simulation of fading radio channels · 2006-05-11 · radio communication propagation channel...
TRANSCRIPT
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Simulation of Fading Radio Channels
Konrad Hofbauer
Graz University of TechnologySPSC – Signal Processing and Speech
Communication laboratory
Advanced Signal Processing inWireless Communications Seminar
May 12, 2005
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Motivation
ProblemTransmitted signal degrades due to the transmission chain.Transmission channel has strong impact on systemperformance.
ObjectiveModelling and simulation
of the narrow-band aeronautic radio channel.
Used ExampleAeronautical radio channel (aircraft to ground)Analogue AM voice radioSame effects for terrestrial channels and digital transm..
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Motivation
ProblemTransmitted signal degrades due to the transmission chain.Transmission channel has strong impact on systemperformance.
ObjectiveModelling and simulation
of the narrow-band aeronautic radio channel.
Used ExampleAeronautical radio channel (aircraft to ground)Analogue AM voice radioSame effects for terrestrial channels and digital transm..
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Motivation
ProblemTransmitted signal degrades due to the transmission chain.Transmission channel has strong impact on systemperformance.
ObjectiveModelling and simulation
of the narrow-band aeronautic radio channel.
Used ExampleAeronautical radio channel (aircraft to ground)Analogue AM voice radioSame effects for terrestrial channels and digital transm..
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Communication ProblemAmplitude ModulationComplex Baseband
Communication Problem
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Communication ProblemAmplitude ModulationComplex Baseband
Communication Problem
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Communication ProblemAmplitude ModulationComplex Baseband
Communication Problem
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Communication ProblemAmplitude ModulationComplex Baseband
Communication Problem
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Communication ProblemAmplitude ModulationComplex Baseband
Communication Problem
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Communication ProblemAmplitude ModulationComplex Baseband
Communication Problem
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Communication ProblemAmplitude ModulationComplex Baseband
Amplitude Modulation
xAM(t) = (A0+kx(t)) cos(2πfc t+ϕ0)
signal x(t)carrier amplitude A0
carrier frequencyfc = 120 MHz
ωc = 2πfcinitial phase ϕ0 = π
4
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Communication ProblemAmplitude ModulationComplex Baseband
AM Spectrum and Complex Baseband
0 0.7 1
0
0.7
1
In−Phase: Re[g(t)]
Qua
drat
ure:
Im[g
(t)]
Complex baseband g(t)
xAM(t) = Re{
(A0 + kx(t))ejωc tejϕ0}
s(t) = Re{
g(t)ejωc t}
gAM(t) = (A0 + kx(t))ejϕ0
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Channel AttenuationAdditive NoiseDoppler EffectMultipath PropagationTime Variation
Propagation ChannelReminder
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Channel AttenuationAdditive NoiseDoppler EffectMultipath PropagationTime Variation
Channel Attenuation
Path loss through distance
proportional to 1dp
d is distance, p is path loss exponentin free space: p = 2
Shading (mountains, buildings, etc.)
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Channel AttenuationAdditive NoiseDoppler EffectMultipath PropagationTime Variation
Additive Noise
Noise is added to the signal during transmission.
thermal noise (electronics)atmospheric noisechannel interferenceman-made noise...
Often simply modeled as additive white gaussian noise(AWGN).
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Channel AttenuationAdditive NoiseDoppler EffectMultipath PropagationTime Variation
Doppler Effect
Frequency shift fD due tomovement v
fD = fD,max cos(α)
Maximum Doppler shift
fD,max =vc
fc
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Channel AttenuationAdditive NoiseDoppler EffectMultipath PropagationTime Variation
Multipath PropagationReflection – Scattering – Diffraction – Absorption
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Channel AttenuationAdditive NoiseDoppler EffectMultipath PropagationTime Variation
Multipath Propagation
Time delays between wavefronts
Phase shiftsConstructive / destructive interferenceChannel is a ‘fading channel’
Time Spread > Symbol Length
Channel is frequency-selective
Different directions of arrival
Different Doppler shiftsFrequency dispersion
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Channel AttenuationAdditive NoiseDoppler EffectMultipath PropagationTime Variation
Time Variation
Time Variant ChannelAll parameters vary over time, and so does the channel !!!
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Large vs. Small Scale Area FadingRayleigh, Rice & Co.Frequency Nonselective FadingRealisation of Coloured Gaussian ProcessesFrequency Selective Fading
Channel ModellingSlow Fading
Large Scale Area Fading
Slow fluctuation of local mean due to shadowingLognormally distributed
Important for channel availability and network planningGeometric modelling is done in some applications.
Millions of parametersSpecific to one situation
Stochastic models as alternative
Various modesl exist, e.g. Okomura, Hata, COST231
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Large vs. Small Scale Area FadingRayleigh, Rice & Co.Frequency Nonselective FadingRealisation of Coloured Gaussian ProcessesFrequency Selective Fading
Channel ModellingFast Fading
Small Scale Area Fading
Local mean of envelope is constantFast signal fluctuation due to multipath
Important for design of (digital) transmission techniquesStochastic Models
Distribution of parameters instead of prediction.Adaptable to many situations.
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Large vs. Small Scale Area FadingRayleigh, Rice & Co.Frequency Nonselective FadingRealisation of Coloured Gaussian ProcessesFrequency Selective Fading
Fast Fading Reference Model
Line-of-sight signal (unmodulated carrier):
LOS: m(t) = A0ej(2πfD+ϕ0)
Assumption: Many scatter components!Sum of all scatter components (µ1,2 are zero-meanGaussian processes):
Scatter: µ(t) = µ1(t) + jµ2(t)
Sum of Scatter and LOS component: Rician channelOnly Scatter: Rayleigh channel (LOS blocked)Only LOS: Deterministic signal
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Large vs. Small Scale Area FadingRayleigh, Rice & Co.Frequency Nonselective FadingRealisation of Coloured Gaussian ProcessesFrequency Selective Fading
Fast Fading Reference ModelRice and Rayleigh – LOS or not
Scatters onlyAmpl. is Rayleigh distributed
0 1 2 3 40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
x
pζ(
x)
σo2=1/2
σo2= 1
σo2= 2
LOS + ScattersAmplitude is Rice distributed
0 1 2 3 40
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x
pξ(
x)
ρ= 0 (Rayleigh)
ρ= 1/2
ρ= 1 σo2=1
Leads to:Computation of level crossing rate, average duration offades, etc.Important for design of coding and error concealmentsystems
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Large vs. Small Scale Area FadingRayleigh, Rice & Co.Frequency Nonselective FadingRealisation of Coloured Gaussian ProcessesFrequency Selective Fading
Doppler SpectrumPower Spectral Density (PSD) of the Received Signal (LOS + Scatters)
Scatters with uniformly distr.angles of arrivalJakes PSD
-100 -50 0 50 1000
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
f (Hz)
Sµ
iµi(f
)
r(τ
)
More realisticGaussian PSD
-200 -100 0 100 2000
1
2
3
4
5
6
7x 10-3
f (Hz)
Sµ
iµi(f
)
Gaussian PSD possibly unsymmetric and/or shifted,depending on distribution of angles of arrivalCharacteristic figures: average Doppler shift and Dopplerspread (the mean and the variance of the PSD).
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Large vs. Small Scale Area FadingRayleigh, Rice & Co.Frequency Nonselective FadingRealisation of Coloured Gaussian ProcessesFrequency Selective Fading
Frequency Nonselective ChannelFlat Fading
Scatter components arrive roughly at the same time inrepsect to symbol interval length.
Signal Bandwidth <1
Multipath Spread(=Coherence Bandwidth)
All frequency components are affected equally!Model: Multiply channel input with a stochastic modelprocess
Rayleigh and RiceSuzuki Models (contains Lognormal and Rayleigh)Loo Models (more flexible)
How to generate the model processes in a simulation?
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Large vs. Small Scale Area FadingRayleigh, Rice & Co.Frequency Nonselective FadingRealisation of Coloured Gaussian ProcessesFrequency Selective Fading
Deterministic Simulation ModelTheory of Deterministic Processes
Efficient computation of realisations of stochastic processneeded!Computation is inherently deterministic.Deterministic processes approximate the properties of thestochastic model processes.Most model processes are based on coloured Gaussianprocesses.
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Large vs. Small Scale Area FadingRayleigh, Rice & Co.Frequency Nonselective FadingRealisation of Coloured Gaussian ProcessesFrequency Selective Fading
Filter Method
Filter white Gaussian noise, so that the output has the desiredPSD
(t) ~ N(0,1)i
WGN
ν
i
µ i (t)H (f)
Difficulties:
Filter design problem (with well-understood limitations)How to compute the WGN (efficiently)?
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Large vs. Small Scale Area FadingRayleigh, Rice & Co.Frequency Nonselective FadingRealisation of Coloured Gaussian ProcessesFrequency Selective Fading
Sum of Sinusoids Method
Rice PrincipleThe superposition of an infinite number of weighted sinusoidswith equidistant frequencies and random phases gives acoloured Gaussian process.
+
+
+f
πcos(2 f i,1 i,1
(t)
θc
c
i,1
i,2
)
πcos(2 f i,2 t
t
i,2 θ )
ci,Ni
πcos(2 i,N t θ )i i,Ni
µ~ i
The weights ci,n = 2√
∆fiSµiµi (fi,n) are determined by thedesired PSD.
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Large vs. Small Scale Area FadingRayleigh, Rice & Co.Frequency Nonselective FadingRealisation of Coloured Gaussian ProcessesFrequency Selective Fading
Sum of Sinusoids - Realisation
Goals
Approximate ideal PSD asclosely as possibleMinimise the number ofsinusoids (for efficiency)
Determine for each sinusoid:
Discrete Frequency fiAmplitude (weigth) ciInitial Phase θi
-300 -200 -100 0 100 200 3000
0.01
0.02
0.03
0.04
0.05
0.06
0.07
S̃µ
iµi(f
)
r̃(τ
)
Big effort made and large number of algorithms available todetermine the best parameters.Attention: Do not forget the initial assumptionsmade! (-> Java animation)
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Large vs. Small Scale Area FadingRayleigh, Rice & Co.Frequency Nonselective FadingRealisation of Coloured Gaussian ProcessesFrequency Selective Fading
Frequency Nonselective ChannelFlat Fading
Scatter components arrive roughly at the same time inrepsect to symbol interval length.All frequency components are affected equally!
Multiply channel input with a stochastic (deterministic)model process!
For frequency nonselective channels (flat flading), this isall!
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Large vs. Small Scale Area FadingRayleigh, Rice & Co.Frequency Nonselective FadingRealisation of Coloured Gaussian ProcessesFrequency Selective Fading
Frequency Selective Channel
High bandwidth, high data rate systems:
Digital symbol intervals become as short as multipathpropagation delaysFrequency components are affected differently
Again, the channel is time-variant!
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Large vs. Small Scale Area FadingRayleigh, Rice & Co.Frequency Nonselective FadingRealisation of Coloured Gaussian ProcessesFrequency Selective Fading
Ellipses Model
For all scatter objects on one given ellipse:
Identical path delaysDifferent Doppler shiftsSum is complex Gaussian (central limit theoreme)
⇒ Tapped delay line structure
τ0
τ 1
τ2
τ 3
Direction ofCmotion
LOS componentRxTx
B
A
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
Large vs. Small Scale Area FadingRayleigh, Rice & Co.Frequency Nonselective FadingRealisation of Coloured Gaussian ProcessesFrequency Selective Fading
WSSUS Model
Channel as linear time-variant filterwith time-variant impulse responses h(t , τ) orwith stochastic system function h(t , τ)
WSSUS modelSimplification of stochastic system functions, assuming
h(t , τ) is wide-sense stationary (WSS)scattering components are uncorrelated (US)
System fully defined by e.g. Scattering functionAll other parameters are derived from this (Delay PSD,Doppler PSD, correlation fcts., ...)Example: COST 207
DGUS model (Deterministic Gaussian, Uncorrelated Scattering)
Deterministic realisation of WSSUS model
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
ImplementationsScenarioResult
Simulation Implementations
Generic Channel Sounder
old FAA/Mitre/MIT channel simulator software in ANSI CErroneous results
probably due to legacy platform issues
Matlab Communications Toolbox
results as expected, easy to use, show example
Direct Matlab implementation of reference models (fromPätzold)
confirmed results
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
ImplementationsScenarioResult
Simulation Scenario
VHF voice channel with sinusoidal inputAircraft with v = 60 m
s and maximum Doppler offD,max = 24 Hz
Frequency nonselective Rician channel with k = 12 dB
Computer based
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
ImplementationsScenarioResult
Simulation ExampleChannel Input Channel Output LOS and Scatter
0 0.7 1
0
0.7
1
In−Phase: Re[g(t)]
Qua
drat
ure:
Im[g
(t)]
0 1 2−0.5
0
0.5
1
1.5
2
In−Phase: Re[g(t)]
Qua
drat
ure:
Im[g
(t)]
0 0.2 0.4 0.6−30
−25
−20
−15
−10
−5
0
Time in s
Com
pone
nts
Pow
er in
dB
Demodulation Bandpass AGC
0 1 2 3 4 5 6 7 8−1.5
−1
−0.5
0
0.5
1
1.5
Time in units of tλ=0.042s
Am
plitu
de
0 0.1 0.2 0.3−1.5
−1
−0.5
0
0.5
1
1.5
Time in s
Am
plitu
de
0 0.1 0.2 0.3−1.5
−1
−0.5
0
0.5
1
1.5
Time in sA
mpl
itude
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
ImplementationsScenarioResult
References
Aeronautical Voice Radio Channel Modelling andSimulation - Konrad Hofbauer & Gernot Kubin - To bepublished at ICRAT 2006
Mobile Radio Systems (Mobilfunktechnik) - Klaus Witrisal -Lecture and Notes
Mobile Fading Channels - Matthias Pätzold - WileyThe Mobile Radio Propagation Channel - J. D. Parsons -Wiley
Proakis&Salehi, Sklar, Barry&Lee&Messerschmitt
Konrad Hofbauer Simulation of Fading Radio Channels
institution-logo
Radio CommunicationPropagation ChannelStochastic Modelling
Hands-On Simulation
ImplementationsScenarioResult
Konrad Hofbauer Simulation of Fading Radio Channels