METHOD FOR GENERATING A MULTI-CARRIER REFLECTOMETRY SIGNAL HAVING THE FORM OF A "CHIRP" SIGNAL

Abstract

A method is provided for generating a multi-carrier reflectometry signal intended to be injected into a transmission line in order to identify the presence of at least one possible fault on the line. The method includes: generating, in the frequency domain, a phase-modulated multi-carrier digital signal by: generating a digital signal, phase-modulating the digital signal based on a constellation of symbols, the phase θ.sub.k of each modulated symbol being determined based on the following equality: θ.sub.k=±(α*k.sup.2), where k is the index of each carrier of the signal and varies between 1 and the number of carriers N of the signal, α is a coefficient within the interval

[00001]$\left[\frac{\pi }{N}-\frac{\pi }{2N};\frac{\pi }{N}+\frac{\pi }{2N}\right],$

rounding the obtained phase θ.sub.k to the phase of the symbol of the constellation that is closest, and converting the generated signal into the time domain.

Claims

1. A method for generating a multi-carrier reflectometry signal intended to be injected into a transmission line in order to identify the presence of at least one possible fault on the line, the method comprising the steps of: generating, in the frequency domain, a phase-modulated multi-carrier digital signal by: generating a digital signal, phase-modulating the digital signal based on a constellation of symbols, the phase θ.sub.k of each modulated symbol being determined based on the following equality: θ.sub.k=±(α*k.sup.2), where k is the index of each carrier of the signal and varies between 1 and the number of carriers N of the signal, wherein α is a coefficient within the interval $\left[\frac{\pi }{N}-\frac{\pi }{2N};\frac{\pi }{N}+\frac{\pi }{2N}\right],$ rounding the obtained phase θ.sub.k to the phase of the symbol of the constellation that is closest, and converting the generated signal into the time domain.

2. The method for generating a multi-carrier reflectometry signal according to claim 1, wherein the phase θ.sub.k of each modulated symbol is determined based on the following equality: ${\theta }_k=\pm \left(\alpha *k^2\right)+\gamma \frac{\pi }{N}k+\delta ,$ where γ is a relative integer and δ is a constant.

3. The method for generating a multi-carrier reflectometry signal according to claim 1, wherein the constellation of symbols is a constellation of a PSK phase modulation or of a QAM phase and amplitude modulation.

4. The method for generating a multi-carrier reflectometry signal according to claim 1, wherein the generated signal is a frequency-modulated pseudo-periodic “chirp” signal.

5. The method for generating a multi-carrier reflectometry signal according to claim 1, further comprising the steps of: converting the generated digital signal into an analogue signal, injecting the analogue signal into a transmission line.

6. The method for identifying the presence of at least one possible fault on a transmission line, the method comprising the steps of: generating a multi-carrier reflectometry signal and injecting it into a transmission line by way of the method according to claim 5, and acquiring and analysing the echo of said reflected reflectometry signal in order to deduce therefrom information relating to the detection and/or the location of an impedance discontinuity characteristic of at least one fault.

7. The method for identifying the presence of at least one fault according to claim 6, wherein the step of analysing the echo of the reflectometry signal comprises the substeps of: computing the intercorrelation between the reflected reflectometry signal and the reflectometry signal injected into the line, in order to obtain a reflectogram, and analysing the reflectogram in order to identify at least one amplitude peak characteristic of the presence of a fault on the line.

8. The method for identifying the presence of at least one fault according to claim 6, wherein the step of analysing the echo of the reflectometry signal comprises the substeps of: multiplying the acquired reflectometry signal by a pseudorandom sequence, applying a low-pass filter to the obtained signal, converting the filtered signal into digital, and reconstructing the signal.

9. A computer program comprising instructions for executing the method for generating a reflectometry signal according to claim 1 when the program is executed by a processor.

10. A recording medium able to be read by a processor and on which there is recorded a program comprising instructions for executing the method for generating a reflectometry signal according to claim 1 when the program is executed by a processor.

11. A device for generating a reflectometry signal intended to be injected into a transmission line in order to identify the presence of at least one possible fault on the line, said device comprising means designed to implement the method for generating a reflectometry signal according to claim 1.

12. A device for generating a reflectometry signal intended to be injected into a transmission line in order to identify the presence of at least one possible fault on the line, said device comprising means designed to implement the method for generating a reflectometry signal according to claim 1, the device comprising: a reflectometry signal generator configured so as to implement the method for generating a reflectometry signal according to claim 1, a digital-to-analogue converter (DAC), and a coupling device for injecting the analogue reflectometry signal into a transmission line.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Other features and advantages of the present invention will become more clearly apparent upon reading the following description with reference to the following appended drawings.

[0052] FIG. 1 shows a diagram illustrating the known principle of time reflectometry and its application to the detection of a soft fault,

[0053] FIG. 2 shows an example of two reflectograms, illustrating the trend of the signature of a soft fault, one obtained by injecting a signal having high-frequency components, the other by injecting a signal having low-frequency components,

[0054] FIG. 3 shows a diagram of an OMTDR reflectometry system according to the prior art,

[0055] FIG. 4 illustrates, on multiple graphs, the characteristics of an OMTDR signal according to the prior art,

[0056] FIG. 5 shows a flowchart detailing the steps for implementing the method for generating an optimized OMTDR signal according to one embodiment of the invention,

[0057] FIG. 6 shows two diagrams of constellations of phase-modulated symbols corresponding to two different steps of the invention,

[0058] FIG. 7 illustrates, on multiple graphs, the characteristics of one example of an OMTDR signal obtained using the method according to the invention,

[0059] FIG. 8 shows a comparative reflectogram illustrating the results obtained with a conventional OMTDR signal and an OMTDR signal generated with the invention,

[0060] FIG. 9 shows, on multiple graphs, certain characteristics of a conventional OMTDR signal, for evaluating its compressibility,

[0061] FIG. 10 shows the same graphs as in FIG. 9, but for an OMTDR signal obtained based on one embodiment of the invention,

[0062] FIG. 11 shows a diagram of a compressed-acquisition reflectometry system according to a second embodiment of the invention.

DETAILED DESCRIPTION

[0063] FIG. 1 schematically shows, as a reminder, the operating principle of a reflectometry-based diagnostic method applied to a transmission line L exhibiting a soft fault DNF. The example described below corresponds to a time-domain reflectometry method.

[0064] A reference signal S is injected into the transmission line at a point P. The reflected signal R is measured at the same point P (or at another point of the line). This signal propagates in the line and encounters, while it is propagating, a first impedance discontinuity at the start of the soft fault DNF. The signal is reflected from this discontinuity with a reflection coefficient Γ.sub.1. If the characteristic impedance Z.sub.c2 in the region of the soft fault DNF is less than the characteristic impedance Z.sub.c1 before the occurrence of the fault, then the reflection coefficient Γ.sub.1 is negative and results in a peak of negative amplitude in the reflected signal R. In the opposite case, the reflection coefficient Γ.sub.1 is positive and results in a peak of positive amplitude in the reflected signal R.

[0065] The transmitted portion T of the incident signal S continues to propagate through the line and then encounters a second impedance discontinuity, creating a second reflection of the incident signal with a reflection coefficient Γ.sub.2 of a sign opposite to the first reflection coefficient Γ.sub.1. If Γ.sub.1<0, then Γ.sub.2>0. If Γ.sub.1>0, then Γ.sub.2<0.

[0066] Thus, by observing the reflected signal R, the signature of the soft fault DNF is characterized by two successive peaks of opposing signs, as shown in FIG. 2.

[0067] FIG. 2 shows a time reflectogram that corresponds either directly to the measurement of the reflected signal R or to the intercorrelation between the reflected signal R and the signal injected into the cable S.

[0068] In the case where the injected reference signal is a time-dependent pulse, this corresponding to the case of a time-domain reflectometry method, the reflectogram may correspond directly to the measurement of the reflected signal R. In the case where the injected reference signal is a more complex signal, for example for MCTDR (multi-carrier time-domain reflectometry) or OMTDR (orthogonal multi-tone time-domain reflectometry) methods, then the reflectogram is obtained by intercorrelating the reflected signal R and the injected signal S.

[0069] FIG. 2 shows two reflectograms 201, 202 corresponding to signals having, respectively, two different maximum frequencies. Curve 201 corresponds to a pulse duration 2.ΔT much longer than the time taken by the signal to pass through the soft fault DNF. With the length of the fault being denoted Ld, this duration is equal to Ld/V, where V is the propagation speed of the signal through the cable. The curve 202 corresponds to a pulse duration 2.ΔT much shorter than the time taken by the signal to pass through the soft fault DNF.

[0070] In both cases, the signature 203 of the soft fault, in the reflectogram, is always composed of the succession of a first peak and second peak the signs of which are opposite.

[0071] The distance between the two peaks characterizes the length of the soft fault, and their amplitude characterizes the severity of the soft fault. Specifically, the larger the variation in the characteristic impedance, the higher the amplitude of the signature of the soft fault in the reflectogram.

[0072] As is known in the field of reflectometry-based diagnostic methods, the position d.sub.DNF of the soft fault in the cable, or in other words its distance from the point P of injection of the signal, may be obtained by directly measuring, in the time reflectogram of FIG. 2, the duration t.sub.DNF between the first amplitude peak recorded in the reflectogram (at the x-coordinate 0.5 in the example of FIG. 2) and the amplitude peak 203 corresponding to the signature of the soft fault.

[0073] Various known methods may be contemplated for determining the position d.sub.DNF. A first method consists in applying the relationship linking distance and time: d.sub.DNF=V.t.sub.DNF/2, where V is the speed of propagation of the signal through the cable. Another possible method consists in applying a proportionality relationship of the type d.sub.DNF/t.sub.DNF=L/t.sub.0, where L is the length of the cable and t.sub.0 is the duration, measured on the reflectogram, between the amplitude peak corresponding to the impedance discontinuity at the injection point and the amplitude peak corresponding to the reflection of the signal off the endpoint of the cable.

[0074] FIG. 3 shows a diagram of a system 300 for analysing a fault in a transmission line L, such as a cable or a wired network, implementing an OMTDR reflectometry method according to the prior art.

[0075] Such a system 300 comprises a generator GEN for generating a digital reference signal. The signal is modulated via a phase modulator MOD using a PSK (phase shift keying) modulation. The PSK modulation is associated with a constellation of symbols CS. The example of FIG. 3 shows a constellation of a 16PSK modulation. The bits of the digital signal are randomly associated with the symbols of the PSK constellation. In other words, the modulated symbols are for example generated directly randomly so as to construct the modulated digital signal. The modulated signal is then synthesized in the time domain by way of an inverse discrete Fourier transform module IDFT. The synthesized signal is then converted into analogue via a digital-to-analogue converter DAC and is then injected at a point of the transmission line L by way of a coupler or any other device for injecting a signal into a line. The signal propagates along the line and reflects off the singularities that it contains. In the absence of a fault on the line, the signal reflects off the endpoint of the line if the termination of the line is not matched. In the presence of a fault on the line, the signal reflects off the impedance discontinuity caused by the fault. The reflected signal is propagated back to a measurement point, which may be the same as the injection point or different. The back-propagated signal is converted into digital by an analogue-to-digital converter ADC. A correlation COR is then made between the measured digital signal and a copy of the digital signal generated prior to injection in order to produce a time reflectogram R(t) corresponding to the intercorrelation between the two signals.

[0076] An OMTDR signal is based on OFDM technology and consists in using mutually orthogonal frequency subcarriers to form the test signal.

[0077] Each amplitude, phase or frequency is used to encode a certain number of bits, called a symbol. The binary data may be random or convey an information message.

[0078] The amplitude and the phase of an OFDM subcarrier are fixed by the binary data to be transmitted in accordance with the chosen type of modulation (M-PSK or M-QAM).

[0079] One example of a possible modulation for an OMTDR signal is M-PSK modulation, since this has good autocorrelation properties due to the fact that the spectrum of the signal is flat.

[0080] In a phase shift keying modulation (M-PSK), M is the order of the modulation (4 for Q-PSK, 8 for 8-PSK, 16 for 16-PSK etc.), and each subcarrier S.sub.k is defined by its amplitude and its phase as follows:

[00004]$.Math.s_k.Math.=1\forall f_n\mathrm{et}\varphi \left(k\right)={\varphi }_n=i\frac{2\pi }{M}$

where i is between 0 and M-1.

[0081] As for any digital modulation technique, the phase in question is able to take only a finite number of values. Each of the values of the phase represents a single binary number (also called a symbol), the size of which (and therefore the amount of information transmitted) depends on the number of possible values for the phase. Generally speaking, for a given PSK modulation, the represented binary numbers are all of the same size.

[0082] For example, for an 8-PSK modulation, the sequence of digital data to be sent: 000 001 011 010 101 corresponds to the sequence of symbols: 5 4 3 2 7 and to the sequence of phases 5π/8,4π/8, 3π/8, 2π/8, 7π/8, according to one exemplary implementation.

[0083] An OMTDR signal with symbols (and therefore phases) that are chosen randomly generally has a poor peak-to-average power ratio PAPR. Moreover, such a signal is not compressible in the time, frequency and time/frequency plane, as illustrated in FIG. 4.

[0084] The graphs in FIG. 4 show various characteristics of a conventional OMTDR signal modulated with a 16-PSK modulation.

[0085] FIGS. 4a) and 4b) correspond, respectively, to the modulus of the frequency response of the signal and to the 16-PSK constellation graph of the signal with randomly generated phases.

[0086] FIG. 4c) shows the temporal response of the signal and FIG. 4d) shows the distribution of the signal in the time/frequency plane, obtained by applying a Wigner-Ville transform to the signal.

[0087] It is noted that the signal is dense in the time/frequency plane, in other words that it is not parsimonious. Such a signal is therefore not compressible.

[0088] The invention aims to propose a novel method for generating an OMTDR signal that makes it possible to construct a signal having a “chirp” form while still complying with the constraints of the adopted modulation.

[0089] FIG. 5 schematically shows, on a flowchart, the steps for implementing the method according to the invention for one example in which the modulation that is used is an MPSK modulation.

[0090] In step 501, a digital signal in the form of a sequence of bits is generated.

[0091] The digital signal is modulated by an MPSK modulation by associating each digital symbol with an MPSK constellation point.

[0092] For this purpose, in step 502, a phase is determined for each symbol to be modulated, using the following expression:

[00005]$\begin{array}{cc}{\theta }_k=\pm \left(\alpha *k^2\right)+\gamma \frac{\pi }{N}k+\delta & \left(1\right)\end{array}$

[0093] k is the index of a carrier of the signal, k varying from 1 to N, where N is the number of subcarriers.

[0094] α is a coefficient within the interval

[00006]$\left[\frac{\pi }{N}-\beta ;\frac{\pi }{N}+\beta \right],$

where

[00007]$\beta =\frac{\pi }{2N}$

[0095] γ is a real number that is positive, negative or zero,

[0096] δ is a constant.

[0097] Relationship (1) notably has the effect of generating a signal having the structure of a “chirp” signal.

[0098] However, the phases that are thus generated do not necessarily correspond to symbols of the chosen MPSK constellation.

[0099] In step 503, the phases generated in step 502 are rounded to the phases of the symbols of the MPSK constellation that are closest.

[0100] Finally, in step 504, an inverse discrete Fourier transform step is applied in order to generate the OMTDR signal.

[0101] The choice of the coefficient a makes it possible to structure the signal so that it has the form of a chirp signal. In particular, a coefficient a chosen close to

[00008]$\frac{\pi }{N},$

for example within the interval

[00009]$\left[\frac{\pi }{N}-\beta ;\frac{\pi }{N}+\beta \right],$

where

[00010]$\beta =\frac{\pi }{2N},$

makes it possible to obtain a signal having a chirp signal form while still minimizing the peak factor (PAPR).

[0102] The coefficients γ and δ influence the reduction of the peak factor (PAPR) of the signal.

[0103] According to a first exemplary embodiment of the invention, the coefficient α is taken to be equal to

[00011]$-\frac{\pi }{N},$

the coefficient γ is taken to be equal to 1 and the coefficient δ is taken to be equal to 0.

[0104] In other words, in this example, the phases are generated using the relationship:

[00012]$\begin{array}{cc}{\theta }_k=-\frac{\pi }{N}{k}^2+\frac{\pi }{N}k& \left(2\right)\end{array}$

[0105] FIG. 6 illustrates, on the phase diagram 601, the phases generated using relationship (2) (step 502) and, on the diagram 602, the symbols of the 16 PSK constellation that are obtained by rounding the phases of the diagram 601.

[0106] FIG. 7 shows, on the same graphs as in FIG. 4, the characteristics of the OMTDR signal that are obtained with the first exemplary embodiment of the invention above.

[0107] It is noted that the representation of the signal in the time/frequency plane (graph d)) follows a linear evolution that is characteristic of a chirp signal. This property makes it possible to obtain a signal that is parsimonious and therefore compressible and that has a low peak factor PAPR.

[0108] By way of illustration, Table 1 below shows examples of peak-to-average power ratio (PAPR) results for various PSK modulations and various numbers N of carriers, for a conventional OMTDR signal.

TABLE-US-00001 TABLE 1 Number of points Constellation 256 512 1024 32 9.81 dB 10.46 dB 10.88 dB 16 9.74 dB 10.10 dB 10.91 dB 8 9.52 dB 10.17 dB 10.96 dB 4 9.27 dB 10.74 dB 11.14 dB

[0109] Table 2 below shows the same results for an OMTDR signal obtained with the first exemplary embodiment of the invention.

TABLE-US-00002 TABLE 2 Number of points Constellation 256 512 1024 32 4.11 dB 3.94 dB 3.65 dB 16  3.9 dB 4.68 dB  4.3 dB 8 4.91 dB 5.46 dB 6.64 dB 4 8.31 dB 7.33 dB 7.22 dB

[0110] It is seen that the peak factor PAPR is greatly reduced thanks to the invention.

[0111] Other examples of phase determination laws for obtaining the same technical effects are for example the following laws:

[00013]${\theta }_k=\frac{\pi }{N}{k}^2-2\frac{\pi }{N}k+\frac{\pi }{N}$${\theta }_k=-\frac{\pi }{N}{k}^2$${\theta }_k=\frac{\pi }{N}{k}^2+\frac{\pi }{N}$${\theta }_k=\frac{\pi }{N-1}{k}^2-\frac{3\pi }{N-1}k+\frac{2\pi }{N-1}$

[0112] The invention is applicable to M-PSK phase modulations, but also to M-QAM phase and amplitude modulations.

[0113] According to a first embodiment, the invention may be implemented by way of the device of FIG. 1, the OMTDR digital signal generator being replaced by a generator configured so as to execute the method for constructing a modified OMTDR signal according to the invention.

[0114] FIG. 8 shows two examples of reflectograms 801, 802 respectively obtained with an OMTDR system from the prior art and an OMTDR system according to the first embodiment of the invention.

[0115] In these two examples, an electrical fault is located at a distance of 30 m from the injection point of the signal. This fault is characterized by a peak 803 in the measured reflectogram. It may be seen in FIG. 8 that the improved OMTDR signal according to the invention makes it possible to amplify the peak 803 in comparison with the conventional OMTDR signal. Due to the improvement in the peak factor PAPR of the signal, the detection gain of the peak 803 is improved.

[0116] The invention thus makes it possible to reduce the peak-to-average power ratio of an OMTDR signal in order to improve fault detection precision through analysis of a reflectogram.

[0117] The invention also makes it possible to make an OMTDR signal parsimonious and compressible in the time/frequency domain.

[0118] FIG. 9 illustrates, in three graphs, the fact that a conventional OMTDR signal with random generation of the modulated symbols is neither parsimonious nor compressible.

[0119] A signal is compressible in a domain if the moduli of its coefficients sorted in this domain decrease rapidly. Consideration is thereafter given to the domain of the DCCT (discrete cosine chirp transform) transform, which is used as a parsimonious signal representation base as indicated in reference [1].

[0120] FIG. 9a) illustrates the time/frequency representation of a conventional OMTDR signal and shows that this signal is dense in the time/frequency plane.

[0121] FIG. 9b) is a graph of the representation of the same OMTDR signal after applying a DCCT transform. It may also be noted that the distribution of the DCCT coefficients is dense and not parsimonious.

[0122] Finally, FIG. 9c) shows a curve of the moduli of the DCCT coefficients obtained in FIG. 9b) sorted in descending order. It is seen that these coefficients have a decrease towards zero that is relatively slow. The distribution of the coefficients is distributed over a wide range of values.

[0123] A conventional OMTDR signal is thus not parsimonious and cannot be compressed in the DCCT domain.

[0124] FIG. 10 illustrates the same graphs as in FIG. 9, but this time for an OMTDR signal generated using the invention.

[0125] FIG. 10a) shows that the time/frequency representation of the signal follows a linear evolution.

[0126] FIGS. 10b) and 10c) show that the distribution of the moduli of the DCCT coefficients of the signal is parsimonious, that is to say that a large number of the coefficients are close to zero.

[0127] The OMTDR signal generated using the invention is therefore compressible in the DCCT domain.

[0128] Document [1] describes in detail a method for reducing the sampling frequency of an analogue-to-digital converter in a reflectometry system when the signal that is used is compressible in the DCCT domain.

[0129] FIG. 11 shows a diagram of a reflectometry system 110 according to a second embodiment of the invention.

[0130] The system 110 comprises a module 100 for generating an OMTDR signal according to the invention, comprising at least a module 101 for generating phases and a module 102 for rounding the generated phases to the closest symbols of the chosen constellation.

[0131] The system 110 then comprises a modulator MOD, an inverse Fourier transform module IDFT and a digital-to-analogue converter DAC. These three elements are identical to those already described in FIG. 1.

[0132] The system 110 differs from the reflectometry system described in FIG. 1 in that the analogue-to-digital converter ADC is replaced by a compressed-acquisition system ACQ that makes use of the parsimonious nature of the generated OMTDR signal.

[0133] The system ACQ is described in detail in document [1], to which those skilled in the art may refer for more information with regard to its implementation.

[0134] The system ACQ comprises a multiplier or mixer MUL that has the role of multiplying the signal measured at the coupler output by a pseudorandom sequence of +/−1 values. The mixer MUL operates at a frequency fp that may be greater than the Nyquist frequency fs.

[0135] The system ACQ then comprises a low-pass filter FIL the cutoff frequency of which depends on the desired compression factor, and then an analogue-to-digital converter ADC that operates at a sampling frequency fm that is lower than the frequency fp of the signal.

[0136] A module RS for reconstructing the signal makes it possible to reconstruct the signal before performing the intercorrelation COR with a copy of the generated signal.

[0137] Various techniques for reconstructing the signal may be implemented by the module RS. One possible exemplary implementation consists in applying a greedy algorithm, making it possible to iteratively construct a parsimonious approximation of the signal. One example of a greedy algorithm is the “orthogonal matching pursuit” algorithm described in reference [2].

References

[0138] [1] “Ajamian, T. (2019). Exploration of Compressive Sampling for Wire Diagnosis Systems Based on Reflectometry (Doctoral dissertation, École centrale de Nantes)” [0139] [2] Joel A Tropp and Anna C Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit”, in: IEEE Transactions on information theory 53.12 (2007), pp. 4655-4666.