Communication System Overview Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech....

Communication System Overview

Gwo-Ruey Lee

Wireless Access Tech. Lab.

CCU Wireless Access Tech. Lab.

Outlines

Communication SystemDigital Communication SystemModulation



Communication System

Input Transducer Transmitter Channel Receiver Output Transducer

Input Transducer ChannelTransmitter Receiver Output Transducer

InputMessage

MessageSignal

TransmittedSignal

ReceivedSignal

OutputSignal

OutputMessage

Carrier

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Input transducer Messages can be categorized as analog (continuous

form)or digital (discrete form). The message produced by a source must be

converted by a transducer to a form suitable for the particular type of communication system employed.

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Transmitter The purpose of the transmitter is to couple the

message to the channel. Modulation

For ease of radiation to reduce noise and interference For channel assignment For multiplexing or transmission of several message over

a single channel To overcome equipment limitation

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Channel Different forms The signal undergoes degradation from transmitter to

receiver Noise, fading, interference……

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Receiver The receiver is to extract the desired message from

the received signal at the channel output and to convert it to a form suitable for the output transducer

Demodulation

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Output Transducer The output transducer completes the communication

system The device converts the electric signal at its input into

the form desired for the system user

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Digital Communication System

InformationSource

&Input Transducer

Source Encodre Channel Encoder

OutpotTransducer

Source Decoder Channel Decoder

DigitalModulator

DigitalDemodulator

ChannelSynchroniz

ation

Output Signal

Transmitted Signal

Received Signal

1/6




Source Encoder/ Decoder The purpose of source coding is to reduce the number

of bits required to convey the information provided by the information source.

The task of source coding is to represent the source information with the minimum of symbols.

High compression rates (Good compression rates) make be achieved with source encoding with lossless or little loss of information.

Source Coding Fixed-length coding

Pulse-code modulation (PCM) Differential Pulse-code modulation (DPCM)

Variable-length coding Huffman Coding/ entropy coding

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Channel Encoder/ Decoder A way of encoding data in a communications channel that

adds patterns of redundancy into the transmission path in order to lower the error rate.

The task of channel coding is to represent the source information in a manner that minimizes the error probability in decoding.

Error Control Coding Error detection coding Error correct coding

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Error Control Coding Linear block code Convolutional code RS code

Modulation Coding Trellis code Turbo code

4/6




Synchronization Symbol/ Timing synchronization

Frequency synchronization Carrier frequency synchronization Sampling frequency synchronization

Two basic types of synchronization Data-aid algorithm

Training sequences Preambles

Non-data-aid algorithm Blind

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Channel Estimation A channel estimate is only a mathematical estimation

of what is truly happening in nature. Allows the receiver to approximate the effect of the

channel on the signal. The channel estimate is essential for removing inter

symbol interference, noise rejection techniques etc.

Two basic types of channel estimation methods Data-aid algorithm

Training sequences pilots

Non-data-aid algorithm Blind

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Modulation

Analog Modulation AM FM PM

Pulse Modulation PAM / PPM / PCM / PWM

Digital Modulation ASK FSK PSK QAM

Amplitude Frequency Phase

cos 2 cfc t tA Carrier:

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Modulation

Mapping The process of mapping the information bits onto the

signal constellation plays a fundamental role in determining the properties of the modulation

Modulation type Phase shift keying (PSK) Quadrature Amplitude Modulation (QAM)

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Modulation

M-ary Phase Shift Keying Consider M-ary phase-shift keying (M-PSK) for which the si

gnal set is

where is the signal energy per symbol, is the symbol duration, and is the carrier frequency.

This phase of the carrier takes on one of the M possible values, namely, , where .

2 12cos 2 0 , 1,2,...,s

i c ss

iEs t f t t T i M

T M

sE sTcf

2 1i i M 1,2,...,i M

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Modulation

An example of signal-space diagram for 8-PSK

sE

2m

3m

4m

5m

6m

7m

8m

Decisionboundary

2

messagepoint

sE

sE

d

d

MM 1m

Decisionregion

1sE

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Modulation

Phase shift keying BPSK

QPSK with Gray code

M-ary PSK

where

0

sinse

Ep erfc

N M

,

1

2e BPSKp erfc

,

1

2e QPSKp erfc

22exp( )

xerfc x z dz

: SNR

5/10



Modulation

BER versus SNR curves in AWGN channel using BPSK, QPSK, 8-PSK,16-PSK .

0 5 10 15 20 25 3010

-6

10-5

10-4

10-3

10-2

10-1

100

SNR Vs BER

SNR

BE

R

BPSK theoretical result BPSK simulation QPSK theoretical result QPSK simulation 8PSK approximate result 8PSK simulation 16PSK approximate result 16PSK simulation

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Quadrature Amplitude Modulation The transmitted M-ary QAM signal for symbol n can be expr

essed as

where E is the energy of the signal with the lowest amplitude, and , and are amplitudes taking on the values

Note that M is assumed to be a power of 4. The parameter a can be related to the average signal energ

y ( ) by

2 2cos 2 sin 2 , 0 , 0, 1, 2,....n n c n c

E Es t a f t b f t t T n

T T

2, , 3 , , log 1n na b a a M a

na nb2E a

3

2 1sE

aM

sE

Modulation 7/10



An example of signal-space diagram for 16-square QAM.

Modulation 8/10



QAM

2

,2

1 11 4 | 4 2 | 2 |

loge M QAMp p c M p c M p cM M

3

2 1sE

aM

2

2

0

2| 1

ap c Q

N

2 2

0 0

2 2| 1 2 1

a ap c Q Q

N N

2

2

0

2| 1 2

ap c Q

N

Modulation 9/10

3aa- a- 3a

a

3a

- a

- 3a

na

nb

: I part

: II part

: III part



BER versus SNR curves in AWGN channel using BPSK/QPSK, 16QAM, 64QAM, 256QAM.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

10-5

10-4

10-3

10-2

10-1

100

Eb/N0 Vs BER

Eb/N0

BE

R

BPSK/QPSK theorem BPSK/QPSK simulation16QAM theorem 16 QAM simulation 64 QAM simulation 64 QAM theorem 256 QAM simulation 256 QAM theorem

Modulation 10/10



Communication System Overview

Readings Any book about communications

Random Process/ Stochastic Process



Outlines

Basic ConceptsStationary ProcessTransmission over Linear Time-Invariant (LTI)

Systems

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Basic Concepts

Why study random processes? Due to the uncertainty of 1. noise and 2. the

unpredictable nature of information itself.

Information signal usually is randomlike We can not predict the exact value of the signal Signal must be distributed by its statistical properties.

Ex: mean, variance…..

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Basic Concepts

Random Variable (r.v.) Consider an experiment with sample space . The element

of are the random outcomes, , of the experiment. If to every , we assign a real value , such a rule is called a random variable (r.v.)

SS

X x

S

Real line

X x

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Basic Concepts

Random Process (r.p.) A random process is the mapping of the outcomes in

into a set of real valued functions of time, called sample function . , iX t

1S

2

n

1

,X t

t

2,X t

t

,n

X t

t

S

0t t

0 1,X t

0 2,X t

0 , nX t r.v.

1. : ensemble 2. : sample function (or a realization)

3. : r.v.

4. : numerical value

,i

X t

2

,X t

20 ,X t

0 ,i

X t

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Basic Concepts

Classification of random process From the perspective of time

Random process: for , t has a continuous of values

Random sequence: for , t can take on a finite or countably infinite numb

er of values

From the perspective of the value of Continuous:

can take on a continuous of values Discrete :

Values of are countable

X t

X t

X t

X n

X t

X t

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Basic Concepts

Classification of random process

Continuous random process Discrete random process Continuous random sequence Discrete random sequence

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Basic Concepts

1st-order distributions function It describes the instantaneous amplitude distribution of a r

andom process Mean:

2nd-order distributions function It distributes the structure of the signal in the time domain Autocorrelation Function (A.F.)

1

,

,

x X

n

i ii

m t E X t x f x t dx

X t p

1 2 1 2

1 2 1 2 1 2 1 2

1 21

,

, , ,

, ,

XX

X

n

i i ii

R t t E X t X t

x x f x x t t dx dx

X t X t p

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Basic Concepts

Autocovariance

Cross-correlation

If and are orthogonal

If and are statistically uncorrelated

1 2 1 1 2 2

1 2 1 2

,

,

XX X X

XX X X

C t t E X t m t X t m t

R t t m t m t

1 2 1 2 1 2

1 21

, , , ,

, , ,

XY XY

n

i i XY i ii

R t t E X t Y t x y f x y t t dxdy

X t Y t p

0XYR X t Y t

XY X YR m m X t Y t

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Basic Concepts

Crosscovariance

The autocorrelation function of a real WSS process is

1 2 1 1 2 2

1 2 1 2

,

,

XY X Y

XY X Y

C t t E X t m t Y t m t

R t t m t m t

X t

,XX XXR t t E X t X t R

9/10



Basic Concepts

The cross-correlation function of two real WSS process and is

If and are orthogonal If and are statistically uncorrelated

Power Spectral Density (PSD) PSD represents the distribution of signal strength (ie, energy

or power) with frequency The PSD of WSS process is the Fourier transform (FT) of t

he A.F.

X t Y t

,XY XYR t t E X t Y t R 0XYR X t Y t

constant

XY X YR m m

X t Y t

2

1 2

j fXX XX XX

j fXX XX XX

S f R R e d

R S f S f e df

X t

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Stationary Process

Stationary A random process whose statistical properties do not

change over time

Stationary Process Strictly-Sense Stationary (SSS) Wide-Sense Stationary (WSS) Strictly-Sense Cyclostationary Wide-Sense Cyclostationary

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Stationary Process

Strictly-Sense Stationary (SSS) A nth-order strictly-sense stationary process is a process in

which for all , all , and all

Note: Mth-order stationary of the above equation holds for all .

Example: 2nd-order SSS process 1st-order SSS process

1 2

1 2

1 2, ,...,

1 2, ,...,

, ,...,

, ,...,

n

n

nX t X t X t

nX t k X t k X t k

f x x x

f x x x

k 1 2, ,..., nt t tn

n M

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Stationary Process

A example of 2nd-order stationary

2t t1t t

1S

2

n

1

,X t

t

2,X t

t

,n

X t

t

2t t k 1t t k

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Stationary Process

Wide-Sense Stationary (WSS) A random process is wide-sense stationary process (W

SS) if

Its mean is constant

Its A.F. depends only on the time difference.

constantxm t E X t

X t

1 2 2 1,xx xx xxR t t R t t R

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Stationary Process

The relationship between SSS and WSS SSS WSS (True) SSS WSS (Fault)

1st-order SSS 2nd-order SSS

For Gaussian process : SSS WSS Since the joint-Gaussian pdf is completely specified by its me

an and A.F.

constantE X t

1 2 2 1,xx xx xxR t t R t t R

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Stationary Process

Strictly-Sense Cyclostationary A nth-order strictly-sense cyclostationary process is a

process in which for all , all , and integer m

( mT is integer multiples of period T )

1 2, ,..., nt t tn

1 2

1 2

1 2, ,...,

1 2, ,...,

, ,...,

, ,...,

n

n

nX t X t X t

nX t mT X t mT X t mT

f x x x

f x x x

6/9



Stationary Process

Wide-Sense Cyclostationary A random process with and is wide-sense cycl

ostationary if

Its mean satisfies

Its a.F. satisfies

X t

x xm t mT m t

1 2 1 2, ,XX XX XXR t mT t mT R t t R

7/9



Stationary Process

Ergodic Process A random process is strictly ergodic process if all time

and ensemble (statistical) average are interchangeable including mean, A.F. PSD, etc.

A random process is wise-sense ergodic if it it ergodic in the mean and the A.F. mean ergodic

A.F. ergodic

lim X XTTm m

lim XX XXTTR R

2

2

1 T

TX TT

X

X t m X t dtT

m E X t

2

2

1

XXT T

T

T

XX

X t X t R

X t X t dtT

R E X X t X t

8/9



Stationary Process

The relationship between ergodic and stationary Ergodic stationary (True) Ergodic stationary (Fault)

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Transmission over LTI Systems

Linear Time-Invariant (LTI) Systems

LTI System

h t x t y t

*

*

y t x h t x t h t

h x t h t x t

Y f X f H f

1/3




Assumptions: and are real-valued and is WSS. The mean of the output

The cross-correlation function

x t h t x t

0x xE y t m h d m H

y t

YX XX

XY XX

R E Y t X t h R

R E X t Y t h R

2/3




The A.F. of the output

The PSD of the output

YY

YX

XY

XX

XX

R E Y t Y t

R h

R h

h R h

R h h

2

YY XXS f S f H f

3/3



Random Process/ Stochastic Process

Readings Communication Systems, 4th edition, Simon Haykin, Wiley

Chapter 1 – 1.1 ~1.7, 1.8

Communication System Overview Gwo-Ruey Lee. Wireless Access Tech. Lab. CCU Wireless Access Tech....

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