Digital Nyquist Spectral Shaping in
DWDM Fiber Communication
Systems for Spectral Efficient
Transmission
Junyi Wang
Email: jxw2808@louisiana.edu
Advisor: Dr. Zhongqi Pan
Dept. of Electrical and Computer Engineering
University of Louisiana at Lafayette
Lafayette, Louisiana, 70504-3890
Outline
1. Motivation – Increase Spectral Efficiency
2. Nyquist Digital Filter and Design
3. Simulation of PDM-QPSK Nyquist-WDM (NWDM) System
4. Simulation Results
5. Conclusion
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Estimate of Year to Reach Fiber Capacity Limits
1000
100
Tb/s
10
1
0.1
Based on current
fiber capacity
estimates and
historical data
0.01
0.001
1990
2000
2010
Year
2020
2030
René-Jean Essiambre, OThL1, OFC’09
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Spectrally Efficient Transmission
Nyquist WDM
(Spectrally Shaped
Single Carrier)
Standard
Single Carrier
Time Domain
time
Multi-Carrier
(OFDM)
time
time
Frequency Domain
Spectral
Shaping
frequency
IFFT
frequency
frequency
Spectrally Efficient
S. L.
Jansen, OTh1B.1, OFC’12
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Spectral Efficiency in Single Carrier System
•
Approaches to increase spectral efficiency in single
carrier WDM systems:
 Use high level modulation formats
 Reduce channel spacing  close to symbol rate
•
Challenges to reduce channel spacing
 Crosstalk: optical filters with very steep profile
 Inter-symbol interference (ISI):
Receiver side DSP such as MAP or MLSE detection
Transmitter side Nyquist spectral shaping (N-WDM)
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Concept of ISI Free N-WDM Channel
N-WDM Signal Spectrum
Symbol Pulse Shape
Amplitude (a.u.)
Power (dB)
10
0
-10
-20
-30
-40
-2
-1
0
1
2
Frequency
(normalized to symbol rate)
1
0.5
0
-4
-2
0
2
4
Time
(Normalized to symbol period)
 Low crosstalk between WDM channels
 Theoretically inter-symbol interference (ISI) free
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Nyquist Criterion in Bandlimited Channel
•

Nyquist Criterion for ISI free
H( f

m 
 m/T)  T
• Rectangular or raised-cosine (RC) spectral shaping:
The channel spacing is close to symbol rate, meanwhile
the system theoretically is ISI free
0.5
1
β=0.4
Amplitude (a.u.)
H(f) (a.u.)
1
Red, =0
Blue, =0.2
Green, =0.4
Red, =0
Blue, =0.2
Green, =0.4
0.5
0
0
-1
-0.5
0
f (symbol rate)
0.5
1
-10
-5
0
5
Time (symbol period)
10
β: roll-off factor; trade-off between spectral width and
impulse response (IR) duration thus the filter length
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Spectral Shaping Through Nyquist Filtering
•
Nyquist Filter (N-Filter): RC/RRC Spectral Shaping
Nyquist Filter
for NRZ-BPSK/QPSK
NRZ-BPSK/QPSK
Spectrum
Nyquist-BPSK/QPSK
Spectrum
=
After
IFFT
Time domain (FIR filter)
or frequency-domain
equalization (FDE)
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Spectral Shaping - Optical Filtering
The main limitation:
• Not particularly steep
(approximately 2-nd
order super-Gaussian),
substantial crosstalk at
symbol-rate spacing
• Not flexible, different
modulation formats
require different
hardware
Example: Finisar Waveshaper filter with tight spectral shaping, highfrequency pre-emphasis. Penalties can be reduced by increasing the
channel spacing to 1.1·Rs when using the standard Finisar filter shape,
or 1.07· Rs with enhanced Finisar filter.
G. Bosco, PTL 2010, & OM3H.1, OFC’12
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Spectral Shaping - Digital Filtering
Nyquist filtering and pre-equalization based on DSP in the Tx:
K. Igarashi, OMR6, OFC’11
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Transmitter with Digital N-filter
Investigates the complexity of digital N-filter at Tx
Odd
sequence
from
PRBS 2131
Even
sequence
from
PRBS 2131
E-signal Digital signal
generator Oversampling 2
Digital
N-Filter
Modulator
Nonlinearity
comp.
DAC
E-filter
Optical
Nyquist-QPSK
QPSK MZI
modulator
E-signal Digital signal
Digital
generator Oversampling 2 N-Filter
Modulator
Nonlinearity
comp.
Digital
DAC
E-filter
Analog
• Oversampling 2 for N-filter w/modulator nonlinearity comp.
• DAC: digital to analog converter
• RC/RRC spectral shaping
•
•
•
H(f): raised-cosine function, f: frequency
RC spectral shaping: spectral shape H2(f)
RRC spectral shaping: spectral shape H(f)
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Digital Filters: FIR Filters
Finite-duration impulse response
(FIR) digital filters are based on
the idea of approximating an ideal
impulse response. Practical CT
filters have infinite-duration
impulse response. The FIR filter
approximates this impulse by
sampling it and then truncating it
to a finite time (N impulses in the
illustration: tap number).
h N n  
N 1
 a  n  m
m
m 0
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Digital Filters: FIR Filters
h N n  
N 1
 a  n  m
m
m 0
The design of an FIR filter is the
essence of simplicity. It
consists of multiple
feedforward paths, each with a
different delay and weighting
factor and all of which are
summed to form the response.
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Frequency-Domain Equalization (FDE)
FFT size
Data stream before FDE
…
Overlap
length
F
F
T
FDE
I
F
F
T
F
F
T
F
F
T
FDE
FDE
FDE
FDE
I
F
F
T
I
F
F
T
…
Data stream after FDE
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Simulation Model
Data 1
DSP
DAC
PMD-QPSK
Modulator
DSP
DAC
PMD-QPSK
Modulator
λ1
Data 2
λ2
Data 3
λ3
DSP
M
U
X
ASE
DAC
PMD-QPSK
Modulator
•
3 channels N-WDM
•
112 Gb/s PDM-QPSK in each channel
•
17.5 GHz modulation bandwidth for MZM
•
100 tests with random fractional delay
and initial phase at transmitter
Coherent
Detection
DSP
BER
Test
•
11.9 GHz bandwidth for Rx
electrical filter
•
Adaptive blind equalizer with 25
taps
•
CD, PMD, and nonlinearity are
not considered
•
Lasers’ line-width and
frequency offset are not
included
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Digital Nyquist Filter Design
•
Determine Nyquist Filter Shape
The Nyquist filter transfer function can be calculated through dividing
RC/RRC function by the Fourier Transform on the digital signal,
YRC/RRC(f) = HNyquist(f)  Xdata(f)
-5
-10
1
Amplitude(a.u.)
Transfer function(dB)
0
RC 0.1
RRC 0.1
-15
-20
-20
10
0
-10
Frequency (GHz)
20
0.5
RC 0.1
RRC 0.1
0
IFT -20
10
0
-10
Time(symbol preiod)
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
20
Normalized Out-of-Band Power (dB)
Normalized Out-of-Band Power
RC 0.1 Spectrum Shape
RRC 0.1 Spectrum Shape
-7
-9
FIR
FFT size, 16 symbols
FFT size, 32 symbols
FFT size, 64 symbols
FFT size, 128 symbols
FIR
FFT size, 16 symbols
FFT size, 32 symbols
FFT size, 64 symbols
FFT size, 128 symbols
-11
-13
-15
-17
-19
-21
-23
0
10
20
30 0
10
20
30
FIR length or FDE overlap Length (symbol)
• The required FIR length is between 10 to 20 symbols
• FFT size is 64 symbols with the overlap length
between 10 to 20
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Simulation Results - FIR
Nyquist QPSK
Optical Intensity Eye Diagram
Nyquist QPSK
Optical Spectrum
• A 65-tap FIR filter
• RC spectral shaping with roll-off factor 0.1 (RC 0.1)
 Side band in spectrum from electrical filtering
between modulation nonlinearity comp. and MZM
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Simulation Results - FIR
Nyquist QPSK
Optical Intensity Eye Diagram
Nyquist QPSK
Optical Spectrum
• A 65-tap FIR filter
• RC spectral shaping with roll-off factor 0.1 (RRC 0.1)
 Side band in spectrum from electrical filtering
between modulation nonlinearity comp. and MZM
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Required OSNR at BER 10-3 with RC N-filter
Required OSNR (dB)
16
Channel spacing 28 GHZ
RC 0.2
RC 0.1
15.5
RC 0.15
RC 0.05
15
• 3×112-Gb/s PDM-QPSK
14.5
• RC spectral shaping with
different roll-off factors
14
Channel spacing 1.1 x 28 GHz
13.5
0
10
20
30
40
50
60
70
Tap number (FIR length)
 Difference < 0.3-dB with different roll-off factors
 Required OSNR for 28-GHz spacing is 0.5 dB
higher than that for 1.1x28-GHz spacing
 Better performance with more taps converges
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Required OSNR at BER 10-3 with RRC N-filter
Required OSNR (dB)
16
Channel spacing 28 GHZ
RRC 0.2
RRC 0.1
15.5
RRC 0.15
RRC 0.05
• 3×112-Gb/s PDM-QPSK
15
• RRC spectral shaping
• Matched filtering
14.5
• Different roll-off factors
14
Channel spacing 1.1 x 28 GHz
13.5
0
10
20
30
40
50
60
70
Tap number
 Maximum difference 0.9-dB with different roll-off factors
 Optimum roll-off factor 0.1
 Better performance with more taps converges
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
RRC N-filter at Different Channel Spacing
Required OSNR (dB)
20
9
9 taps
taps
17
17 taps
taps
33
33 taps
taps
19
18
13
13 taps
taps
25
taps
25 taps
17
16
• 3×112-Gb/s PDM-QPSK
• RRC spectral shaping
(matched filtering at
receiver)
• Optimum roll-off factor 0.1
15
14
13
0.95
1
1.05
1.1
1.15
Channel spacing (× 28GHZ)
 17 taps is good for 1.1×28-GHz Channel spacing
 < 1-dB penalty with frequency drift of 5%×28-GHz
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Simulation Results - FDE
Nyquist QPSK
Optical Intensity Eye Diagram
Nyquist QPSK
Optical Spectrum
For RRC with 0.1 roll off factor
• The FFT size is 64 with oversampling of 2.
• The overlap length of 60 points (to avoid cyclic extension).
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Required OSNR at BER 10-3 with RC N-filter
Required OSNR (dB)
15.5
RC 0.2
RC 0.1
Channel spacing 28 GHZ
15
RC 0.15
RC 0.05
• 3×112-Gb/s PDM-QPSK
14.5
• RC spectral shaping with
different roll-off factors
14
• FFT size: 64,
oversampling of 2
Channel spacing 1.1 x 28 GHz
13.5
0
10
20
30
40
50
Overlap length (point)
60
 Optimum roll-off factor is 0.05 or o.1 (no significant difference)
 0.5 dB better for 1.1x28-GHz spacing than 28-GHz spacing
 Overlap length  8
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Required OSNR at BER 10-3 with RRC N-filter
Required OSNR (dB)
15.5
Channel spacing 28 GHZ
RRC 0.2
RRC 0.1
15
RRC 0.15
RRC 0.05
• 3×112-Gb/s PDM-QPSK
14.5
• RC spectral shaping with
different roll-off factors
14
Channel spacing 1.1 x 28 GHz
• FFT size: 64,
oversampling of 2
13.5
0
10
20
30
40
50
Overlap length (point)
60
 Maximum difference 0.9-dB with different roll-off factors
 Optimum roll-off factor 0.1
 Overlap length  8
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
RRC N-filter at Different Channel Spacing
Required OSNR (dB)
20
19
0 point
4 points
• 3×112-Gb/s PDM-QPSK
18
8 points
12 points
17
• RRC spectral shaping
(matched filtering at
receiver)
16
• Optimum roll-off factor 0.1
15
14
13
0.95
1
1.05
1.1
1.15
Channel spacing (× 28 GHz)
 8 points is good for 1.1×28-GHz Channel spacing
 < 1-dB penalty with frequency drift of 5%×28-GHz
WILLIAM HANSEN HALL Department of Electrical & Computer Engineering
Summary
 Nyquist digital filters can reduce the channel spacing
in WDM system close to the symbol rate, thus
increasing the spectral efficiency and overall
capacity.
 Digital FIR filters with 17 taps, or FDE with FFT size of
64 and overlap length of 8 allow channel spacing of
1.1 times symbol rate.
< 1-dB penalty w/ frequency drift of 5% symbol rate
 RRC spectral shaping is 0.3-dB better than RC
spectral shaping with an optimum roll-off factor 0.1 at
1.1×28-GHz channel spacing.