U.S. patent application number 14/539504 was filed with the patent office on 2015-03-12 for complexity reduced feed forward carrier recovery methods for m-qam modulation formats.
The applicant listed for this patent is AT&T Intellectual Property I, L.P.. Invention is credited to Yifan Sun, Xiang Zhou.
Application Number | 20150071395 14/539504 |
Document ID | / |
Family ID | 46234591 |
Filed Date | 2015-03-12 |
United States Patent
Application |
20150071395 |
Kind Code |
A1 |
Zhou; Xiang ; et
al. |
March 12, 2015 |
COMPLEXITY REDUCED FEED FORWARD CARRIER RECOVERY METHODS FOR M-QAM
MODULATION FORMATS
Abstract
The present disclosure provides a method of carrier phase error
removal associated with an optical communication signal. The method
includes estimating and removing a first phase angle associated
with an information signal using coarse phase recovery, the
information symbol being associated with a digital signal, the
digital signal representing the optical communication signal;
estimating a carrier frequency offset between a receiver light
source and a transmitter light source by using the estimated first
phase angle, the carrier frequency offset being associated with the
information signal; removing carrier phase error associated with
the carrier frequency offset; and estimating and removing a second
phase angle associated with the information signal, the estimated
second phase angle being based on the estimated first phase angle
and the estimated carrier frequency offset.
Inventors: |
Zhou; Xiang; (Holmdel,
NJ) ; Sun; Yifan; (Naperville, IL) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
AT&T Intellectual Property I, L.P. |
Atlanta |
GA |
US |
|
|
Family ID: |
46234591 |
Appl. No.: |
14/539504 |
Filed: |
November 12, 2014 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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12968454 |
Dec 15, 2010 |
8908809 |
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14539504 |
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Current U.S.
Class: |
375/371 |
Current CPC
Class: |
H04L 2027/0055 20130101;
H04L 2027/0026 20130101; H04B 10/6165 20130101; H04L 27/0014
20130101; H04L 7/033 20130101; H04L 2027/0032 20130101; H04L
2027/0067 20130101; H04L 27/3818 20130101 |
Class at
Publication: |
375/371 |
International
Class: |
H04L 7/033 20060101
H04L007/033 |
Claims
1. A method of carrier phase error removal, the method comprising:
removing, using a coarse phase recovery device, a first phase angle
associated with an information symbol to provide a coarse phase
recovered signal, the information symbol being associated with a
digital signal, the digital signal being an optical high-order
communication signal; removing a carrier frequency offset by using
the first phase angle to provide a carrier frequency offset removed
signal, the carrier frequency offset being associated with a
current information symbol; removing carrier phase error associated
with the carrier frequency offset; and removing, using the coarse
phase recovered signal and the carrier frequency offset removed
signal, a second phase angle associated with the optical high-order
communication signal modulated with the current information symbol
to provide a refined phase recovered signal, the second phase angle
being removed by performing a maximum likelihood carrier phase
estimation.
2. The method of claim 1, wherein removing the first phase angle
comprises estimating the first phase angle using a
decision-directed phase-locked loop.
3. The method of claim 1, wherein removing the first phase angle
comprises estimating the first phase angle using a coarse blind
phase search.
4. The method of claim 1, wherein removing the second phase angle
comprises performing a maximum likelihood estimate based on the
first phase angle and the carrier frequency offset.
5. The method of claim 1, wherein removing the second phase angle
comprises performing a phase-constrained blind phase search.
6. The method of claim 1, further comprising removing a third phase
angle associated with the information symbol, the third phase angle
being based on the second phase angle and the carrier frequency
offset.
7. The method of claim 6, wherein removing the third phase angle
comprises performing a maximum likelihood estimate to generate a
maximum likelihood estimator, the maximum likelihood estimator
being used to adjust the carrier frequency offset based on the
second phase angle.
8. An apparatus to perform carrier phase error removal, the
apparatus comprising: a processing device; and a receiver, the
receiver receiving an information symbol, the information symbol
being associated with a digital signal, the digital signal being an
optical high-order communication signal, the receiver transmitting
the information symbol to the processing device, the processing
device removing a first phase angle associated with the information
symbol using coarse phase recovery to provide a coarse phase
recovered signal, the processing device removing a carrier
frequency offset using the first phase angle to provide a carrier
frequency offset removed signal, the carrier frequency offset
removed signal being associated with the optical high-order
communication signal modulated with a current information symbol,
the processing device removing carrier phase error associated with
the carrier frequency offset, the processing device removing a
second phase angle associated with the optical high-order
communication signal modulated with the current information symbol
to provide a refined phase recovered signal, the second phase angle
being removed using the coarse phase recovered signal and the
carrier frequency offset removed signal by performing a maximum
likelihood carrier phase estimation.
9. The apparatus of claim 8, wherein removing the first phase angle
by the processing device comprises estimating the first phase angle
using a decision-directed phase-locked loop.
10. The apparatus of claim 8, wherein removing the first phase
angle by the processing device comprises estimating the first phase
angle using a coarse blind phase search.
11. The apparatus of claim 8, wherein removing the second phase
angle by the processing device comprises performing the maximum
likelihood carrier phase estimation based on the first phase angle
and the carrier frequency offset.
12. The apparatus of claim 8, wherein removing the second phase
angle by the processing device comprises performing a
phase-constrained blind-phase search.
13. The apparatus of claim 12, further comprising removing a third
phase angle associated with the information symbol by the
processing device, the third phase angle being based on the second
phase angle and the carrier frequency offset.
14. The apparatus of claim 13, wherein removing the third phase
angle by the processing device comprises performing a maximum
likelihood estimate to generate a maximum likelihood estimator used
to adjust the carrier frequency offset based on the second phase
angle.
15. A computer-readable storage medium storing instructions that,
when executed by a processing device, cause the processing device
to perform operations comprising: removing a first phase angle
associated with an information symbol using coarse phase recovery
to provide a coarse phase recovered signal, the information signal
being associated with a digital signal, the digital signal being an
optical high-order communication signal; removing a carrier
frequency offset by using the first phase angle to provide a
carrier frequency offset removed signal, the carrier frequency
offset being associated with the optical high-order communication
signal modulated with a current information symbol; removing
carrier phase error associated with the carrier frequency offset;
and removing, using the coarse phase recovered signal and the
carrier frequency offset removed signal, a second phase angle
associated with the optical high-order communication signal
modulated with the current information symbol to provide a refined
phase angle recovered signal, the second phase angle being removed
by performing a maximum likelihood carrier phase estimation.
16. The computer-readable storage medium of claim 15, wherein
removing the first phase angle comprises estimating the first phase
angle using a decision-directed phase-locked loop.
17. The computer-readable storage medium of claim 15, wherein
removing the first phase angle comprises estimating the first phase
angle using a coarse blind phase search.
18. The computer-readable storage medium of claim 15, wherein
removing the second phase angle comprises performing a
phase-constrained blind phase search.
19. The computer-readable storage medium of claim 15, wherein the
operations further comprise removing a third phase angle associated
with the information symbol, the third phase angle being based on
the estimated second phase angle and the carrier frequency
offset.
20. The computer-readable storage medium of claim 19, wherein
removing the third phase angle comprises performing a maximum
likelihood estimate to generate a maximum likelihood estimator used
to adjust the carrier frequency offset based on the second phase
angle.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application is a continuation of, and claims priority
to, co-pending U.S. application Ser. No. 12/968,454, filed Dec. 15,
2010, which is incorporated by reference herein in its
entirety.
FIELD
[0002] The present disclosure relates generally to optical
communications, and more particularly to using the carrier phase
angles recovered from the coarse phase recovery stage to estimate
and remove carrier frequency offset for a carrier system.
BRIEF DESCRIPTION OF THE RELATED ART
[0003] In order to meet growing capacity demands in core optical
networks, spectrally efficient techniques, such as digital coherent
detection, have attracted recent attention. These techniques allow
the use of advanced modulation formats; especially M-ary quadrature
amplitude modulation (QAM) modulated systems. However, one major
challenge in implementing high-performance coherent detection is in
accurate phase and frequency offset recovery, which is caused by
intrinsic laser phase noise and signal-local oscillator frequency
offset. As a result, for high-order M-QAM modulation formats (where
M>4), tolerance to laser phase noise decreases as the modulation
level increases, because the Euclidean distance decreases (Yu, X.
Zhou and J., "Multi-level, Multi-dimensional Coding for High-Speed
and High Spectral-Efficiency Optical Transmission." to be published
in the August issue of J. Light wave Technology, 2009). In
particular, while frequency offset is relatively slow-changing,
phase drift caused by laser phase noise (characterized by laser
linewidth) is fast-changing. Given the small tolerance of
high-order M-QAM systems to phase and frequency noise, the quality
of phase tracking significantly influences performance of the
communication system.
[0004] Presently, there are three published carrier phase recovery
schemes. The first is a decision-directed digital feedback loop
(Irshaad Fatadin, David Ives, Seb J. Savory., "Compensation of
Frequency Offset for Differentially encoded 16- and 64-QAM in the
presence of laser phase noise." IEEE Photonics Technology Letters.
Feb. 1, 2010, p. 2010; H. Louchet, K. Kuzmin, and A. Richter.,
Improved DSP algorithms for coherent 16-QAM transmission, Brussels,
Belgium: Tu.1.E.6, 2008. Proc. ECOC'08. pp. Sep. 21-25, 2008; A.
Tarighat, R. Hsu, A. Sayed, and B. Jalali., Digital adaptive phase
noise reduction in coherent optical links, J. Lightw. Technol.,
vol. 24, no. 3, March 2006, pp. 1269-1276). Since this method
relies on negative feedback, its performance depends heavily on the
ability of previous samples to be relatively current, which places
demands on the sampling frequency. This is especially a problem in
parallel and pipeline architectures, in which sampling is both
sparse and delayed.
[0005] The second method uses a classic feed-forward phase
correction technique based on an Mth-power Viterbi-Viterbi
algorithm, in which the phase quadrant information is deliberately
removed to calculate phase error (Seimetz, M., "Laser linewidth
limitations for optical systems with high-order modulation
employing feed forward digital carrier phase estimation." San
Diego, Calif.: OTuM2, Feb. 24-28, 2008. Proc. OFC/NFOEC). However,
this method can only be applied to certain constellation points
having equal phase spacing, and therefore only a small subset of
incoming signals can be used--this again reduces the linewidth
tolerance of the system.
[0006] A third method proposes using a blind exhaustive phase
search to find phase error based on the phase distance to the
nearest constellation point, for a collection of points (T. Pfau,
S. Hoffmann and R. Noe., Hardware-Efficient Coherent Digital
Receiver Concept With Feed forward Carrier Recovery for M-QAM
Constellations, Journal of Lightwave Technology, Vol. 27, No. 8,
Apr. 15, 2009). While this method is both feed-forward and
high-performing, it requires high complexity to process a large
collection of points simultaneously. In addition, because of the
need to process in parallel, each group of computations required to
process the collection of points must be repeated for each parallel
branch. Therefore, though this method is high-performing, it is not
feasible to implement.
SUMMARY
[0007] The present disclosure includes a method to use a
decision-directed digital phase lock loop (PLL), which may be
implemented with parallel and pipeline architecture, for coarse
phase recovery, and one or more feed forward maximum likelihood
(ML) estimators to fine-tune the estimate. Additionally, the use of
a weighted ML phase estimator for improved performance is
contemplated. For the case with carrier frequency offset between
the transmitter laser and the local oscillator laser, the present
disclosure proposes to use the carrier phase angles recovered from
the coarse phase recovery stage to estimate and remove carrier
phase angles recovered from the coarse phase recovery stage to
estimate and remove carrier frequency offset. Specifically, the
present disclosure proposes a novel time-domain edge detection
algorithm to perform carrier frequency recovery prior to the ML
phase estimator. The method of the present disclosure performs well
even for a highly parallelized system, and the required
computational efforts can be reduced by one order of magnitude as
compared to the prior art using single-stage based blind phase
search method.
[0008] Further, the present disclosure includes a method of carrier
phase error removal associated with an optical communication
signal. The method includes estimating and removing a first phase
angle associated with an information signal using coarse phase
recovery, the information symbol being associated with a digital
signal, the digital signal representing the optical communication
signal; estimating a carrier frequency offset between a receiver
light source and a transmitter light source by using the estimated
first phase angle, the carrier frequency offset being associated
with the information symbol; removing carrier phase error
associated with the carrier frequency offset; and estimating and
removing a second phase angle associated with the information
symbol, the estimated second phase angle being based on the
estimated first phase angle and the estimated carrier frequency
offset. Estimating and removing the first phase angle may include
estimating the first phase angle using a decision-directed
phase-locked loop, a decision-aided feedback phase recovery method,
or estimating the first phase angle using a coarse blind phase
search. Estimating and removing the second phase angle may include
performing a maximum likelihood estimate based on the estimated
first phase angle and the estimated carrier frequency offset, or
estimating an average phase rotation based on the estimated first
phase angle and the estimated carrier frequency offset. The method
may further include estimating and removing a third phase angle
associated with the information symbol, the third phase angle being
based on the estimated second phase angle and the estimated carrier
frequency offset. Estimating and removing the third phase angle may
include performing a maximum likelihood estimate to generate a
maximum likelihood estimator used to adjust the estimated carrier
frequency offset based on the estimated second phase angle.
[0009] Additionally, the present invention includes an apparatus
for carrier phase error removal associated with an optical
communication signal. The apparatus includes a processing device
having a processor and a receiver. The receiver receives an
information symbol being associated with a digital signal, the
digital signal representing the optical communication signal. The
processor is configured to estimate and remove a first phase angle
associated with an information symbol using coarse phase recovery,
an information symbol being associated with a digital signal, the
digital signal representing the optical communication signal, the
processing device being configured to estimate a carrier frequency
offset between a receiver light source and a transmitter light
source by using the estimated first phase angle, the carrier
frequency offset being associated with the information symbol, the
processing device being configure to remove carrier phase error
associated with the carrier frequency offset, the processing device
being configure to estimate and remove a second phase angle
associated with the information symbol, the estimated second phase
angle being based on the estimated first phase angle and the
estimated carrier frequency offset.
[0010] Further, the present disclosure includes a non-transitory
computer-readable storage medium storing computer instructions
that, when executed by a processing device, perform a carrier phase
error removal associated with an optical communication signal. The
instructions include estimating and removing a first phase angle
associated with an information symbol using coarse phase recovery,
the information symbol being associated with a digital signal, the
digital signal representing the optical communication signal;
estimating a carrier frequency offset between a receiver light
source and a transmitter light source by using the estimated first
phase angle, the carrier frequency offset being associated with the
information symbol; removing carrier phase error associated with
the carrier frequency offset; and estimating and removing a second
phase angle associated with the information symbol, the estimated
second phase angle being based on the estimated first phase angle
and the estimated carrier frequency offset.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] The drawings constitute a part of this specification and
include exemplary embodiments, which may be implemented in various
forms. It is to be understood that in some instances various
aspects may be shown exaggerated or enlarged in the drawings to
facilitate understanding of the embodiments.
[0012] FIG. 1 shows a schematic of a generic optical communications
system;
[0013] FIG. 2 shows a schematic of an optical transmitter;
[0014] FIG. 3 shows a schematic of an optical receiver;
[0015] FIG. 4a is a block diagram of a second-order
decision-directed phase locked loop (PLL).
[0016] FIG. 4b is a block diagram of a second order decision
directed phase-locked loop (DD-PLL) with k parallel branches.
[0017] FIG. 5 is a block diagram of a first embodiment in
accordance with the present disclosure.
[0018] FIG. 6 is a block diagram of a second embodiment in
accordance with the present disclosure.
[0019] FIG. 6a is a high-level block diagram of the embodiment of
FIG. 6.
[0020] FIG. 6b is a high-level block diagram of the embodiment of
FIG. 6.
[0021] FIG. 6c is a block diagram of a third embodiment of FIG. 6
for carrier frequency offset estimation purpose.
[0022] FIG. 6d is a block diagram of a fourth embodiment of FIG. 6
introducing a feedback configuration.
[0023] FIG. 7 is a plot diagram of phase offset detection of
samples with a frequency offset of 1 MHz.
[0024] FIG. 8 is a block diagram of a multi-branch method for edge
detection compatible with wide-range frequency detection.
[0025] FIG. 9 is a plot diagram of simulated bit error ration (BER)
as a function of a number of parallel branches with different phase
recovery schemes, where there is no frequency offset in the
system.
[0026] FIG. 10 is a plot diagram of simulated BER as a function of
carrier frequency offset by using a three-stage PLL+2ML phase
recovery method with a different number of parallel branches.
[0027] FIG. 11 is a plot diagram of simulated BER versus carrier
frequency offset by using both phase (PLL+2ML) and frequency
recovery methods.
DETAILED DESCRIPTION
[0028] There is a need for further reducing the implementation
complexity of carrier recovery for high-order M-QAM system.
Moreover, the single-stage, blind-phase search algorithm and
multi-stage algorithm do not consider carrier frequency offset (the
frequency offset between the signal source and the local
oscillator). However, in the real world, significant carrier
frequency offset (>10 MHz) may occur in many cases, especially
for long-haul transmission systems using intradyne detection and
coarse automatic frequency tracking techniques (Z. Tao, H. Zhang,
A. Isomura, L. Li, T. Hoshida, J. C. Rasmussen, "Simple, Robust,
and Wide-Range Frequency Offset Monitor for Automatic Frequency
Control in Digital Coherent Receivers," ECOC 2007, paper 03.5.4).
Thus, a carrier recovery method capable of recovering the carrier
phase in the presence of carrier frequency offset is also
needed.
[0029] FIG. 1 shows a schematic of a generic optical
telecommunications system. Multiple optical transceivers (XCVRs)
send and receive lightwave signals via optical transport network
102. Shown are four representative transceivers, referenced as XCVR
1 104, XCVR 2 106, XCVR 3 108, and XCVR 4 110, respectively. In
some optical telecommunications systems, optical transport network
102 can include all optical components. In other optical
telecommunications systems, optical transport network 102 can
include a combination of optical and optoelectronic components. The
transport medium in optical transport network 102 is typically
optical fiber; however, other transport medium (such as air, in the
case of free-space optics) can be deployed.
[0030] Each transceiver has a corresponding transmit wavelength (,T
n 1) and a corresponding receive wavelength (,R n 1), where n=1-4.
In some optical telecommunications systems, the transmit and
receive wavelengths for a specific transceiver are the same. In
other optical telecommunications systems, the transmit and receive
wavelengths for a specific transceiver are different. In some
optical telecommunications systems, the transmit and receive
wavelengths for at least two separate transceivers are the same. In
other optical telecommunications systems, the transmit and receive
wavelengths for any two separate transceivers are different.
[0031] FIG. 2 shows a schematic of an example of an optical
transmitter. Transmit (Tx) laser optical source 202 transmits a
continuous wave (CW) optical beam 201 (with wavelength 1) into
electro-optical modulator 204, which is driven by electrical signal
203 generated by electrical signal source 206. Electrical signal
203 consists of an electrical carrier wave modulated with
information symbols (data symbols). The output of electro-optical
modulator 204 is carrier optical beam 205, which consists of a
corresponding optical carrier wave modulated with information
symbols. In general, the amplitude, frequency, and phase of the
optical carrier wave can be modulated with information symbols.
Carrier optical beam 205 is transmitted to optical transport
network 102 (see FIG. 1).
[0032] FIG. 3 shows a schematic of an example of an optical
receiver. Carrier optical beam 301, with wavelength 1, is received
from optical transport network 102 (see FIG. 1). Carrier optical
beam 301 has an optical carrier wave modulated with information
symbols. In general, the optical receiver determines the amplitude,
frequency, and phase of the modulated optical carrier wave to
recover and decode the information symbols. Carrier optical beam
301 is transmitted into optical coherent mixer 302. Local
oscillator laser optical source 304 generates a reference optical
beam 303, with wavelength 1, modulated with an optical reference
wave with tunable reference amplitudes, reference frequencies, and
reference phases. Reference optical beam 303 is transmitted into
optical coherent mixer 302.
[0033] Optical coherent mixer 302 splits carrier optical beam 301
into carrier optical beam 301A and carrier optical beam 301B.
Optical coherent mixer 302 splits reference optical beam 303 into
reference optical beam 303A and reference optical beam 303B, which
is phase-shifted by 90 degrees from reference optical beam 303A.
The four optical beams are transmitted into optoelectronic
converter 306, which contains a pair of photodetectors (not shown).
One photodetector receives carrier optical beam 301A and reference
optical beam 303A to generate analog in-phase electrical signal
307A. The other photodetector receives carrier optical beam 301B
and reference optical beam 303B to generate analog quadrature-phase
electrical signal 307B. Analog inphase electrical signal 307A and
analog quadrature-phase electrical signal 307B are transmitted into
analog/digital converter (ADC) 308. The output of ADC 308,
represented schematically as a single digital stream, digital
signal 309, is transmitted into digital signal processor 310.
Digital signal processor 310 performs multiple operations,
including timing synchronization, equalization, carrier frequency
recovery, carrier phase recovery, and decoding.
[0034] The carrier phase recovery refers to estimate and remove the
phase error caused by inherent laser phase noise as well as the
unknown transmission delay from the information symbol. Carrier
frequency recovery refers to estimate and remove the phase error
caused by carrier frequency offset (or difference) between the
transmitter laser source and the receiver laser source from the
information symbol. The information symbol refers to the physical
representation of a digital signal such as the binary-modulated
signal symbol. QAM-modulated signal symbol in the electrical field
form. Coarse phase recovery refers to not very accurate phase
recovery. The first phase angle refers to the estimated phase
deviation of the received information symbol based on the coarse
phase recovery. The second phase angles refers to the phase
deviation of the received information symbol based on the second
refined phase recovery.
[0035] An optical signal degrades as it propagates from the optical
transmitter to the optical receiver. In particular, laser phase
noise introduces some uncertainty in the carrier phase of the
received signal relative to the carrier phase of the transmitted
signal assuming no laser phase noise. Carrier phase recovery refers
to recovery of the correct carrier phase (carrier phase as
originally transmitted assuming no laser phase noise) from the
received signal. In practice, a best estimate of the carrier phase
is determined from the received signal such that a decoded
information symbol at the receiver is a best estimate of the
corresponding encoded information symbol at the transmitter.
Carrier phase recovery determines the phase angle by which an
initial decoded information signal is rotated to yield the best
estimate of the corresponding encoded information signal.
[0036] FIGS. 4a and 4b show block diagrams 10, 11 of a
decision-directed second-order digital phase lock loop (PLL) 10 and
its parallel form 11, respectively, which are based on a system
described in "Compensation of Frequency Offset for Differentially
encoded 16- and 64-QAM in the presence of laser phase noise", by
Irshaad Fatadin, David Ives, Seb J. Savor., IEEE Photonics
Technology Letters. Feb. 1, 2010, p. 2010. The presently claimed
embodiment would benefit these systems as discussed below in
detail.
[0037] The feedback phase error .phi..sub.error is calculated as
follows:
.phi. error ( k ) = Im { a ^ k * y k - j .DELTA. .phi. ^ ( k ) } a
^ k * y k ( 1 ) ##EQU00001##
where k is the time index, y.sub.k is the kth received sample (one
sample per symbol, after equalization), a*.sub.k is the conjugate
of the kth decided bit, and .DELTA.{circumflex over (.phi.)}(k) is
the kth estimated phase offset. Here,
y.sub.ke.sup.-j.DELTA.{circumflex over (.phi.)}(k) is the received
sample with phase correction based on an estimated phase offset. By
multiplying y.sub.ke.sup.-j.DELTA.{circumflex over (.phi.)}(k) with
a*.sub.k, any phase information encoded in the sample is removed,
and the symbol is rotated to the x-axis. Any deviation of this
result from the x-axis is, therefore, representative of the error
in phase estimation. For small angles, .phi..apprxeq.sin(.phi.).
Thus, to simplify calculations, the angle is estimated by measuring
the imaginary component, and normalizing for magnitude scaling.
This normalization is not present in the prior art (i.e., Irshaad
Fatadin, David Ives, Seb J. Savory., "Compensation of Frequency
Offset for Differentially encoded 16- and 64-QAM in the presence of
laser phase noise." IEEE Photonics Technology Letters. Feb. 1,
2010, p. 2010). However, this normalization of the presently
claimed embodiment significantly improves the performance of the
phase-locked loop (PLL).
[0038] The remaining PLL equations are as follows:
.phi..sub.i(k)=.phi..sub.i(k-1)+g.sub.i.phi..sub.error(k) (2)
.phi..sub.B(k+1)=g.sub.p.phi..sub.error(k)+.phi..sub.i(k) (3)
.DELTA.{circumflex over (.phi.)}(k+1)=.DELTA.{circumflex over
(.phi.)}(k)+.phi..sub..delta.(k+1) (4)
a.sub.k=y.sub.ke.sup.-j.DELTA.{circumflex over (.phi.)}(k) (5)
[0039] The PLL can only be used for coarse phase recovery. This is
because the PLL performance relies heavily on negative feedback,
and therefore used for dense sampling. However, in order to support
high optical data rates (greater than 10 Gbaud), electronic
processing has to be parallelized, and therefore must rely on
sparse sampling.
[0040] FIGS. 5 and FIG. 6 describe PLL-based phase recovery method.
PLL is the preferable coarse phase recovery method in accordance
with the present disclosure due to its hardware efficiency.
Specifically, FIG. 5 shows the basic scheme 20 of the present
disclosure, which relies on a series of maximum likelihood (ML)
phase estimators 22 to adjust the phase offset and improve the bit
error ration (BER). Because the ML phase estimator 22 is a
feed-forward method, its performance does not degrade due to system
parallelization.
[0041] The ML phase estimator 22 is implemented as follows
(Proakis, J. G., Digital Communications, 4th edition, Chapter 6,
pp. 348):
H ( k ) = Y ( k ) X ^ old * ( k ) ( 6 ) H k , k + 1 , , k + P - 1 =
H ( k ) + H ( k + 1 ) + + H ( k + P - 1 ) ( 7 ) .DELTA. .phi. ^ MLE
( k , k + 1 , , k + P - 1 ) = tan - 1 ( Im { H k , k + 1 , , k + P
- 1 } Re { H k , k + 1 , , k + P - 1 } ) ( 8 ) X ^ new ( k ) = Y (
k ) - j .DELTA. .phi. new ( k ) ( 9 ) ##EQU00002##
Here, Y(k), and {circumflex over (X)}.sub.old(k) denote the kth
received sample 24 (before carrier recovery) and the decided symbol
from the previous coarse phase recovery stage 26, respectively, and
{circumflex over (X)}.sub.new(k) and .DELTA.{circumflex over
(.phi.)}.sub.MLE(k) are the newly decided symbol and phase offset,
respectively. For each ML phase estimator 22, the decided symbols
of the previous stage are used as a reference. Through simulation,
this cascade works best with two or fewer stages, as performance
quickly reaches a BER floor.
[0042] The performance of the ML phase estimator 22 can be improved
by weighting the phase estimates inversely to the magnitudes of the
symbols, due to the fact that symbols further from the origin have
a higher probability of error, and therefore contribute more to
phase error. A weighted ML phase estimator is implemented by
substituting H(k) in with
H w ( k ) = Y ( k ) X ^ old * ( k ) X ^ old ( k ) + d ( 10 )
##EQU00003##
where, d is a very small number to prevent division by 0. For
systems with only one ML phase estimator, this normalization step
will improve performance. However, for cascaded ML systems, the
improvement may not be significant.
[0043] For a highly parallelized system of FIG. 5, the above
discussed PLL 28 and ML phase estimator 22 multistage solution
works well only for the case with no carrier frequency offset or
with very small carry frequency offset. Its performance degrades
when frequency offset is present. This is because the ML phase
estimator 22 acts as a smoothing filter, and will attempt to remove
the slope in .DELTA.{circumflex over (.phi.)} caused by the
frequency offset .DELTA.f. To address this problem, estimation and
removal of this frequency offset is proposed prior to the ML phase
estimation 22 by using the estimated phase offset 29 from the first
PLL coarse phase recovery stage 28. A time-domain edge detection
algorithm of the present disclosure performs such carrier frequency
offset estimation. This frequency offset estimation method in
general can also be used in the case that the first phase recovery
stage employs different coarse phase recovery methods (e.g. the
coarse blind phase search method). In addition, although the
proposed time-domain edge detection based frequency detection
method has the advantage of simple implementation, more complicated
fast-fourier-transform (FFT) based method or time-domain phase
slope based method may also be employed to detect the carrier
frequency offset by using the recovered carrier phase angles
obtained from the first coarse phase recovery stage.
[0044] Although phase offset changes quickly, frequency offset
changes slowly, and can be corrected on a separate time scale than
phase offset. This is an additional advantage, in that frequency
estimation can be performed on a much slower timescale, thereby
decreasing complexity. The schematic illustration for the proposed
carrier recovery 30 method with the presence of carrier frequency
offset is shown in FIG. 6.
[0045] The coarse phase recovery shown in FIGS. 6a-6d is not
limited to PLL, other phase estimation methods such as the blind
phase search based methods or the decision-aided feedback phase
recovery method reported in IEEE PHOTONICS TECHNOLOGY LETTERS, VOL.
21, NO. 19, Oct. 1, 2009, entitled "Parallel Implementation of
Decision-Aided Maximum-Likelihood Phase Estimation in Coherentary
Phase-Shift Keying Systems," by S. Zhang, C. Yu, Member, P. Y. Kam,
and J. Chen, may also be used as the coarse phase recovery method.
The ML estimator shown in FIG. 6 corresponds to 2nd-stage refined
phase recovery in FIG. 6a-6d. Although ML estimator is preferable
choice for the 2nd-stage refined phase recovery, some other phase
estimators such as the known phase-range constrained blind phase
search method may also be used in the second stage phase
recovery.
[0046] FIG. 6a shows a high-level block diagram 60 of the
embodiment shown in FIG. 6. In this embodiment, the carrier phase
recovered from the first coarse phase recovery stage 61 is used as
the input of a carrier frequency offset detection/estimation
circuit 62, where the carrier frequency offset 63 between the
incoming signal source 64 and the local oscillator light source 65
is estimated by either the proposed time-domain edge detection
method or some other known carrier frequency offset detection
methods such as the fast Fourier transform (FFT)-based frequency
domain methods or time-domain phase slope detection based methods.
The frequency offset of a copy of the original signal can then be
removed 66 and the frequency offset-removed signal 67 along with
the phase recovered signal 68 from the first coarse phase recovery
stage 61 are then used as two inputs of the second-stage refined
carrier recovery circuit 69 where a maximum likelihood (ML) based
carrier phase estimation method or phase-constrained blind phase
search method may be applied to do a more accurate carrier phase
recovery. The phase recovered signal 70 from the second phase
recovery stage 69 and a copy of the frequency-offset removed signal
67 can be further used as two inputs of the third carrier phase
recovery circuit 71 to further refine the carrier phase
recovery.
[0047] FIG. 6b shows another embodiment of a high-level block
diagram of FIG. 6. The second embodiment 72 is similar to
embodiment 60 of FIG. 6a except that the phase-recovered signal 68
resulted from the first coarse phase recovery stage 61 is made to
pass through a frequency offset removal circuit 73 before entering
into the second phase recovery stage 69. The second embodiment 72
may achieve better performance than the first embodiment 60 if the
coarse phase is estimated in a block-by-block basis (i.e the
carrier phase is assumed identical for all the symbols within the
same block). For this case, carrier frequency offset 74 introduces
an additional phase error 75 if without performing carrier
frequency offset removal.
[0048] FIG. 6c shows the third embodiment 80 of the present
disclosure. For third embodiment 80, the coarse phase recovery
circuits serve only for carrier frequency offset estimation
purpose. The estimated carrier phase angles 62 from the coarse
phase recovery circuit 61 is used for carrier frequency offset
detection 76 but the coarse phase-recovered signal 77 does not pass
to the second phase recovery stage 69, instead, the carrier
frequency offset removal operation 66 is applied to the original
signal 81 and then the frequency offset-removed signal 67 goes to
the second phase recovery stage 69 and then the third phase
recovery stage 71 for carrier phase recovery. This embodiment may
achieve better performance than the first embodiment 60 and the
second embodiment 72 when the frequency offset is significant.
[0049] FIG. 6d shows that the fourth embodiment 82 is an
improvement of the third embodiment 80 of FIG. 6c by introducing a
feedback configuration 83 such that the phase recovered signal 62
from the first coarse phase recovery stage 61 can be used along
signal 84 by the second phase recovery circuit 69 even for large
carrier frequency offset. Note that if phase locked loop (DD-PLL)
based methods are employed for the coarse phase recovery, the PLL
may fail to lock for a large frequency offset. For this case,
scanning of the frequency offset at the system acquisition stage
(i.e. the starting stage) with a frequency step smaller than the
maximum tolerable frequency offset of the PLL is done. Once the PLL
can lock (i.e. the test frequency is within its locking range), the
system can switch to the normal operation state.
[0050] The basic idea for the frequency offset estimation is to
exploit the periodicity of the measured phase offset
.DELTA.{circumflex over (.phi.)} caused by range-limiting the value
to [-.pi.,.pi.), eg:
.DELTA.{circumflex over
(.phi.)}.apprxeq.mod(2.pi.(.DELTA.ft+.DELTA..phi.(t)), 2.pi.)
(11)
Since .DELTA.ft>>.DELTA..phi.(t) for most values of t, this
modulo operation will cause the detected .DELTA.{circumflex over
(.phi.)} to resemble a nearly perfect sawtooth wave with
frequency.apprxeq..DELTA.f. Additionally, because of the sharp
edges in a sawtooth wave, a simple edge detection technique can be
used to find the average period of .DELTA.{circumflex over
(.phi.)}, thereby estimating .DELTA.f.
[0051] FIG. 7 is an example plot of .DELTA.{circumflex over
(.phi.)} for .DELTA.f=1 MHz. The measured period is very close to
1/.DELTA.f; however, in instances with high jitter, one edge may
manifest itself as several edges, which can be corrected. An
example of a simple edge detection scheme is shown below, where K
is the set of sample indices closest to each edge.
.delta.[k]=.DELTA.{circumflex over (.phi.)}[k]-.DELTA.{circumflex
over (.phi.)}[k-1] (12)
K={k:|.delta.[k]|>.pi.} (13)
Because .DELTA.ft>.DELTA..phi., the sawtooth gives very sharp
edges, making these frequency estimates very precise. However, as
FIG. 7 also shows, there can sometimes be jitter in the system,
causing one sawtooth edge to appear as a cluster of edges. If this
is not corrected, the distance between edges within the cluster can
skew the estimate dramatically. One way to identify edges caused by
jitter is that these edges will be followed by an edge going the
opposite direction. For example, an edge going from .pi. to -.pi.
caused by jitter will be soon followed by an edge going from -.pi.
to .pi.. Therefore, of all the edges detected in K, the edges
actually pertaining to the sawtooth, K.sub.c, can be found as:
K.sub.c={k .di-elect cons. K:.delta.[k]+.delta.[k-1]>2.pi.}
(14)
[0052] Then, the average frequency magnitude can be found as
d = mean spacing in K c ( 15 ) .DELTA. f ^ = d F s ( 16 )
##EQU00004##
where F.sub.s is the sampling frequency. The sign of the frequency
can then be found by summing the slopes of the edges, or
s = sign ( k .delta. [ k .di-elect cons. K ] ) ( 17 )
##EQU00005##
[0053] Frequency offset can then be estimated and removed:
.DELTA.{circumflex over (f)}=s|.DELTA.{circumflex over (f)}|
x.sub.B=xe.sup.-2.pi..DELTA.ft (18)
where x.sub.B is the baseband transmit signal.
[0054] Since this method includes additions and thresholding, the
only major complexity comes from the number of samples L needed for
good frequency estimation. For a 64 QAM system with 26 dB
open-source cognitive radio (OSNR) or higher, it is possible to
achieve a frequency precision of 1 MHz for the entire dynamic range
with L=1000 samples by downsampling at the appropriate rate. This
rate must be chosen such that the sampling window is wide enough to
include two or more sawtooth periods, while also sampling dense
enough that edges are detected closely. Since systems with more
parallel branches can only sync to a smaller range of frequencies,
a highly parallelized system can achieve good frequency estimation
for the entire effective frequency range with a very small number
of samples. For example, in a 64-QAM system and 100 kHz laser
linewidth, with a PLL with 4 or more parallel branches, a sampling
rate of 300 MHz for 1000 samples works well for all the possible
frequency offsets in which the PLL will sync (.ltoreq.20 MHz), and
can consistently predict .DELTA.f to within 1 MHz error. A PLL with
fewer parallel branches can sync to higher frequencies, making it
difficult to achieve frequency precision for the entire dynamic
range with a small number of samples. In this case, a
multi-branched method is used in which the estimation is done with
multiple L-sample banks, all sampling the data at different rates.
FIG. 8 shows a multi-branch method for edge detection compatible
with wide-range frequency detection 50. Each branch 51,52 and 53
then performs edge detection (Equations(12)-(14)) in parallel, and
the best window 54 produces K.sub.c for Equation (15). In this
case, the best window is the one with the densest sampling but
includes more than T sawtooth edges (.apprxeq.3). This method grows
in complexity, in that it requires L.times.M samples, where M is
the number of branches. However, in most cases, M is very small. In
64-QAM, for example, for fewer than 4 PLL branches, M=2 is
sufficient to acquire 1 MHz accuracy in all effective frequency
ranges (.ltoreq.100 MHz). Here, the preferred choice for the two
sampling rates is 300 MHz and 4.75 GHz.
[0055] The frequency offset estimate .DELTA.{circumflex over (f)}
is removed from Y as follows:
Y.sub.B=Ye.sup.-j.DELTA.ft (19)
After this, Y.sub.B, a baseband version of Y, is fed into the ML
phase estimation. For a sampling speed of 300 MHz and window of
1000 samples, the time needed to acquire each window is about 3.3
.mu.s. This means that this method will consistently remove
frequency offset correctly if the frequency offset changes at a
rate of 300 kHz per microsecond or less. Typically, frequency
offset changes much more slowly, in which case the frequency
estimation can be applied less frequently.
[0056] In the above, a time domain edge detection solution 55 is
used to decide both the magnitude and sign of the carrier frequency
offset 56. Time-domain based solution 55 such as the one described
in `Frequency Estimation in Intradyne Reception", by A. Leven, N.
Kaneda, U. V. Koc, Y. K. Chen, (See IEEE Photonics Technology
Letters, Vol. 19, No. 6, Mar. 15, 2007) and an FFT based solution
as described in "Frequency Estimation for Optical Coherent MPSK
System Without Removing Modulated Data Phase," by Y. Cao, S. Yu, J.
Shen, W. Gu, Y. Ji (See IEEE Photonics Technology Letters, Vol. 22,
No. 10, May 15, 2010) can also be used for carrier frequency offset
estimation by using the phase offset output from the first stage
PLL. The method of the present disclosure provides more accurate
frequency offset estimation than the alternative time-domain based
solution, which cannot provide good estimation for M-QAM based
systems, where M>4. Additionally, the method of the present
disclosure is much less complex than the FFT-based solutions, which
requires at least a 2048-length FFT to achieve our performance
level. In contrast, the method of the present disclosure requires
1000 or 2000 samples (depending on the number of PLL branches), and
uses only additions and thresholding.
[0057] Although the above discussed time-domain edge detection
method used the PLL to remove the data modulation and find the
phase offset. Other data modulation-removing methods (such as the
well known Mth-power algorithm used for phase-shifting key (M-PSK
system) can also be used to find the phase offset. Once phase
offset is found, the time-domain edge detection method can then be
used to estimate the carrier frequency offset.
[0058] The effectiveness of these methods has been verified by
numerical simulations of resulting BER for back-to-back
transmission. In all cases, the following assumptions were made:
the symbols constituted a square 64 QAM constellation, transmitted
at a baud rate of 38 Gsym/s, with an optical signal to noise ratio
(OSNR) at 0.1 nm noise bandwidth to be 28 dB, and a laser linewidth
of 100 kHz for both the signal source and local oscillator. At the
receiver, the 3 dB electrical receiver bandwidth is 0.55.times.baud
rate, sampling performed at 38 Gb/s (1 sample per symbol, after
equalization), and receiver filtering effects is equalized by using
a cascaded multi-modulus algorithm based adaptive equalizer (X.
Zhou, J. Yu., 200-Gb/s PDM-16 QAM generation using a new
synthesizing method. s.1.: paper 10.3.5, 2009. ECOC) prior to
carrier recovery. The resulting BER for these schemes are shown in
FIGS. 9-11.
[0059] FIG. 9 shows the simulated BER performance versus the number
of parallel branches for a cascaded PLL and ML system as
illustrated in FIG. 5 for the case that there is no frequency
offset in the system. Dashed lines are systems where ML phase
estimators use weighted estimates. FIG. 9 shows that the BER
performance of the PLL decreases as the number of parallel branches
increase, showing that negative feedback systems do not perform
well with many parallel branches. However, this degradation in
performance is not apparent after two ML phase estimators, showing
that our cascaded system works well with parallel systems despite
the negative feedback PLL. The third ML phase estimator does not
improve performance, showing that two ML phase estimators is
optimal. Additionally, though a weighted ML phase estimator
improves performance for one ML, the improvement is negligible when
two or more ML phase estimators are cascaded. In the remaining
figures, our system consists of a PLL, followed by two unweighted
ML phase estimators.
[0060] In FIG. 10, the embodiment in FIG. 5 is used in a receiver
with phase and frequency offset. FIG. 10 shows the simulated BER
versus carrier frequency offset by using three-stage PLL+2ML phase
recovery method with different number of parallel branches. The
labels show number of parallel PLL branches used. Here, the
performance decreases for increasing frequency offset, for two
reasons. For lower frequency offsets, the performance of the ML
phase estimator degrades, resulting in a slowly rising BER. This
results from the block implementation of the ML phase estimator,
which attempts to filter out the frequency offset component of the
phase detection. Additionally, for .DELTA.f too high,
.DELTA.{circumflex over (.phi.)} changes too quickly, and the PLL
cannot sync, causing the BER to jump to maximum error. This is
especially a problem as the number of parallel branches increases,
as the feedback delay is greater.
[0061] In FIG. 11, the embodiment presented in FIG. 6 is used to
mitigate frequency offset. By removing the frequency offset after
the PLL, the performance degradation caused by the ML phase
estimator smoothing effect is eliminated. However, because
frequency removal depends on data from the PLL, it cannot help with
the PLL's inability to sync to high-frequency systems. FIG. 11
shows simulated BER versus carrier frequency offset by using both
phase (PLL+2ML) and frequency recovery method. The labels show
number of parallel PLL branches used.
[0062] Overall, these plots show that the multistage PLL, frequency
removal, and ML phase estimator can successfully perform phase
recovery for low frequency offset. Although a highly parallelized
PLL cannot sync to high frequency offsets, it is possible to use a
PLL with fewer branches for systems with smaller frequency offsets,
in which the performance is just as good as if there is no
frequency offset at all. For a large frequency offset, an
independent frequency recovery should be performed prior to the
above discussed PLL/ML multi-stage phase recovery.
[0063] Additionally, the ML phase estimator stages can be replaced
by other phase estimate methods. For example, the carrier phase can
be estimated by directly calculating the average phase rotation of
the original signal relative to the decoded signal obtained from
the previous stage. In addition, the blind phase search method with
refined/reduced phase scan range may also be used in the second and
the third stages.
[0064] High-order M-QAM is the most promising modulation formats to
realize high-spectral efficiency optical transmission at a data
rate beyond 100-Gb/s. Because high-order M-QAM is very sensitive to
laser phase noise, laser linewidth-tolerant and hardware-efficient
feedforward carrier recovery method is critical important for
practical implementation of these high-order modulation formats. So
far, among all the published carrier recovery algorithms, only
single-stage blind phase search method can achieve high laser
line-width tolerance. But the required computational efforts are
very high for this method, especially for highly paralleled
systems. The multi-stage method of the present disclosure can
achieve high laser line-width tolerance (comparable to the blind
phase search method because the method not only use feedforward
configuration but also use the most current symbol for the phase
estimate) with substantially lower implementation complexity. The
reason that the method of the present disclosure has lower
implementation complexity is due to the fact that the method of the
present disclosure requires only one phase estimate in each of the
two or three stages, while the blind phase search (BPS) method
require many phase estimates.
[0065] For example, using 64 QAM, the single stage BPS requires
testing of more than 64 different phase angles (T. Pfau, S.
Hoffmann and R. Noe., "Hardware-Efficient Coherent Digital Receiver
Concept With Feed-forward Carrier Recovery for M-QAM
Constellations." JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 8,
Apr. 15, 2009). Table 1 shows the hardware complexity required for
one block of 2N symbols. In order to find one phase estimate, 64
such blocks are required.
TABLE-US-00001 TABLE 1 BPS complexity for 64 QAM system, for a
single block of 2N symbols. Complex Real Real multiplier multiplier
adder Slicer Other BPS (.times.64) 2N 0 2N + 1 2N 1 comparator 2N
selectors Total 128N 0 128N + 64 128N 64 comparator 128N
selectors
[0066] In contrast, the multistage DD-PLL and ML scheme requires
more hardware per 2N symbols (Table 2), but requires only one
calculation per phase estimate. In this respect, this scheme has a
complexity reduction of almost 10 times.
TABLE-US-00002 TABLE 2 DD-PLL with 2 ML phase estimators complexity
for a 64 QAM system, for a single block of 2N symbols in phase
recovery, and 2L symbols in a 2-branch frequency recovery. Complex
Real Real multiplier multiplier adder Slicer Other PLL 2N 4N 6N 2N
ML (.times.2) 4N 2N 4N 2N Arctangent Freq. <8L 2L removal Total
10N 8N 10N + 8L 4N + 2L Arctangent
[0067] In addition to the complexity reduction for carrier phase
recovery, the present disclosure also proposes a complexity-reduced
frequency recovery method that essentially enables accurate carrier
phase recovery in the presence of carrier frequency offset for the
first time.
[0068] The present disclosure includes a new laser
linewidth-tolerant multi-stage feed-forward carrier phase recovery
algorithm for arbitrary M-QAM modulation formats. As compared to
the prior art, it is shown that the proposed new algorithm can
significantly reduce the required computational efforts for
high-order modulation formats. We also propose an edge detection
frequency recovery method that essentially enables us to perform
accurate carrier phase recovery even with carrier frequency
offset.
[0069] The Abstract is provided to comply with 37 C.F.R.
.sctn.1.72(b) and will allow the reader to quickly ascertain the
nature and gist of the technical disclosure. It is submitted with
the understanding that it will not be used to interpret or limit
the scope or meaning of the claims. In addition, in the foregoing
Detailed Description, it can be seen that various features are
grouped together in a single embodiment for the purpose of
streamlining the disclosure. This method of disclosure is not to be
interpreted as reflecting an intention that the claimed embodiments
require more features than are expressly recited in each claim.
Rather, as the following claims reflect, inventive subject matter
lies in less than all features of a single disclosed embodiment.
Thus the following claims are hereby incorporated into the Detailed
Description, with each claim standing on its own as a separately
claimed subject matter.
* * * * *