Patent Publication Number: US-9846188-B2

Title: Detecting, localizing and ranking copper connectors

Description:
FIELD OF THE INVENTION 
     Embodiments of the present invention relate to cable fault measurements and, more particularly, to detecting, localizing and ranking faulty copper connectors. 
     BACKGROUND OF THE INVENTION 
     In testing and troubleshooting electrical cables a typical test involves using test instruments that transmit stimulus signals into one end of a cable and receive and measure any reflections that return. Both time-domain reflectometry (TDR) and time-domain crosstalk (TDX) measurements are subject to two major types of problems. One is attempting to identify all modes of failure and the other is attempting to identify all time domain events. These problems typically introduce many false positive results and often hinder attempts to locate connectors. 
     As data transmission rates have steadily increased, modular connectors with improved crosstalk performance have been designed to meet the increasingly demanding standards. In particular, recent connectors have introduced predetermined amounts of crosstalk compensation to cancel offending near end crosstalk (NEXT). As a result, TDX measurements no longer can robustly detect all connector faults in the cable. 
     SUMMARY OF THE INVENTION 
     The purpose and advantages of the illustrated embodiments will be set forth in and apparent from the description that follows. Additional advantages of the illustrated embodiments will be realized and attained by the devices, systems and methods particularly pointed out in the written description and claims hereof, as well as from the appended drawings. 
     In accordance with a purpose of the illustrated embodiments, in one aspect, a method for detecting failures in electrical cable assemblies is provided. A cable testing instrument obtains frequency domain data representing electrical characteristics of a cable link under test. A number of connectors in the cable link under test is determined based on the obtained frequency domain data. An estimated location of each of the connectors along the length of the cable link under test is determined by the cable testing instrument. The connectors are ranked in accordance with their respective contribution to detected failures in the cable link under test. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying appendices and/or drawings illustrate various, non-limiting, examples, inventive aspects in accordance with the present disclosure: 
         FIG. 1  is a high level flowchart of operational steps for carrying out the failure detection method, in accordance with an illustrative embodiment of the present invention; 
         FIG. 2  a diagram illustrating an exemplary RJ-45 connector type in accordance with the prior art; 
         FIG. 3  is a diagram illustrating a Common-to-Differential Near-End Crosstalk (CDNEXT) signal path, in accordance with an embodiment of the present invention; 
         FIG. 4  is a detailed flowchart of connector detection, localization and ranking step in  FIG. 1 , in accordance with an illustrative embodiment of the present invention; 
         FIG. 5  is a graph illustrating uncompensated TDX signal, in accordance with the prior art; 
         FIG. 6  is a graph illustrating TDX signal compensated for attenuation and dispersion, in accordance with an illustrative embodiment of the present invention; 
         FIG. 7  is a graph showing Hilbert envelope, in accordance with an illustrative embodiment of the present invention; 
         FIG. 8  is a block diagram of a constant false alarm rate (CFAR) detector, in accordance with an illustrative embodiment of the present invention; 
         FIG. 9  illustrates a comparison between the flat and adaptive thresholds, in accordance with an illustrative embodiment of the present invention; 
         FIG. 10  graphically illustrates Dynamic Time Warping (DTW) search path principle, in accordance with an illustrative embodiment of the present invention; 
         FIG. 11  graphically illustrates a potential problem with estimating connector locations based on signal measurements collected by a single test instrument, in accordance with an illustrative embodiment of the present invention; and 
         FIGS. 12A and 12B  illustrate mapping of connector positions from CDX trace to TDX trace, according to some embodiments of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF CERTAIN EMBODIMENTS 
     The present invention is now described more fully with reference to the accompanying drawings, in which illustrated embodiments of the present invention are shown wherein like reference numerals identify like elements. The present invention is not limited in any way to the illustrated embodiments as the illustrated embodiments described below are merely exemplary of the invention, which can be embodied in various forms, as appreciated by one skilled in the art. Therefore, it is to be understood that any structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a basis for the claims and as a representative for teaching one skilled in the art to variously employ the present invention. Furthermore, the terms and phrases used herein are not intended to be limiting but rather to provide an understandable description of the invention. 
     Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Although any methods and materials similar or equivalent to those described herein can also be used in the practice or testing of the present invention, exemplary methods and materials are now described. It must be noted that as used herein and in the appended claims, the singular forms “a”, “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a stimulus” includes a plurality of such stimuli and reference to “the signal” includes reference to one or more signals and equivalents thereof known to those skilled in the art, and so forth. 
     It is to be appreciated the embodiments of this invention as discussed below are preferably a software algorithm, program or code residing on computer useable medium having control logic for enabling execution on a machine having a computer processor. The machine typically includes memory storage configured to provide output from execution of the computer algorithm or program. 
     As used herein, the term “software” is meant to be synonymous with any code or program that can be in a processor of a host computer, regardless of whether the implementation is in hardware, firmware or as a software computer product available on a disc, a memory storage device, or for download from a remote machine. The embodiments described herein include such software to implement the equations, relationships and algorithms described below. One skilled in the art will appreciate further features and advantages of the invention based on the below-described embodiments. Accordingly, the invention is not to be limited by what has been particularly shown and described, except as indicated by the appended claims. 
     In one aspect, various embodiments of the present invention provide a method for detecting failures in electrical cable assemblies. This method includes determining the number of connectors present in the cable link under test, their positions along the length of the cable link and their ranking in accordance with their respective contribution to detected failures in the cable link under test. Given this information, according to an embodiment of the present invention, an “event map” of the tested link may be generated. The generated event map graphically represents the topology of the link along with any additional failure diagnostic information that can be inferred from fault indicators, for example. In a preferred embodiment, the event map illustrates the likely causes of one or more failures in the link under test and their estimated positions along the link, where applicable. 
     Referring to  FIG. 1  of the drawings,  FIG. 1  is a high level flowchart of operational steps for carrying out the failure detection method, in accordance with an illustrative embodiment of the present invention. At step  102 , a frequency-based cable test instrument synthesizes a virtual stimulus by sending a series of sinusoidal frequencies, or “tones”, into a cable link under test. Reflected responses are received as the frequency domain data. 
     In one embodiment, collected frequency domain data may be represented by s-parameters. The s-parameters comprise a set of parameters that describe the scattering and reflection of traveling electromagnetic waves that occur in a link under test. The s-parameters are normally measured as a function of frequency, the measurement representing a complex gain (i.e., magnitude and/or phase). Accordingly, s-parameters are often termed complex scattering parameters. The s-parameters can be used to accurately describe the electronic behavior of a link under linear conditions in the microwave frequency range. 
     The frequency domain is the best domain to collect this information as it can be measured with high Signal-to-Noise Ratio (SNR) leading to accurate results. In a particular embodiment of the present invention, two test instruments may be provided, with a first test instrument (generally referred to hereinafter as a “main unit” or simply as a “test instrument) connected to one end of the link under test, and a second test instrument (generally referred to hereinafter as a “remote unit”) connected to the other end of the link under test. It is noted that both the first and second test instruments may comprise portable or hand held test instruments. The main and remote units may cooperate to effect testing, and may comprise either both active test instruments or an active and more passive test instrument, with the active instrument (e.g., main unit) controlling the testing, and the more passive instrument providing measurement results back to the active instrument. 
     In one embodiment, the frequency domain data acquired by the main and remote units in step  102  may include NEXT measurements and Common-to-Differential NEXT (CDNEXT) measurements on both the main and remote units. Distortion, such as crosstalk, is a common impairment in communication systems. NEXT refers to the undesirable coupling of a signal transmitted in one direction into the signal transmitted in the opposite direction. NEXT is important as it represents the domain in which connectors have the largest impact on performance and may cause a test failure. However, due to manufacturing improvements in NEXT over the years, it has become more and more difficult to detect connectors via measurement of NEXT alone. In particular, recent connectors have introduced predetermined amounts of crosstalk compensation to cancel offending NEXT. 
     The present inventor discovered that empirically connectors exhibit distinctive performance in CDNEXT measurements. Therefore, in a preferred embodiment, CDNEXT measurements can be used for connector detection purposes. CDNEXT concepts are discussed below with reference to  FIG. 3 . While a reliable detection of connector faults method in the link under test requires NEXT and CDNEXT measurement points, in various embodiments, other frequency domain data may also be gathered at step  102  by the main and/or remote units for use in fault diagnosis. 
     Referring back to  FIG. 1 , at step  104 , the main unit may detect, localize and rank connectors in the link under test. Each of these sub-steps is discussed in greater detail below with reference to  FIG. 4 . The end result of step  104  may represent a diagnostic list of connectors detected in the link. This list of connectors may be sorted in accordance with their respective contribution to detected failures in the link under test. At  106 , all detected failures may be analyzed to determine the most likely causes for each of the failures. In one embodiment, the analysis may be based on empirical knowledge, which may be stored in a knowledge-based system. For example, Technical Assistance Center (TAC) agents may have extensive experience debugging failed links. TAC agents&#39; experiential knowledge may be acquired and encoded in the knowledge-based system. In one embodiment, an analysis of the knowledge-based system may be handled by an inference engine using well-known reasoning techniques such as Model Based Reasoning, Rule Based Reasoning or Case Based Reasoning. The inference engine may attempt to determine the most likely causes of each failure and, given this information, may attempt to localize these faults (if possible). For instance, the root cause of failure may be a damaged cable in a link with multiple segments. The inference engine or another suitable knowledge-based system may attempt to determine which segments are problematic in this instance. The end result of step  106  is a list of the most likely causes of failure as well as the location of localizable failures. 
     At step  108 , a graphical representation of topology of the link under test may be presented to a user, for example, via a graphical user interface of the main unit. This graphical representation may be based on information acquired at step  102  and based on the analysis preformed at steps  104  and  106 . In one embodiment, distance values may be displayed, representing the distance from the test instrument to the various located events, as well as connector information and fault information related to connectors along the link under test. Link topology information may also include the failure list generated at step  106 . 
     Various embodiments of the present invention apply in particular to RJ-45 connectors. The description given hereinafter concerns this type of connector. However, the present invention is not limited to this type of connector and may be extended to other types of suitable cable connectors. A conventional RJ-45 connector  200  is shown in  FIG. 2 . Such a connector  200  is common in computer networking, and consists of a cable  210  which contains eight wires and terminates in a plastic or metal housing or plug  214 . More specifically, the eight wires  201 - 208  terminate at pins which are exposed at the end of the plug  214 . The wires  201 - 208  (and corresponding pins) are numbered 1 through 8. The plug  214  is insertable in a corresponding receptacle, and causes the pins on the connector  200  to conductively contact corresponding pins in the receptacle. The overall structure and operation of an RJ45 connector is well known in the art.  FIG. 2  shows that one pair of wires, referred to hereinafter as a first pair,  204 , 205  is centrally positioned and a second pair  203 , 206  straddles the first pair  204 , 205 . Due to this unique geometry, the first pair  204 , 205  and second pair  203 , 206  are the critical areas for the worst cross talk problems in the link under test. However, for CDNEXT, the arrangement of RJ-45 connector  200  results in different performance across the pairs due to the reasons explained below. 
       FIG. 3  is a diagram illustrating a CDNEXT signal path in accordance with an embodiment of the present invention. For purposes of the present invention, CDNEXT is defined as generating a Common Mode (CM) signal  302  on one pair  304   a - b  and measuring a Differential Mode (DM) signal  306  on a different pair  308   a - b  on the same end. A person of skill in the art should recognize an important difference between NEXT and CDNEXT. For NEXT, there are only 6 unique pair combinations due to the symmetric geometry. For example, pairs  201 , 202 - 203 , 206  and  203 , 206 - 201 , 202  are equivalent with respect to NEXT measurements. However, this assumption cannot be made for CDNEXT since the generated and received modes are not the same (the former is CM signal  302  and the latter is DM signal  306 ). Therefore, there are 12 unique combinations for CDNEXT. Generally, for cables, there is no one particular pair that always shows the worst case performance as the geometry in cables is constantly changing down the length of the cable. However, this is not true with respect to RJ-45 connectors. 
     Due to a common mode input signal  302 , the majority of the crosstalk between pairs  304  and  308  is made up of common mode signal. The output is a differential signal  306 , which means that if the crosstalk is similar between the output wires  308   a  and  308   b , the measured crosstalk will be small. Conversely, if the crosstalk is very different between the output wires  308   a  and  308   b , the measured crosstalk will be large. Referring back to  FIG. 2 , said observation means that pairs  201 , 202 - 203 , 206  and  207 , 208 - 203 , 206  (by symmetry) will necessarily have the largest amount of CDNEXT in the RJ-45 connector  200  because the  203 , 206  pair has the largest distance between the wires of any pair and will therefore have the largest difference in the crosstalk received on each wire. This also means that  203 , 206 - 204 , 205  will necessarily have the smallest amount of CDNEXT which is directly opposite of the NEXT results described above with reference to  FIG. 2 . Empirical studies have shown that with respect to time domain and in reference to connector related peak values against so called “noise floor” set by crosstalk in the cable itself, CDNEXT has better SNR than NEXT in the majority of cases. Accordingly, various embodiments of the present invention utilize CDNEXT measurements for connector detection purposes, as described below. 
       FIG. 4  is a detailed flowchart of connector detection, localization and ranking corresponding to step  104  in  FIG. 1 , in accordance with an illustrative embodiment of the present invention. Before turning to description of  FIG. 4 , it is noted that the flow diagram in  FIG. 4  shows example in which operational steps are carried out in a particular order, as indicated by the lines connecting the blocks, but the various steps shown in this diagram can be performed in any order, or in any combination or sub-combination. It should be appreciated that in some embodiments some of the steps described below may be combined into a single step. In some embodiments, one or more steps may be omitted. In some embodiments, one or more additional steps may be included. As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a method or computer program product. Accordingly, aspects of the present invention may take the form of an entirely software embodiment. Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon. In one embodiment, the program code may execute entirely on the cable test instrument (e.g., main unit). 
     At step  402 , frequency domain data in the form of frequency domain NEXT and CDNEXT measurements may be obtained by a test instrument. This step at least partially overlaps with step  102  of  FIG. 1  and is included in  FIG. 4  for ease of illustration. Generally, there is an inherent lack of localization information in the frequency domain data as it represents a weighted sum over all time points for each frequency. Therefore, various embodiments of the present invention contemplate transforming the frequency domain data to the time domain in order to localize connectors. The traditional method for changing between the frequency and time domains is the Inverse Discrete Fourier Transform (IDFT). Typically, this transform is implemented using well-known Inverse Fast Fourier Transform (IFFT). However, some parts of the frequency domain data may have to be corrected because distortion exists in the frequency domain data in the form of attenuation and dispersion due to the natural characteristics of copper cable. In one embodiment of the present invention, the test instrument may utilize a distortion compensation method, described below in conjunction with step  404 , which advantageously converts frequency domain measurements to the time domain measurements and in the process, corrects for distortions leading to traces that may be analyzed for localized information. Traditionally, this distortion compensation method has been applied to calculate Return Loss (RL) and NEXT of events which produce corresponding TDR waveform trace and TDX waveform trace, respectively. However, according to embodiments of the present invention, the same technique may be applied to CDNEXT measurements to produce a Common-to-Differential Crosstalk (CDX) waveform trace which may be utilized for connector detection. 
     At step  404 , the test instrument may generate a CDX trace using distortion compensation method based on acquired CDNEXT measurements. The distortion compensation method will be illustrated below using a mathematic model. 
     In one embodiment, the test instrument may use a swept sine approach with amplitude of 1 and frequency ranging from 1 MHz up to a current maximum of 1200 MHz. This is, in essence, an approximation of an impulse in the time domain. In other words, the frequency domain can be considered as unity over the frequencies of interest, approximating white noise (which is unity over all frequencies). In addition, it is well known that
 
 F   −1 {1}=δ( t )  (1)
 
     where F −1  represents an inverse Fourier transform and δ(t) is a Dirac delta (impulse) in the time domain. It is therefore the case that, because not all frequencies are represented and that an IDFT is used, a swept sine input approximates an impulse response. Under the assumption of linearity, the output Y(f), given an input X(f), is a scaled and phase-shifted version of X(f) at each frequency f. Therefore, under this assumption, a swept sine input will yield the desired output Y(f). 
     It should be noted that to obtain the transfer function R(f) of the link under test in the frequency domain, the output of a linear system is the multiplication of the input by the transfer function of the system. Mathematically, the transfer function can be retrieved through 
     
       
         
           
             
               
                 
                   
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     where the last equality is asserted under the assumption that that X(f)≈1. Furthermore, R(f) can be represented as 
     
       
         
           
             
               
                 
                   
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     where Γ(k) is the crosstalk coefficient at time point k and y(f) is the propagation constant at frequency f. The propagation constant represents a distortion due to the natural characteristics of the link under test and is made up of y(f)=α(f)+jβ(f), where α(f) is the attenuation constant, β(f) is the phase constant, and j is the imaginary unit=√{square root over (−1)}. 
     While the distortion has a natural occurrence in the link under test, for detection purposes, it is necessary to retrieve the underlying undistorted crosstalk coefficients Γ(k). In other words, it is desirable to view the undistorted crosstalk coefficients as a function of time (or distance). To obtain this result, it is noted that in equation (3) above the first index is an undistorted crosstalk coefficient Γ(0) while the remainder of the indices are in some form distorted by e −2ky (f). To compensate for the distortion, the transfer function R(f) can be multiplied by e 2y(f) , which leads to the following equation:
 
 R ( f ) e   2y(f) =Γ(0) e   2y(f) +Γ(1)+ . . . +Γ( N− 1) e   −2(N−2)y(f)   (4)
 
     This transformation can be seen as shifting the crosstalk coefficients such that Γ(1) is shifted to time index k=0. Furthermore, this transformation can be achieved for each time index k=0, 1, . . . , N−1. To actually isolate and retrieve the crosstalk coefficients, the IDFT can be used which results in the following: 
     
       
         
           
             
               
                 
                   
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     However, for each time index k, only the effects from the time point at t=0 are needed for the purposes of this method. Therefore, the crosstalk coefficients can be obtained by: 
                     Γ   ⁡     (   k   )       =       1   N     ⁢       ∑     l   =   0       N   -   1       ⁢           ⁢     Re   ⁢     {       R   ⁡     (   l   )       ⁢     e     2   ⁢           ⁢     ky   ⁡     (   f   )             }                   (   6   )               
for k=0, 1, . . . , N−1, where Re {•} is the real operator. Equation (6) can be rationalized as performing an IDFT for each value of k and only keeping the first point. Equation (6) can also be represented in matrix form as a matrix multiplication (in the same way an IDFT can be represented as a matrix multiplication),
 
                     Γ   ⁡     (   k   )       =       1   N     ⁢     C   ⁡     (   f   )       ⁢     R   ⁡     (   f   )                 (   7   )               
where C(f) is the compensation matrix:
 
     
       
         
           
             
               
                 
                   
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     It should be noted that m may not necessarily be equal to n, but rather may be equal to n/2. The result of this is approximately equivalent to doing a Hilbert transform of Γ(k):
 
 H {Γ( k )}=Γ( k )+ jΓ   1 ( k )  (9)
 
where H denotes a Hilbert transform and F 1  (k) is a 90° phase-shifted version of Γ(k). It is noted that Γ(k) can be found through the use of the real operator Re {•}. The rationale behind the assertion expressed in equation (9) is the definition of the Hilbert transform which considers the positive frequencies only and effectively zeros out the negative frequencies. Therefore, the compensation equation becomes:
 
     
       
         
           
             
               
                 
                   
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     The compensation equation (10) can be refined further to produce a more palatable waveform. Since, as indicated above, frequencies may go up to 1200 MHz, it would be desirable to evaluate only the lower frequency “character” of the waveform and disregard the higher frequency “details” which may have substantially large variance. Therefore, it is preferable to consider only a smaller subset of frequencies, ranging, for example, from approximately 1 MHz up to approximately 400 MHz. The effect of higher frequencies on the end result can be further reduced (while maintaining resolution) through the use of tapering (or windowing). 
     A Fourier transform is a mathematical method of converting an infinitely long, or repetitive, time domain signal into a frequency domain spectrum—a sum of a set of sine waves. A Discrete Fourier Transform (DFT) is a mathematical method of estimating the frequency domain power spectrum of an infinitely long signal, based on a finite length piece of the signal, represented by a finite number of samples of the signal waveform. An IDFT is a method of estimating a time-domain waveform, from a finite set of frequency domain samples covering a finite bandwidth. In either case, i.e. DFT or IDFT, artifacts or errors are made in the process due to the finite nature of the data. In the case of the DFT, sidelobes appear that are caused largely by the abrupt ends of the finite data set. In the case of the IDFT, the time-domain waveform exhibits blurring as well as erroneous peaks and ringing. 
     The classic way of reducing sidelobes is to taper the data set so that the data amplitudes are dropping toward zero at the ends of the finite data. The various classic window taper types, like Rectangular, Hann, Hamming, Blackman, Nutall, Kaiser, Chebyshev (lowest sidelobes but poorest resolution), represent different tradeoffs between resolution and sidelobe levels. In a preferred embodiment, the Blackman taper type may be utilized. Tapering the data is important as there is inherent periodicity in a data record when using a DFT. If the end points do not align, there is a perceived discontinuity between the end points, causing spectral leakage in the frequency domain (also known as bias). This bias tends to dump energy across a wide range of frequencies (as a discontinuity theoretically has energy at all frequencies). The downside of using windows in this context is that the frequency domain data tends to smear slightly due to the wider main lobe of the window&#39;s frequency response. It is noted, due to the convolution property of Fourier transforms, multiplication in one domain is convolution in the other. By multiplying a given data record by a window, the frequency response is convolved with the frequency response of the window. Without applying a data taper, the default window is a rectangular window (due to a finite number of samples) whose frequency response has a narrow main lobe and large side lobes. The narrow main lobe allows for better resolution of events but the large side lobes introduce bias into the frequency response. By using a data taper, the resolution is reduced due to a larger main lobe but much smaller side lobes reduce bias in the frequency response. 
     For similar reasons, windows are preferably applied to the frequency domain measurements prior to compensation. However, in the frequency domain this may be perceived as a low pass filter, as the window is centered at f=0 (DC) and tapers to 0 at f max =400 MHz. Therefore, the final compensation equation can be defined as: 
                     Γ   ⁡     (   k   )       =       1   N     ⁢   Re   ⁢     {       C   ⁡     (   f   )       ⁢     R   ⁡     (   f   )       ⁢     h   ⁡     (   f   )         }               (   11   )               
where h(f) is the aforementioned window. Equation (11) advantageously allows observing the crosstalk values without attenuation or dispersion. This distortion compensation step significantly improves the disclosed connector detection technique as attenuation can bury crosstalk in noise.
 
       FIG. 5  is a graph illustrating uncompensated TDX signal, in accordance with the prior art.  FIG. 5  illustrates an exemplary waveform graph  500  depicting the relationship of signal amplitude and distance. The X-axis  502  represents the distance; the Y-axis  504  represents signal amplitude. In  FIG. 5 , amplitude values corresponding to four different connectors are graphically depicted as regions  506 . The exemplary waveform graph  500  illustrates that when TDX signal is not compensated for attenuation and dispersion the increase in signal amplitude corresponding to connector crosstalk is not easily detectable. 
       FIG. 6  is a waveform graph  600  illustrating TDX signal compensated for attenuation and dispersion, in accordance with an illustrative embodiment of the present invention. Similarly to  FIG. 5 , the X-axis  602  represents the distance; the Y-axis  604  represents signal amplitude. Regions  606  graphically depict increasing amplitudes of an overall detected TDX signal pattern attributed to crosstalk generated by four different connectors. However, in this case, the detected TDX signal is compensated using the distortion compensation method described above. The waveform graph  600  depicted in  FIG. 6  illustrates that it is easier to detect signal amplitude peaks when TDX is compensated for attenuation and dispersion. The waveform graph  600  also shows that crosstalk pulse responses are, in general, bipolar. In other words, crosstalk responses oscillate both positively and negatively. These bipolar responses may be difficult to detect robustly as the positive and negative peaks need not be equivalent in magnitude. It is therefore preferable to convert bipolar responses to unipolar ones. In one embodiment of the present invention, this is done by using the Hilbert envelope. The Hilbert envelope is the inverse Fourier transform of the autocorrelation of the single sided (positive frequency) spectrum. In other words, this envelope is the absolute value of the Hilbert transform of the signal x(t). The most efficient method (and simplest) to calculate the Hilbert transform is by setting the negative frequencies equal to zero and converting to the time domain. In other words,
 
 X ( f )= F{x ( t )}
 
 X (− f ):=0
 
{circumflex over ( x )}( t )= F   −1   {X ( f )}= x ( t )+ jx   1 ( t )  (12)
 
where {circumflex over (x)}(t) is the Hilbert transformed version of x(t) and x 1 (t) is a 90° phase-shifted version of x(t). The Hilbert envelope, also known as the analytic signal, can be arrived at by taking the absolute value of the quantity expressed by equation (12). Thus, the Hilbert envelope is represented by the following equation:
 
 {circumflex over (x)}   A ( t )=|{circumflex over ( x )}( t )|=| x ( t )+ jx   1 ( t )|  (13)
 
It should be noted that if only the positive frequencies are used during the distortion compensation method and an absolute value is used in place of the real operator, no Hilbert transform needs to be directly computed. Therefore, the final compensation equation becomes:
 
     
       
         
           
             
               
                 
                   
                     
                       Γ 
                       A 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       N 
                     
                     ⁢ 
                     
                        
                       
                         
                           C 
                           ⁡ 
                           
                             ( 
                             f 
                             ) 
                           
                         
                         ⁢ 
                         
                           R 
                           ⁡ 
                           
                             ( 
                             f 
                             ) 
                           
                         
                         ⁢ 
                         
                           h 
                           ⁡ 
                           
                             ( 
                             f 
                             ) 
                           
                         
                       
                        
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
       FIG. 7  is a graph showing Hilbert envelope, in accordance with an illustrative embodiment of the present invention.  FIG. 7  depicts both a bipolar signal waveform  702  which oscillates both positively and negatively and a unipolar signal waveform  704  which includes only positive frequencies. Hilbert envelopes are depicted as regions  706 .  FIG. 7  illustrates that it is easier to detect amplitude peaks in the Hilbert envelope  706  than in the original signal as the peak heights of regions  706  are larger and have only positive values. 
     Referring back to  FIG. 4 , after CDX trace is generated, at  406 , the test instrument may determine which pair is best for connector detection as there are twelve distinct pairs associated with this measurement. Continuing the discussion of CDNEXT with respect to conventional RJ-45 connectors, the best pairs for CDX-based connector detection are typically  201 , 202 - 203 , 206  and  207 , 208 - 203 , 206  whereas the best pairs for TDX-based detection are typically  203 , 206 - 204 , 205 . However, this is not always the case for CDNEXT. Therefore, at  406 , the test instrument preferably determines which pairs  201 , 202 - 203 , 206  or  207 , 208 - 203 , 206  are the best for connector detection purposes. In order to quantify the detection quality of each pair of wires, it is desirable to develop some measure of SNR. In one embodiment, this can be done by attempting to estimate the noise floor without the presence of signal events. This data related noise can be removed (without losing too much precision) by using a flat threshold, zeroing out the noise and calculating the energy in the remaining signal. To set the threshold, it can be speculated that connector contributions make up less than 5% of the signal as a whole. Using a normal distribution approximation, it can be assumed that 95% of the signal will be below the mean plus two standard deviations. Accordingly, the threshold can be expressed as:
 
 T= μ + 2 σ   (15)
 
where  μ  is the sample mean and  σ  is the sample variance. These quantities can be calculated from the original signal as:
 
                       μ   _     =       1   N     ⁢       ∑     i   =   0       N   -   1       ⁢           ⁢     x   ⁡     (   i   )             ,           ⁢       σ   _     =       1   N     ⁢         ∑     i   =   0       N   -   1       ⁢           ⁢     (       x   ⁡     (   i   )       -         μ   )     _     2                         (   16   )               
Given value of T, a threshold for signal x(t) can be set, such that:
 
                       x   ~     ⁡     (   t   )       =     {             x   ⁡     (   t   )       ,             x   ⁡     (   t   )       ≥   T               0   ,         otherwise                   (   17   )               
Accordingly, the test instrument can calculate the signal energy for each pair, noting that the threshold is different for every pair:
 
ε j =Σ i=0   N−1     x     j ( i ) 2   (18)
 
where j is the pair number/index. To summarize, at  406 , the test instrument may choose the best pair for detecting connectors by using equation (18) and maximizing ε over j. The pair with the highest energy is preferably chosen.
 
     As previously mentioned, in a particular embodiment of the present invention, two test instruments may be used to collect data, with the main unit connected to one end of the link under test and the remote unit connected to the other end of the link under test. In this particular embodiment the main and remote units may comprise either identical or substantially similar test instruments. It is further noted that detected events close to respective units tend to have high SNR values, decreasing as signal moves further away from the test instruments. Various embodiments of the present invention contemplate the utilization of these large SNR values in combination with the fact that the information provided by the main and remote units is substantially similar. However, according to an embodiment of the present invention, prior to performing connector detection step, the test instrument preferably calculates an adaptive threshold. 
     Referring back to  FIG. 4 , at  408 , the test instrument may calculate an adaptive threshold based on the combination of a flat threshold and a CFAR detector. As discussed above, one of the main problems associated with detecting signal peak values is related to detecting the presence of noise in the signal. The most common solution is to set the signal threshold (i.e., flat threshold) at a certain level and disregard the remaining portion of the signal. For stationary noise, a flat threshold may be appropriate. However, when noise is variable over time or distance, a flat threshold may no longer be sufficient. 
     A commonly used method, intended to produce a constant false alarm rate, is referred to herein as the constant false alarm rate (CFAR) detector. The principle of the CFAR detector is to provide a threshold at each data point based on the local noise present around the so called “Cell Under Test” (CUT). By setting a threshold in this manner, non-stationary noise may be considered if the movement in the noise distribution is “slow enough”. 
       FIG. 8  is a block diagram of a constant false alarm rate (CFAR) detector function, in accordance with an illustrative embodiment of the present invention. The illustrated CFAR function is a cell-averaging constant false alarm rate (CA-CFAR) detector and operates along the training cells  806  (data points). The guard cells  804  are used to prevent from factoring the events present at the CUT  802  into the training cells  806 . According to this method, it is preferable to choose the number of training cells  806  such that the noise distribution present in the training cells  806  is substantially fixed. Given this information, the CFAR detector function can set an adaptive threshold based on finding the sample mean in the training cells  806  for each CUT  802  and multiplying the result by particular factor dependent upon the false alarm rate (probability). It is known in the art that the optimal factor based on CA-CFAR can be calculated using the following equation: 
                   α   =     N   (       P   FA     -     (     1   N     )         -   1     )             (   19   )               
where N is the number of training cells  806  and P FA  represents the probability of false alarm.
 
       FIG. 9  illustrates a comparison between the flat and adaptive thresholds, in accordance with an illustrative embodiment of the present invention. The X-axis  902  represents the distance; the Y-axis  904  represents signal amplitude. First waveform graph  906  in  FIG. 9  represents a discrete signal, second waveform graph  908  represents adaptive threshold with P FA =0.05, third waveform graph  910  represents adaptive threshold with P FA =0.01 and a line  905  represents a flat threshold. Given the two sample events present,  FIG. 9  illustrates that the adaptive threshold  908 ,  910  has the potential for improved performance over flat threshold  905 . In  FIG. 9 , amplitude values corresponding to two detected events are graphically depicted as regions  912 . It can be seen, that in the presented case the flat threshold  905  is not able to isolate both events  912  without capturing noise. 
     It is further noted that for the adaptive threshold to work, a reasonable threshold value should be selected. While it is highly desirable to minimize false alarms, lowering the adaptive threshold value has the undesired side effect of making it more difficult to detect the proper events  912  as well. Theoretically speaking, a P FA  value equal to 0 has a probability of 0 of detecting events and P FA =1 has a probability of 1 of detecting events. This observation leads to the conclusion that the probability of detecting events is directly related to P FA . In other words, a CFAR detector can be selected based on the following degrees of freedom: P FA , N and the number of guard cells. It is important to determine the correct values for those parameters in order to achieve the desired performance from the adaptive thresholds  908 ,  910 . As shown in  FIG. 9 , second waveform  908  representing adaptive threshold with P FA =0.05 captures both events  912  and third waveform graph  910  representing adaptive threshold with P FA =0.01 misses both events  912  because its noise floor estimate values are higher than peak amplitude values corresponding to both events  912 . It is noted that various embodiments of the present invention contemplate usage of other variants of CFAR detector method to calculate the adaptive threshold. Two simplest of these are modifications of the CFAR detector known as the “greatest of” (GO-CFAR) and “least of” (LO-CFAR). These techniques consider the difference in noise levels left and right of the CUT  802 , where the GO-CFAR method uses the larger of the two noise floor estimates and the LO-CFAR method uses the smaller of the two. 
     In some embodiments of the present invention, at  408 , the test instrument may also calculate a composite threshold based on the flat and adaptive thresholds described above. The distortion compensation method discussed above with reference to step  404  relies on estimation of α(f) and β(f) for the link (i.e., cable) under test, where α(f) is the attenuation constant and β(f) is the phase constant. However, these values are not dynamically calculated, but rather being estimated based, for example, on various characteristics of the cable. This estimation has inherent error in precision in generating the proper distortion compensation parameters. Due to the exponential growth of correction from α(f), any estimation error tends to be compounded as distance of the cable under link increases. In addition, points at the remote end of the cable under test tend to be buried in noise generated from measurement noise of the test instrument. Even with distortion compensation, the noise floor tends to rise as signal progresses along the length of cable as depicted by region  608  in  FIG. 6 . This non-stationary nature of the noise floor warrants the use of the adaptive threshold. 
     However, in determining the estimated local noise floor, large point sources corresponding to connectors may be present. These sources may increase the estimate value of the noise floor beyond accurate levels. In order to avoid this problem, all data points above a flat threshold may be set to be equal to the sample mean of the signal. An appropriate choice of flat threshold is the threshold T F  expressed by equation (15) above. Therefore, in order to determine the adaptive threshold signal, the equation (17) can be replaced with the following: 
     
       
         
           
             
               
                 
                   
                     ⁢ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             CDX 
                             , 
                           
                         
                         
                           
                             CDX 
                             ≥ 
                             
                               
                                 μ 
                                 _ 
                               
                               + 
                               
                                 2 
                                 ⁢ 
                                 
                                   σ 
                                   _ 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               μ 
                               _ 
                             
                             , 
                           
                         
                         
                           otherwise 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     It should be noted that in a preferred embodiment, the test instrument performs this manipulation on a copy of CDX trace used for thresholding purposes, rather than the CDX trace generated at step  404 . Applying adaptive thresholding to  (t) signal expressed above (by using, for example CA-CFAR detector) results in generating an adaptive threshold signal. However, due to the increasing of a noise floor as distance increases, this adaptive threshold is more useful for distances closer to the remote end of the cable under test. At smaller distances, the flat threshold T F  performs rather well due to higher SNR value in the cable under test. Therefore, to accommodate both thresholds and gain the benefit of both, at  408 , the test instrument may calculate the overall composite threshold by taking the pointwise maximum of the two thresholds:
 
 T ( k )=max k=0,1, . . . ,N−1   {T   F ( k ), T   A ( k )}  (21)
 
where T F  represents the flat threshold value and T A  represents the adaptive threshold. It should be noted that test instrument may use equation (21) to calculate the composite threshold if the length of the cable under test exceeds a predetermined value. In one embodiment, this predetermined value may be equal to approximately 50 ft.
 
     Referring back to  FIG. 4 , at step  410 , the main and remote units may attempt to find connectors in their respective portions of the link under test using adaptive thresholds described above. For instance, the main unit may detect connectors at one end (closest to the main unit) of the link under test, while the remote unit may detect connectors at the other end (closest to the remote unit). It is noted that in this embodiment, events from the respective remote ends of link under test appear backwards at both units as signal propagates away from each unit. Therefore, according to an embodiment of the present invention, at step  412 , the main unit preferably obtains information related to connectors in the remote portion of the link under test from the remote unit. 
     Next, at  414 , the main unit preferably aligns the connectors in the two signals. In one embodiment of the present invention, the main unit may use dynamic time warping (DTW) to align time domain data corresponding to the respective signals. Generally, when dealing with large amounts of data in multiple time series and trying to discern information across all the time series, data corresponding to different time series is usually not aligned in time exactly. DTW represents a well-known alignment algorithm. The DTW algorithm tries to find, given two sequences or time series, the optimum path (the optimum sequence of matching points) between their start and end points via dynamic programming techniques. Given two time series x 1 , . . . x N  and y 1 , . . . , y M  (of length N and M, respectively), DTW determines the position in the second sequence that the current position in the first sequence should be matched to for each point in the sequence. The end result is a pair of vectors (q 1 , p 1 ), . . . (q T , p T ) of length T that specify that x q     i    and y q     i    occur at the same “corrected” time step. The size of T varies depending on how shifted the events in x are as compared to y. Typically, the larger the shift, the larger the value of T will be and vice-versa. By finding vectors (q, p), the two signals can be overlaid in time by using vectors (q, p) as indices into (x,y) such that x(q) and y(p) will overlap. In one embodiment, at step  414  the conventional DTW algorithm can be implemented. 
       FIG. 10  is a diagram showing the concept of DTW, in accordance with an illustrative embodiment of the present invention. Since DTW is a well-known process, the concept of DTW is graphically shown in  FIG. 10 , with a detailed explanation being omitted. In one embodiment, the X-axis  1002  represents the time domain data collected by remote unit; the Y-axis  1004  represents reference template data, which may comprise time domain data collected by the main unit. DTW uses dynamic programming optimization techniques to achieve some degree of enhanced temporal alignment. The identity time warp waveform  1008  of  FIG. 10  is achieved through the “stretching” and “shrinking” in time by DTW to make one time domain data best match the second time domain data.  FIG. 10  also graphically depicts maximum bandwidth  1006 , which may be used by the DTW algorithm to ensure that the path does not “warp” too far if measurements have been collected by a single test instrument rather than both main and remote units. It is noted that other well-known time-alignment techniques, such as, but not limited to, Hidden Markov Models (HMMs) may be employed in step  414  as well. 
     Referring again to  FIG. 4 , at step  416 , the main unit preferably combines time domain data collected by the main and remote units based on the time-alignment performed at step  414 . The combined aligned time domain data yields better results since it is possible for a single test instrument to miss at least some connectors at the remote end of the cable, as the SNR value is substantially smaller in that portion of the cable under test. 
       FIG. 11  graphically illustrates a potential problem with estimating connector locations based on signal measurements collected by a single test instrument, in accordance with an illustrative embodiment of the present invention. Similarly to  FIGS. 5 and 6 , the X-axis  1102  represents the distance; the Y-axis  1104  represents signal amplitude. The waveform graph  1106  represents a plurality of signal measurements collected only by the main unit and the dotted line  1108  represents a composite threshold calculated in accordance with embodiments of the present invention. Regions  1110  graphically depict peaks of increasing signal amplitudes corresponding to crosstalk generated by a plurality of different connectors along the link under test.  FIG. 11  shows that by using only self-collected data the main unit may fail to detect the last connector corresponding to region  1110   a . However, detecting the same connector will be much easier for the remote unit, since the detectable SNR value as measured by the remote unit at that cable region should be significantly higher, thus making the connector detection much easier for the remote unit. In one embodiment, the main unit may detect connectors at step  416  by zeroing out all data points located below the composite threshold  1108  and by attempting to find the relevant remaining amplitude peaks  1110 . This step may include identifying all local maxima amplitude points (such that the points around the local maxima point are all smaller in magnitude) with a possible constraint that if two local maxima points are discovered in close proximity to each other, the larger of the two local maxima points is chosen and the other is ignored. This aspect may become important as there may be large local oscillations around peaks  1110  that may factor into detection. Thus, by utilizing local maxima amplitude points the main unit may effectively create so called “dead zones” around peak values to simplify the detection practice. It should be noted that, in various embodiments, such dead zones may comprise a few feet depending on the overall length of the cable under test. 
     In summary, step  416  provides mapping of connector positions detected by both devices in respective remote portions of the link under test. It should be further noted that segmentation of the link under test into the first and second portions (as referred to in steps  410 - 416 ) can be done based on the overall length of the link under test estimated by the main unit. 
     At  418 , the main unit may generate TDX trace by performing the aforementioned IDFT calculations on NEXT measurements collected at step  402 . IDFT is an operation for deriving a time series data values from the given frequency domain measurements, as described above. 
     At  420 , the test instrument preferably determines which pair of the wires is best for connector detection purpose with respect to TDX trace. According to an embodiment of the present invention, the test instrument may determine the best pair by identifying the pair with the worst margin. Typically, the pair with the worst margin will have a better SNR value and may provide a more accurate connector ranking based on the failure. Once the test instrument selects the signals corresponding to the pair of interest, the analytic waveform versions of these signals may be obtained according to the description provided above with reference to  FIG. 7 . In accordance with one embodiment of the present invention, this bipolar to analog conversion is done to make it easier to analyze and align the signals. It is noted that the TDX waveform generated at step  418  directly through an IDFT is uncompensated. This waveform is used to provide an accurate ranking of the contributions of each connector on the overall NEXT performance. To illustrate this point, consider that the cable link under test attenuates signals with distance. The NEXT measurements in frequency domain represent this attenuation inherently. Therefore, if NEXT measurements indicate a failure, in order to determine the cause of the failure, the attenuation factor on all the potential sources of failure should be considered. 
     Accordingly, at  422 , to find connectors in the TDX trace, the test instrument preferably analyzes the following waveforms:
 
 CDX=C   −1   {CD NEXT},
 
 TDX=F   −1 {NEXT}  (22)
 
     where C −1  represents the distortion compensation method discussed above with reference to step  404  and where F −1  represents the conventional IDFT method. According to an embodiment of the present invention, all connector positions in CDX trace determined at step  416  can be translated to their respective positions in TDX trace. However, prior to the mapping, the test instrument may adjust the TDX scale to correspond to the CDX scale according to the following formula: 
     
       
         
           
             
               
                 
                   TDX 
                   := 
                   
                     TDX 
                     · 
                     
                       
                         max 
                         ⁡ 
                         
                           ( 
                           CDX 
                           ) 
                         
                       
                       
                         max 
                         ⁡ 
                         
                           ( 
                           TDX 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     In order to align TDX signal with the CDX signal, the test instrument may employ DTW algorithm described above with reference to step  414 . It is noted that for this operation the maximum bandwidth  1006  value may be on the order of 20 units. In other words, the assumption is made that the skew between CDX and TDX positions will be less than 20 units. As a result, the DTW operation, provides two warping vectors (q, p) mapping CDX(q) to TDX(p), which in turn enables the test instrument to map connector locations from the generated CDX trace to the generated TDX trace. 
     According to an embodiment of the present invention, once the test instrument identified all amplitude peak value of interest as described above with reference to step  416  and  FIG. 11 , at step  424  the test instrument preferably uses the warping vectors (q, p) to map connector locations from CDX trace to TDX trace. 
       FIGS. 12A and 12B  illustrate mapping of connector positions from CDX trace to TDX trace, according to some embodiments of the present invention. The waveform graph  1202  in  FIG. 12A  shows uncompensated TDX trace signal generated by IDFT operation based on NEXT measurements. The waveform graph  1204  in  FIG. 12B  shows CDX trace signal compensated for attenuation and dispersion in accordance with embodiments of the present invention. It should be noted that a plurality of dots  1203  in  FIG. 12B  graphically depicts the determined connector positions in CDX trace. At step  424 , the test instrument maps these determined positions  1203  to positions  1201  in TDX trace  1202 . Furthermore,  FIG. 12A  illustrates advantages of the method described herein, as the attenuation effect makes it substantially impossible to detect the last connector position  1201   a  through conventional thresholding means. 
     According to an embodiment of the present invention, at  426 , the test instrument preferably ranks the connectors in accordance with their respective contribution to detected failures in the link under test. Once the test instrument determines an estimated location of each of the connectors as shown in  FIG. 12B , the connector ranking step may be reduced to relative sorting of the amplitude values corresponding to each peak. In other words, connectors corresponding to the tallest peak values  1201   c  will have the largest impact on the failure in NEXT while connector corresponding to the smallest peak value  1201   a  will have the smallest impact. In one embodiment, both CDX trace  1204  and TDX trace  1202  may be presented to a user at step  104  shown in  FIG. 1 . The presented information allows the user to know which connector he should focus on fixing first when the test instrument detects a plurality of failures. 
     In summary, various embodiments of the present invention provide a method for detecting, localizing and ranking copper connectors in electrical cabling assemblies. In one aspect, for connector detection, the preferred embodiment uses CDNEXT measurements to generate a CDX trace. It has been shown that CDX has superior SNR value as compared to TDX in the majority of cases. Furthermore, various embodiments of the present invention utilize the CDX trace to determine the number of connectors. In another aspect, embodiments of the present invention employ conventional DTW method to align time domain data provided by two test instruments connected to the opposing ends of the cable under test. This alignment procedure along with the greater SNR values at respective ends and a calculation of composite threshold based on adaptive thresholding technique enables more robust detection of connectors in CDX trace. In yet another aspect, given detection of connectors in CDX, DTW may be used again to map the connector positions in CDX trace to their respective positions in uncompensated TDX trace. This step facilitates determination of the relative rank of each connector&#39;s contribution to a NEXT failure as this information can only truly be identified in the uncompensated domain. Utilization of DTW method is preferable for this mapping as the connector positions do not align in time. These aspects, collectively, yield the advanced benefits of a robust cable testing method capable of illustrating the likely causes of detected failures and their estimated positions along the link under test. Various other aspects of the invention embodiments are also presented above. 
     The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions. 
     The descriptions of the various embodiments of the present invention have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.