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Modul 3

Small Scale Fading

Wireless Communication System

1

Faculty of Electrical Communication

IT Telkom

October 2012Modul 3 Small Scale Fading

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Subject

a. Introduction Fading Channel Manifestationsb. Small Scale Fading

c. Kl sifik si Sm ll Sc le F din

2

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Multipath Components

Component 2

Component 1

Radio Signals Arriving from different directions to receiver

3

Component N

Receiver may be stationary or mobile.

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Multipath Components

At a receiver point

Radio waves generated from the same transmitted signalmay come

from different directions

with different propagation delays

with ossibl different am litudes random

4

with (possibly) different phases (random)

with different angles of arrival (random).

These multipath components combine vectorially at the

receiver antenna and cause the total signal to fade

to distort

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5

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6 Multipath Propagation

In general, the received signal at the receiver point is the sum of the directsignal and the number of signals reflected from various objects. In mobilecommunication, reflection will be caused by:

Surface terrain

Buildings Moving objects as an example vehicle

Wave reflection magnitude and phase will change, depending on thereflection coefficient, the wave trajectory, and also depending on the angle of

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. ,terms of:

Amplitude, depending on the magnitude of reflection coefficient Phase, depending on the phase change of reflection and the

path distance difference between the direct wave and the

reflected waveThe worst condition occurs when the direct wave and reflection wave hasthe same magnitude and different phases 180o. In such conditions, betweenthe direct wave and the reflected waves will occur eliminate each other(complete cancellation)

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7

Phase difference of 180o

occur if there are differences in the path distancetraveled by the waves as follows:

=

2

)1n2(d

The best condition is achieved if the direct wave and reflection wave has thesame phase or a multiple of 360o (In Phase Combination). Difference distancedirect wave and reflection on this condition can be expressed as follows:

Multipath Propagation

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= nd where:n = 1,2, 3, etct = wave length

The variation of wave amplitude and phase depending on thevariety of conditions and due to various factors, which causeFading occurs, we will discuss in this module.

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Amplitudo

Amplitudo sinyal terimatergantung dari lokasi danfrekuensi

Jika antena bergerak,maka lokasi x akanberubah linear terhadap

Small Scale Fading8

Frekuensi Waktu

wa u x= v

Parameters:

probability of fades

duration of fades bandwidth of fades

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Delay Spread Model dan Time Varying Model

Fokus pada multipath fading, disebabkan 2 hal:

Time spreadingsinyal Akibat sinyal datangdengan delay yang berbeda-beda, dianalisis denganDelay Spread Model

Time varying of channel akibat pergerakan,

Karakterisasi Kanal Multipath10

ana s s engan me ary ng o e

Evaluasi/analisis biasa dilakukan dalam

Domain waktu, dan

Domain frekuensi

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Delay Spread Model

To know the characteristics of channel delay, usually conducted Channel

sounding (with impulse response)

Maximum excess delay digitize into N groups of paths, each path separated

Multipath channel

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.

The model used to analyze signals with BW < 1/(2).

The total power received is the sum of all multipath components, if the

components can be resolved / processed.

If the signal BW BW al multipath channel can not be overcome

SIRCIM (Simulation ofIndoorRadioChannelIMpulse response)

SMRCIM (Simulation ofMobileRadioChannelIMpulse response.)

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h(d,t)x(t) y(d,t)

Received signal, is a function of distance (d) and time (t)

+

== d)t,d(h)(x)t,d(h)t(x)t,d(y

=

Small Scale Fading - Multipath Channel Impulse Response Model

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, ,

=t

d)t,t.v(h)(x)t,t.v(y

Assumption of constant v, then d is only a function of velocity (v) andtime (t)

==t

d)t,t.v(h)(x)t,t.v(h)t(x)t(y

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( ) ( ) = +=N

1k k0krtf2cosate

Received signal can be expressed as follows :

Where,=

Multipath Signal Analysis, Assumptions: Vehicles without moving

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N = number of track multipathak , k = amplitude and phase of the kth

multipath component-k

( ) ( ) = +=N

1k k0kr tf2cosate

( ) ( ) ( ) ( ) ( )k0k0k0 sintf2sincostf2costf2cos =+Recall :

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( ) ( ) ( ) ( ) ( ) == =N

1k kk0

N

1k kk0rsinatf2sincosatf2coste

( ) ( ) ( )tf2sinYtf2cosXte 00r = X

Yr

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Asuming :N Large N (many paths) theoretically infinite, practically > 6k uniformly distributed in (0 to 2)ak respectively can be compared (no one is quite dominant)X and Y are mutually independent identical distributed Gaussian

Then :

22 YXrEnvelopeSinyal +== RAYLEIGH distibuted!!

Identically Independently Distributed(IID)

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as c eory _ ma ca e a ng multipath signal analysis

Mobile RadioPropagation

The received signal is a sum of real

signals that have experienceattenuation, reflection, refractionand diffraction according to its path.

Mobile station movement

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Rayleigh Distribution

( )( )

( )

>

Coherence time < periodesimbol

Variasi kanal lebih cepat darivariasi sinyal baseband

Doppler spread periode

simbol

Variasi kanal lebih lambat darivariasi sinyal baseband

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22%------------------

% fading parameters%------------------

c_light = 3E8; % speed of light (m/s)

v = 10; % vehicle's speed (kph)

B = 40; % number of bit per slot

R = 60; % bit rate (kbps)

T = 1/(R*1E3); % symbol duration (s)

f = 1.8; % carrier frequency (GHz)

fd = (v*1E3/3600)*f*1E9/c_light; % Doppler freq (Hz)

N = 34;

N0 = (N/2 - 1)/2;alpha = pi/4;

xc = zeros(len,1);

xs = zeros(len,1);

sc = sqrt(2)*cos(alpha);

ss = sqrt(2)*sin(alpha);

ts = 0:len-1;

ts = ts'.*T + round(rand(1,1)*10000)*T;

wd = 2*pi*fd;

xc = sc.*cos(wd.*ts);

xs = ss.*cos(wd.*ts);

Fading Simulator : Jakes Method22

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%-----------------------

% variable in simulation

%-----------------------

Tp = 1000; % number of data slot

len = B*Tp; % number of symbol (Bsymbols/slot)

% function y = fading(len, fd, T)

%--------------------------

% parameter in Jakes Method

%---------------------------

for lx =1:N0

wn = wd*cos(2*pi*lx/N);

xc = xc + (2*cos(pi*lx/N0)).*cos(wn.*ts);

xs = xs + (2*sin(pi*lx/N0)).*cos(wn.*ts);

end;

y = (xc + i.*xs)./sqrt(N0+1);

%plot fading signalfigure(1);

plot(ts*T,abs(y));

title('Fading Signals')

xlabel('time (sec)')

ylabel('amplitude')

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mu a on esuSignal Analysis on Rayleigh Channel

Mobile station speed 5km/hour,fd=4,023Hz

mobile station speed25km/hour, fd=20,27Hz

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Mobile station speed 100km/hour, fd=80,52Hz Amplitude fluctuation (Fading) will increase asthe mobile station (MS) speed increase, it can

be seen as follow:

MS speed 5km/hour, fd=4,023Hz.Received signal will achieve maximalattenuation 11db, amplitude fluctuation is notoccurs many times.

MS speed 25km/hour, fd=20,27Hz.Received signal will achieve maximalattenuation 13dB, amplitude fluctuation is moreoften than MS 25km/hour.

MS speed 100km/hour, fd=80,52Hz.Maximal attenuation 17dB, amplitudefluctuation is the most often in this threeexperiment.

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