CSM Equalization, Diversity and Channel Coding PART1

8/7/2019 CSM Equalization, Diversity and Channel Coding PART1

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Equalization, Diversity and Channel Coding

1. Introduction

2. Equalization Concept

3. Equalization Simulation

4. Diversity Concept

5. Diversity Techniques

6. Combining Techniques

7. Channel Coding Concept

8. Block Codes

9. Convolutional Codes

10. Coding Gain

Introduction (1)

- Multipath propagation causes fading

- Fading causes poor signal quality or bit errors on systems using digital

modulation

- Wireless systems need to use one or more techniques to reduce the effects of

multipath.

- Three most effective techniques are equalization diversity and channel

coding


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Introduction (2)

- Compensate for intersymbol Interference (ISI) create by multipath within

time dispersive channels

Equalization

- Compensate for fading channel impairments

Diversity

- Used by the receiver to detect or correct some (or all) of the errors introduced

by the channel in a particular sequence of message bits

Channel coding

Techniques are used to improve radio link performance

Equalization Concept (1)

- Structure of the inverse filter can become very complicated to implement

- Multipath channel structure is not always known

- Channel changes in real time so equalization must be adaptive

Equalization Characteristic


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- Algorithm to evaluate the channel and estimate filter coefficients

- Pseudorandom or fixed binary signal which is prescriptive bit pattern

Training

Tracking

Operating mode

Block diagram of a simplified communications system using an adaptive

equalizer at the receiver



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Equalizer condition

( ) ( ) ( ) ( )tntftxty b+=

( ) ( ) ( ) ( ) ( ) ( )thtnthtftxtd eqbeq +=

( ) ( ) ( )tthtf eq =

( ) ( ) 1= fHfF eq


Linear equalizer (transversal filter) with feedforward tap,

and is called a finite impulse response (FIR) filter



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Linear equalizer (transversal filter) with both feedforward and feedback taps,

and is called an infinite impulse response (IIR) filter


Equalization Simulation (1)

s.Ts = 001

s. = 121

Symbol period

RMS delay spread

Frequency selective fading

Time domain


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Frequency selective fading

Frequency domain


Intersymbol interference (ISI)

Receive Signal


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Frequency selective fading Flat fading



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- Send same bits over independent fading paths

- Combine paths to mitigate fading effects

- Provide two or more inputs to the receiving site for that fading on

among those inputs are uncorreleated

- If one radio path undergoes a deep fade, another independent path

may have a strong signal

Diversity Concept (1)

Basic idea

- Two kind of fading, long term (large scale) and short term (small

scale) fading

- Long term fading can be mitigated by macroscopic diversity (apply

on separated antenna sites) like the diversity using two base stations

- Short term fading can be mitigated by microscopic diversity (apply on

locally located antenna site) like the diversity using multiple

antennas on the base station or mobile unit


Basic idea (Cont.)


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Graph for probability distributions

of SNR for M branch selection

diversity


None Diversity

Single Input Single Output (SISO)

Receiving Diversity

Single Input Multi Output (SIMO)


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Transmit Diversity

Multi Input Single Output (MISO)

Transmit/Receiving Diversity

Multi Input Multi Output (MIMO)

- Signal level and phase due to multipath fading is a function of

position, frequency and time (if the paths are time-varying)

- Diversity reception makes use of multiple independent fading sources

to mitigate the effects of fading

- For example, if the signal at one location is faded, at another position

a fraction of a wave-length away it may be unfaded

- There are many ways of getting independent fading sources (diversity

techniques)


Independent fading sources


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Diversity Techniques

Space diversity

- Multiple antenna elements separated by decorrelation distance

Angle or direction diversity

- One or multiple directional antenna(s), each responds to a narrow

direction of arrival (DOA) spread

Polarization diversity

- Two transmit or receive antennas with different polarizations

Diversity Techniques (1)

Diversity Techniques (Cont.)

Frequency diversity

- Multiple narrowband channels separated by channel coherence bandwidth

Time diversity

- Multiple timeslots separated by channel coherence time

Path diversity

- Multiple antennas received multipath signal and separated by using RAKE

receiver



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- Radio wave polarization given by direction of electric field vector

- Polarization of the signal can change when it reflects

- Can use antennas sensitive to different polarizations

- Can make use of orthogonal polarization (horizontal and vertical polarization

or clockwise and anticlockwise polarizations

- Advantage is that dont need any spatial separation between antennas


Polarization Diversity

- Same information is transmitted on frequencies separated by more than

coherence bandwidth

- Problem is that each diversity path (frequency) increases the bandwidth

required

- Not commonly used


Frequency Diversity


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- Same information is transmitted on times with interval separated by the

coherence time of the channel

- Problem is that each diversity path (time) increases the bandwidth

required

- Not commonly used

- Interleaving

- Automatic repeat request (ARQ)


Time Diversity


Interleaving

- Interleaving is a form of time

diversity

- Interleaving scrambles input

bit stream

- Spreads burst errors over

many code words

- Code words correct a small

number errors


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Automatic repeat request (ARQ)

- When the receiver detects errors in a packet, it will automatically request

the retransmission of missing packets or packets with errors

Common schemes

- Stop & wait

- Go back N

- Selective repeat


Stop & wait

- Transmits one packet at a time and wait for acknowledge (ACK)

- Transmits next packet after received ACKs packet

- Retransmits packet after a timeout


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- Fading cause multipath of signal

- Used in wideband channel such as spread spectrum and CDMA system

- RAKE receiver is used for separate the path of signal


Path Diversity

Rake diversity receiver



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Combining Techniques (1)

Combining Techniques

Selection combining (SC)

- Fading path with highest gain used (selecting the strongest signal among

the M diversity branches)

Switched (scanning) combining

- Receiver switches to another branch when ever it experience fading in the

current branch


Combining Techniques (Cont.)

Equal gain combining (EGC)

- All paths co-phased and summed with equal weighting

Maximal Ratio Combining

- All paths co-phased and summed with optimal weighting to maximize

combiner output SNR


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Equal Gain Combining (EGC)

- It is a co-phase combining that brings all phases to a common point and combines

- Combined signal is the sum of the instantaneous envelops of the individual

branches

- It is simple but not optimum, mostly used


Maximum Ratio Combining (MRC)

- Optimal technique (maximizes output SNR)

- Phase-shift the signals from the branches so the received signals have the same

phase and weight them according to their SNR

- Circuitry to provide maximal-ratio combining is complicated, so it is not often used


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Errors

- Errors occur due to noise or interference on a communication channel

- Error detection and correction codes are used for bit errors

- Retransmission (ARQ) is used for packets

Channel coding

- Channel codes that are used to detect errors are called error detection codes

- Channel codes that can detect and correct errors are called error correction

codes

Channel Coding Concept (1)

Basic idea

- Encoder at the transmitter adds redundancy to transmitted data

- Decoder at the receiver uses this redundancy to detect and/or correct for

possible errors in the received data

- Two main types: block codes and convolutional codes

Channel Coding Concept (2)


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- Block codes are forward error correction (FEC) codes that enable a limited

number of errors to be detected and corrected without retransmission

- Data is broken up into blocks of equal length

- Each block is mapped onto a larger block

- Block code is referred to as an (n,k) code where

n : Block length

k : Number of data bits

n-k : Number of checked bits

R = k/n : Code rate

Block Codes (1)

Example

- (6,3) code - Block length (n) = 6

- Number of data bit (k) = 3 - Code rate (R) = 1/2

Block Codes (2)


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Distance of a code

- Distance of a code word is the number of elements in which two

codewords and

Block Codes (3)

Block Code Parameters

iC jC

( ) =

=N

l

l,jl,iji CCC,Cd

1

- Minimum distance is the smallest distance for the given set and is

given as

jimin C,CdMind =

Weigh of a code

- Weight of a codeword is given by the number of nonzero element

in the code word

Block Codes (4)

Block Code Parameters (Cont.)

( ) =

=N

l

l,ii CCw

1


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Example - (4,2) code

Block Codes (5)

Block Code Parameters (Cont.)

111111

101010

010101

000000

4

3

2

1

=

=

=

=

C

C

C

C

( )

( )( )

( )

( )

( ) 2

2

4

4

2

2

43

42

32

41

31

21

=

=

=

=

=

=

C,Cd

C,Cd

C,Cd

C,Cd

C,Cd

C,Cd

2=mind

( )

( )

( )

( ) 4

2

2

0

4

3

2

1

=

=

=

=

Cw

Cw

Cw

Cw


Block Codes (6)

Properties of Block Codes

Linearity

- Let and be any two elements selected from the alphabet

- Code will be linear only if is also a code word

1 2

2211 CC +

111111

101010

010101

000000

4

3

2

1

=

=

=

=

C

C

C

C


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Block Codes (7)

Properties of Block Codes (Cont.)

Systematic

- For an (n,k) code, the first k bits are identical to the information bits, and

the remaining n-k bits of each code word are linear combinations of the

k information bits

111111

101010

010101

000000

4

3

2

1

=

=

==

C

C

C

C


Block Codes (8)

Properties of Block Codes (Cont.)

Cyclic

- If is a code word of a cyclic code, then

obtained by a cyclic shift of the elements of

is also a code word

111111

101010

010101

000000

4

3

2

1

=

=

=

=

C

C

C

C

[ ]021 c,,c,cC nn K=

[ ]102 = nn c,c,,cC K C


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- Output is provided by looking at a sliding window of input

Convolutional Codes

- Coding gain describes how much better the decoded message performs

as compared to the raw bit error performance of the coded transmission

Coding Gain (1)

( )+=

n

ti

inc

icB PPini

nP

1

11

: Decoded message error probability

: Channel BER probability

: Number of errors that can be corrected in an (n,k) block code

: Block length

BP

CP

t

n


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Example of coding gain

Given : Channel BER probability ( ) = 1%

Number of errors that can be corrected in an (4,2) block code ( ) = 1

Find : Decoded message error probability

Coding Gain (2)

CP

t

( )

( )

( ) ( ) ( )[ ]

%..

......

......

..ii

PPi

ni

nP

i

ii

n

ti

inc

icB

0297010972

9900101499001043990010624

1

9900104

44990010

3

43990010

2

42

4

1

01010104

4

1

11

4

041322

444343242

4

2

4

1

=

++

+

+

=

+=

Solution of coding gain

Coding Gain (3)

CSM Equalization, Diversity and Channel Coding PART1

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