Pioneer Paper

8/3/2019 Pioneer Paper

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A

Paper Prepared on

WIRELESS COMMUNICATION

BY

Kulkarni Amey Shrikant (T.E. Eln, WCE, Sangli,)

Bhide Chinmay Milind (T.E.Eln, WCE, Sangli)

For the event

PIONEER 2010

Organized by KIT COE, Kolhapur.

Author Details:

1. Kulkarni Amey Shrikant - [email protected], + 91 9975273828

2. Bhide Chinmay Milind - [email protected], +91 9403045649

Discipline: Electronics and Telecommunication Engg.

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INDEX

Sr.no

Contents Page No.

1 Abstract 2

2 Introduction 3

3 Channel analysis

a. Propagation Mechanisms and

Path loss Models

b. Basic LTI two path model

c. Statistical Analysis of received

signal

d. Characterization of system

4

4

5

7

4 Equalization

a. Concept of adaptive equalization

b. Channel model for Equalizationc. Types of Equalizer

i. Linear

ii. Non line

10

11

12

5 References 13

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ABSTRACT

Wireless communication belongs to one of the greatest milestones in the era of electronic

evolution. Every communication system involves three major sections namely transmitter,

receiver and channel. Wireless Communication System utilizes air or atmosphere as channel.

Uneven properties of channel result in uncertain system performance. Hence, study of

propagation channel plays vital role in design of transmitter and receiver.

In this paper, we have discussed in detail about mathematical analysis of channel from design

perspective. In later part, equalizers are discussed which nullify the effect imposed by the

channel. Channel analysis is discussed in flow of mathematical simplicity. In initial stages,

channel is considered to be only LTI narrowband system and then other practical conditions like

time variance, non stationary receiver state and wideband system are considered step by step and

mathematical treatment is modified accordingly. In later part, equalizers are discussed in a

typical manner. Adaptive equalization technique is implemented in Advance Wireless

Communication systems like GSM. Hence the concept of adaptive equalization and the types of

equalizers namely linear and non linear are considered in principle.

Statistical methods provide good approximations to random behavior of channel. Good

approximation yields to efficient design of the transmitters and receivers. The channel propertieswhen estimated, there effect on the signal can be nullified at the receiver by use of equalizer.

Adaptive equalization technique is practically used in advanced communication systems like

GSM and OFDM.

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Introduction:

Wireless Communication is one of the big engineering stories from last 25 years, not only from

scientific point of view but also from market size and impact on society.The Wireless

Communication Field can be divided into following sections viz. ( a ) Communication Channel

( B ) Design of Transmitter and Receiver ( C ) Signal Processing Techniques and Algorithms

( D ) Communication Protocols. The present paper is centered on the study of Communication

Channel inclusive of its time variance, Impulse response and narrowband, wideband distinction

and process of equalization which is to get back the signal to its original form as affected by

propagating through the channel which is finally a system.

There is considerable difference between Wired Communication systems and Wireless

Communication Systems that should be understood before entering into details of wireless

communication. In case of wired communication systems, a specific path is assigned to the

signal flow whereas the signal has got a lot many space to deviate from the desired path in case

of wireless communication. In scientific point of view, wireless communication systems face

problems of Interference and fading whereas wired communication systems totally get rid of this

issue.

Wireless Propagation Channel is a medium linking the transmitter and receiver. Its properties

eventually limit the performance of Wireless Communication System. So it is essential to

understand wireless communication channel in order to design transmitter, receiver and other

signal processing algorithms. The paper is organized in such a way that mathematical treatments

are given due emphasis especially in modeling of the channel as a system. The concepts are so

elaborated in a flow of Specific General. The specific case, easy to model mathematically is

considered first and then it is generalized. E.g. The LTI narrowband model of the system is

elaborated first and then the time variant wideband model is considered.

Propagation Mechanisms and Path loss Models

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It is essential to determine the behavior of Radio Wave when it is propagating through the

channel. The detailed information of propagation mechanisms helps in determining the overall

response of the channel system & thereby designs of equalizer and other receiver components.

Propagation Mechanisms involve following 4 factors

1. Free Space Loss

2. Reflection and Scattering

3. Diffraction

4. Scattering.

Propagation Channel Models: Link Budget is another important term in Wireless

Communication. Link budget is the clearest and institutive way to know the required transmitter

power and design. The formulation of the link budget involves transmitter power and receiver

SNR (Signal to noise ratio) including all possible factors that may affect the wave propagation.

The Link budget thus will be site specific. The exhaustive survey of the concerned region and

thereby knowing the different types of losses due to above mentioned propagation mechanisms

go to decide the Link Budget of the particular region. There are different kinds of path loss

models specified which associate the propagation factors to know the cumulative path loss of the

channels. These models include ( 1 ) Okumura - Hata Model ( 2 ) COST 231 Model ( 3)

COST 207 model ( 4 ) Motley Keenan Model. Etc. These models have their specified formulae

by which effective numerical response of the channel system can be determined.

BASIC ANALYTICAL TWO PATH MODEL OF CHANNEL --- CHANNEL AS LTI SYSTEM

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As shown in the figure, lets consider the simplest two path model with sinusoidal signal.

ETrans. = E0 cos ( 2 f c t ) and Received signal E Received = E0 cos ( 2 f c t k0 d )

where k0 = wave number d = distance travelled by the wave.

In complex base band notation it is represented as E received = E0 e j k0 d

Hence the interference of the two waves is taken as E received = E0 e j k0 d + E0 e

j k1 d

The interference pattern is represented as follows in 3 dimensions:

Two Path Time Variant Model:

Now, suppose if the receiver is non stationary, Doppler Shift will be introduced and the equation

of the resulting wave is given as E Received = E0 cos ( 2 t { f v/ } k0 d )

Being the receiver is non stationary, it will receive two waves each with Doppler Shift of

different amount. This will cause the phenomenon of beating.

Statistical Analysis of Signal received at Receiver:

The signal received at the receiver end can be treated as a random variable with no dominating

component. It indicates the probability of reception to all possible components is equally likely.

So it follows from the central limit theorem that such a set of variables will have Gaussian

distribution. Being complex sinusoid, it should be analyzed in terms of both amplitude and

phase. The statistical analysis shows that the amplitude pdf will have Rayleigh Distribution and

the phase pdf will have uniform distribution.

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Gaussian Distribution of Received Power:

Rayleigh Distribution of Amplitude

The Rayleigh distribution is found to be very convenient in wireless communication because

1. It is an excellent approximation in a large number of practical cases.

2. It is the worst case scenario in the sense that there is no dominant signal component and

thus there is large number of fading dips.

3. It depends on single parameter, the mean received power, once this parameter is known

the complete signal statistics can be known. It is easier and less error prone to obtain this

single parameter instead of making the case complicated by integrating other possible

terms.

4. It is also convenient for mathematical computations and modeling

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PROPAGATION CHANNEL AS A SYSTEM & ITS CHARACTERIZATION:

The propagation channel can be certainly treated as a system. The generalized system properties

like Impulse Response, Frequency Response and Transfer Function are justified for the

propagation channel too.

Continuing to the previously followed analogy, lets consider the two path model of the channel

with different run times say t1 = d1/ c and t2= d2/ c

For the sake of simplest approximation, lets consider the system to be LTI (Linear Time

Invariant) ; so the impulse response of the system is found to be

h ( t ) = a1 . ( t -- t1) + a2 . ( t -- t2 ) ; where a = |a| exp ( j )

The Fourier transform of the Impulse Response will give the Frequency response

H ( f ) = a1 exp( -j 2 f 1 ) + a2 exp( -j 2 f 2)

The magnitude of the transfer function is | H ( f ) | = [ a12 + a2

2 + 2 a1 a2 cos ( 2 f

) ]We observer that the transfer function depends on the frequency, so we have frequency

selective fading. The notches are observed in the transfer function plot, those are the

frequencies at which the two waves have 1800 phase shift.

The More General Case:

After the simple two path model, we now progress to the more general case where Interacting

Objects can be at any place in the plane. If imaginary ellipses are considered with TX & RX at its

foci. All rays undergo a single interaction with objects on a specific ellipse arrive at the receiver

at the same time. Signals that interact with objects on different ellipses arrive at different times.

Thus the channel is delay dispersive. It is obvious that IOs will never lie exactly on a single

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ellipse. So for the channel to be non dispersive, the strictness of the condition is released

depending on the bandwidth of the system. A receiver bandwidth cannot distinguish between

echoes arriving at time interval for


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1. For narrowband system

2. For Wideband System . The impulse response is same for period equal to unit maximum

delay amount and it varies in the further one.

It should be emphasized strictly that the definition of Wideband is different from its conventional

one. Conventional one states it in terms of comparison between System bandwidth and the

carrier frequency. In Wireless Communication System properties and Channel properties are

compared from time domain point of view. Hence it is possible that a system is narrowband for a

particular kind of channel and necessarily wideband for another channel.

Time Variance of Channel System:

For the time variant system, the practical systems are so defined; the impulse response will be

time variant. The impulse response will be function of both and t. Fourier transform can be

applied to either of them or both of them to result into four different kinds of representations.

They can be mentioned as follows.

1. Integration with respect to i.e. Time Variant Transfer function

It represents the spectrum of the input signal multiplied by the currently valid transfer

function to give the spectrum of the output signal. Abbreviated as H ( f, t )

2. Integration with respect to t i.e. Delay Doppler Function

It is better known as Spreading Function S ( , )

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3. Doppler variant Transfer Function

It is the more generic to above two Frequency Domain representations. It is better knownas Doppler Variant Transfer Function abbreviated as B ( , f )

Characterization of Wideband Systems:

The Wide band systems can be characterized by associating the above discussed points

viz. time variance, delay dispersion and implementation of impulse response in a finite

delay bin (). In order to be specific within certain practical limits, Wideband systems

are characterized by well accepted models. These models mainly include WSSUS (Wide

Sense Stationary Uncorrelated Scatters) and another specific model which is derived

from WSSUS model is Tapped Delay Line Model. These models are developed by

considering Statistical Dependencies or Correlations between various affecting factors.

Mathematical Identities of these models involve extensive statistical analysis which is not

in the scope of the paper. Hence the brief conclusion of these models can be drawn in

terms of the impulse response of the system which is given as

N

ci (t) ( ti )

i=1

Equalization

It is the process at receiver by means of which the distortions and other effects by channel are

reversed.

Equalizer:

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These are receiving structures that work to reduce or eliminate ISI, inter symbol

interference and also at the same time exploit delay diversity inherent in the channel.

Need of equalization:

Delay dispersion, i.e. multipath components can have different runtimes from transmitter

to receiver, leads to inter symbol interference. If delay spread is comparable to or greater

than symbol duration then BER (Bit error Rate) increases acceptably as happens in 2G-

3G cellular communication networks.

Concept of adaptive equalization:

In case of wireless communication, channel is having two characteristics which hamper

the design of equalizers by above equation.

1. Unknown

2. Time-variant

First problem is solved by training sequence (known sequence of bits) is transmitted

from transmitter to receiver from knowledge of received and transmitted bits impulse

response of channel is found out. This is called channel estimation. Later problem is

solved by repeating training sequence at sufficient short intervals so that equalizer is

adapted to channel state at regular intervals. This is called adaptive equalization.

Modeling of channel for equalization:

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ui = Lc

n=0 fnCi-n + nb --------------------------------------

Where, terms are ith sample of

fi= impulse response of channel

Ci= complex transmitted symbol

Lc= length of fc

Nb= Gaussian uncorrelated terms (equivalent noise)

Disadvantages

o Reduced spectral efficiency: There is no information in training sequence hence

efficiency reduces. e.g. GSM service uses 26 bits per 148 bit frame

o Sensitivity to noise: To improve spectral density training sequence should be

short and hence sensitive to noise since longer sequence will average out noise.

o Outdated estimates: If the channel changes after transmission the receiver could

not detect the variations.

Types of Equalizers

o Linear:These are simple filters structures that try to invert the channel in the

sense that the product of the transfer function of the channel and equalizer fulfills

a certain criterion. Following the equation for linear equalizers we can write the

linear filter by equation,

Ci= k

n=-k en ui-n

---------------------------------------------------

Where , en= coefficients for equalization

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un= received signal at equalizer output

Ci= estimate of transmit symbol Ci

Structure of basic linear equalizer (the taps are the coefficients e i in above equation &Ts is delay

by one sample)

Examples for linear equalizers:

o Zero forcing equalizer:

In frequency domain it can be interpreted as enforcing a completely

flat transfer function of the combination of channel and equalizer by

choosing the equalizer transfer function as E(z)= 1/F(z).

It is optimum for elimination of inter symbol interference. But here

noise added by channel is also amplified. Hence

o Noise becomes colored

o Noise power at detector input is larger than that without

equalizer.

o Non linear equalizers

Decision feedback equalizer.

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1. It consists of forward filter which is conventional linear equalizer with transfer function E(z),

and a feedback filter with transfer function D(z) .

2. As soon as receiver has decided on received symbol, its impact on all future samples (post

cursor ISI) can be computed, and via f/b subtracted from the received signal.

3. This equalizer results in a smaller error probability.

4. The disadvantage of this type of equalizer is error propagation. If receiver decides incorrectly

for one bit the computed post cursor ISI will be erroneous. for small BER this effect does not

play role.

Conclusion:

Propagation channel is the fundamental aspect of wireless communication. Behavior of channel

is that way not deterministic. Statistical methods provide good approximations to random

behavior of channel. Good approximation yields to efficient design of the transmitters and

receivers. Huge research in this field has given many models for channel properties which has

lead to better accuracy in communication systems. The channel properties when estimated there,

effect on the signal can be nullified at the receiver by use of equalizer. Adaptive equalization

technique is practically used in advanced communication systems like GSM and OFDM.

References:

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1. Wireless Communication, Andres F. Molisch, John Wiley India Ltd.

2. Fundamentals of Wireless Communication, David Tse and Pramod Vishwanathan

Cambridge University Press, Cambridge, England.

3. Web Resources :

a. www. google.com

b. www.wikipedia.com

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