Frequency Source Requirements for Digital Communications Systems

8/7/2019 Frequency Source Requirements for Digital Communications Systems

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freq reqs for comm.ppt, V. S. Reinhardt. Page 1Copyright 2005 Victor S. Reinhardt--Rights to copy material is granted so long as a source

reference is listed on each page, section, or graphic utilized.

The Calculation of Frequency SourceRequirements for Digital

Communications Systems

Victor S. Reinhardt

08/25/04

IEEE International Ultrasonics, Ferroelectrics, andFrequency Control 50th Anniversary JointConference, Montreal, August 24-28, 2004


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The Calculation of Frequency SourceRequirements for Digital Comm Systems

Introduction

Frequency sources (oscillators, synthesizers, etc.) are animportant part of digital communications systems

Paper will discuss the derivation of frequency sourcerequirements from over-all digital comm system parameters

Will be tutorial treatment for those not familiar with digital commtheory but familiar with time & frequency theory

Frequency source properties directly impact the performance ofdigital comm systems

Impact link acquisition & loss of acquisitionT&F community familiarwith synchronization issuesWill not be covered here

Impact bit error rate (BER) performance--Paper will address this

Will utilize quadrature phase shift keyed (QPSK) systems forconcrete examples

But theory applicable to other systems


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Basic Digital Comm ConceptsSignals Carrying Digital Information

At the transmitter a carrieris modulated in a regular time sequenceofsymbols to produce a digital communications signal or waveform

A symbol is a temporal waveform in some modulation spacerepresenting a single digital word of information

At the receiver the signal is sampled at discrete decision epochs todetermine a modulation value of the carrier

The modulation value is converted into a digital or data word bycomparing it to decision thresholds

The symbols occur at a symbol rate Rs=1/Tc (Tc= clock period)

The bit or data rate R = WRs (W = bits persymbol orword)

Example: Unshaped (Rectangular)Symbols in PAM

Decision Epochs

Time

Value

Decisi on

Threshold

s

Symbol3

Symbol2

Symbol1

(1,0)

(1,1)

(0,1)

(0,0)(2-Bit)Digital

Words

Tc t3t2

t1

Carrie

rAxis

Signal


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Shaped Symbols

Unshaped (rectangular) symbols are notbandwidth efficient Sinc functions in freq domain

Shaped symbols are sinc-like functionsin time domain Produce more bandwidth efficient

trapeziodal functions in freq domain

Do not interfere with each other at decisionepochs

The price one pays for shaping is morestringent timing

-3 -2 -1 0 1 2 3

Un-shaped

Shaped

tn/Tc

Symbols in Time Domain

Shaped Transmission

0 1 2 3 4 5 6

-1

1

0

Composite Signal

tn/Tc

-3 -2 -1 0 1 2 3

Un-shaped

Shaped

f/Rs

Symbols in Freq Domain


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Inter-Symbol Interference (ISI) & EyePatterns

Eye Pattern = Graph of the modulationvalue vs time at the receiver plotted

modulo 1-symbol period (as in a scopetrace)

Eye opening = region with no valuetrajectories in it

Inter-symbol Interference (ISI) =Contamination at decision epoch of

modulation value by adjacent symbols Ideal Decision epochno ISI Clock errors cause the decision epoch to

wander off the best decision epochincreasing the ISI

Sensitivity of ISI to clock timing = Slope ofeye opening at decision epoch

Even unshaped (square) symbolsgenerate such eye patterns because ofreceiver and channel filtering necessaryto limit signal BW & noise

Shaped symbols have narrower eyewidths than unshaped ones

From: Telecom Glossary 2000, AmericanNational Standard forTelecommunications, T1.523-2001,www.atis.org/tg2k/images/epdplot1.gif

Modulo Symbol Time0- +

Eye Pattern

Inter-SymbolInterference

Ideal Decision Epoch

Eye Opening

(No Trajectories)

ShapingNarrows

Eye Width


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Types of Digital Modulation

Type of carrier: RF carrier or subcarrier,baseband voltage, etc.

Parameter modulated: amplitude, phase,frequency, etc.

Modulation Order (or number of digitalstates 2W): binary, quadrature, M-ary

Shaped or unshaped

Coherent, incoherent, differential phase

Synchronous & asynchronous dataclock timing (used in hardline systems)

Binary, M-aryFSK

Freq

(0) (1)

FrequencyShift Keyed

Time

PulsePosition

or WidthModulation

PWM

Time

PulseAmplitude

Shift Keyedor Modulation

Amplitude

PAM

Hybrid ModulationM-ary Quadrature AmplitudeShift Keyed or Modulation

Coherent Phase-FrequencyShift Keyed

Minimum Shift Keyed (BinaryCPFSK)

16-QAMor 16-QASK(4-Bit word)

. .

. .

. .

. .

. .

. .

. .

. .

I

Q

Phase Shift KeyedBPSK, QPSK, 8PSK, .., DPSK

(0,0)(0,1)

(1,0) (1,1)

Complex RF Envelope

I

Q


7/21freq reqs for comm.ppt, V. S. Reinhardt. Page 7Copyright 2005 Victor S. Reinhardt--Rights to copy material is granted so long as a source


Bit Error Rate (BER) vs Eb/NoKey Comm System Parameter

Rx thermal noise must limited by a filter

For an ideal system the Rx filters bandwidth isequal to the symbol rate Rs = R/W

The ideal SNR = Prx/(NoRs) = Pb/(NoR) = Eb/No

No = Thermal noise density

Pb = Prx/W = Power per bit

Eb = Pb/R = Prx/Rs = Energy per bit

BER vs Eb/No the canonical comm link

characterization

BER degradation is the extra Eb/No over idealsystem to achieve same BER as ideal

Error correction coding (ECC) allows up to Nbit errors to be corrected in a group or block of

bits--Improves BER above a certain Eb/No

The bit error rate (BER) is the probability that a received bit isincorrect

The BER is a function of the SNR at the digitalreceiver

Uncoded BER

10-3

10-4

10-5

10-6

10-7

- Ideal- Actual

Eb/No - dB

10-3

10-410-5

10-6

10-7

- Ideal- Actual

Error CorrectionCoded BER

BERDegrad-ation

BERDegrad-ation

Eb/No - dB




BER Degradation and ISI

Causes of ISI Symbol distortion

RF carrier phase errors & jitter

Data clock errors & jitter

Simple BER degradation Models Worst case model:

BER deg = -20Log10 (1- V/V) Noise Model: Use theoretical

curve with Eb/NoPrx/(NoRs + V2)

Decisionthresholds

Thermal noise in BW Rs ( = NoRs)causes occasional bit errors BER (uncoded) = *Erfc(2-0.5 V/ )

= *Erfc((Eb/No))

ISI generates non-thermal jitter Vn When V + Vn is closer to decision

threshold higher BER with thermal noise

Net effect to increase BER for given Eb/No

Actual QPSK system

(no thermal noise)

Sampled valuesV(1 j)/20.5 atdecision epoch

No ISI (jitter)without thermalnoise

Jitter Vn

Ideal QPSK System




LO Phase Jitter Requirements in RFCarrier Digital Comm Systems

At the transmitter (Tx) an LO and a clock are required

At the Receiver (Rx)

a clock recovery loop is always required to track the Rx clock to the Txclock

a carrier rec loop at the Rx LO required for phase coherent symbols

Recovery loops track out relative Rx-Tx LO and clock jitter forfourier frequencies < recovery loop bandwidths

This is very important in defining the appropriate jitter statistics interms of power spectral densities (PSD)

SymbolModulator

DataEncode

User

Data

ErrorCorrection

Encryption

Framing

~~

SymbolDemod-ulator

Data(Sampling)

Clock~ ~

LO

RF

Xmission

DataDecode

Recover Loops

User

Data

Data(Sampling)

ClockLO

Transmitter (Tx) Receiver (Rx)

Rx LOrecovery

loop only for

phasecoherentsymbols

Typical RF Carrier Comm System




Carrier Phase Jitter and ISI

Phase jitter produces ISI in quadrature systems through I-Q cross-

talk Phase jitter much less of an issue in BPSK because there is no Q

channel (Just produces loss of power)

The definition of the appropriate of phase variance 2 isdetermined by the phase coherence properties of the system

PhaseJitter

Q-Symboljitter produces

cross-talkin I-Channel, etc.

Rx Q-Axis

Rx I-Axis

RMS ISI V*Sin( )

V




RF Carrier Phase Jitter and Coherent,Incoherent, and Differential Systems

Coherent symbols Tx symbols decoded relative to

phase of Rx LO

Rx-Tx LO phase independent overmany symbols (recovery loop timeconstant Tp 1/ Bp >> Tc)

Must have Tp >> Tc so thermal noise

does not degrade BER throughrecovery loop

(Phase) Incoherent symbols Inter-symbol phase unimportant

Ex: Freq or amplitude modulation

Differential symbols

Data coded so change in symbolphase carries information

Phase matters only from symbol tosymbol

No Rx carrier recovery loop needed

BER vs Eb/No worse than for coherent

systems

Incoherent (i.e., FSK, ASK)Freq

Symbols

Coherent (i.e., QPSK)

Xmitted Symbols

Differential (i.e., DPSK)

Phase only mattersover one symbol

Rx & Tx LO phase differenceimportant over many symbols

Phase unimportant

Decoded SymbolX




Definition of phase jitter variancefor coherent systems

2 = 2 0Rs/2 L (f)|1-Hp(f)|2df 2 2 Bp Rs/2 L (f)df Hp(f) = recovery loop response

function

Assumes channel bandpass filterwidth = symbol rate Rs

L (f)= sum of SSB -PSDs of allLOs

Because of the high pass cut-offfrom the carrier recovery loop, thisstandard variance exists even forflicker of frequency noise

Rule of thumb for QPSK phase jitter

should be < 1-3 for < 0.1 dBBER degradation

Calculating LO Phase Jitter for CoherentSystems

For oscillator x N

The phase jitter req must bereduced by N to compensate

for x N multiplication

L (f) (single sideband noise)

f

Sum of all LOs

Carrier RecoveryLoop BW

Bp

Phase JitterIntegration

Region

Filter atSymbol

Rate Rs/2

RecoveryLoop

tracksout thisregion




Typical L (f) Requirements for QPSK LOs(vs Symbol Rate)

-140

-120

-100

-80

-60

-40

0 10 20 30 40 50 60 70 80 90Fourier Frequency-dBHz

L

(f)-dBc/Hz

- 10 Hz

- 100 Hz- 1 KHz- 10 KHz- 100 KHz- 1 MHz- 10 MHz- 100 MHz

- 1 GHz

SymbolRate Rs

Composite Spec

Rs = 10 Hz - 1 MHz

The curves above show typical L (f) requirements vs symbol rate 0.5 phase jitter allocated to particular LO Oscillator model: flicker frequency + white phase

Flicker freq and white phase each contribute equally to jitter

Carrier recovery loop BW optimized for data rate = 0.01 x Data Rate but 100 KHz (assumed hardware limit for VCO modulation rate) For multi-data-rate units, LOs must satisfy worst case composite

spec for all rates covered by that unit




LO Vibration Sensitivity and CarrierPhase Jitter

Vibration induces phase jitter throughFreq source g-sensitivity

Hg(f) =( f/f)/ g = y/ g The vibration PSD Sg(f) generates f/f-

PSD Sy (f) directly through Hg(f)

Sy(f) = |Hg(f)|2 Sg(f)

S(f) = double-sided PSDs

This can be converted to a phase PSD byadding a (fo/f)

2 factor

S (f) = |Hg(f)|2 Sg(f)*(fo/f)2 fo = carrier frequency

As before, S (f) is integrated from Bp to Rsto produce a phase variance

2 = 0Rs/2 |Hg(f)|2 Sg(f)*(fo/f)2 |1-Hp(f)|2df 2 Bp Rs/2 |Hg(f)|2 Sg(f)*(fo/f)2 df

Because of the (fo/f)2 dependence of S (f),

there is a strong 1/Bp dependence in 2

Sg(f)

f

Vibration Spectrum

|Hg(f)|2

f

Oscillator gsensitivity

StructuralResonances

f

Vibration Induced

Phase Noise

S (f) (fo/f)2 factorbecause vibgeneratesfrequencysidebands




Typical Vibration Levels in a CommercialAircraft

From: PHASE NOISE PERFORMANCE OF SAPPHIRE MICROWAVE OSCILLATORS IN AIRBORNE RADARSYSTEMS, T. Wallin, L. Josefsson, B. Lofter, GigaHertz 2003, Proceedings from the Seventh Symposium, November 45,

2003, Linkping, Sweden, Linkping ISSN 1650-3740 (www) , Issue: No. 8, URL: http://www.ep.liu.se/ecp/008/.

-80

-70

-60-50

-40

-30

-20

-10

10 20 30 40

Sg(f)dBg2/Hz

Fourier Frequency - dBHz

WithVibrationDamper

WithoutVibrationDamper

Sg Level

0.003 g2/Hz

Double Sideband Spectrum Damper Response

-80

-60

-40

-20

0

20

-20 -10 0 10 20 30

f/fres - dB

Respon

sedB

fres = 14.3 Hz

Q = 3

Vibration levels at a crystal oscillator with and without avibration damper




Typical LO Hg Required vs Data Rate

Using this vib data (scaled by peak Sg without damper), one cangenerate the above curves of required Hgvs symbol rate

Assumes: 0.25 allocated to vibration induced phase jitter, Bp = 0.01Rs,

fo = 10 GHz, and constant Hg vs freq

Note (because of strong Bp dependence in 2) : (1) Hg regs morestringent for lower symbol rates, (2) vibration damper helps more athigher symbol rates & can make things worse at lower rates

With Vibration DamperNo Vibration Damper

Sg=0.003 Sg=0.01 Sg=0.03 Sg=0.1

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1020304050607080

Symbol Rate-dBHz

Hg-g

2/Hz

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1020304050607080

Symbol Rate-dBHz

Hg-g

2/Hz


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18/21freq reqs for comm.ppt, V. S. Reinhardt. Page 18

Copyright 2005 Victor S. Reinhardt--Rights to copy material is granted so long as a sourcereference is listed on each page, section, or graphic utilized.

Decision Epoch Jitter from Data Clocks

Analysis of decision jitter similar tothat of phase jitter

x

2 = 2 0

Rs/2 Lx (f)

|1-Hp

(f)|2df

x2 2 Bp Rs/2 Lx(f)df = ( Tc)2 x = /(2 Rs) = clock reading error Lx(f)

= sum of SSB x-PSDs of clocks

Rec loop: Hp(f) = response Bp = BW

Rule of thumb: should be < 0.3-0.9 %for < 0.1 dB DER deg

Data clock phase jitter = 2 Rs x = 2 (in radians) L (f)= sum of SSB -PSDs of clocks 2 = 2 0Rs/2 L (f)|1-Hp(f)|2df 2 2 Bp Rs/2 L (f)dfRule of thumb: should be < 1-3

for < 0.1 dB BER degradation

Same curves as LO L (f)vs Rs (for samephase jitter and Bp)

Clock Jitter Reqsvs Symbol Rate

-12

-11

-10

-9-8

-7

-6

-5

30 40 50 60 70 80 90Symbol Rate - dBHz

Jtter-lo

g(s)

0.3% of Tc

0.9% of Tc




Effect of Sampling Clock Jitter in DigitalImplementations

Digital implementations use A/Dand D/A converters to convertbetween analog and digitaldomains

Jitter tj in aperture clockgenerates random amplitudenoise in digitizing a signal withcarrier frequency f

Phase noise generated = 2 fSW tj = V/A Limits SNR of digital output

to 1 Can be converted to an effective

number of bits (ENOB) of theconverter (with assumptionsabout the size of A)

From: Analog Devices, Mixed-Signal and DSP Design Techniques, Section 2, Sampled Data Systems,

http://www.analog.com/Analog_Root/static/pdf/dataConverters/MixedSignal_Sect2.pdf, p35

Modulated SinewaveInput at Frequency fSW

Time Jitter tj

AmplitudeJitter V

Phase Jitter = 2 fSW tj

2A




SNR due to Aperture (Sampling) ClockJitter for Full Scale Sinewave Input

From: Analog Devices, Mixed-Signal and DSP Design Techniques, Section 2, Sampled Data Systems,http://www.analog.com/Analog_Root/static/pdf/dataConverters/MixedSignal_Sect2.pdf, p36

0

20

40

60

80

100

120

60 65 70 75 80 85 90

4

8

12

16

E

NOB

Sinewave Frequency - dBHz

SNR

-dB

1ns

0.1ns

10ps

1ps

0.1ps

ClockJitter

S C


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Copyright 2005 Victor S Reinhardt--Rights to copy material is granted so long as a source

Summary--Conclusions

T&F specs for frequency sources in comm systems can bederived by understanding the relationship between BER

degradation and frequency source phase and clock jitter

Recovery loops act as high pass filters that allow the use ofstandard variances even in the presence of flicker of frequencynoise

The critical jitter statistics are derived from PSDs by integratingfrom the loop recovery BW to the symbol rate

Spurs must be included in jitter integrations (not covered in talk)

Quadrature systems have more stringent phase jitterrequirements because of I-Q crosstalk

Frequency source vibration requirements are more critical for lowdata rate systems

Frequency Source Requirements for Digital Communications Systems

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