagation
Propagation on straight lineSignal strength is proportional to 1/d² in free space
â In practice can be modeled by 1/dc, for c up to 4 or 5Energy consumption
â for transmitting a radio signal over distance d in empty space is d²Basic properties
â Reflectionâ Refraction (between media with slower speed of propagation)â Interferenceâ Diffractionâ Attenuation in air (especially HV, VHF)
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-8
Radio Propagation
VLF, LF, MFâ follow the curvature of the globe (up zu 1000 kms in VLF)â pass through buildings
HF, VHFâ absorbed by earthâ reflected by ionosphere in a height of 100-500 km
>100 MHzâ No passing through wallsâ Good focus
> 8 GHz absorption by rain
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-9
Radio Propagation
Multiple Path Fadingâ Because of reflection, diffraction and diffusion the signal arrives on
multiple pathsâ Phase shifts because of different path length causes interferences
Problems with mobile nodesâ Fast Fading
⢠Different transmission paths⢠Different phase shifts
â Slow Fading⢠Increasing or decreasing the distance between sender and receiver
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-10
Signal Interference NoiseRatio
Receiving-power = Transmission-power â path-loss
â path loss ~ 1/rβ
â β â [2,5]
Signal to Interference + Noise Ratio = SINRâ S = receiving power from desired senderâ I = receiving power from interfering sendersâ N = other interfering signals (e.g. noise)
Necessary for recognizing the signal:
!
SINR =S
I + N" Threshold
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-11
Frequency allocation
Some frequencies are allocated tospecific uses
âCellular phones, analogtelevision/radio broadcasting, DVB-T,radar, emergency services, radioastronomy, âŚ
Particularly interesting: ISM bands(âIndustrial, scientific, medicineâ) âlicense-free operation
Some typical ISM bands
24 â 24.25 GHz
WLAN5.725 â 5.875 GHz
WLAN/WPAN2.4 â 2.5 GHz
Americas900 â 928 MHz
Europe433 â 464 MHz
40.66 â 40.70 MHz
26.957 â 27.283 MHz
13.553-13.567 MHz
CommentFrequency
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-12
Example: US frequencyallocation
http://www.ntia.doc.gov/osmhome/allochrt.pdf
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-13
Transceivers and thePhysical Layer
Frequency bandsModulationSignal distortion â wireless channelsFrom waves to bitsChannel modelsTransceiver design
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-14
Modulation and keying
How to manipulate a given signal parameter?â Set the parameter to an arbitrary value: analog modulationâ Choose parameter values from a finite set of legal values: digital keyingâ Simplification: When the context is clear, modulation is used in either
caseModulation?
â Data to be transmitted is used select transmission parameters as afunction of time
â These parameters modify a basic sine wave, which serves as a startingpoint for modulating the signal onto it
â This basic sine wave has a center frequency fc
â The resulting signal requires a certain bandwidth to be transmitted(centered around center frequency)
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-15
Modulation (keying!)examples
Use data to modify theamplitude of a carrierfrequency ! Amplitude ShiftKeying
Use data to modify thefrequency of a carrier frequency! Frequency Shift Keying
Use data to modify the phase ofa carrier frequency ! PhaseShift Keying
Š Tanenbaum, Computer Networks
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-16
Amplitude Shift Keying(ASK)
Let Ei(t) be the symbol energy at time t
The first term is a convention such that Ei denotes the energyExample: E0(t) = 1, E1(t)=2 for all t
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-17
Phase Shift Keying (PSK)
For phase signals Ďi(t)
Example:
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-18
Frequency Shift Keying(FSK)
For frequency signals Ďi(t)
Example:
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-19
Receiver: Demodulation
The receiver looks at the received wave form and matches it with thedata bit that caused the transmitter to generate this wave form
â Necessary: one-to-one mapping between data and wave formâ Because of channel imperfections, this is at best possible for digital
signals, but not for analog signalsProblems caused by
â Carrier synchronization: frequency can vary between sender and receiver(drift, temperature changes, aging, âŚ)
â Bit synchronization (actually: symbol synchronization): When does symbolrepresenting a certain bit start/end?
â Frame synchronization: When does a packet start/end?â Biggest problem: Received signal is not the transmitted signal!
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-20
Overview
Frequency bandsModulationSignal distortion â wireless channelsFrom waves to bitsChannel modelsTransceiver design
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-21
Transmitted signal â received signal!
Wireless transmission distorts any transmitted signalâ Received <> transmitted signal; results in uncertainty at receiver about which
bit sequence originally caused the transmitted signalâ Abstraction: Wireless channel describes these distortion effects
Sources of distortionâ Attenuation â energy is distributed to larger areas with increasing distanceâ Reflection/refraction â bounce of a surface; enter materialâ Diffraction â start ânew waveâ from a sharp edgeâ Scattering â multiple reflections at rough surfacesâ Doppler fading â shift in frequencies (loss of center)
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-22
Attenuation results in pathloss
Effect of attenuation: received signal strength is a function of thedistance d between sender and transmitter
Captured by Friis free-space equationâ Distance: Râ Wavelength: Îť
â Pr: power at receive antenna
â Pt: power at transmit antenna
â Gt: transmit antenna gain
â Gr: receive antenna gain
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-23
Suitability of differentfrequencies â Attenuation
Attenuation depends on the usedfrequency
Can result in a frequency-selectivechannel
â If bandwidth spans frequencyranges with differentattenuation properties
http://www.geographie.uni-muenchen.de/iggf/Multimedia/Klimatologie/physik_arbeit.htm
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-24
Distortion effects: Non-line-of-sight paths
Because of reflection, scattering, âŚ, radio communication is not limitedto direct line of sight communication
â Effects depend strongly on frequency, thus different behavior at higherfrequencies
Different paths have different lengths =propagation time
â Results in delay spread of the wireless channelâ Closely related to frequency-selective fading
properties of the channelâ With movement: fast fading
Line-of-sight path
Non-line-of-sight path
signal at receiver
LOS pulsesmultipathpulses
Š Jochen Schiller, FU Berlin
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-25
Wireless signal strength ina multi-path environment
Brighter color = stronger signalObviously, simple (quadratic) free space
attenuation formula is not sufficient tocapture these effects
Š Jochen Schiller, FU Berlin
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-26
To take into account stronger attenuation than only caused by distance(e.g., walls, âŚ), use a larger exponent Îł > 2
â Îł is the path-loss exponent
â Rewrite in logarithmic form (in dB):
Take obstacles into account by a random variationâ Add a Gaussian random variable XĎ with 0 mean, variance Ď2 to dB
representationâ Equivalent to multiplying with a lognormal distributed r.v. in metric units !
lognormal fading
Generalizing theattenuation formula
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-27
Transceivers and thePhysical Layer
Frequency bandsModulationSignal distortion â wireless channelsFrom waves to bitsChannel modelsTransceiver design
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-28
Noise and interference
So far: only a single transmitter assumedâ Only disturbance: self-interference of a signal with multi-path âcopiesâ of
itself In reality, two further disturbances
â Noise â due to effects in receiver electronics, depends on temperature⢠Typical model: an additive Gaussian variable, mean 0, no correlation
in timeâ Interference from third parties
⢠Co-channel interference: another sender uses the same spectrum⢠Adjacent-channel interference: another sender uses some other part
of the radio spectrum, but receiver filters are not good enough tofully suppress it
Effect: Received signal is distorted by channel, corrupted by noise andinterference
â What is the result on the received bits?
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-29
Symbols and bit errors
Extracting symbols out of a distorted/corrupted wave form is fraughtwith errors
â Depends essentially on strength of the received signal compared to thecorruption
â Captured by signal to noise and interference ratio (SINR) given indecibel:
SINR allows to computebit error rate (BER) for a given modulation
â Also depends on data rate (# bits/symbol) of modulation
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-30
Overview
Frequency bandsModulationSignal distortion â wireless channelsFrom waves to bitsChannel modelsTransceiver design
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-31
Channel models âanalog signal
How to stochastically capture the behavior of a wireless channelâ Main options: model the SNR or directly the bit errors
Signal modelsâ Simplest model: assume transmission power and attenuation are constant,
noise an uncorrelated Gaussian variable⢠Additive White Gaussian Noise model, results in constant SNR⢠For expectation Âľ and standard deviation Ď the density function is
defined as:
â Situation with no line-of-sight path, but many indirect paths: Amplitude ofresulting signal has a Rayleigh distribution (Rayleigh fading)
⢠Ί = E(R2). Then the density function is
⢠One dominant line-of-sight plus many indirect paths: Signal has a Ricedistribution (Rice fading)
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-32
Channel models â digital
Directly model the resulting bit error behaviorâ Each bit is erroneous with constant probability, independent of the other
bits ! binary symmetric channel (BSC)â Capture fading modelsâ property that channel be in different states !
Markov models â states with different BERs⢠Example: Gilbert-Elliot model with âbadâ and âgoodâ channel states
and high/low bit error rates
â Fractal channel models describe number of (in-)correct bits in a row by aheavy-tailed distribution
good bad
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-33
WSN-specific channelmodels
Typical WSN propertiesâ Small transmission rangeâ Implies small delay spread (nanoseconds, compared to micro/milliseconds
for symbol duration) ! Frequency-non-selective fading, low to negligible inter-symbol
interference⢠Coherence bandwidth
often > 50 MHzSome example
measurementsâ Îł path loss exponentâ Shadowing variance Ď2
â Reference pathloss at 1 m
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-34
Sharing the Medium
Space-Multiplexingâ Spatial distanceâ Directed antennae
Frequency-Multiplexingâ Assign different frequencies
to the sendersTime-Multiplexing
â Use time slots for eachsender
Spread-spectrumcommunication
â Direct Sequence SpreadSpectrum (DSSS)
â Frequency Hopping SpreadSpectrum (FHSS)
Code Division Multiplex
University of FreiburgInstitute of Computer Science
Computer Networks and TelematicsProf. Christian Schindelhauer
Wireless Sensor Networks 07.11.2006 Lecture No. 04-35
Frequency HoppingSpread Spectrum
Change the frequency while transfering the signalâ Invented by Hedy Lamarr, George Antheil
Slow hoppingâ Change the frequency slower than the signals
comeFast hopping
â Change the frequency faster
36
University of FreiburgComputer Networks and Telematics
Prof. Christian Schindelhauer
Thank you(and thanks go also to Holger Karl for providing some slides)
Wireless Sensor NetworksChristian Schindelhauer
4th Lecture07.11.2006