Transcript Frequency Source Requirements for Digital Communications

The Calculation of Frequency Source
Requirements for Digital
Communications Systems
Victor S. Reinhardt
08/25/04
IEEE International Ultrasonics, Ferroelectrics, and
Frequency Control 50th Anniversary Joint
Conference, Montreal, August 24-28, 2004
Copyright 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.
freq reqs for comm.ppt, V. S. Reinhardt. Page 1
The Calculation of Frequency Source
Requirements for Digital Comm Systems
Introduction
• Frequency sources (oscillators, synthesizers, etc.) are an
important part of digital communications systems
• Paper will discuss the derivation of frequency source
requirements from over-all digital comm system parameters
• Will be tutorial treatment for those not familiar with digital comm
theory but familiar with time & frequency theory
• Frequency source properties directly impact the performance of
digital comm systems
– Impact link acquisition & loss of acquisition—T&F community familiar
with synchronization issues—Will not be covered here
– Impact bit error rate (BER) performance--Paper will address this
• Will utilize quadrature phase shift keyed (QPSK) systems for
concrete examples
– But theory applicable to other systems
Copyright 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.
freq reqs for comm.ppt, V. S. Reinhardt. Page 2
Basic Digital Comm Concepts
Decision
Thresholds
Signals Carrying Digital Information
•
•
•
•
•
•
Value
Symbol
1
(1,1)
(1,0)
Symbol Symbol
2
3
t1
(0,1)
(0,0)
(2-Bit)
Digital
Words
Signal
Time
t2
Tc
t3
Carrie
Decision Epochs
r
Example: Unshaped (Rectangular) Symbols in PAM
Axis
At the transmitter a carrier is modulated in a regular time sequence
of symbols to produce a digital communications signal or waveform
A symbol is a temporal waveform in some modulation space
representing a single digital word of information
At the receiver the signal is sampled at discrete decision epochs to
determine a modulation value of the carrier
The modulation value is converted into a digital or data word by
comparing 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 per symbol or word)
Copyright 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.
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Shaped Symbols
• Unshaped (rectangular) symbols are not
bandwidth efficient
– Sinc functions in freq domain
• Shaped symbols are sinc-like functions
in time domain
– Produce more bandwidth efficient
trapeziodal functions in freq domain
– Do not interfere with each other at decision
epochs
Symbols in Time Domain
— Unshaped
-3 -2 -1
• The price one pays for shaping is more
stringent timing
Shaped Transmission
Composite Signal
—
Shaped
0 1
tn/Tc
2
3
Symbols in Freq Domain
— Unshaped
1
—
Shaped
0
-1
0
1
2
3
tn/Tc
4
5
6
Copyright 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.
-3 -2 -1
0 1
f/Rs
2
3
freq reqs for comm.ppt, V. S. Reinhardt. Page 4
Inter-Symbol Interference (ISI) & Eye
Patterns
• Eye Pattern = Graph of the modulation
value vs time at the receiver plotted
modulo 1-symbol period (as in a scope
trace)
• Eye opening = region with no value
trajectories in it
• Inter-symbol Interference (ISI) =
Contamination at decision epoch of
modulation value by adjacent symbols
Eye Pattern
Inter-Symbol
Interference
Eye Opening
(No Trajectories)
– Ideal Decision epoch—no ISI
– Clock errors cause the decision epoch to
wander off the best decision epoch
increasing the ISI
– Sensitivity of ISI to clock timing = Slope of
eye opening at decision epoch
• Even unshaped (square) symbols
generate such eye patterns because of
receiver and channel filtering necessary
to limit signal BW & noise
• Shaped symbols have narrower eye
widths than unshaped ones
Copyright 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.
Shaping
Narrows
Eye Width
Ideal Decision Epoch
-
+
0
Modulo Symbol Time
From: Telecom Glossary 2000, American
National Standard for
Telecommunications, T1.523-2001,
www.atis.org/tg2k/images/epdplot1.gif
freq reqs for comm.ppt, V. S. Reinhardt. Page 5
Types of Digital Modulation
Phase Shift Keyed
BPSK, QPSK, 8PSK, .., DPSK
Binary, M-ary
FSK
Q
(0,1)
(0,0)
I
(1,0)
Frequency
Shift Keyed
(0)
Pulse
Pulse
Amplitude
Position
Shift Keyed
or Width
or Modulation Modulation
PAM
(1)
Amplitude
(1,1)
Complex RF Envelope
PWM
Freq
• Type of carrier: RF carrier or subcarrier,
baseband voltage, etc.
• Parameter modulated: amplitude, phase,
frequency, etc.
• Modulation Order (or number of digital
states 2W): binary, quadrature, M-ary
• Shaped or unshaped
• Coherent, incoherent, differential phase
• Synchronous & asynchronous data
clock timing (used in hardline systems)
Copyright 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.
Time
Time
Hybrid Modulation
M-ary Quadrature Amplitude
Shift Keyed or Modulation
Coherent Phase-Frequency
Shift Keyed
Minimum Shift Keyed (Binary
CPFSK)
16-QAM
or 16-QASK
(4-Bit word)
.
.
.
.
.
.
.
.
Q
.
.
.
.
.
.
.I
.
freq reqs for comm.ppt, V. S. Reinhardt. Page 6
Bit Error Rate (BER) vs Eb/No
Key Comm System Parameter
• The bit error rate (BER) is the probability that a received bit is
incorrect
• The BER is a function of the SNR at the digital
Uncoded BER
receiver
- Ideal
– Rx thermal noise must limited by a filter
– For an ideal system the Rx filter’s bandwidth is
equal to the symbol rate Rs = R/W
– The ideal SNR = Prx/(NoRs) = Pb/(NoR) = Eb/No
10-3
10-4
10-5
10-6
10-7
• 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 ideal
system to achieve same BER as ideal
• Error correction coding (ECC) allows up to N
bit errors to be corrected in a group or block
of bits--Improves BER above a certain Eb/No
Copyright 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.
- Actual
BER
Degradation
Eb/No - dB
Error Correction
Coded BER
10-3
10-4
10-5
10-6
10-7
- Ideal
- Actual
BER
Degradation
Eb/No - dB
freq reqs for comm.ppt, V. S. Reinhardt. Page 7
BER Degradation and ISI
Sampled values
V(±1 ±j)/20.5 at
decision epoch
• No ISI (jitter)
without thermal
noise
Ideal QPSK System
• Thermal noise in BW Rs (s = NoRs)
causes occasional bit errors
• BER (uncoded) = ½*Erfc(2-0.5V/s)
= ½*Erfc((Eb/No) ½)
Decision
thresholds
Actual QPSK system
(no thermal noise)
• ISI generates non-thermal jitter dVn
• When V + dVn is closer to decision
threshold higher BER with thermal noise
• Net effect to increase BER for given Eb/No
• Causes of ISI
– Symbol distortion
– RF carrier phase errors & jitter
– Data clock errors & jitter
Jitter dVn
• Simple BER degradation Models
• Worst case model:
BER deg = -20Log10(1-dV/V)
• Noise Model: Use theoretical
curve with Eb/No  Prx/(NoRs + sV2)
Copyright 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.
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LO Phase Jitter Requirements in RF
Carrier Digital Comm Systems
Typical RF Carrier Comm System
User
Data
Data
Encode
Symbol
Modulator
• Error
Correction
• Encryption
Data
LO
• Framing (Sampling)
Clock
~ ~
RF
Xmission
Data
(Sampling)
Clock
Symbol
Demod
-ulator
~ ~
Data
Decode
LO
Recover Loops
Transmitter (Tx) Receiver (Rx)
• At the transmitter (Tx) an LO and a clock are required
• At the Receiver (Rx)
User
Data
Rx LO
recovery
loop only for
phase
coherent
symbols
– a clock recovery loop is always required to track the Rx clock to the Tx
clock
– a carrier rec loop at the Rx LO required for phase coherent symbols
• Recovery loops track out relative Rx-Tx LO and clock jitter for fourier
frequencies < recovery loop bandwidths
• This is very important in defining the appropriate jitter statistics in
terms of power spectral densities (PSD)
Copyright 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.
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Carrier Phase Jitter and ISI
Phase
Jitter
f
V
Q-Symbol
jitter produces
cross-talk
in I-Channel, etc.
Rx I-Axis
Rx Q-Axis
RMS ISI  V*Sin(sf)
• Phase jitter produces ISI in quadrature systems through I-Q crosstalk
• 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 sf2 is
determined by the phase coherence properties of the system
Copyright 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.
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RF Carrier Phase Jitter and Coherent,
Incoherent, and Differential Systems
• Coherent symbols
Coherent (i.e., QPSK)
– Tx symbols decoded relative to
phase of Rx LO
– Rx-Tx LO phase independent over
many symbols (recovery loop time
constant Tp  1/ Bp >> Tc)
– Must have Tp >> Tc so thermal noise
does not degrade BER through
recovery loop
Symbols
Rx & Tx LO phase difference
important over many symbols
Incoherent (i.e., FSK, ASK)
• (Phase) Incoherent symbols
Freq
Phase unimportant
– Inter-symbol phase unimportant
– Ex: Freq or amplitude modulation
• Differential symbols
– Data coded so change in symbol
phase carries information
– Phase matters only from symbol to
symbol
– No Rx carrier recovery loop needed
– BER vs Eb/No worse than for
coherent systems
Differential (i.e., DPSK)
Xmitted Symbols
Copyright 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.
Phase only matters
over one symbol
X
Decoded Symbol
freq reqs for comm.ppt, V. S. Reinhardt. Page 11
Calculating LO Phase Jitter for Coherent
Systems
• Definition of phase jitter variance
for coherent systems
sf2 = 20Rs/2 Lf(f) |1-Hp(f)|2df
sf2  2BpRs/2 Lf(f) df
Lf(f) (single sideband noise)
Sum of all LO’s
Recovery
Loop
tracks
out this
region
Phase Jitter
Integration
Region
Carrier Recovery
Loop BW
Bp
f
Filter at
Symbol
Rate Rs/2
For oscillator x N
The phase jitter req must be
reduced by N to compensate
for x N multiplication
– Hp(f) = recovery loop response
function
– Assumes channel bandpass filter
width = symbol rate Rs
– Lf(f) = sum of SSB f-PSD’s of all
LO’s
• Because of the high pass cut-off
from the carrier recovery loop, this
standard variance exists even for
flicker of frequency noise
• Rule of thumb for QPSK phase
jitter
– sf should be < 1-3 ° for < 0.1 dB
BER degradation
Copyright 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.
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Typical Lf(f) Requirements for QPSK LOs
(vs Symbol Rate)
Composite Spec
Rs = 10 Hz - 1 MHz
Symbol
Rate Rs
- 10 Hz
- 100 Hz
- 1 KHz
- 10 KHz
- 100 KHz
- 1 MHz
- 10 MHz
- 100 MHz
- 1 GHz
• The curves above show typical Lf(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, LO’s must satisfy worst case composite
spec for all rates covered by that unit
Copyright 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.
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LO Vibration Sensitivity and Carrier
Phase Jitter
|Hg(f)|2
Structural
Resonances
– Hg(f) =(df/f)/dg = dy/dg
f
Oscillator g
sensitivity
• The vibration PSD Sg(f) generates df/fPSD Sy (f) directly through Hg(f)
– Sy(f) = |Hg(f)|2 Sg(f)
– S(f) = double-sided PSD’s
Sg(f)
• This can be converted to a phase PSD
by adding a (fo/f)2 factor
f
Vibration Spectrum
Sf(f)
• Vibration induces phase jitter through
Freq source g-sensitivity
– Sf(f) = |Hg(f)|2 Sg(f)*(fo/f)2
– fo = carrier frequency
(fo/f)2 factor
because vib
generates
frequency
sidebands
• As before, Sf(f) is integrated from Bp to
Rs to produce a phase variance
f
• Because of the (fo/f)2 dependence of
Sf(f), there is a strong 1/Bp dependence
in sf2
Vibration Induced
Phase Noise
– sf2 = 0Rs/2 |Hg(f)|2 Sg(f)*(fo/f)2 |1-Hp(f)|2df
– sf2  BpRs/2 |Hg(f)|2 Sg(f)*(fo/f)2 df
Copyright 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.
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Typical Vibration Levels in a Commercial
Aircraft
-10
-20
-30
-40
-50
-60
-70
-80
Damper Response
20
Sg Level
0.003 g2/Hz
With
Vibration
Damper
Without
Vibration
Damper
Response – dB
Sg(f) – dBg2/Hz
Double Sideband Spectrum
0
-20
-40
-60
fres = 14.3 Hz
Q =3
-80
10
20
30
40
Fourier Frequency - dBHz
-20 -10 0 10 20 30
f/fres - dB
Vibration levels at a crystal oscillator with and without a
vibration damper
From: PHASE NOISE PERFORMANCE OF SAPPHIRE MICROWAVE OSCILLATORS IN AIRBORNE RADAR
SYSTEMS, T. Wallin, L. Josefsson, B. Lofter, GigaHertz 2003, Proceedings from the Seventh Symposium, November 4–5,
2003, Linköping, Sweden, Linköping ISSN 1650-3740 (www) , Issue: No. 8, URL: http://www.ep.liu.se/ecp/008/.
Copyright 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.
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Typical LO Hg Required vs Data Rate
With Vibration Damper
1.E-06
1.E-06
1.E-07
1.E-07
1.E-08
1.E-08
2
Hg-g /Hz
2
Hg-g /Hz
No Vibration Damper
1.E-09
1.E-10
1.E-09
1.E-10
1.E-11
1.E-11
1.E-12
1.E-12
10 20 30 40 50 60 70 80
10 20 30 40 50 60 70 80
Symbol Rate-dBHz
Sg=0.003
Sg=0.01
Symbol Rate-dBHz
Sg=0.03
Sg=0.1
• Using this vib data (scaled by peak Sg without damper), one can
generate the above curves of required Hg vs 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 sf2) : (1) Hg regs more
stringent for lower symbol rates, (2) vibration damper helps more at
higher symbol rates & can make things worse at lower rates
Copyright 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.
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Clock Jitter Requirements for Data and
Sampling Clocks
• Decision epoch jitter from data clocks
– Clock jitter requirement value determined by eye pattern behavior
• Sampling or aperture clock jitter in A/Ds & D/As (in digitally
implemented Tx’s and Rx’s)
– Jitter in aperture clock causes non-thermal SNR degradation in A/D’s
and D/A’s (creates amplitude jitter)
– Reduces effective number of bits (ENOB)
– Causes BER degradation
Decision Epoch Jitter
Data Clock Jitter
ISI
ISI
Symbol Period
Typical Digital Implementation
SNR of N-Bit word
degraded by clock jitter
Decision
Threshold
Effective
eye
Opening
reduced
Modulo
time
Analog
Input
Copyright 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.
A/D
Sampling
or Aperture
Clock
Demod
Recovery
Loops
freq reqs for comm.ppt, V. S. Reinhardt. Page 17
Decision Epoch Jitter from Data Clocks
• Analysis of decision jitter similar to
that of phase jitter
Jtter - log(s)
Clock Jitter Reqs
vs Symbol Rate
-5
-6
-7
-8
-9
-10
-11
-12
0.9% of Tc
– sx2 = 2 0Rs/2 Lx (f) |1-Hp(f)|2df
– sx2  2 BpRs/2 Lx(f) df = (eTc)2
– x = f/(2Rs) = clock reading error
– Lx(f) = sum of SSB x-PSD’s of clocks
– Rec loop: Hp(f) = response Bp = BW
– Rule of thumb: e should be < 0.3-0.9 %
for < 0.1 dB DER deg
• Data clock phase jitter sf
0.3% of Tc
30 40 50 60 70 80 90
Symbol Rate - dBHz
– sf = 2Rssx = 2e (in radians)
– Lf(f) = sum of SSB f-PSD’s of clocks
– sf2 = 2 0Rs/2 Lf(f) |1-Hp(f)|2df
– sf2  2 BpRs/2 Lf(f) df
–Rule of thumb: sf should be < 1-3 °
for < 0.1 dB BER degradation
–Same curves as LO Lf(f) vs Rs (for same
phase jitter and Bp)
Copyright 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.
freq reqs for comm.ppt, V. S. Reinhardt. Page 18
Effect of Sampling Clock Jitter in Digital
Implementations
• Digital implementations use A/D
and D/A converters to convert
between analog and digital
domains
• Jitter tj in aperture clock
generates random amplitude
noise in digitizing a signal with
carrier frequency f
• Phase noise generated
Modulated Sinewave
Input at Frequency fSW
2A
df = 2fSWdtj = dV/A
• Limits SNR of digital output
to df-1
• Can be converted to an effective
number of bits (ENOB) of the
converter (with assumptions
about the size of A)
Amplitude
Jitter dV
Time Jitter
dtj
Phase Jitter
df = 2fSWdtj
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
Copyright 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.
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SNR due to Aperture (Sampling) Clock
Jitter for Full Scale Sinewave Input
16
80
12
SNR - dB
100
60
40
20
8
ENOB
120
4
0
60 65 70 75 80 85 90
Sinewave Frequency - dBHz
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
Copyright 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.
freq reqs for comm.ppt, V. S. Reinhardt. Page 20
Summary--Conclusions
• T&F specs for frequency sources in comm systems can be
derived 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 of
standard variances even in the presence of flicker of frequency
noise
• The critical jitter statistics are derived from PSD’s by integrating
from 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 jitter
requirements because of I-Q crosstalk
• Frequency source vibration requirements are more critical for low
data rate systems
Copyright 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.
freq reqs for comm.ppt, V. S. Reinhardt. Page 21