Digital Communication System

Chapter 5 : Synchronization

• Lecture 1: Introduction & Receiver Synchronisation

– Introduction

• Definition

• Cost-Benefit Issues

• Approach & Assumptions

– Receiver Synch

• Frequency & Phase Synch

• Lecture 2: Receiver Synch (cont’d)

– Costas Loops

– High-Order Suppressed Carrier Loops

– Acquisition

– Phase Tracking Errors & Performance

– Spectrum Analysis Techniques

– Symbol Synch – Discrete Case

• Lecture 3: Receiver Synch (cont’d)

– Synch with CPM

– Data-Aided Synch

– Non-Data-Aided Synch

– Frame Synch

• Lecture 4: Network Synch

– Open-Loop Transmitter

Synch

– Closed-Loop Transmitter

Synch

– Conclusion

Synchronization Defined

• Phase synchronization.

• Symbol Synchronization.

• Frame Synchronization.

• Frequency Synchronization.

• Network Synchronization.

Tradeoff • There are added cost to receiver design due to

the implementation of acquisition and tracking

circuits.

• Time required for synchronization to be

achieved.

• Energy expended, for instance on pilot signals,

for the purpose of synchronization.

• Complexity due to error control.

– Frame, block, message synchronization.

• Complexity due to spread spectrum technique.

– PN sequence synchronization.

Receiver Synchronization.

• All digital communication receivers require

some degree of synchronization to the

incoming signal.

Frequency and Phase

Synchronization.

• A Phase-Locked-Loop (PLL) is at the heart

of nearly all synchronization circuits.

Frequency and Phase

Synchronization.

• PLL are servo-control loops, whose

controlled parameter is the phase of a

locally generated replica of the incoming

carrier signal.

• Components of a PLL:

– A phase detector

– A loop filter

– A voltage-controlled oscillator (VCO).

Frequency and Phase

Synchronization.

• A phase detector determines the difference in phase

between the incoming signal and the reference signal.

• The loop filter controls the response of the PLL to the

error signal.

• The VCO is an oscillator whose output frequency is a

linear function of its voltage over some range of input

and output. – +ve signal increase frequency beyond the uncontrolled value.

– -ve signal reduce frequency below the uncontrolled value.

Frequency and Phase

Synchronization.

• For a normalized

input signal of the

form:

• Consider a

normalized VCO

output of the form:

)](cos[)( 0 ttwtr

)](ˆsin[2)( 0 ttwtx

Frequency and Phase

Synchronization.

• Output error signal at

the phase detector

output:

• If the filter output is

low-pass, we will

have

)](ˆ)(2sin[)](ˆ)(sin[

)](cos[)](ˆsin[2)()()(

0

00

tttwtt

ttwttwtrtxte

)](ˆ)(sin[)( ttty

Frequency and Phase

Synchronization.

• The low pass filter produces an output that is

solely the function of difference in phase between

the two signals.

• The VCO output will be a linear function of y(t).

• Deviation in frequency is given as

)(*)](ˆ)([)(*)(

)()](ˆ[

)(

tfttKtfteK

tyKdt

tdt

oo

o

Gain of the VCO Loop filter impulse response

Frequency and Phase

Synchronization.

• The Fourier transform of the difference equation

leads to

Reorganizing, we have

)(*)](ˆ)([)(*)(

)()](ˆ[

)(

tfttKtfteK

tyKdt

tdt

oo

o

)()](ˆ)([)( wFKj o

)()(

)(

)(

)(ˆ

H

wFKj

wFK

o

o

Closed-loop transfer function

Frequency and Phase

Synchronization.

• The order of the PLL is the order of the

highest term in jwin the denominator of

H(w).

Steady state tracking Characteristic

of the PLL.

• The expression for the Fourier transform of the

phase error can be given as:

• The steady-state error is the residual error after all

transients have died away.

)(

)()())(1()(ˆ)()}({)(

wFKj

jHteFE

o

)(

)()()}({)(

2

0limlim wFKj

jteFjte

ojt

Performance in noise

• The input might be noisy, as is the case in many

communication systems.

• n(t) can be expanded into quadrature

components.

)(]cos[)( 0 tntwtr

twtntwtntn sc 00 sin)(cos)()(

Performance in noise

• The output of the phase detector can be written as

• The loop filter eliminates the high-frequency components. We are then left with

• Let us denote the variance of n/(t) by σn.

• It can be shown that the variance of the output phase is:

• For the special case of white noise

• This is related to the

frequency)carrier theat twice terms(]ˆcos[)(]ˆsin[)(]ˆsin[)()()( tntntrtxte cs

]ˆcos[)(]ˆsin[)(]ˆsin[)( tntntn cs

dHG 22

ˆ |)(|)(2

1

dHNo 22

ˆ |)(|2

LoBN22

ˆ

Acqusition.

• Acquisition is the process of getting the

PLL to lock with the incoming signal.

– Aided acquisition

• With the aid of external circuits.

– Self-acqusition

• Without the aid of extrnal signals

Symbol synchronization.

• Symbol synchronization is needed in order to achieve

optimum demodulation.

– Non-Data Aided (NDA).

– Data Aided (DA).

Open-loop symbol synchronization.

Closed-loop symbol

synchronization.

Closed-loop symbol

synchronization.

Frame Synchronization