U.S. patent application number 15/984117 was filed with the patent office on 2019-11-21 for dynamic constellation adaptation for slicer.
The applicant listed for this patent is MACOM Technology Solutions Holding, Inc.. Invention is credited to Yehuda AZENKOT.
Application Number | 20190356528 15/984117 |
Document ID | / |
Family ID | 68533192 |
Filed Date | 2019-11-21 |
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United States Patent
Application |
20190356528 |
Kind Code |
A1 |
AZENKOT; Yehuda |
November 21, 2019 |
DYNAMIC CONSTELLATION ADAPTATION FOR SLICER
Abstract
System and method of demodulation by adapting constellation
values based on statistic distributions of received data symbols.
To determine an adapted constellation, an expected ratio of
received symbols with values in a certain range is preset based on
an expected statistic distribution of data symbols across the
multiple constellations. For a set of received symbols, a count
ratio of symbols falling in a first range to all the symbols in the
set is compared with the expected ratio, where the first range is
defined as below a first value. The first value is repeatedly
adjusted to adjust the first range until the count ratio equals the
expected ratio. The final fist value is then designated as the
optimal adapted constellation.
Inventors: |
AZENKOT; Yehuda; (San Jose,
CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
MACOM Technology Solutions Holding, Inc. |
Lowell |
MA |
US |
|
|
Family ID: |
68533192 |
Appl. No.: |
15/984117 |
Filed: |
May 18, 2018 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H04L 25/03019 20130101;
H04L 25/066 20130101; H04L 27/3405 20130101; H04L 2025/0342
20130101; H04L 27/06 20130101; H04L 25/06 20130101; H04L 27/3881
20130101 |
International
Class: |
H04L 27/38 20060101
H04L027/38; H04L 27/34 20060101 H04L027/34; H04L 25/03 20060101
H04L025/03 |
Claims
1. A method of dynamically determining adapted constellations for
constellation selection in demodulation, the method comprising:
accessing a first plurality of sampled inputs to a slicer and that
are generated in response to a signal received at a receiver;
comparing each of said first plurality of sampled inputs with a
first value; based on said comparing with said first value,
determining a first count ratio that represents a ratio of first
sampled inputs to said first plurality of sampled inputs, wherein
each of said first sampled inputs is comprised in said first
plurality of sampled inputs and has a value encompassed in a first
range that is defined by said first value; comparing said first
count ratio with a preset count ratio; determining an adapted
constellation based on said first value, and said comparing with
said preset count ratio; and selecting said adapted constellation
as an output in response to a sampled input based on one or more
constellation selection thresholds.
2. The method of claim 1 further comprising adjusting said first
value until said first count ratio equals said preset count
ratio.
3. The method of claim 1, wherein said adapted constellation equals
said first value if said first value results in said first count
ratio equal to said preset count ratio.
4. The method of claim 1, wherein said first plurality of sampled
inputs are inputs to the slicer configured to use a Pulse Amplitude
Modulation (PAM) scheme comprising N constellation levels, wherein
said preset count ratio equals j N - 1 2 N , ##EQU00023## wherein j
is an integer greater than 0 and smaller than or equal to N.
5. The method of claim 1, wherein said first plurality of sampled
inputs are inputs to the slicer configured to use Quadrature
Amplitude Modulation (QAM) comprising 2.times.N constellation
levels, wherein said preset count ratio equals j N - 1 2 N ,
##EQU00024## wherein j is an integer greater than 0 and smaller
than N.
6. The method of claim 4, wherein said adapted constellation
offsets from a nominal constellation of said PAM scheme used in
modulation of said signal at a transmitter.
7. The method of claim 4, wherein said first range encompasses any
value smaller than or equal to said first value.
8. The method of claim 1 further comprising: performing
analog-to-digital conversion on said signal to generate sampled
inputs; and performing equalization on said sampled inputs to
generate said first plurality of sampled inputs.
9. A device comprising: a slicer decision unit configured to:
select a first constellation as an output responsive to an input
greater than a threshold; and select a second constellation as an
output responsive to an input smaller than said threshold; and a
constellation adaptation unit coupled to said slicer decision unit
comprising: a comparator configured to compare each of a first
plurality of inputs with a first value, wherein said first
plurality of inputs are supplied to said slicer decision unit; a
first counter configured to, responsive to comparison decisions
output from said comparator, produce a number of first inputs
comprised in said first plurality of inputs and each having a value
encompassed in a first range, wherein said first range is defined
by said first value; and logic configured to: determine a first
count ratio of said number of said first inputs to a total number
of said first plurality of inputs; determine an adapted
constellation based on said first value and said first count ratio;
and send said adapted constellation to said slicer decision
unit.
10. The device of claim 9, wherein the first constellation and said
second constellation are adapted constellations offset from nominal
constellations used in modulation.
11. The device of claim 10, wherein said constellation adaptation
unit is further configured to vary said first value until said
first count ratio equals a preset count ratio.
12. The device of claim 11, wherein said slicer decision unit is
configured to use a Pulse Amplitude Modulation (PAM) scheme
comprising N constellation levels, and wherein further said preset
count ratio equals j N - 1 2 N , ##EQU00025## wherein i is an
integer greater than 0 and smaller than or equal to N.
13. The device of claim 11, wherein said slicer decision unit is
configured to use Quadrature Amplitude Modulation (QAM) comprising
2.times.N constellation levels, and wherein further said preset
count ratio equals j N - 1 2 N , ##EQU00026## wherein j is an
integer greater than 0 and smaller than or equal to N.
14. The device of claim 9, wherein said first range encompasses any
value below said first value.
15. A receiver comprising: an analog-to-digital converter (ADC)
configured to converted received analog signals to digital signals;
an equalizer coupled to said ADC and configured to: generate
equalized signals responsive to digital signals; and send said
equalized signals as inputs to a slicer decision unit; said slicer
decision unit coupled to said equalizer and configured to: select a
first constellation as an output responsive to an input greater
than a threshold; and select a second constellation as an output
responsive to an input smaller than said threshold; and a
constellation adaptation unit coupled to said slicer decision unit
and configured to: access a first plurality of inputs; compare each
of said first plurality of inputs with a first value; based on said
comparing with said first value, determine a first count ratio of
first inputs to said first plurality of inputs, wherein each of
said first inputs is comprised in said first plurality of inputs
and has a value encompassed in a first range that is defined by
said first value; compare said first count ratio with a preset
count ratio; determine an adapted constellation based on said first
value and said comparing with said preset count ratio.
16. The receiver of claim 15, wherein said constellation adaptation
unit is further configured to determine said first value by
adjusting said first value until said first count ratio equals said
preset count ratio.
17. The receiver of claim 15, wherein said slicer decision unit is
configured to use one of: Pulse Amplitude Modulation (PAM)
comprising N constellation levels; and Quadrature Amplitude
Modulation (QAM) comprising 2.times.N constellation levels.
18. The receiver of claim 15, wherein said first range encompasses
any value below said first value, and wherein said second range
encompasses any value below said second value.
19. The receiver of claim 15, wherein said first constellation and
said second constellation are adapted constellations determined by
said constellation adaptation unit.
Description
TECHNICAL FIELD
[0001] The present disclosure relates generally to the field of
signal processing in communication systems, and, more specifically,
to the field of demodulation mechanisms in receivers.
BACKGROUND OF THE INVENTION
[0002] Multi-level Pulse Amplitude Modulation (PAM) has become a
favored modulation mechanism in signal transmission, whether
between chips on a Printed Circuit Board (PCB) or from one end of a
long-haul optical fiber to another. On the transmitter side, the
amplitudes of carrier pulses are varied according to the sample
value of the message signal and based on the constellation levels
of the particular PAM-N scheme. Correspondingly, on the receiver
side, demodulation is performed based on the constellation levels
by detecting the amplitude level of the carrier at every
period.
[0003] As a signal transmitted from a transmitter to a receiver, a
wide range of factors in the communication channel can cause the
shape and amplitude of the signal to be altered, also called
non-linearity, such as due to noise and phase interference. When
characterized by using eye diagrams, non-linearity or amplitude
compression can alter the eye height of different transition eyes,
leading to errors due to a lower Signal-Noise-Ratio (SNR).
[0004] At the receiver side, when a noise-affected signal is
converted to a digital signal and subject to demodulation, it is
likely mapped to a constellation point that does not correspond
identically to a signal constellation level. A slicer is used to
determine which signal constellation level lies closest to the
received symbol based on a set of thresholds which are typically
defined to be evenly spaced. Unfortunately, non-linearity likely
causes a received symbol to move closer to another constellation
level than the one transmitted. Hence incorrect modulation tends to
occur as the nominal thresholds used in the slicer do not factor in
non-linearity. In the existing art, various computationally
intensive calculations have been developed for identifying the
actual closest signal constellation level. These calculations
consume a significant amount of the valuable computation resources
in a receiver.
SUMMARY OF THE INVENTION
[0005] Embodiments of the present disclosure provide cost-effective
mechanisms of dynamically adapting the constellation selection
thresholds and the constellation levels to signal nonlinearity
distortions for a slicer and thereby facilitating accurate data
recovery during, demodulation at a receiver.
[0006] Embodiments of the present disclosure use threshold
adaptation logic to dynamically adapt the thresholds of a slicer to
nonlinearity or other distortions in the received signals based on
statistic distributions of the data symbols. In some embodiments,
the slicer is configured for an N-level Pulsed Amplitude Modulation
(PAM-N) scheme which uses N-1 thresholds to map received symbols to
N constellations. Collectively speaking, the data symbols as
modulated and transmitted are distributed across the N nominal
constellations substantially in certain known percentages or
ratios. Typically, when they are transmitted, a large number of
symbols are distributed substantially evenly across the N nominal
constellations. Therefore, at the slicer of the receiver, the
inputs in a particular range that is defined by an optimal adapted
threshold (e.g., below the specific threshold) is expected to
constitute a corresponding certain ratio (the expected ratio) of
the total inputs regardless of the signal nonlinearity. To discover
this optimal adapted threshold that offsets from the nominal
threshold, the threshold adaption logic (1) identifies a first
value which causes the slicer inputs that fall in a first range to
constitute a first ratio of the total slicer inputs, where the
first ratio is the expected ratio minus an error ratio that is
substantially smaller than the expected ratio; and (2) identifies a
second value which causes the slicer inputs in a second range to
constitute a second ratio of the total slicer inputs, where the
second ratio is the expected ratio plus the same error ratio. The
adapted threshold is then derived based on the first and the second
values. In some embodiments, the threshold adaptation logic uses a
comparator to compare the slicer inputs with the first or second
value and accordingly uses a counter to keep count of slicer inputs
that falls below the first or second value (the first or second
range). A ratio of the inputs in the first or second range to the
total inputs can thus be calculated based on the count. The first
or second value is adjusted until the first or second ratio is
reached. The final first or second value is then used to calculate
the optimal adapted threshold in a simple arithmetic operation.
[0007] In accordance with embodiments of the present disclosure, a
set of thresholds of a slicer can be dynamically determined and
adapted to signal non-linearity and amplitude compression in a
statistical approach. As a result, data demodulation and data
recovery at the receiver can be advantageously performed with
significantly reduced error rates. The threshold adaptation process
does not involve complicated processing or computationally
intensive calculations and can be implemented by using simple
circuitry, e.g., including a comparator and counters. Thus,
compared with the conventional approaches, the present disclosure
offers reduced design and development costs as well as operational
power consumption.
[0008] According to another aspect of the present disclosure,
constellation adaptation logic is used to dynamically adapt the
values of constellations to signal nonlinearity and other
distortions at a slicer based on statistic distributions of the
data symbols. In some embodiments, to discover an optimal adapted
constellation which offsets from a nominal constellation, the
constellation adaption logic compares a first value with a set of
slicer inputs and keeps count of the slicer inputs that fall in a
certain range defined by the first value (e.g., below the first
value) based on the comparison results. The count ratio of the
number of inputs in the certain range (e.g., lower than the first
value) to the number of the set of inputs is also derived. The
first value is adjusted until the count ratio reaches an expected
ratio associated with the nominal constellation. The first value is
then designated as the adapted constellation to be used by the
slicer.
[0009] According to embodiments of the present disclosure,
constellation levels of a slicer can be dynamically determined and
adapted to signal non-linearity and amplitude compression in a
statistical approach. As a result, data demodulation and data
recovery can be advantageously performed with further reduced error
rates at the receiver. Similarly, the constellation adaptation does
not involve computationally intensive calculations or complicated
circuitry design. Thus, design and development costs and
operational power consumption can be advantageously further
reduced, compared with the conventional approaches.
[0010] The foregoing is a summary and thus contains, by necessity,
simplifications, generalizations, and omissions of detail;
consequently, those skilled in the art will appreciate that the
summary is illustrative only and is not intended to be in any way
limiting. Other aspects, inventive features, and advantages of the
present invention, as defined solely by the claims, will become
apparent in the non-limiting detailed description set forth
below.
DETAILED DESCRIPTION
[0011] Reference will now be made in detail to the preferred
embodiments of the present invention, examples of which are
illustrated in the accompanying drawings. While the invention will
be described in conjunction with the preferred embodiments, it will
be understood that they are not intended to limit the invention to
these embodiments. On the contrary, the invention is intended to
cover alternatives, modifications, and equivalents, which may be
included within the spirit and scope of the invention as defined,
by the appended claims. Furthermore, in the following detailed
description of embodiments of the present invention, numerous
specific details are set forth in order to provide a thorough
understanding of the present invention. However, it will be
recognized by one of ordinary skill in the art that the present
invention may be practiced without these specific details. In other
instances, well-known methods, procedures, components, and circuits
have not been described in detail so as not to unnecessarily
obscure aspects of the embodiments of the present invention.
Although a method may be depicted as a sequence of numbered steps
for clarity, the numbering does not necessarily dictate the order
of the steps. It should be understood that some of the steps may be
skipped, performed in parallel, or performed without the
requirement of maintaining a strict order of sequence. The drawings
showing embodiments of the invention are semi-diagrammatic and not
to scale and, particularly, some of the dimensions are for the
clarity of presentation and are shown exaggerated in the drawing
Figures. Similarly, although the views in the drawings for the ease
of description generally show similar orientations, this depiction
in the Figures is arbitrary for the most part. Generally, the
invention can be operated in any orientation.
BRIEF DESCRIPTION OF THE DRAWINGS
[0012] Embodiments of the present invention will be better
understood from a reading of the following detailed description,
taken in conjunction with the accompanying drawing figures in which
like reference characters designate like elements.
[0013] FIG. 1 illustrates exemplary data ranges used to determine
optimal adapted thresholds of constellation selection based on an
expected statistic distribution of data symbols across multiple
constellations in accordance with an embodiment of the present
disclosure.
[0014] FIG. 2 illustrates the configuration of an exemplary
threshold adaptation unit capable of dynamically adapting
constellation selection thresholds used in a slicer in accordance
with an embodiment of the present disclosure.
[0015] FIG. 3A is a flow chart depicting an exemplary process of
determining adapted thresholds for constellation selection in
accordance with an embodiment of the present disclosure.
[0016] FIG. 3B is a flow chart depicting an exemplary process of
determining a first value or a second value associate with a
threshold in accordance with an embodiment of the present
disclosure
[0017] FIG. 4 illustrates exemplary data ranges used to determine
optimal adapted constellations based on an expected statistic
distribution of data symbols across multiple constellations in
accordance with an embodiment of the present disclosure.
[0018] FIG. 5 illustrates the configuration of an exemplary
constellation adaptation unit capable of dynamically determining
optimal adapted constellations in accordance with an embodiment of
the present disclosure.
[0019] FIG. 6 is a flow chart depicting an exemplary process of
determining optimal adapted constellations for demodulation in
accordance with an embodiment of the present disclosure.
[0020] FIG. 7 illustrates a network signal transmission system that
includes constellation adaptation logic and constellation selection
threshold adaptation logic at the receiver in accordance with an
embodiment of the present disclosure.
[0021] FIG. 8 shows a set of simulated results comparing the symbol
error rates (SERs) resulting from using default slicer thresholds
and the SERs resulting from optimal adapted thresholds obtained in
accordance with an embodiment of the present disclosure.
[0022] FIG. 9 shows another set of simulated results comparing the
SERs resulting from default slicer thresholds and SERs resulting
from the optimal adapted thresholds obtained in accordance with an
embodiment of the present disclosure.
Dynamic Constellation Adaptation for Slicer
[0023] Embodiments of the present disclosure provide a threshold
adaptation mechanism of determining optimal adapted thresholds for
constellation selection by a slicer at a receiver based on
statistic distributions of the data symbols across multiple
constellations in a modulation. scheme. More specifically, to
determine an optimal adapted threshold, threshold adaptation logic
coupled to, or included in, the slicer is configured with an
expected ratio of received symbols that have values in a certain
range, e.g., below the optimal threshold that has shifted from the
nominal threshold due to nonlinearity. This optimal threshold is to
be discovered as the adapted threshold. The expected ratio can be
determined based on an expected statistic distribution of data
symbols across the multiple constellations. A first ratio and a
second ratio are defined based on the expected ratio, the first
ratio equal to the expected ratio minus an error ratio and the
second ratio equal to the expected ratio plus the error ratio. The
threshold adaptation logic then determines a first value that can
make the received symbols in a first range (e.g., below the first
value) to constitute the first ratio of a set of slicer inputs, and
determine a second value that can make the received symbols in the
second range. (e.g., below the second value) to constitute the
second ratio of a set of slicer outputs. The adapted threshold is
then obtained based on the first and the second value.
[0024] Embodiments of the present disclosure also provide a
constellation adaptation mechanism of determining adapted
constellations of a slicer at a receiver based on statistic
distributions of the data symbols across the multiple
constellations. More specifically, to determine an optimal
constellation that offsets from the nominal constellation,
constellation adaptation logic is provided with an expected ratio
of received symbols that have values in a certain range, e.g.,
below the optimal constellation value that has shifted from the
nominal value due to nonlinearity. This optimal constellation is to
be discovered as the adapted constellation. The expected ratio can
be determined based on an expected statistic distribution of the
slicer inputs across the multiple constellations. The constellation
adaption logic compares a first value with a set of received
symbols and keeps count of the symbols in the certain range that is
defined by the first value (e.g., below the first value) based on
the comparison results. The count ratio of the number of inputs in
the first range to the total number of the set of inputs is also
derived. The first value is adjusted until the ratio reaches the
expected ratio. The first value is then designated as an optimal
adapted constellation to be used by the slicer.
[0025] Embodiments herein are described in detail with reference to
4-level PAM slicers. However, it will be appreciated that the
present disclosure is not limited to any particular modulation
scheme or any specific number of constellations in a modulation
scheme. The constellation adaption and threshold adaptation
mechanisms provided herein can be used in any suitable demodulation
devices besides slicers.
[0026] Statistically speaking, data symbols as modulated and
transmitted at the transmitter are distributed across the multiple
constellation levels substantially in certain known percentages or
ratios. For example, a large number of symbols are distributed
substantially evenly across the N nominal constellations as a
result of modulation. During signal transmission, the received
symbols are altered in an unpredictable fashion because
nonlinearity and amplitude compression can cause different noise
levels for constellations and different constellation offsets.
However, the collective symbol distribution with respect to the
multiple constellations is expected to carry over the receiver side
despite impairment on the signals during transmission.
Particularly, for a large number of received symbols at the
receiver, the symbols falling, in a particular data range that is
defined by the actual constellations or the actual thresholds is
expected to constitute a known ratio of the overall received
symbols regardless of signal nonlinearity or amplitude
compression.
[0027] FIG. 1 illustrates exemplary data ranges used to determine
optimal adapted thresholds of constellation selection based on an
expected statistic distribution of data symbols across multiple
constellations in accordance with an embodiment of the present
disclosure. Constellation selection may be performed at a slicer.
In this example, data symbols are modulated and demodulated
according to the PAM-4 scheme, the nominal constellations
C(1).about.C(4) being [-3,-1,+1, +3] respectively. Accordingly, a
slicer uses 3 thresholds TH(1).about.TH(3) to decide which
constellation is assigned to a received symbol, the nominal
thresholds being [-2,0,+2] respectively.
[0028] As dictated by the modulation process at the transmitter
side, the data symbols are distributed across the 4 constellations
evenly. Accordingly, the data symbols falling below the optimal
adapted TH (1) should all be associated with the constellation C(1)
and are expected to constitute 25% of the overall received symbols.
The data symbols falling between the optimal adapted TH(1) and the
optimal adapted TH(2) should all be associated with the
constellation C(2), and therefore the data symbols falling below
the optimal adapted TH(2) are expected to constitute 50% of the
overall received symbols. By the same token, the data symbols
falling below the optimal adapted TH(3) should constitute 75% of
the overall received symbols.
[0029] To find an optimal TH(i) (i=1, 2 and 3), two values TH(i)1
and TH(i)2 are first determined based on the definitions that (1)
the symbols below TH(i)1 take up
( 100 .times. t N - P ) / 100 ##EQU00001##
(alternatively expressed as
1 N - P 100 ) ##EQU00002##
of the overall received symbols, and (2) the symbols below TH(i)2
take up
( 100 .times. t N - P ) / 100 ##EQU00003##
(alternatively expressed as
1 N + P 100 ) ##EQU00004##
of the overall received symbols. In this case, N equals 4 and
P 100 ##EQU00005##
is a programmable error ratio that is substantially smaller
than
1 N , ##EQU00006##
e.g., P=5 or less.
[0030] As illustrated, with respect to TH(1), TH((1)1 is defined as
a value that (25-P) % symbols are below it and TH(1)2 is defined as
a value that (25+P) % symbols are below it. With respect to TH(2),
TH(2)1) is defined as a value that (50-P) % symbols are below it
and TH(2)2 is defined as a value that (50+P) % symbols are below
it. With respect to TH(3), TH(3)1 is defined as a value that (75-P)
% symbols are below it and TH(3)2 is defined as a value that (75+P)
% symbols are below it. TH(i) can then be derived as TH(i)=mean
(TH(i)1, TH(i)2). That is, TH(1)=mean (TH(1)1, TH(1)2); TH(2)=mean
(TH(2)1, TH(2)2); and TH(3)=mean (TH(3)1, TH(3)2).
[0031] It will be appreciated that the present disclosure is not
limited to any specific data ranges and the corresponding expected
ratios selected for determining adapted thresholds. For example, in
some embodiments, an optimal adapted threshold TH(i) can be
determined based on the expected ratios of the symbols that are
above a first value TH(i)1 and a second value TH(i)2. In some other
embodiments, more than two data ranges can be defined and used to
generate an optimal adapted threshold. In still some other
embodiments, a single data range can be used to find the optimal
adapted threshold. For example, 50% of the symbols are expected to
be below an optimal adapted threshold TH(2). The error ratio may be
set to a lower value if the difference between two thresholds is
too high. In some embodiments, different P values may be used for
discovering different thresholds.
[0032] FIG. 2 illustrates the configuration of an exemplary
threshold adaptation unit 200 capable of dynamically adapting
constellation selection thresholds used in a slicer 210 in
accordance with an embodiment of the present disclosure. The slicer
210 includes decision circuitry configured to map each input to one
of the multiple constellations by comparing the input with the
constellation thresholds. For example, each input is a sampled
digital data output from an equalizer. The slicer 210 can be
implemented in any manner that is well known in the art. The slicer
inputs are also fed to the threshold adaptation unit 200 which uses
a comparator 201 to compare each input with a "TH" value, e.g.,
stored in a register. Applied in the example shown in FIG. 1, The
TH value is either TH(i)1 or TH(i)2. The threshold adaptation unit
200 includes Counter 1 205 for keeping count of all the inputs
subject to comparison with the TH value. Counter 2 204 is coupled
to the output of the comparator 201 and keeps count for the inputs
that fall in the particular value range defined by the TH based on
the comparison results.
[0033] Using the example shown in FIG. 1, to discover an optimal
adapted threshold TH(1), the TH register 202 is first set to be an
initial TH(1)1 value. The total number of inputs to the slicer is
programmed to be 2.sup.M which can be tracked by the Counter 1 205.
Each time the comparator outputs a result indicating that the
current input r is smaller than the TH, the Counter 2 204
increments by 1. For each window of 2.sup.M inputs, the TH
adjustment logic 203 determines the ratio of inputs below TH value
by calculating
counter 2 counter 1 . ##EQU00007##
If the ratio is not equal to the expected ratio (25-P) %, the TH
adjustment logic 203 adjusts the TH value accordingly. Another
window of 2.sup.M inputs are then compared with the new TH value to
obtain the ratio of inputs below the new TH by
counter 2 counter 1 . ##EQU00008##
This process is repeated for multiple windows of 2.sup.M inputs
until finding a TH value that makes
counter 2 counter 1 = ( 25 - P ) % . ##EQU00009##
This TH value is then designated as the TH(1)1. In the same manner,
by varying the TH value to obtain
counter 2 counter 1 = ( 25 + P ) % , ##EQU00010##
TH(1)2 can be determined. The TH adjustment logic 203 can then
generate the optimal adapted TH(1) by averaging the determined
TH(1)1 and TH(1)2.
[0034] The threshold adaptation unit 200 can be used to
sequentially determine the TH(1)1, TH(1)2, TH(2)1, TH(2)2, TH(3)1,
TH(3)2, etc. In some other embodiments, the threshold adaptation
unit 200 includes duplicate circuits shown in FIG. 2 which can
generate different TH(i)X (X=1 or 2) values in parallel. The
resultant adapted thresholds are supplied to the slicer for making
constellation selection decisions accordingly for the subsequent
inputs. The threshold adaptation process may be performed
periodically as well as based on needs.
[0035] The TH adjustment logic 203 may be implemented in software,
firmware, hardware or a combination thereof. The counters 204 and
205 may have a resolution of 32 bits for instance. For a bit-error
rate of 10.sup.-6, the number of sampled inputs of one symbol that
yields on sample at the threshold is 4.times.10.sup.6. For 100
samples at the threshold, the total number of samples is
100.times.4.times.10.sup.6, which is equivalent to 29 bits.
[0036] In accordance with embodiments of the present disclosure, a
set of optimal adapted thresholds for use of constellation
selection can be dynamically determined and adapted to signal
non-linearity and amplitude compression in a statistical approach.
As a result, data demodulation and data recovery can be
advantageously performed with reduced error rates at the receiver.
Further, the threshold adaptation does not involve computationally
intensive calculations and can be implemented by using simple
circuitry, e.g., including a comparator and counters. Thus, design
and development costs and operational power consumption can be
advantageously reduced, compared with the conventional
approaches.
[0037] FIG. 3A is a flow chart depicting an exemplary process 300
of determining adapted thresholds for constellation selection in
accordance with an embodiment of the present disclosure. Process
300 may be performed by a threshold adaptation unit coupled to, or
included in, a slicer as shown in FIG. 2 for example. At 301, the
index of threshold i is initialized, where i<N, and N represents
the number of constellations defined in the modulation scheme.
Particularly, N is 4 for PAM-4. At 302, i increments to 1. At 303,
a first value TH(i)1 associated with TH(i) is determined. TH(i)1
defines a certain data range (e.g., <TH(i)1) and is associated
with a first preset count ratio
( e . g . , i N - P 100 ) . ##EQU00011##
The optimal TH(i)1 is defined as one that causes the inputs falling
in the data range to meet the first preset count ratio. For
example, for i=3, the data range associated with the first value
TH(3)1 encompasses any value smaller than TH(3)1 and the preset
count ratio for this range is (75-P) %.
[0038] At 304, a second value TH(i)2 associated with TH(i) is
determined. TH(i)2 defines another data range (e.g., <TH(i)2)
and is associated with another preset count ratio
( e . g . , i N + P 100 ) . ##EQU00012##
An optimal TH(i)2 is defined as one that causes the inputs falling
in this data range to meet the second preset count ratio. For
example, for i=3, the data range associated with the first value
TH(3)2 encompasses any value below TH(3)2 and the preset count
ratio in this range is (75+P) %. At 305, the average of TH(i) 1 and
TH(i)2 is assigned as the optimal adapted TH(i), e.g., TH(i)=mean
(TH(i)1,TH(i)2). The process 302.about.305 is repeated to determine
each optimal threshold.
[0039] FIG. 3D is a flow chart depicting an exemplary process of
determining a first value or a second value TH(i)X (X=1 or 2)
associate with a threshold TH(i) in accordance with an embodiment
of the present disclosure. At 351, a plurality of inputs of a
slicer are accessed. For example, the total number of inputs used
for each TH(i)X variation can be preset to a window of 2.sup.M
inputs. At 352, each of the plurality of inputs is compared with
the current TH(i)X value (as set in the TH register 202 in FIG. 2).
At 353, the count ratio of the number of inputs below TH(i)X
(counter 2) to the total number of inputs subject to the comparison
(counter 1) is determined. At 354, it is determined if
counter 2 counter 1 ##EQU00013##
equals the preset count ratio associated with the TH(i)X. If not,
the TH(i)X value is adjusted at 555 and the process 551.about.554
are repeated for the adjusted TH(i)X value. The process
551.about.555 is repeated until
counter 2 counter 1 ##EQU00014##
equals the preset count ratio. At 556, the final TH(i)X is assigned
as the optimal TH(i)X to be used for deriving TH(i).
[0040] It will be appreciated that the present disclosure is
applicable to various other suitable modulation schemes. For
example, for a quadrature amplitude modulation (QAM) with 2N
constellations, the same threshold adaptation process shown in
FIGS. 3A and 3B can be performed on an individual constellation
dimension as well to discover optimal adapted thresholds and
adapted constellations. The data ranges shown in FIG. 1 and the
associated preset count ratios may also be applied to an individual
constellation dimension in a QAM-2N scheme.
[0041] According to another aspect of the present disclosure,
constellation levels can be dynamically adapted based on the
statistic distribution of the received symbols with respect to the
multiple constellations. Collectively speaking, the inputs in a
certain data range and mapped to a specific constellation are
expected to constitute a certain ratio (expected ratio) of the
total inputs as dictated by the statistic distribution. FIG. 4
illustrates exemplary data ranges used to determine optimal adapted
constellations based on an expected statistic distribution of data
symbols across multiple constellations in accordance with an
embodiment of the present disclosure. In this example, data symbols
are modulated and demodulated according to PAM-4 scheme, the
nominal constellations C(1).about.C(4) being [-3,-1,+1, +3]
respectively. Accordingly, a slicer uses 3 thresholds
TH(1).about.TH(3) to decide which constellation is assigned to a
received symbol, the nominal thresholds being [-2,0,+2]
respectively.
[0042] As dictated by the modulation process at the transmitter
side, the data symbols are distributed across the 4 constellations
evenly. Accordingly, the inputs to the slicer falling below the
optimal adapted C(1) are expected to constitute 12.5% (=0+12.5%) of
the overall inputs. The inputs falling below the optimal adapted
C(2) are expected to constitute 37.5% (=25%+12.5%) of the overall
inputs. By the same token, the inputs falling below the optimal
adapted C(3) should constitute 62.5% (=50%+12.5%)) of the overall
inputs, and the data symbols falling below the optimal adapted C(4)
should constitute 87.5% (=75%+12.5%) of the overall inputs. This is
equivalent to median of the points that belong to a constellation.
There is no assumption of Gaussian noise.
[0043] It will be appreciated that the present disclosure is not
limited to any specific data ranges and the corresponding expected
ratios selected for determining optimal adapted constellations. For
example, in some embodiments, an optimal adapted constellation can
be determined based on the expected ratios of the symbols that are
above the constellation level. In some other embodiments, more than
one data ranges can be defined and used to generate an optimal
adapted constellation, in a similar manner in the threshold
adaptation process described above.
[0044] FIG. 5 illustrates the configuration of an exemplary
constellation adaptation unit 500 capable of dynamically
determining optimal adapted constellations in accordance with an
embodiment of the present disclosure. The slicer 510 includes
decision circuitry configured to map each input to one, of the
multiple constellations by comparing the input with the
constellation thresholds. The slicer 510 can be implemented in any
manner that is well known in the art. The slicer inputs are also
fed to the constellation adaptation unit 500 which uses a
comparator 501 to compare each input with a "C(j)" value, e.g.,
stored in a register 502. The constellation adaptation unit 500
includes Counter 1 505 for keep count of all the inputs used in a
constellation adaptation process. The Counter 2 504 is coupled to
the output of the comparator 501 and keeps count for the inputs
that falls in the particular value range defined by C(j) based on
the comparison results.
[0045] Using the example shown in FIG. 4, to discover an optimal
adapted threshold C(1), the C(j) register is first set to be an
initial value. The total number of inputs to the slicer is
programmed to be 2.sup.M which can be tracked by the Counter 1 505.
Each time the comparator outputs a result that the input r is
smaller than C(j), the Counter 2 204 increments by 1. For each
window of 2.sup.M inputs, the C(j) adjustment logic 503 determines
the ratio of inputs below C(j) by calculating
counter 2 counter 1 . ##EQU00015##
If the ratio is not equal to the expected ratio 12.5%, the C(j)
adjustment logic 503 adjusts the C(j) value accordingly. Another
window of 2.sup.M inputs are then compared with the new C(j) value
to obtain the ratio of inputs below the C(j) value in the register
502 based on
counter 2 counter 1 . ##EQU00016##
This process is repeated for multiple windows of 2.sup.M inputs
until finding a C(j) value that results in
counter 2 counter 1 = 12.5 % . ##EQU00017##
This C(j) value is then designated as the optimal adapted C(1). By
the same token, by varying the C(j) value to obtain
counter 2 counter 1 = 37.5 % , ##EQU00018##
C(2) can be determined. The same process is performed to generated
the adapted C(3) and C(4) by using preset count ratios of 62.5% and
87.5%, respectively.
[0046] The constellation adaptation unit 500 can be used to
sequentially determine the C(1).about.C(4). The constellation
adaption unit 500 can also be used to perform a threshold adaption
process as described with reference to FIGS. 1-3B. In some other
embodiments, the constellation adaptation unit 500 includes
duplicate circuits shown in FIG. 5 which can generate different
levels of adapted constellations in parallel. The adapted
constellations are supplied to the slicer for making constellation
selection decisions accordingly for the subsequent inputs. The
constellation adaptation process may be performed periodically as
well as based on needs.
[0047] The constellation adjustment logic 503 may be implemented in
firmware, software, hardware or a combination, thereof. The
counters may have a resolution of 32 bits for instance. For a
bit-error rate of 10.sup.-6, the number of sampled inputs of one
symbol that yields on sample at the threshold is 4.times.10.sup.6.
For 100 samples at the threshold, the total number of samples is
100.times.4.times.10.sup.6, which is equivalent to 29 bits.
[0048] In some embodiments, to prevent interaction with
equalization gain at the receiver, the gain of the 4 optimal
constellations can be maintained at a fixed value. For example,
.SIGMA..sub.j=1.sup.4|C(j)|=Constant, where Constant=sum
(abs[-3,-1,+1,+3]).
[0049] FIG. 6 is a flow chart depicting an exemplary process 600 of
determining optimal adapted constellations for demodulation in
accordance with an embodiment of the present disclosure. Process
600 may be performed by a constellation adaptation unit coupled to
a slicer as shown in FIG. 5 for example. At 601, the index of
constellation j is initialized, where j.ltoreq.N, and N represents
the number of constellations defined in the modulation scheme. At
602, j increments by 1. At 603, a plurality of inputs of a slicer
are accessed. For example, the total number of inputs used for each
C(j) variation can be preset to a window of 2.sup.M inputs.
[0050] At 604, each of the plurality of inputs is compared with the
current C(j) value. At 605, a total number of inputs subject to the
comparison (counter 1) is determined. At 606, the number of inputs
below the current C(j) value is determined (counter 2). At 606, it
is determined if
counter 2 counter 1 ##EQU00019##
equals the preset count ratio associated with the C(j), which
is
( j N - 1 2 N ) . ##EQU00020##
If not, the C(j) value is adjusted at 608, and the foregoing
602.about.607 are repeated for the adjusted C(j) value. The
foregoing 602.about.608 is repeated until
counter 2 counter 1 ##EQU00021##
equals the preset count ratio
( j N - 1 2 N ) . ##EQU00022##
At 609, the final C(j) value is assigned as the optimal adapted
constellation C(j) which is supplied to the slicer for use.
[0051] FIG. 7 illustrates a network signal transmission system 700
that includes constellation adaptation logic 739 and constellation
selection threshold adaptation logic 738 at the receiver 730 in
accordance with an embodiment of the present disclosure. In a
simplified form, the system 700 includes an optical transmitter
710, an optical fiber cables 740, an optical receiver 720 and an
electrical receiver 730. The optical transmitter 710 has a driver
711 and a Mach-Zehnder interferometer (MZI) 712 and operates to
receive data modulated according to PAM-4. The modulated data is
sent for transportation through the optical fiber cable 740. The
optical receiver 720 has a photodetector (PD) 721 and a
transimpedance amplifier (TIA) 722 and operates to receive data
from the optical fiber cable 740. The electrical receiver 730
receives the signals from the optical receiver 720 and performs
data and clock recovery. The electrical receiver 730 includes an
analog-to-digital converter (ADC) 731, an equalizer 734, a slicer
735, a timing recovery (TR) system 737 and a phase interpolator
736. The slicer 735 is coupled to, or integrates, the threshold
adaptation logic 739 and the constellation adaptation logic 739
that can generate optimal adapted thresholds and optimal adapted
constellations that vary over time due to nonlinearity or other
signal distortions. The threshold adaptation logic 738 and
constellation adaptation logic 739 can be used in any other
suitable signal transmission and processing systems. In some
embodiments, a single circuit as shown in FIG. 2 or 5 can be
implemented to perform both the threshold adaptation and
constellation adaptation using different configurations of data
ranges, TH/C(j) values and the expected count ratios.
[0052] FIG. 8 shows a set of simulated results comparing the symbol
error rates (SERs) resulting from using default slicer thresholds
and the SERs resulting from optimal adapted thresholds obtained in
accordance with an embodiment of the present disclosure. The data
presented in diagrams 810, 820 and 830 are obtained using different
input Signal-Noise-Ratio (SNRs) of constellations in PAM-4. In each
plot, the SNRs for all 4 constellations are identical, 16 dB in
810, 18 dB in 820 and 20 dB in 830. Each data plot shows SER
variation as a function of the amount of constellation #2 shift by
using the default slicer thresholds (811, 821 and 831) and by using
the optimal adapted thresholds (812, 822 and 832). Comparing the
two curves in each plot, it demonstrates that using the optimal
adapted thresholds can significantly reduce SER, and the amount of
SER reduction increases with constellation shift.
[0053] FIG. 9 shows another set of simulated results comparing the
symbol error rates (SERs) resulting from default slicer thresholds
and SERs resulting from the optimal adapted thresholds obtained in
accordance with an embodiment of the present disclosure. The data
presented in diagrams 910 and 920 are obtained using different sets
of input SNRs of constellations in PAM-4. For plot 910, the input
SNRs for the 4 constellations are [18, 18, 18, 14] dB. For plot
920, the input SNRs for the 4 constellations are [20, 20, 20, 16]
dB. Each data plot shows SER variation as a function of
constellation #2 shift by using the default slicer thresholds (911
and 921) and by using the optimal adapted thresholds (912 and 922).
Comparing the two curves in each plot, it demonstrates that using
the optimal adapted thresholds can significantly reduce SER, and
the SER reduction effect increases with constellation shift.
* * * * *