U.S. patent application number 14/819798 was filed with the patent office on 2015-12-03 for methods and systems for analyzing decomposed uncorrelated signal impairments.
The applicant listed for this patent is Tektronix, Inc.. Invention is credited to Maria Agoston, Kan Tan, Pavel R. Zivny.
Application Number | 20150350042 14/819798 |
Document ID | / |
Family ID | 46753966 |
Filed Date | 2015-12-03 |
United States Patent
Application |
20150350042 |
Kind Code |
A1 |
Zivny; Pavel R. ; et
al. |
December 3, 2015 |
METHODS AND SYSTEMS FOR ANALYZING DECOMPOSED UNCORRELATED SIGNAL
IMPAIRMENTS
Abstract
Method and systems are described for estimating signal
impairments, in particular jitter that includes uncorrelated,
non-periodic signal impairments. One system may take the form of an
oscilloscope. The estimates may take the form of a probability
density function (PDF) for uncorrelated signal impairments that has
been modified to replace low probability regions with a known
approximation and an extrapolation of the known approximation.
Inventors: |
Zivny; Pavel R.; (Portland,
OR) ; Agoston; Maria; (Beaverton, OR) ; Tan;
Kan; (Portland, OR) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Tektronix, Inc. |
Beaverton |
OR |
US |
|
|
Family ID: |
46753966 |
Appl. No.: |
14/819798 |
Filed: |
August 6, 2015 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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13337052 |
Dec 24, 2011 |
9130751 |
|
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14819798 |
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61448574 |
Mar 2, 2011 |
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Current U.S.
Class: |
375/226 |
Current CPC
Class: |
H04L 1/205 20130101;
H04L 43/087 20130101; H04L 43/045 20130101 |
International
Class: |
H04L 12/26 20060101
H04L012/26 |
Claims
1. A method for estimating a probability density function (PDF) for
uncorrelated signal impairments comprising: modifying a compound
distribution representing acquired data that comprises uncorrelated
signal impairments by, identifying low probability regions in the
distribution; identifying a known approximation that models a
distribution of the low probability regions; removing the low
probability regions; and replacing the low probability regions with
the known approximation and an extrapolation of the known
approximation.
2. The method as in claim 1 wherein the low probability regions are
located at extremes of the compound distribution.
3. The method as in claim 1 further comprising extrapolating the
known approximation to extremes of a specified probability.
4. The method as in claim 1, wherein the known approximation
comprises a polynomial approximation.
5. The method as in claim 1, further comprising generating a
cumulative distribution function (GDF) estimate based on the
compound distribution.
6. The method as in claim 5, wherein the known approximation
comprises a linear polynomial approximation having a Gaussian
distribution in Q space.
7. The method as in claim 5, further comprising converting the GDF
estimate into a modified PDF distribution.
8. The method as in claim 7, wherein the signal impairments
comprise uncorrelated jitter, the method further comprising
generating an accurate estimate of total jitter by convolving the
modified PDF distribution with a data-dependent deterministic PDF
in order to calculate a total jitter distribution and a total
jitter value at a specified bit error rate.
9. The method as in claim 1, further comprising: Identifying lower
probability regions of the compound distribution of uncorrelated
signal impairments, whose probability of occurrence of impairments
is lower than a probability of occurrence of impairments within a
central region of the distribution; determining that the
probability of occurrence of the impairments within the lower
probability regions is sufficiently characterized by the acquired
data to model the lower probability regions as the known
approximation; identifying lowest probability regions of the
compound distribution of uncorrelated signal impairments, whose
probability of occurrence of impairments is lowest than a
probability of occurrence of impairments within the central region
of the estimate and insufficiently represented by the acquired
data; and replacing the lower probability region with the known
approximation and replacing the lowest probability region with at
least an extrapolation of the known approximation.
10. The method as in claim 1, wherein the uncorrelated signal
impairments comprise comprises non-periodic, uncorrelated
jitter.
11. The method as in claim 1, wherein the uncorrelated signal
impairments comprise noise.
12. A system for estimating a probability density function (PDF)
for uncorrelated signal impairments comprising: a controller
operable to execute instructions for modifying a compound
distribution representing acquired data that comprises uncorrelated
signal impairments by, identifying low probability regions in the
distribution; identifying a known approximation that models a
distribution of the low probability regions; removing the low
probability regions; and replacing the low probability regions with
the known approximation and an extrapolation of the known
approximation.
13. The system as in claim 12, wherein the known approximation
comprises a polynomial approximation.
14. The system as in claim 12, wherein the controller is further
operable to execute instructions for generating a cumulative
distribution function (GDF) estimate based on the compound
distribution.
15. The system as in claim 14, wherein the known approximation
comprises a linear polynomial approximation having a Gaussian
distribution in Q space.
16. The system as in claim 14, wherein the signal impairments
comprise non-periodic, uncorrelated jitter, and the controller is
further operable to execute instructions for, converting the GDF
estimate into a modified PDF distribution, and generating an
accurate estimate of total jitter by convolving the modified PDF
distribution with a data-dependent deterministic PDF in order to
calculate a total jitter distribution and a total jitter value at a
specified bit error rate.
17. The system as in claim 12, wherein the system comprises an
oscilloscope.
18. The system as in claim 12, further comprising: a user interface
for activating signal impairment analysis, and for indicating when
the analysis is completed; and a display unit for displaying the
user interface.
Description
RELATED APPLICATIONS
[0001] This application claims priority to U.S. Non-provisional
application Ser. No. 13/337,052 filed Dec. 24, 2011, which in turn
claims the benefit of U.S. Provisional Application No. 61/448,574
filed Mar. 2, 2011, both of which are incorporated by reference
herein.
[0002] This application is also related to U.S. Non-Provisional
application Ser. No. 13/081,369 filed Apr. 6, 2011, incorporated by
reference herein. To the extent that any of the disclosure in U.S.
Non-Provisional patent application Ser. No. 13/081,369 conflicts or
appears to conflict with the disclosure of the present
specification, the disclosure of the present specification shall
take precedence and govern the resolution of any such conflict.
BACKGROUND
[0003] In the field of high-frequency (e.g., 1 to 40
gigabits/second (Gb/s)) telecommunications and data communications,
a signal that is transmitted from one location to another may
become degraded due to a number of factors. Such factors are
generally referred to as signal impairments. Two types of signal
impairments are jitter and noise. Jitter and noise may be caused by
various types of sources, such as electromagnetic interference,
crosstalk, data-dependent effects, random sources, and so
forth.
[0004] In general, jitter may be identified on the horizontal axis
of an oscilloscope (typically measured in units of time), while
noise may be identified on the vertical axis of an oscilloscope
(typically measured in units of voltage). In slightly more detail,
the term jitter refers to the horizontal displacement from an ideal
position of various aspects of pulses of a signal or waveform, such
as, for example, the displacement of various aspects of pulses of a
signal or waveform within the time domain, phase timing, or the
width of the pulses themselves. The term noise refers to the
vertical displacement of various aspects of pulses of a signal or
waveform, such as for example amplitude error in the signal or
other vertical noise effects.
[0005] Jitter and noise may be "decomposed" (e.g., separated) into
various components in order to aid in the analysis of the total
impairment of a communications link or an associated system (e.g.,
transmitter, receiver, transmitter and receiver pair, electronic
device or component, etc.), as well as to extrapolate or predict
impairments that are typically associated with events of low
probability. Conventional approaches for decomposing jitter include
separating deterministic jitter (DJ) from random jitter (RJ),
extrapolating lower probability events by "reassembling" or
convolving the jitter components to analyze total jitter at a
specific bit error rate (BER), sometimes referred to as TJ@BER.
Similar methods of decomposition can be applied to noise as well.
Complete two-dimensional probability waveforms or eye diagrams may
be developed by combining those two orthogonal distributions.
[0006] FIG. 1 illustrates the decomposition of total jitter. As
shown, deterministic jitter (DJ) 1 may be comprise: (1) periodic
jitter (PJ) 1a, which may include periodic variations of signal
edge positions over time; (2) data-dependent jitter (DDJ) 1b, which
may be dependent on the bit pattern being transmitted within a
given signal, including inter-symbol interference (ISi); and (3)
duty cycle distortion (DCD) 1c, which may be dependent on
transitions between symbols in a given data pattern. While
deterministic jitter 1 may be completely characterized, the
remaining component of total jitter 3, referred to as random jitter
2, can only be described by its statistical properties, e.g. a
distribution. This is sufficient, however, to perform an accurate
analysis of the impairments associated with a given signal.
[0007] FIG. 2 is an illustration of the so-called "spectral"
approach to the analysis of jitter. A jitter spectrum is displayed,
for example, using a logarithmic vertical scale measured in
decibels (dB) and a horizontal scale showing jitter modulation
frequency in gigahertz (GHz). The spectrum can be seen to contain a
number of prominent spikes, some appearing at regular frequency
intervals and others at apparent random locations. These spikes
correspond to deterministic jitter. In a known spectral approach,
the remaining spectral "floor" 200 is assumed to be composed
entirely of random jitter with a Gaussian probability
distribution.
[0008] One limitation of the spectral approach or methodology is
that it appears to require a repeating pattern, at least to some
degree. Another limitation is that the presumption that the random
jitter in the "floor" 200 is best represented by a Gaussian
probability distribution is not always valid. For example, jitter
associated with crosstalk may be non-periodic and uncorrelated with
a given data pattern, while possessing a bounded probability
distribution. The consequence of mistaking bounded jitter for
unbounded (i.e., random) jitter is particularly severe, especially
when jitter measurements are extrapolated and used to measure the
performance of a communication link or device at low bit rates.
Said another way, the spectral approach may fail to isolate random
jitter from other forms of uncorrelated jitter when, for example,
crosstalk is present. As is known in the art, crosstalk occurs
between high-speed channel links, and is mostly characterized as
bounded noise. In its most general form, it is uncorrelated to the
data streams within the links (i.e., the links being analyzed).
When at least some of the crosstalk spectral lines broaden and
flatten they may become undistinguishable from the jitter spectral
floor 200. This increase in the noise and jitter floors (such as
floor 200 in FIG. 2) makes the components of crosstalk
indistinguishable from residual, random elements.
[0009] In sum, while the spectral approach may identify and remove
periodic jitter components, non-periodic, uncorrelated jitter
components may remain. One result is that random jitter
measurements may be severely inaccurate (i.e., overestimated)
which, in turn, results in inaccurate (i.e., overly pessimistic)
estimates of TJ@BER.
[0010] Similar problem exist in other methods as well (i.e., other
than the spectral method). For example, a different approach,
referred to as a "correlation method", is directed at the
separation of jitter components of a data stream even when an
associated data pattern is unknown or non-repeating. In particular,
the correlation approach measures Time Interval Errors (TIE) of the
data stream, estimating ISi and DGD associated with the data
pattern and then subtracting out the ISi and DGD components from
the measured TIE. A spectral approach may then be used to separate
the remaining TIE into periodic and random components. In contrast
to the "repeating pattern" requirement illustrated by the spectral
approach, however, the correlation method may be useful even when a
waveform carries a non-repeating data pattern. Further, the
correlation method may be combined with the spectral approach such
that the correlation method identifies and removes jitter
associated with data dependency, after which the spectral method
identifies the jitter associated with other deterministic
processes. Unfortunately, however, random (but bound) jitter that
is mixed with unbound Gaussian jitter cannot be separately
identified.
[0011] U.S. Pat. No. 7,899,638 entitled "Estimating Bit Error Rate
Performance of Signals", issued to M. Miller on Mar. 1, 2011
(referred to as Miller) appears to describe an estimated cumulative
distribution function (GDF) method, where an estimate of the TIE's
probability density function (PDF) may be obtained from a TIE
histogram. Because it is known that Gaussian, random jitter is only
dominant in the unbounded left and right extremes of Miller's PDF,
the standard deviation of this random jitter may be estimated by
varying the standard deviation of a Gaussian jitter model and
comparing the results to the measured distribution.
[0012] In one specific implementation, a histogram (i.e., sampling
of the PDF) may be mathematically integrated to form an estimated
GDF, which is then plotted using the so-called Q-scale. As is
known, the Q-scale is a mathematical transformation of the GDF's
probability axis, such that a Gaussian distribution may be plotted
as a straight line with a slope inversely related to its standard
deviation. Once the estimated GDF is plotted on the Q-scale,
straight lines may be fit to the left and right asymptotic regions
(according to a predefined minimization criteria), where the slope
of the lines may reveal the standard deviation of the Gaussian
distributions. This process is illustrated by FIGS. 3(A) and (B),
which show two simulated data sets for which this process may be
applied. In each case, the darker line is an estimated GDF derived
from a histogram of measured TIE values. In FIG. 3(A), the data set
is from a random process with a (solely) Gaussian distribution.
Once plotted on the Q-scale, this distribution approximates a
straight line, having a slope equal to 1/.sigma., where .sigma. is
the standard deviation of the Gaussian distribution. In FIG. 3(8),
the data set includes multiple uncorrelated bounded distributions,
as well as at least one Gaussian distribution. The two dotted lines
4, 5 may be used to indicate that linear fits may be made to the
asymptotic extremes of the GDF, as a means of estimating the
standard deviation, CJ, of the Gaussian model parameter for this
data set.
[0013] However, there are several limitations to Miller's
"estimated GDF" method. For example, the method appears to only
provide a way to model Gaussian and aggregated deterministic
components; no modeling parameters are presented to model or
estimate individual bounded jitter components that may be present.
Further, the presence of multiple bounded components (which
typically make up a majority of the jitter being observed,
especially when crosstalk is present) may bias attempts to
accurately measure the standard deviation, .sigma., of the
relatively small Gaussian components. For example, multiple
uncorrelated bound distributions may combine into a distribution
that has extremes resembling a Gaussian distribution (i.e., see the
well known "Central Limit Theorem"). The more (uncorrelated, bound
signal impairment) components are present, the closer the
resemblance. This makes the separation or distinctions
error-prone.
[0014] Heretofore, the limitations discussed above have prevented
the total jitter of a given signal or waveform to be measured
accurately. Lacking accurate estimates, it is difficult to diagnose
the source of jitter much less design a communications system that
minimizes or prevents jitter from interfering with the quality and
integrity of signals within such a system.
[0015] One approach to addressing these limitations is described in
U.S. application Ser. No. 13/081,369 (referred to as the '369
application), mentioned above and assigned to the same assignee as
the present application. As described in the '369 application,
jitter is decomposed into correlated and uncorrelated components,
and the uncorrelated component is further decomposed into bounded,
uncorrelated jitter and random (i.e., unbound) jitter, for example,
by integrating a probability density function (PDF) of the residual
jitter and analyzing the resulting cumulative distribution function
(GDF) curve in Q-space.
[0016] While this approach overcomes some of the limitations
discussed above, it does not address the circumstance where unbound
(random) components and some bound, uncorrelated components of
signal impairments may co-exist. More particularly, because the
unbound component is very difficult to separate from the bound
component, it cannot be easily replaced by a desired, unbound
component's PDF (e.g., an ideal or near-ideal PDF that includes
very low probabilities, far from the mean). Collectively, the
combination of the unbound (random) component and bound,
non-periodic uncorrelated component of signal impairment(s) may be
referred to herein as "residual jitter".
SUMMARY
[0017] In accordance with embodiments of the present invention,
uncorrelated, bounded non-periodic jitter components and an
unbounded, random jitter component are included in an analysis of
so-called residual jitter. Heretofore, the uncorrelated, bounded
non-periodic component was largely ignored--leading to exaggerated
values of BER, particularly in the presence of crosstalk between
signals.
[0018] In particular, the present invention provides methods and
related systems (e.g., an oscilloscope) for estimating a
probability density function (PDF) for uncorrelated signal
impairments (e.g., including non-periodic, uncorrelated jitter or
alternatively, noise components). An exemplary embodiment of such a
method and related system comprises: modifying a compound
distribution representing acquired data that comprises uncorrelated
signal impairments by: (a) identifying low probability regions in
the distribution; (b) identifying a known approximation that models
a distribution of the low probability regions; (c) removing the low
probability regions; and (d) replacing the low probability regions
with the known approximation and an extrapolation of the known
approximation, where the known approximation may be a modeled,
polynomial approximation, or a polynomial approximation having a
Gaussian distribution in Q space when the compound distribution is
integrated to generate a cumulative distribution function (GDF)
estimate.
[0019] In a further embodiment of the invention the GDF estimate
may be converted into a modified PDF distribution, and, thereafter
the modified PDF distribution may be convolved with a
data-dependent deterministic PDF in order to calculate an accurate
estimate of total jitter that includes a total jitter distribution
and a total jitter value at a specified bit error rate.
[0020] In still a further embodiment of the invention, the method
and related system may: (i) identify lower probability regions of
the compound distribution of uncorrelated signal impairments, whose
probability of occurrence of impairments is lower than a
probability of occurrence of impairments within a central region of
the distribution; (ii) determine that the probability of occurrence
of the impairments within the lower probability regions is
sufficiently characterized by the acquired data to model the lower
probability regions as the known approximation; (iii) identify
lowest probability regions of the compound distribution of
uncorrelated signal impairments, whose probability of occurrence of
impairments is lowest than a probability of occurrence of
impairments within the central region of the estimate and
insufficiently represented by the acquired data; and (iv) replace
the lower probability region with the known approximation and
replacing the lowest probability region with at least an
extrapolation of the known approximation.
[0021] In the embodiments directed at the related system, such a
system may comprise a controller operable to execute instructions
for completing the exemplary methods set forth above.
[0022] It should be understood that while the discussion that
follows may be described in terms of the decomposition and analysis
of jitter impairments, the same or substantially similar methods
and related systems may be applied to noise impairments.
[0023] Other and further aspects and advantages of the present
invention will become apparent during the course of the following
discussion and by reference to the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0024] Referring now to the drawings,
[0025] FIG. 1 is a simplified illustration of a conventional,
standard model used to explain the decomposition of jitter
components in signal analysis;
[0026] FIG. 2 is a plot of jitter (on a log scale), as a function
of frequency, showing the presence of spikes (deterministic jitter)
above a "floor" component of random jitter;
[0027] FIGS. 3(A) and (B) contain two plots in Q-space of a
cumulative distribution function (GDF) of a signal, the plot in
FIG. 3(A) being essentially Gaussian, which is depicted as linear
in Q-space, and the plot in FIG. 3(B) containing both Gaussian
components and non-Gaussian components;
[0028] FIG. 4A illustrates a simplified block diagram of one
embodiment of system that includes a jitter decomposition module
for impairment analysis according to embodiments of the present
invention;
[0029] FIG. 4B illustrates a user interface that is a part of a
system for activating and indicating completion of impairment
analyses according to embodiments of the present invention;
[0030] FIG. 5 is a variation of the standard decomposition model of
FIG. 1 that illustrates an overview of a decomposition method
associated with residual jitter in accordance with embodiments of
the present invention;
[0031] FIG. 6 is an estimated probability density function (PDFe)
curve, in particular, a compound distribution curve including
contributions from both an unbound (random), uncorrelated jitter
component and a bound, uncorrelated jitter component according to
an embodiment of the present invention;
[0032] FIG. 7 is an estimated cumulative distribution function
(CDFe) formed from the PDFe of FIG. 6 according to an embodiment of
the present invention;
[0033] FIG. 8 is a truncated version of the CDFe of FIG. 7
according to an embodiment of the present invention;
[0034] FIG. 9 is a CDFe formed in accordance with an embodiment of
the present invention, where ideal, unbound distribution curves
(straight lines in Q-space) are spliced into locations where the
truncations are formed in FIG. 8;
[0035] FIG. 10 is a PDFe formed from the CDFe of FIG. 9 according
to an embodiment of the present invention; and
[0036] FIG. 11 is a high level flow diagram according to
embodiments of the present invention.
DETAILED DESCRIPTION, WITH EXAMPLES
[0037] As mentioned above, it is difficult to properly identify and
analyze the various components of unbounded (random) signal
impairments, particularly in the presence of crosstalk. The present
invention addresses this problem in the manner discussed above and
below, by identifying and separating the contributing factors--both
conventional, "random" jitter (i.e., the unbounded component) and
remaining, bounded components of uncorrelated non-periodic jitter
(a contributor to jitter in the presence of crosstalk), where the
non-periodic jitter is a component decomposed from bounded,
uncorrelated jitter (BUJ). Again, as a reminder to the reader,
though the discussion that follows may be described in terms of the
decomposition and analysis of jitter impairments, the same or
substantially similar methods and related systems may be applied to
noise impairments.
[0038] More particularly, while the inventive techniques disclosed
herein are generally discussed in the context of jitter rather than
noise, the embodiments of the invention disclosed herein can be
used to decompose, isolate, convolve, and/or analyze either jitter
or noise, or both, associated with a signal or waveform. In sum,
the following discussion of jitter should be considered as merely
exemplary of a specific type of signal impairment.
[0039] Prior to describing the details of embodiments of the
inventive methodologies, an embodiment of a related system that may
be used to implement such methodologies will be briefly
described.
[0040] FIG. 4A illustrates a simplified block diagram of one
embodiment of a system 10, which may be an oscilloscope, In
alternative embodiments of the invention the system 10 may comprise
a spectrum analyzer, or a signal analyzer, some combination of the
two, or another type of comparable test and measurement instrument
or device or a simulation of such system whose function(s) is (are)
substantially the same as system 10. In accordance with embodiments
of the present invention, the system 10 may include jitter
decomposition means or module 12. The system 10 may implement or
include various exemplary embodiments of the present invention,
which may be applied in a variety of ways and in a variety of
different applications, including for example, the measurement and
analysis of impairments associated with digital or analog signals
(actual or simulated signals). The signals can be associated with,
for example, high-frequency wired or wireless communication
systems, high-speed memory or other logic circuits, storage
devices, networks, may be simulated, and so forth. The system 10,
and in particular module 12, may be used for precision decomposing,
convolving, and/or analyzing either the jitter or noise impairment
of a signal (actual or simulated), or both.
[0041] In one embodiment of the invention the oscilloscope 10 may
include, for example, one or more input means 14 (for example,
terminals), acquisition means 16, memory means 18, controller or
control means 20 (including jitter decomposition means 12), and a
display unit 22. Control means 20 and, more specifically, jitter
decomposition means 12, alone or in combination with other
components of oscilloscope 10, may implement or cause to be
implemented any of the various embodiments of the present
invention.
[0042] Oscilloscope 10 may have one, two, four, or any number of
channels that are connected to input means 14, suitable for use
with various embodiments as described herein. While components of
oscilloscope 10 are shown to be directly coupled to each other, it
should be understood that oscilloscope 10 may include a variety of
other circuit or software components, inputs, outputs, and/or
interfaces, which are not necessarily shown, but that are disposed
between or otherwise associated with the illustrated components of
oscilloscope 10.
[0043] One or more actual or simulated, analog or digital waveforms
or electrical signals (collectively referred to as "signals") may
be received at input means 14. Acquisition means 16 may include,
for example, known electronic circuitry and/or devices for at least
receiving the signal from terminals 14, sampling the signal and
converting the signal into digitized samples. The so "acquired
data" may then be stored in memory means 18. The acquired data may
include one or more data patterns 24. As used herein the term
"acquired data" will be understood to include the reception of an
original input signal, sampling of such a signal and the conversion
of such a signal into digital samples or bits when the signal is an
analog signal. Memory means 18 may be any suitable recordable
medium or storage medium capable of storing the acquired data,
including the one or more data patterns 24. Memory means 18 may,
for example, take the form of RAM, ROM and/or cache memory. RAM
memory may be operable to store volatile data, such as the acquired
data and corresponding data patterns 24 generated by the
acquisition means 14. If required or desired, the memory means 18
may also store one or more time interval error (TIE) values (not
shown) for comparison with the one or more data patterns 24. Yet
further, memory means 18 may also store executable instructions
that may be accessed by control means 20.
[0044] Alternatively, the acquired data, corresponding data
patterns 24, TIE values and executable instructions may be stored
in a recordable medium separate from memory means 18.
[0045] Control means 20 may be operatively coupled to memory means
18 and display unit 22. Control means 20, and in particular the
jitter decomposition module 12, may be operable to access and
process acquired data from memory means 18 in order to generate
corresponding jitter distributions, histograms, probability density
function curves, cumulative distribution function curves, Q-space
plots, traces and/or other jitter measurements, and all of the
elements of the inventive methods and processes described herein,
any and or all of which may be displayed by, and on, display unit
22. As indicated above, control means 20 may include the jitter
decomposition module 12. Components of control means 20 and/or
jitter decomposition module 12 may take the form of, or be
implemented using, hardware, software, firmware, or by some
combination thereof. For example, executable instructions for
implementing the inventive methods and processes described herein
and for otherwise controlling the oscilloscope 10 may be stored and
accessed from memory means 18, more particularly, for example from
a ROM, by processing means 20 which includes the jitter
decomposition module 12. Alternatively, the executable instructions
may be stored and accessed from external or internal mass storage
media of a mass storage unit which in some embodiments may be
included within memory means 18. The control means 20 may be
implemented as, for example: one or more programmable
microprocessors, such as those designed and developed by Intel
Corporation; or multiple programmable controllers; and/or one or
more programmable digital signal processors (may be collectively
referred to as "controller" or "controllers" herein). In yet
another embodiment, when the control means 20 is implemented using
multiple controllers one may be used to control the acquisition and
processing of input signals while the second may control the other
operations of the oscilloscope 10. The oscilloscope 10 may be
further controlled using a Windows.RTM. Operating System, such as
Windows XP.RTM., designed and developed by Microsoft, Corporation
that is stored, for example, within associated memory means 18 and
accessed, for example, by one or more controllers 20.
[0046] In some embodiments, control means 20 may exchange
information related to impairments (e.g., jitter) with an external
device 30 via a conductor such as a bus or a wire. External device
30 may include, for example, a computer separate from oscilloscope
10, or an external memory device (e.g., mass storage unit), among
other possibilities. Control means 20 may transmit information
concerning jitter analysis to external device 30, and/or receive
information from external device 30 to enhance the jitter analysis
performed by oscilloscope 10.
[0047] Turning to FIG. 4B, there is depicted a user interface 90
that may be part of the system 10 for activating signal impairment
analysis (e.g., estimation of a probability density function (PDF)
for non-periodic, uncorrelated jitter), and for indicating when the
analysis is completed. In one embodiment the user interface 90 may
be a part of the display unit 22, and, thus, the display unit may
be operable to display the user interface 90. In accordance with an
embodiment of the invention, an activation icon 92 may be included
in the interface 90 which when clicked with a mouse, touched with a
finger or otherwise activated begins the process of executing the
signal impairment methods and process(es) described herein. A save
icon 102 may be selected to (e.g., clicked, touched) to save the
results of such methods and processes, for example in memory means
18. The user interface 90 may also include icon 103 that may be
displayed for indicating when the methods and processes described
herein are completed. It should be understood that the positioning
of the icons 92, 102 and 103 is only for illustrative purposes and
that their position may be altered without changing their function
or the scope of the invention. Further, though shown as three
separate icons, one or more of the icons 92, 102 and/or 103 may be
combined into as few as one icon (e.g., an icon that blinks at a
certain rate depending on its function, or uses different colors
depending on its function) or may be further separated into
additional icons.
[0048] FIG. 5 is a diagram which illustrates an overview of a
decomposition method associated with residual jitter in accordance
with embodiments of the present invention. As shown, the method
involves separating total jitter 100 into deterministic
(correlated) jitter 110 and uncorrelated jitter 120.
[0049] Deterministic jitter 110 includes the following components:
periodic jitter 111, data-dependent jitter 112, and duty cycle
distortion 113, all of which may be processed in a conventional
manner.
[0050] The present invention is concerned with understanding and
evaluating the components of uncorrelated jitter 120. As mentioned
above, particularly in the presence of crosstalk, uncorrelated
jitter will comprise both bounded and unbounded components.
Therefore, any measurement that presumes that this component can
merely be represented as Gaussian-distributed random (i.e.,
"unbound") jitter may improperly characterize total jitter @bit
error rate (TJ@BER).
[0051] Uncorrelated jitter 120 may be decomposed into both random
jitter 121 and bounded uncorrelated jitter (BUJ) 122 using, for
example, the techniques set forth in U.S. application Ser. No.
13/081,369. Further, BUJ 122 may be further decomposed in the
frequency domain into a periodic jitter (BPJ) component 123 and a
non-periodic jitter (NPJ) component 124. Periodic component 123 may
be converted from the frequency domain to the time domain, and
studied in the same manner as the deterministic components using
techniques known in the art.
[0052] What remains is to extract the remaining uncorrelated
elements of jitter, namely, the bounded, uncorrelated non-periodic
jitter (NPJ) component 124 and random jitter (RJ) 121 that is
referred to as residual jitter herein in order to, ultimately,
accurately estimate a total jitter at bit error rate (TJ@BER). In
accordance with an embodiment of the invention, this may be
accomplished by analyzing a compound probability density function
estimate (PDFe), which includes information associated with both of
these components.
[0053] FIG. 6 depicts an exemplary compound PDFe 600 of
uncorrelated unbound and bound components (residual jitter) in
accordance with an embodiment of the present invention. In this
embodiment of the invention: 1) it is assumed that regions A-D of
the PDFe 600 are indicative of low probability distribution
behavior associated with random jitter components; 2) the random
jitter distribution in regions A-D may be modeled or estimated as a
single sigma (.sigma.) Gaussian function (and generally different
for the rise and fall edges of a given data pattern); 3) it is
assumed that a statistically significant amount of data has been
acquired by the acquisition means 16 in FIG. 4A, for example, and
is able to populate bins representing low probability events; 4) it
is assumed that a non-periodic jitter component exhibits a bounded
distribution; and 5) it is assumed that jitter, including
crosstalk-induced impairments, is stationary.
[0054] It should be noted here that, as is known in the art, a test
and measurement instrument referred to as a bit error rate test set
(BERT) may be used to measure a bit error rate. While BERTs offer
the advantage of being able to sample large amounts of data
associated with an incoming signal, thus making their measurement
of BER highly accurate, the time it takes to complete such a
measurement is sometimes unacceptably long for a given application.
Thus, the ability to make BER computations using a relatively
small, yet statistically significant amount of acquired data, using
an oscilloscope or another comparable device offers significant
advantages. Such computations must, however, be accurate in order
to be reliable. In relation to the present invention this accuracy
may be obtained by ensuring that the components of residual jitter
in regions A-D are identified and accurately estimated.
[0055] Yet further, it should also be noted here that prior to the
present invention, prior art techniques were unable to accurately
model or convert the non-periodic, uncorrelated jitter impairments
represented by regions A-D in FIG. 6--whose occurrence or
probability is either: (a) lower when compared to the impairments
represented by central region CR (regions A and B) or (b) the
lowest when compared to central region CR (regions C and D)
(collectively lower and lowest may be referred to as "low")--to
regions which are associated with known, predictable distributions,
such as regions E and F in FIG. 9. In the embodiment of FIG. 9,
regions E and F may comprise linear polynomial approximations with
slopes of 1/.sigma. (i.e., Gaussian distributions).
[0056] In more detail, regions A and B in FIG. 6 represent regions
that include impairments that may be modeled by polynomial
approximations, such as linear polynomial approximations (e.g.,
when the PDFe is converted to a CDFe in Q-space) having a Gaussian
distribution. Specifically, the acquired data used to create
regions A and B represents impairments that have a lower
probability of occurrence (i.e., distribution) than the central
region CR. Even though their probability of occurrence is low, the
present inventors discovered that the amount of acquired data from
an input signal is enough for the controller 20, and in particular
the jitter decomposition module 12, to process and determine that
the probability distribution, though lower, can be modeled as a
known approximation, such as a polynomial approximation (in
Q-space, a linear polynomial approximation with a slope of
1/.sigma. (e.g., Gaussian distribution).
[0057] The present inventors use this discovery to convert not only
regions A and B, but also regions C and D of the PDFe estimate 600
into an estimate that accurately and properly describes unbounded,
random impairments, and bounded, uncorrelated non-periodic
(residual jitter) impairments. Further, though it is preferable for
the PDFe 600 to already have had correlated and periodic jitter
impairments removed, the inventive methods and related systems may
also be applied to situations where some periodic jitter
impairments remain.
[0058] In accordance with an embodiment of the invention, such an
estimate may be generated as follows.
[0059] In an embodiment of the invention, given a compound
distribution (e.g., PDFe 600 in FIG. 6) representing acquired data
that includes uncorrelated unbound and bound components (residual
jitter), such a compound distribution may be modified by: (a)
identifying low probability regions in the distribution; (b)
identifying a known approximation that models a distribution of the
low probability regions; (c) removing the low probability regions;
and (d) replacing the low probability regions with the known
approximation.
[0060] By "known approximation" is meant, for example, a known
probability model that is used to estimate an actual probability
distribution of impairments in the low probability regions.
[0061] Regarding steps (a) and (b), the identification of low
probability regions may include identifying "lower" probability
regions, such as regions A and B in FIG. 6, whose probability of
occurrence of impairments is lower than the probability of
occurrence of impairments within a central region, CR, in FIG. 6.
Once identified, the embodiments of the present invention may then
determine that the probability of occurrence of the impairments
within regions A and B, though lower than region CR, is nonetheless
sufficient enough for the controller 20, and in particular the
jitter decomposition module 12, to determine that the probability
distribution can be modeled as a known approximation, such as a
polynomial approximation (e.g., linear polynomial approximation
with a slope of 1/.sigma. (e.g., a Gaussian distribution). Said
another way, the amount of data (probability distribution) that has
been input and acquired by acquisition means 16, though low, is
sufficient to allow the jitter decomposition module 12 to allow
characterize the acquired data using a model of a known
approximation (e.g., as a polynomial approximation, in particular a
linear polynomial approximation having a Gaussian distribution when
represented as a CDFe in Q-space).
[0062] In addition, steps (a) and (b) include the identification of
"lowest" probability regions, such as regions C and D in FIG. 6,
whose probability of occurrence of impairments is lowest when
compared to the probability of occurrence of impairments within
central region, CR, in FIG. 6. Once identified, in embodiments of
the present invention, unlike regions A and B, the present
inventors discovered that the probability of occurrence of
impairments within regions C and D is too low to initially model
these regions as a known approximation, such as a polynomial
approximation. Said another way, the amount of data (probability
distribution) that has been input and acquired by acquisition means
16, stored in memory means 18 is insufficient, such that the jitter
decomposition module 12 cannot initially characterize the acquired
data (i.e., determine that the probability distribution can be
modeled as a known approximation). Nonetheless, the present
inventors next discovered and determined that this problem could be
solved by extrapolating the known approximation, such as the
polynomial approximations used to model regions A and B, to model
regions C and D as well.
[0063] As used herein, it should be understood that the term "low",
as used in the phrase "low probability region" is meant to include
both a "lower" probability region and "lowest" probability
region.
[0064] In one embodiment of the invention, the PDFe 600 shown in
FIG. 6 may be converted into the CDFe 700 shown in FIG. 7 using the
identification and determining steps described above and below.
[0065] In yet more detail the identification and determination
steps may be completed as follows. First, the controller 20 may be
operable to access stored executable instructions from the memory
means 18 that enable the controller 20 to identify data that has
been input and acquired by acquisition means 16 and stored in
memory means 18 representing regions A through D in FIG. 6.
Continuing, again, even though the probability of occurrence of
data in regions A-D is low, the amount of identified, acquired data
(probability distribution) in regions A and B is sufficient enough
for the controller 20, and in particular the jitter decomposition
module 12, to process and determine that the probability
distribution for regions A and B can be modeled as a known
approximation, such as a polynomial approximation (e.g., a linear
polynomial approximation with a slope of 1/.sigma., having for
example, a Gaussian distribution when depicted as a CDFe in
Q-space), a model that can be extrapolated into regions C and D.
Thus, in accordance with the present invention the controller 20
may be operable to first identify acquired data associated with low
probability of occurrence in regions A through D of the PDFe
estimate shown in FIG. 6, and then process the data in order to
determine that the data can be modeled as (i.e., corresponds to) a
known approximation, such as a polynomial approximation Once the
controller 20 has determined that the data within regions A-D may
be so approximated, the controller 20 may be operable to generate
an estimate of the PDFe in Q-space in the form of a CDFe. In
particular, the controller 20 may be operable to generate an
estimate CDFe 700 in FIG. 7. The estimate includes linear
polynomial approximations with slopes of 1/a, having for example,
Gaussian distributions (i.e., lines m1 and m2 in FIG. 7).
[0066] In an embodiment of the invention, to complete the
identification and determination steps in the generation of the
CDFe in FIG. 7, the controller 20 may be operable to access and
execute stored instructions from memory means 18 and access
acquired data from memory means 18. Further, to model the acquired
data representing regions A-D as a linear polynomial approximation
(e.g., straight lines m.sub.1 and m.sub.2 in FIG. 7), the
controller 20 may be operable to access and execute stored
instructions in memory means 18 and acquired and unacquired data
(e.g., data based on a stored model) from memory means 18 that
represent a known probability distribution, for example a linear
polynomial approximation having a Gaussian distribution.
[0067] CDFe 700 depicted in FIG. 7 represents an intermediate CDFe
that may be generated by the controller 20.
[0068] Regarding steps (c) and (d) above, once the present
inventors discovered that regions A-D of the PDFe 600 estimate in
FIG. 6 could be modeled as known approximations, such as linear
polynomial approximations using, for example, the Q-space CDFe 700
in FIG. 7, the inventors then discovered a way to complete this
modeling. In an embodiment of the invention, regions A-D of PDFe
600 in FIG. 6 or regions modeled by the lines m1 and m2 in FIG. 7
may be truncated or otherwise removed and replaced by such known
approximations.
[0069] FIG. 8 depicts another intermediate CDFe estimate that may
be generated by the controller 20 upon truncation of the low
probability regions of the CDFe estimate 700 in FIG. 7.
[0070] FIG. 9 depicts yet another intermediate CDFe estimate that
may be generated by the controller 20 upon replacement of the low
probability regions with "spliced in" known approximations, such as
linear polynomial approximation regions having, for example,
Gaussian distributions.
[0071] In more detail, in an embodiment of the invention to
complete the truncation and replacement steps, the controller 20
may be operable to execute instructions from memory means 18 to
first truncate or remove the acquired data representing the low
probability regions and then replace the truncated regions with
data that comprises a known approximation, such as polynomial
approximations or linear polynomial approximations (when the
impairments are displayed in a Q-space, CDFe) where the
approximations may be extrapolated into the lowest probability
regions. It should be understood that the data corresponding to the
known approximation (e.g., best fits lines m1 and m2) may be
generated by the controller 20 based on the acquired data and
unacquired or generated data that fits a known probability model
that is used to estimate an actual probability distribution of
impairments in the lower and lowest probability regions. (e.g.,
best fit curves of polynomial approximations that may be stored in
memory means 18 and accessed by controller 20).
[0072] It should be noted that while the low probability regions in
FIG. 6 are located at extremes (left and right) of the compound
distribution, such regions may be located elsewhere and still be
identified, truncated and replaced as described herein. Further, it
should be understood that the known approximation may be
extrapolated to extremes of a specified probability (i.e., a
specified BER).
[0073] Because PDFs are traditionally used, in an alternative
embodiment of the invention the CDFe shown in FIG. 9 may be
converted to a modified PDF 1000, as shown in FIG. 10. It should be
understood that the modified PDF 1000 shown in FIG. 10 may be
generated by the controller 20 using executed instructions and
acquired and unacquired data generated by controller 20 and/or
stored within memory means 18. Further, it should be understood
that the modified PDF 1000 includes known, ideal unbound
distribution regions (polynomial approximation regions) E, F
(associated with regions A, C and B, D respectively) instead of the
low probability regions. Such a modified PDF estimate 1000 may be
viewed as partially a PDF (in low probability regions) and
partially a PDFe (in the central, high probability region), where
this estimate has the property of closely matching the convolution
of an ideal PDF with a bound PDFe.
[0074] In accordance with an embodiment of the invention, an
accurate estimate of total jitter (RJ) may be generated by
convolving the modified PDFe shown in FIG. 10 with a PDF of
data-dependent deterministic components (as represented in FIG. 5,
for example) in order to measure total jitter at bit error rate (TJ
@ BER) using the controller 20 in conjunction with the memory means
18.
[0075] FIG. 11 depicts a simplified flow diagram that summarizes
the elements of the embodiments described above.
[0076] An exemplary method begins at step 200, where an analog
input waveform or signal is input into oscilloscope 10, for
example, and acquired by acquisition means 16. At step 210,
acquired data (e.g., one or more data patterns 24) representing the
input signal may be stored in memory means 18. At step 220, an
uncorrelated jitter histogram may be generated from the acquired
data. At step 230, data dependent jitter may be separated from
uncorrelated jitter using one or more known techniques (e.g.,
spectral, averaging, or the like), and then processed using known
techniques in step 240.
[0077] In accordance with the present invention, the remaining
uncorrelated jitter is further decomposed to separate the bounded
uncorrelated jitter (BUJ) from random jitter. For example, the
uncorrelated jitter component may be subjected to a spectral
analysis at step 250 to remove the periodic component at step 260,
which may be analyzed in the time domain.
[0078] The remaining non-periodic component of the BUJ and the
unbounded jitter may then be used to generate a compound
distribution of these components, such as PDFe 600 in FIG. 6, at
step 270. As set forth above, the non-periodic component of the BUJ
and unbounded jitter is referred to as residual jitter.
[0079] Thereafter, a CDFe such as the intermediate CDFe 700 in FIG.
7 is generated in step 280. Next, regions of low probability may be
identified in step 290, and determined to be modeled as known
approximations, such as linear polynomial approximations in step
290, as shown in the intermediate Q-space CDFe 700 in FIG. 7.
[0080] The low probability regions are truncated (i.e., removed) in
step 300 as shown in the CDFe 800 in FIG. 8. The truncated, low
probability regions are replaced with known, ideal, unbound
distribution functions (polynomial approximation(s)) in step 310,
as shown by the CDFe 900 in FIG. 9. The polynomial approximations
may be linear polynomial approximations having Gaussian
distributions when depicted in Q-space as a CDFe. The truncation
includes replacement of lower probability regions with a model,
known approximation and replacement of lowest probability regions
with extrapolations or extensions of the known approximations that
correspond to specified bit error rates.
[0081] The CDFe may then be converted to a modified PDF that has a
distribution that is partially a PDF (in low probability areas),
and a PDFe in the remaining, high probability areas in step 320, as
shown by the modified PDF 1000 in FIG. 10.
[0082] Although particular embodiments of the invention have been
described, it will be appreciated that the principles of the
present invention are not limited to these embodiments. For
example, while shown as being at the end portions of a PDFe or CDFe
estimate, it should be understood that low probability regions may
also be found at other locations. These regions are defined as
locations where the distribution has already reached the shape of
an estimated distribution function. Further, other predictable or
known approximations, other than linear polynomial approximations
with Gaussian distributions, may be used to model the low
probability regions. Still further, though the above embodiments
focused on analyzing uncorrelated jitter that included non-periodic
components it should be understood that the same or substantially
same methodologies and systems may be used or modified to include
periodic components as well and still fall within the scope of the
present invention. Yet other variations and modifications may be
made without departing from the principles of the invention as set
forth in the following claims.
* * * * *