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LOVELY PROFESSIONAL UNIVERSITY

TERM PAPER 

OF

(ECE-304)

DIGITAL COMMUNICATION SYSTEM

ON

CHANNEL FADING AND CHANNEL

EQUALIZATION

SUBMITTED TO: SUBMITTED BY:

Mr. Gagandeep Singh Walia Saurav SinghR B 6703 B 64

3460070065

ABSTRACT:

This demonstration illustrates the

application of adaptive filters to channel

equalization in digital communications.Channel equalization is a simple way of 

mitigating the detrimental effects caused by

a frequency-selective and/or dispersive

communication link between sender and

receiver. For this demonstration, all signals

are assumed to have a digital baseband

representation Frequency-selective time-

varying fading causes a cloudy pattern to

appear on a spectrogram. Time is shown on

the horizontal axis, frequency on the vertical

axis and signal strength as grey-scaleintensity. In wireless 

communications, fading is deviation of 

the attenuation that a carrier-modulated

telecommunication signal experiences over 

certain propagation media. The fading may

vary with time, geographical position and/or 

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radio frequency, and is often modelled as

a random process. A fading channel is a

communication channel that experiences

fading. In wireless systems, fading may

either be due to multipath propagation,

referred to as multipath induced fading, or 

due to shadowing from obstacles affecting

the wave propagation, sometimes

referred to as shadow fading.

Fading:

In wireless communications, fading is

deviation of the attenuation that a carrier-

modulated telecommunication signal

experiences over certain propagation media.The fading may vary with time,

geographical position and/or radio

frequency, and is often modelled as a

random process. A fading channel is a

communication channel that experiences

fading. In wireless systems, fading may

either be due to multipath propagation,

referred to as multipath induced fading, or 

due to  shadowing from obstacles affecting

the wave propagation, sometimes referred toas shadow fading.

 Slow versus fast fading:

The terms slow and fast fading refer to the

rate at which the magnitude and phase

change imposed by the channel on the signal

changes. The coherence time is a measure of 

the minimum time required for the

magnitude change of the channel to becomeuncorrelated from its previous value.

• Slow fading arises when the

coherence time of the channel is

large relative to the delay constraint

of the channel. In this regime, the

amplitude and phase change imposed

  by the channel can be considered

roughly constant over the period of 

use. Slow fading can be caused by

events such as shadowing, where a

large obstruction such as a hill or 

large building obscures the main

signal path between the transmitter 

and the receiver. The amplitude

change caused by shadowing is often

modeled using a log-normal 

distribution with a standard deviation

according to the log-distance path 

loss model.

• Fast fading occurs when the

coherence time of the channel is

small relative to the delay constraint

of the channel. In this regime, the

amplitude and phase change imposed

 by the channel varies considerably

over the period of use.

In a fast-fading channel, the transmitter may

take advantage of the variations in thechannel conditions using time diversity to

help increase robustness of the

communication to a temporary deep fade.

Although a deep fade may temporarily erase

some of the information transmitted, use of 

an error-correcting code coupled with

successfully transmitted bits during other 

time instances (interleaving) can allow for 

the erased bits to be recovered. In a slow-

fading channel, it is not possible to use time

diversity because the transmitter sees only a

single realization of the channel within its

delay constraint. A deep fade therefore lasts

the entire duration of transmission and

cannot be mitigated using coding.

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Flat versus frequency-selective fading:

As the carrier frequency of a signal is

varied, the magnitude of the change in

amplitude will vary. The coherence 

 bandwidth measures the separation in

frequency after which two signals will

experience uncorrelated fading.

• In flat fading, the coherence

  bandwidth of the channel is larger 

than the bandwidth of the signal.

Therefore, all frequency components

of the signal will experience the

same magnitude of fading.

• In frequency-selective fading, the

coherence bandwidth of the channel

is smaller than the bandwidth of the

signal. Different frequency

components of the signal therefore

experience decorrelated fading.

Since different frequency components of the

signal are affected independently, it is

highly unlikely that all parts of the signalwill be simultaneously affected by a deep

fade. Certain modulation schemes such as

OFDM and CDMA are well-suited to

employing frequency diversity to provide

robustness to fading. OFDM divides the

wideband signal into many slowly

modulated narrowband subcarriers, each

exposed to flat fading rather than frequency

selective fading. This can be combated by

means of  error coding, simple equalization or adaptive bit loading. Inter-symbol

interference is avoided by introducing a

guard interval between the symbols. CDMA

uses the Rake receiver  to deal with each

echo separately.

Frequency-selective fading channels are also

dispersive, in that the signal energy

associated with each symbol is spread out in

time. This causes transmitted symbols that

are adjacent in time to interfere with each

other. Equalizers are often deployed in such

channels to compensate for the effects of the

intersymbol interference.

Fading models:

Examples of fading models for the

distribution of the attenuation are:

•  Nakagami fading

• Weibull fading

• Rayleigh fading 

• Rician fading 

• Dispersive fading models, with

several echoes, each exposed to

different delay, gain and phase shift,

often constant. This results in

frequency selective fading and inter-

symbol interference. The gains may

  be Rayleigh or Rician distributed.The echoes may also be exposed to

Doppler shift, resulting in a time

varying channel model.

• Log-normal shadow fading

Rayleigh fading:

Rayleigh fading is a statistical model for the

effect of a  propagation environment on a

radio signal, such as that used by wireless devices. Rayleigh fading models assume that

the magnitude of a signal that has passed

through such a transmission medium (also

called a communications channel) will vary

randomly, or  fade, according to a Rayleigh 

distribution — the radial component of the

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sum of two uncorrelated Gaussian  random 

variables.

Rayleigh fading is viewed as a reasonable

model for  tropospheric and ionospheric 

signal propagation as well as the effect of 

heavily built-up urban environments on

radio signals.[1][2] Rayleigh fading is most

applicable when there is no dominant

  propagation along a line of sight between

the transmitter and receiver. If there is a

dominant line of sight, Rician fading may be

more applicable.

 Properties:

Since it is based on a well-studied

distribution with special properties, the

Rayleigh distribution lends itself to analysis,

and the key features that affect the

  performance of a wireless network have

analytic expressions.

 Note that the parameters discussed here are

for a non-static channel. If a channel is notchanging with time, clearly it does not fade

and instead remains at some particular level.

Separate instances of the channel in this case

will be uncorrelated with one another owing

to the assumption that each of the scattered

components fades independently. Once

relative motion is introduced between any of 

the transmitter, receiver and scatterers, the

fading becomes correlated and varying in

time.

Generating Rayleigh fading:

As described above, a Rayleigh fading

channel itself can be modelled by generating

the real and imaginary parts of a complex

number according to independent normal

Gaussian variables. However, it is

sometimes the case that it is simply the

amplitude fluctuations that are of interest

(such as in the figure shown above). There

are two main approaches to this. In both

cases, the aim is to produce a signal which

has the Doppler power spectrum given

above and the equivalent autocorrelation

 properties.

Rician fading:

Rician fading is a stochastic model for radio 

 propagation anomaly caused by partial

cancellation of a radio signal by itself — the

signal arrives at the receiver by two different

  paths (hence exhibiting multipath 

interference), and at least one of the paths is

changing (lengthening or shortening). Rician

fading occurs when one of the paths,

typically a line of sight signal, is much

stronger than the others. In Rician fading,

the amplitude gain is characterized by a

Rician distribution.

Rayleigh fading is the specialised model for 

stochastic fading when there is no line of  

sight signal, and is sometimes considered as

a special case of the more generalised

concept of Rician fading. In Rayleigh

fading, the amplitude gain is characterized

 by a Rayleigh distribution

The model behind Rician fading is similar to that for  Rayleigh fading, except that in

Rician fading a strong dominant component

is present. This dominant component can for 

instance be the line-of-sight wave. Refined

Rician models also consider that

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• that the dominant wave can be a

 phasor sum of two or more dominant

signals, e.g. the line-of-sight, plus a

ground reflection. This combined

signal is then mostly treated as a

deterministic (fully predictable)

 process, and that

• the dominant wave can also be

subject to shadow attenuation. This

is a popular assumption in the

modelling of satellite channels.

Besides the dominant component, the

mobile antenna receives a large number of 

reflected and scattered waves.

Phasor Diagram of Rician fading signal

Rician factor:

The Rician K-factor is defined as the ratio of 

signal power in dominant component over 

the (local-mean) scattered power. In the

expression for the received signal, the power 

in the line-of-sight equals C2/2. In indoor  

channels with an unobstructed line-of-sight

 between transmit and receive antenna the K-

factor is between, say, 4 and 12 dB.

Rayleigh fading is recovered for K = 0 (-

infinity dB).

Rician Channels:

Examples of Rician fading are found in

• Microcellular channels

• Vehicle to Vehicle communication,

e.g., for AVCS 

• Indoor propagation

• Satellite channels

Scales of Fading:

Large scale Fading

Small Scale Fading

Small Scale Fading Types:

Frequency selective fading

Flat fading

Fast fading

Frequency Selective fading:

Selective fading causes a "cloudy" pattern to

appear on a spectrogram display.

Selective fading or frequency selective

fading is a radio propagation anomaly

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caused by partial cancellation of a radio

signal by itself — the signal arrives at the

receiver by two different paths, and at least

one of the paths is changing (lengthening or 

shortening). This typically happens in the

early evening or early morning as the

various layers in the ionosphere move,

separate, and combine. The two paths can

 both be skywave or one be groundwave.

Selective fading manifests as a slow, cyclic

disturbance; the cancellation effect, or 

"null", is deepest at one particular 

frequency, which changes constantly,

sweeping through the received audio.

The effect can be counteracted by applying

some diversity scheme, for example OFDM 

(with subcarrier  interleaving and forward 

error correction), or by using two receivers 

with separate antennas spaced a quarter-

wavelength apart, or a specially-designed

diversity receiver  with two antennas. Such a

receiver continuously compares the signals

arriving at the two antennas and presents the better signal.

Flat fading:

If the mobile radio channel has a constant

gain and linear phase response over a

 bandwidth

which is greater than the bandwidth of the

transmitted signal, then the received signal

willundergo flat fading. This type of fading is

historically the most common type of fading

described

in the technical literature. In flat fading, the

multipath structure of the channel is such

that the

spectral characteristics of the transmitted

signal are preserved at the receiver.

However the

strength of the received signal changes with

time, due to fluctuations in the gain of the

channel

caused by multipath. The characteristics of a

flat fading channel are illustrated in Figure

5.12.

It can be seen from Figure 5.12 that if the

channel gain changes over time, a change of 

amplitude occurs in the received signal.

Over time, the received signal r(t) varies in

gain, but

the spectrum of the transmission is  preserved. In a flat fading channel, the

reciprocal bandwidth

of the transmitted signal is much larger than

the multipath time delay spread of the

channel, and can be approximated

as having no excess delay (i.e., a single delta

function with

Frequency Selective Fading:

If the channel possesses a constant-gain andlinear phase response over a bandwidth that

is

smaller than the bandwidth of transmitted

signal, then the channel creates frequency

selective

fading on the received signal. Under such

conditions, the channel impulse response has

a multipath delay spread which is greater 

than the reciprocal bandwidth of the

transmitted message

waveform. When this occurs, the received

signal includes multiple versions of the

transmitted

waveform which are attenuated (faded) and

delayed in time, and hence the received

signal is distorted. Frequency selective

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fading is due to time dispersion of the

transmitted symbols within the channel.

Thus the channel induces intersymbol

interference (ISI). Viewed in the frequency

domain, certain frequency components in

the received signal spectrum have greater 

gains than

others. Frequency selective fading channels

are much more difficult to model than flat

fading

channels since each multipath signal must be

modeled and the channel must be considered

to be a linear filter. It is for this reason that

wideband multipath measurements are

made, and models are developed from thesemeasurements. When analyzing mobile

communication systems, statistical impulse

response models such as the two-ray

Rayleigh fading model (which considers the

impulse response to be made up of two delta

functions which independently fade and

have sufficient time delay between them to

induce frequency selective fading upon the

applied signal), or computer generated or 

measured impulse responses, are generallyused for analyzing frequency selective

small-scale fading. Figure 5.13 illustrates

the characteristics of a frequency selective.

Equalization in Digital Communications

This demonstration illustrates the

application of adaptive filters to channel

equalization in digital communications.

Channel equalization is a simple way of 

mitigating the detrimental effects caused by

a frequency-selective and/or dispersive

communication link between sender and

receiver. For this demonstration, all signals

are assumed to have a digital baseband

representation. During the training phase of 

channel equalization, a digital signal s[n]

that is known to both the transmitter and

receiver is sent by the transmitter to the

receiver. The received signal x[n] contains

two signals: the signal s[n] filtered by the

channel impulse response, and an unknown

 broadband noise signal v[n]. The goal is to

filter x[n] to remove the inter-symbol

interference (ISI) caused by the dispersive

channel and to minimize the effect of the

additive noise v[n]. Ideally, the output signal

would closely follow a delayed version of 

the transmitted signal s[n].

The transmitted input signal s[n]:

A digital signal carries information through

its discrete structure. There are several

common baseband signaling methods. We

shall use a 16-QAM complex-valued symbol

set, in which the input signal takes one of 

sixteen different values given by all possible

combinations of {-3, -1, 1, 3} + j*{-3, -1, 1,

3}, where j = sqrt(-1). Let's generate a

sequence of 5000 such symbols, where eachone is equiprobable.

ntr = 5000;

 j = sqrt(-1);

s =

sign(randn(1,ntr)).*(2+sign(randn(1,ntr)))

+j*sign(randn(1,ntr)).*(2+sign(randn(1,ntr))

);

 plot(s,'o');

axis([-4 4 -4 4]);axis('square');

xlabel('Re\{s(n)\}');

ylabel('Im\{s(n)\}');

title('Input signal constellation');

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Fig 1.2.1

The transmission channel:

The transmission channel is defined by the

channel impulse response and the noise

characteristics. We shall choose a particular 

channel that exhibits both frequency

selectivity and dispersion. The noise

variance is chosen so that the received

signal-to-noise ratio is 30 dB.

 b = exp(j*pi/5)*[0.2 0.7 0.9];

a = [1 -0.7 0.4];

% Transmission channel filter channel = dfilt.df2t(b,a);

% Impulse response

hFV = fvtool(channel,'Analysis','impulse');

legend(hFV, 'Transmission channel');

  Fig.1.3.1

% Frequency response

set(hFV, 'Analysis', 'freq')

Fig 1.3.2

 The received signal x[n]:

The received signal x[n] is the signal s[n]

filtered by the channel impulse response

with additive noise v[n]. We assume a

complex Gaussian noise signal for the

additive noise. sig =

sqrt(1/16*(4*18+8*10+4*2))/sqrt(1000)*no

rm(impz(channel));

v = sig*(randn(1,ntr) +

 j*randn(1,ntr))/sqrt(2);

x = filter(channel,s) + v;

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 plot(x,'.');

xlabel('Re\{x[n]\}');

ylabel('Im\{x[n]\}');

axis([-40 40 -40 40]);

axis('square');

title('Received signal x[n]');

  Fig.1.4.1

The training signal:

The training signal is a shifted version of the

original transmitted signal s[n]. This signal

would be known to both the transmitter and

receiver.

d = [zeros(1,10) s(1:ntr-10)];

Trained equalization:

To obtain convergence, we use the

conventional version of a recursive least-

squares estimator. Only the first 2000

samples are used for training. The output

signal constellation shows clusters of values

centered on the sixteen different symbol

values--an indication that equalization has

 been achieved.

P0 = 100*eye(20);

lam = 0.99;

h = adaptfilt.rls(20,lam,P0);

ntrain = 1:2000;

[y,e] = filter(h,x(ntrain),d(ntrain));

 plot(y(1001:2000),'.');

xlabel('Re\{y[n]\}');

ylabel('Im\{y[n]\}');

axis([-5 5 -5 5]);

axis('square');

title('Equalized signal y[n]');

  Fig.1.6.1

Training error e[n]:

Plotting the squared magnitude of the error 

signal e[n], we see that convergence with the

RLS algorithm is fast. It occurs in about 60

samples with the equalizer settings chosen.

semilogy(ntrain,abs(e).^2);xlabel('Number of iterations');

ylabel('|e[n]|^2')

title('Squared magnitude of the training

errors');

Fig 1.7.1

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References :

www.google.com

www.wikipedia.com

www.answers.com