lecture 13 symbol timing synchronization · 2016-11-09 · lecture 13 symbol timing...

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EE4900/EE6720 Digital Communications Suketu Naik

EE4900/EE6720: Digital Communications

Lecture 13

Symbol Timing

Synchronization

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Block Diagrams of Communication System

Digital Communication System

Informatio

n (sound,

video, text,

data, …)

Transducer &

A/D ConverterModulator

Source

Encoder

Channel

Encoder

Tx RF

System

Output

Signal

D/A Converter

and/or output

transducer

DemodulatorSource

Decoder

Channel

Decoder

Rx RF

System

Channel

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Symbol Timing Error can create,

1) Uncertainty: where is the

starting sample out

of the matched filter?

2) Scattered constellation points:

close to the decision boundaries

This can happen regardless of

Carrier Phase synchronization

and absence of noise

How to address the timing error?

Symbol Timing Synchronization: Estimating the receiver

clock that is aligned in both phase and frequency with the

transmitter clock

Problem: Where is the starting sample?

Scattered constellation points

due to symbol timing error

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Symbol Timing SynchronizationGoal: Estimate the receiver clock

The clock must be extracted from the noisy received signal

When Matched Filter (M.F.) is used, the clock signal can identify

the sampling instant when the output of the M.F. must be sampled

This optimum instant is at the center of the eye diagram

The center of the eye diagram=max. eye opening

Effect of Timing Error in QPSK Receiver

1) Optimum sampling instant is when

we have maximum eye opening

2) Any other sampling instant will

generate the symbol timing error1 2

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Continuous-time

M-ary PAM

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Basic Problem Formulation

Goal: Estimate the unknown time-delay

M-ary PAM signal: Eq. 8.1

Output of the M.F.: Eq. 8.2-8.3

Timing Error and Timing Error Signal: Eq. 8.5

Symbol Timing PLL generates the timing error and the clock

Binary PAM Demodulator with Symbol Timing PLL

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Continuous-time Symbol Timing PLL

Three components:1) Timing Error Detector (TED): finds the phase error (timing

error) between the output of the M.F. and VCC

2) Loop Filter F(s): filters the timing error and generates

control voltage for VCC

3) Voltage Controlled Clock (VCC): produces the receiver clock

which aligns with the symbols

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Continuous-time Symbol Timing PLL

Comparison with generic PLL1) TED => Phase Detector

2) Loop Filter => Loop Filter

3) VCC => VCO

Symbol Timing PLL Generic PLL

Key component in the Symbol Timing PLL is the TED because it

must extract the embedded clock from the M.F. output

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TED: How to generate the timing error

Eye Diagram

Optimum

sampling instant is

when we have

maximum eye

opening

Optimum sampling

instant is when slope of

the eye diagram = 0

Slope of the eye diagram

can be used to generate the

timing error

Note that the derivative of

the eye diagram shows:

1) zero to pos. or zero to neg.

transition

2) pos. to zero or neg. to zero

transition

This means symbol timing

PLL must have data sign

transitions (-1 to 1 or 1 to -1)

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TED: How to generate the timing error

Sampling Instant is early,

Increase VCC clock period

Sampling Instant is late,

Decrease VCC clock period

-1 to +1

transition

+1 to -1

transition

Goal:

Slope=Zero

Sampling Instant is early,

Increase VCC clock period

+1 to -1

transition

-1 to +1

transition

Sampling Instant is late,

Decrease VCC clock period

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Timing Error Signal for PAM

Timing error signal for the Decision-directed PLL: Eq. 8.7

Binary PAM symbol estimate: Eq. 8.8

Note that the error signal is zero (oval) when there are no data

transitions (repetitive symbols): this is addressed by randomizer at

Tx

Timing Error Signal

Data transitions are necessary

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Approximating the Derivative

Use the difference equation: Eq. 8.11

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Continuous-time

M-ary QAM

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Continuous-time MQAM Symbol Timing

M-ary QAM signals: Eq. 8.13-8.14

Timing Error Signal: Eq. 8.18-8.20

QPSK Symbol

Timing PLL

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Discrete-time

M-ary PAM

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Discrete-time MPAM Symbol Timing

Goal: given symbols at a symbol rate and corresponding

sampling rate, one of the N samples is aligned

Generic MPAM Symbol Timing Sync

Sampling Rate Symbol Rate

Interpolator Output:

One of the N samples is aligned

Matched Filter Output:

No alignment

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Discrete-time MPAM Symbol Timing

Discrete Symbol Timing PLL will move the samples at

the desired time instants: also known as interpolation

Interpolator must be adaptive to accommodate unknown

time delay τ

Sampling Rate Symbol Rate

Interpolator Output:

One of the N samples is alignedMatched Filter Output:

No alignment

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Discrete-time PLL for Symbol Timing

Four Components:

Interpolator & Timing Error Detector (TED)=>PD

Loop Filter F(z) => Loop Filter F(z)

Interpolation Control => DDS

From

Matched

Filter

To Decision

Block

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Timing Error Detector (TED)

Maximum Likelihood Timing Error Detector (MLTED)

Early-Late Timing Error Detector (ELTED)

Zero Crossing Timing Error Detector (ZCTED)

Gardner Timing Error Detector (GTED)

Mueller and Muller Timing Error Detector (MMTED)

From

Matched

Filter

To Decision

Block

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Goal: TED in general produces error signal once per

symbol

Eq. 8.24 where, Timing Error 𝝉𝒆 = 𝝉 − ො𝝉 TED will produce 𝝉𝒆 just as generic PLL produces

phase error

𝝉𝒆 a function of interpolated matched filter outputs

and the symbols (or their estimates)

ZCTED finds zero crossings in the eye diagram

ZCTED operates at 2 samples/symbol

ZCTED produces zero error at every other sample

aligned with zero crossing of the interpolated M.F. symbol

ZCTED produces other samples that are aligned with

the optimum sampling instant

ZCTED error signal (decision-directed PLL): Eq. 8.37

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Symbol

Estimate

Symbol

EstimateInterpolated M.F.

outputs at 2

samples/symbol)

Pos. Timing

Error: data

transition is

pos. to neg.

Neg. Timing

Error: data

transition is

neg. to pos.

Bin-PAM Symbol

Estimates: Eq. 8.38

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ZCTED Example

From

Interpolator

Signum

Function

(Zero

Crossing

Threshold)

Fig. 8.4.25

To

Loop

Filter

From Interpolation

Control

Symbol

Estimate a(k)Symbol

Estimate

a(k-1)

2 Samples/Symbol

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Four Components:




From

Matched

Filter

To Decision

Block

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Interpolation

Goal: Synchronize (or align) the symbol samples

to an optimum sampling instant

Q: How do we determine that?

A: By looking at the eye diagram (center aligned?)

Optimum

Sampling Instant

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Interpolation

Fractional

Interval

Basepoint

Index

Goal: Interpolate (or insert) the “optimally”

located sample in between two successive samplesTI = Interpolation Interval

T = Sampling Time

Desired sample or

Interpolant

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Interpolation

Interpolation is done by computing a weighted

sum of the available samples: Eq. 8.54

Interpolation can be viewed as sync pulse filter:

Eq. 8.55

Example: DAC

Samples

Sync pulses

Reconstructed

waveform

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Interpolation

Three major types: Linear, Quadratic and Cubic

Linear

Quadratic

Cubic

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Piecewise Linear Interpolation

Eq. 8.61, 8.62, 8.63

Interpolant (desired sample at TI=Ts) is a linear

combination of available samples

Filter coefficients depend on the fractional

interval, μ(k)

Basepoint index, m(k) tells you which samples to

use to find the interpolant

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Piecewise Parabolic Interpolation

FIR filter impulse response

Hardware efficient

implementation (Farrow): Eq. 8.78

Coefficients: Table 8.4.1

“Quadratic Sync”

Impulse Response of

Interpolation Filter

Farrow Structure for

efficient hardware

implementationμ(k) and m(k) come

from interpolation

control

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Four Components:




From

Matched

Filter

To Decision

Block

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Interpolation Control

Goal: provide the interpolator with a strobe signal that

indicates the kth basepoint index m(k) and kth interval μ(k)

Two methods:

Modulo-1 Counter Interpolation Control

Recursive Interpolation Control

Underflow

Strobe

Signal

m(k)

μ(k)

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Decrementing counter: decrements by 1/N so that underflow

occurs every N samples

Loop filter output v(n) adjusts the decrement number

m can be viewed as “alignment clock”, mu = alighment

period

Underflow

Strobe

Signal

m(k)

μ(k)

Interpolation

Control ≈ DDS

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Four Components:




From

Matched

Filter

To Decision

Block

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Proportional-Plus-Integrator Loop Filter

Loop Transfer Function Loop Constants

Eq. C.51Eq. C.61

From

TED

To

Interpolation

Control

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Discrete-time

M-ary QAM

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Discrete-time MQAM Symbol Timing

Goal: given I & Q components at a symbol rate and

corresponding sampling rate, find the optimum sampling

instant

Generic MQAM

Symbol Timing Sync

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Discrete-time MQAM Symbol Timing

All components are the same as MPAM except two

interpolators (one for I and one for Q) and two TEDs (one for I

and one for Q)

M.F. outputs: x(nT)= Eq. 8.23 x cos, y(nT)=Eq. 8.23 x sin

ZCTED error signal: Eq. 8.100 with I estimates ෝ𝒂𝟎(k-1), ෝ𝒂𝟎(k)

and Q estimates ෝ𝒂𝟏(k-1), ෝ𝒂𝟏(k)

lecture 13 symbol timing synchronization · 2016-11-09 · lecture 13 symbol timing...

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