Simulation of Fading Radio Channels · 2006-05-11 · Radio Communication Propagation Channel Stochastic Modelling Hands-On Simulation Simulation of Fading Radio Channels Konrad Hofbauer

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


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..


institution-logo


Hands-On Simulation

Motivation






institution-logo


Hands-On Simulation

Motivation






institution-logo


Hands-On Simulation

Communication ProblemAmplitude ModulationComplex Baseband

Communication Problem


institution-logo


Hands-On Simulation




institution-logo


Hands-On Simulation




institution-logo


Hands-On Simulation




institution-logo


Hands-On Simulation




institution-logo


Hands-On Simulation




institution-logo


Hands-On Simulation


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


institution-logo


Hands-On Simulation


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


institution-logo


Hands-On Simulation

Channel AttenuationAdditive NoiseDoppler EffectMultipath PropagationTime Variation

Propagation ChannelReminder


institution-logo


Hands-On Simulation


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.)


institution-logo


Hands-On Simulation


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).


institution-logo


Hands-On Simulation


Doppler Effect

Frequency shift fD due tomovement v

fD = fD,max cos(α)

Maximum Doppler shift

fD,max =vc

fc


institution-logo


Hands-On Simulation


Multipath PropagationReflection – Scattering – Diffraction – Absorption


institution-logo


Hands-On Simulation


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


institution-logo


Hands-On Simulation


Time Variation

Time Variant ChannelAll parameters vary over time, and so does the channel !!!


institution-logo


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


institution-logo


Hands-On Simulation


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.


institution-logo


Hands-On Simulation


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


institution-logo


Hands-On Simulation


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


institution-logo


Hands-On Simulation


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).


institution-logo


Hands-On Simulation


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?


institution-logo


Hands-On Simulation


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.


institution-logo


Hands-On Simulation


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)?


institution-logo


Hands-On Simulation


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.


institution-logo


Hands-On Simulation


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)


institution-logo


Hands-On Simulation


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!


institution-logo


Hands-On Simulation


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!


institution-logo


Hands-On Simulation


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


institution-logo


Hands-On Simulation


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


institution-logo


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


institution-logo


Hands-On Simulation


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


institution-logo


Hands-On Simulation


Simulation ExampleChannel Input Channel Output LOS and Scatter

0 0.7 1

0

0.7

1


Qua

drat

ure:

Im[g

(t)]

0 1 2−0.5

0

0.5

1

1.5

2


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


institution-logo


Hands-On Simulation


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


institution-logo


Hands-On Simulation



Simulation of Fading Radio Channels · 2006-05-11 · Radio Communication Propagation Channel Stochastic Modelling Hands-On Simulation Simulation of Fading Radio Channels Konrad Hofbauer

Documents