FR2965625A1 - Method for estimating pulse response of e.g. optical fiber network, by short-sighted deconvolution in reflectometry system in electronics field, involves carrying out fine estimation of pulse response by deconvolution using core - Google Patents

Abstract

The method involves introducing a test signal into an input point of a network. A signal is measured in an output point of the network, where the input point and the output point are same. A pulse response is initially estimated (300) by deconvolution of the signal with a core corresponding to the test signal. A deconvolution core is estimated (301) by using the result of the initial estimation of pulse response while considering the distortions introduced by the network. A fine estimation of the pulse response is carried out (302) by the deconvolution using the core. An independent claim is also included for a reflectometry device comprising a unit for generating a test signal.

Description

The invention relates to a method and a device for estimating the impulse response of a cable network by myopic deconvolution and is particularly applicable to the evaluation of the pulse response of a cable network by myopic deconvolution. field of electron reflectometry.

Cables are ubiquitous in all electrical systems, for powering or transmitting information. These cables are subject to the same constraints as the systems they connect and may be subject to failures. It is therefore necessary to be able to test their status and provide information on the detection of defects, but also their location and type, to help with maintenance and prevention. For this, so-called reflectometry methods are implemented. These can also be used to detect faults in an optical fiber network. The principle of OTDR is based on the injection of a test signal. The shape of this signal changes significantly during its propagation back and forth in a cable, these changes being the consequence of physical phenomena of attenuation and dispersion. OTDR methods use a principle similar to that of radar: an electrical signal, the test signal, often broadband, is injected in one or more places of the cable to be tested. Said signal propagates in the cable or network and returns a portion of its energy when it encounters an electrical discontinuity. An electrical discontinuity may result, for example, from a junction, the end of the cable or a fault. The analysis of the signals returned to the injection point makes it possible to deduce information on the presence and the location of these discontinuities, thus possible defects. The analysis of the reflected signals makes it possible to detect singularities, that is to say cable characteristic impedance breaks, the latter also being able to correspond to faults. The signal resulting from the reflectometry is called reflectogram and consists of a plurality of peaks corresponding to the singularities of the network. There may be several peaks by singularity, some corresponding to multiple reflections. In a complex network, the objective is then to determine which peak corresponds to a fault and then isolate it correctly in order to precisely locate said fault. In order to be able to detect a fault within an arbitrarily complex network, it is necessary to measure the variations of the electrical response of said network. The difficulty is then to identify the peak corresponding to the defect in order to be able to locate it. In embedded non-destructive testing systems and in particular for wiretap diagnostics by reflectometry, the bandwidth of the systems is limited. The objective is to obtain signals with the best possible resolution, the resolution being directly dependent on the bandwidth. In order to optimize this resolution, various processing based on a deconvolution of signals can be applied. In the case of reflectometry, high resolution treatments are known, such as those presented in the article by C. Buccella, M. Feliziani and G. Manzi entitled Detection and localization of defects in shielded cells by timedomain measurements with uwb pulse injection and clean algorithm postprocessing, IEEE Transactions on Electromagnetic Compatibility, 46 (4), pp. 597-605, November 2004, as well as in S. Schuet's article entitled Wiring Diagnostics via I1 - regularized least squares, Sensors Journal, IEEE, 20 10 (7) pages 1218-1225, July 2010. The so-called "high resolution" methods correspond to treatments that make it possible to improve the estimation of the delay times in the reflectogram and to distinguish, with respect to one another, several peaks that can be very close. These treatments can be integrated in an embedded system, but they do not take into account the various phenomena of linear distortions which alter the signal, the latter being generally unknown. These linear distortion phenomena are the consequence, for example, of the dispersion in the cables of the network to be tested and the characteristics of the components of the reflectometry measuring system which act as low-pass filters. Taking these distortions into account improves the resolution. Since these distortions are unknown, it is necessary to implement myopic deconvolution methods, also called semi-blind methods. Several methods of this type exist, as described in the article by O. Rosec, JM Boucher, B. Nsiri and T. Chonavel entitled Marine Blind Seismic Deconvolution Using Statistical Methods, IEEE Journal of Oceanic Engineering, 28 (3), pages 502-512, July 2003. A disadvantage of the existing methods is that they require a large amount of calculations which makes it difficult to integrate them into a reflectometry system. An object of the invention is in particular to overcome the aforementioned drawbacks. To this end, the subject of the invention is a method of estimating the impulse response h (t) of a cable network by myopic deconvolution, a test signal s (t) being introduced at an entry point of the network and a signal y (t) being measured at a network exit point, the entry point and the exit point being preferably the same. The method comprises a step of initial estimation of the impulse response h (t) by deconvolution of the signal y (t) with a core corresponding to the test signal s (t), a step of estimating a deconvolution kernel g (t) using the result of the initial estimate of the impulse response h (t), said kernel taking into account the distortions (t) introduced by the network. The method further comprises a step (302) of refined estimation of h (t) by deconvolution using the core g (t). According to one aspect of the invention, the initial estimate of the impulse response h (t) is obtained by applying the CLEAN algorithm. The refined estimate of h (t) is obtained, for example, by deconvolution L1. According to another aspect of the invention, it is assumed in the step of estimating the deconvolution kernel g (t) that the function f (t) is centered around the instant t = 0. In one embodiment, the deconvolution nucleus g (t) is obtained by contruction and resolution of a tridiagonal system, which system corresponds to the expression: g = FH (FHHHFH +, u1I +, u2DHD) 1 FHHy. in which: g is a vector corresponding to the deconvolution nucleus; 35, u1 and, u2 are actual adjustment parameters;

I represents the identity matrix of dimension NxN; H is a circulating matrix representative of the convolution operation with the vector h representative of the initial estimate of the impulse response hW; F represents the unitary Fourier matrix of dimension NxN; D represents a diagonal matrix of dimension NxN arranged in the following way: do -d1 d1 D = -dN-2 dN-2 -dN-1 dN-1 the elements of D having do = 0 and dn = 1 for n> 0 ; HH, FH and DH represent the conjugated transpose matrices of the matrices H, F and D. N can be chosen so as to implement a fast Fourier transform algorithm such as Radix-2. The tridiagonal system is solved, for example, using the Thomas algorithm. According to one embodiment, after the initial estimation of the impulse response h (t), the estimation steps of the kernel g (t) and the refined estimate of hW are applied successively and iteratively. The invention also relates to a reflectrometry device comprising means for generating a test signal s (t), transmitting it in a network to be tested, measuring a signal y (t) resulting from the course of s (t) in the network. analyze the signal y (t). The device comprises means for implementing the method according to any one of the preceding claims.

Other features and advantages of the invention will become apparent with the aid of the description which follows given by way of nonlimiting illustration, with reference to the appended drawings in which: FIG. 1 shows a modeling of the phenomena modifying a signal test during its propagation in a network tested using a reflectometry system; FIG. 2 gives an example of a high resolution reflectogram obtained by simulation with and without taking into account the distortion; FIG. 3 gives a simplified example of a deconvolution process according to the invention; FIG. 4 presents simulation results relating to the implementation of the myopic deconvolution according to the invention; FIG. 5 gives an example of a reflectogram obtained by applying the method according to the invention. FIG. 1 shows a modeling of the phenomena modifying the test signal during its propagation in a network tested using a reflectometry system. A signal noted y (t) corresponds to the signal measured by the reflectometry system resulting in particular from the propagation of the test signal in the network and can be modeled using the following expression: y (t) = s (t) * h (t) * (t) + n (t) (1) where: * represents the convolution product operation; S (t) represents the test signal 100; hW represents the signal sought by the reflectometry system and corresponds to the impulse response 101 of the tested network; f (t) represents various filtering phenomena 102, not necessarily known, related inter alia to the bandwidth limitation of the various elements and components present in the path of the wave corresponding to the test signal; n (t) represents an additive measurement noise 103. The signal hW is composed of a series of peaks whose positions give the delays of the different reflections of the test signal, also called echoes, and can be described with the help of the following expression: 10 h (t) = lak 8 (t-Zk), (2) k> 0 in which: ak represents the amplitude of the echoes; Zk represents delays associated with echoes; 8 (t) represents the Dirac distribution. The signal hW belongs to the category of parsimonious signals because it has few non-zero values. The function (t) is called in the rest of the description 1 o function of distortion. This function usually corresponds to a low-pass filter 102 whose characteristics are not known. It is for this reason that the effect of this filter is often neglected by the reflectometry systems to the detriment of the fault localization accuracy of the tested network. The method described below aims in particular to estimate the distortion function (t) by processing methods that can be embedded in a reflectometry system, this estimate is then used to compensate for this distortion. The measured signal y (t) is usually processed in a matched filter reflectometry system, which is equivalent to a cross correlation between y (t) and the test signal s (t). The signal r (t) obtained at the output of this filter can be described using the expression: r (t) = rss (t) * h (t) (3) in which: rs (t) is the function d autocorrelation of s (t). Here it is assumed that the transmitted signal s (t) is chosen to have triangle-shaped autocorrelation by the following expression: iK-In1 if I n1 <K r (n) - K 0 otherwise :

K is a real constant;

n represents the index of the samples of the signal.

When the distortion function (t) is not taken into account, that is to say that we put (t) = 1, the elimination of s (t) in the expression (1) constitutes a classic deconvolution problem. Indeed, in this case, the deconvolution nucleus is equal to s (t) and is itself known.

In this context, the principle of these algorithms is based on the parsimonious nature of the hW signal to be found and falls into the category of pulse deconvolution methods. Among the best methods

adapted to the context of embedded systems, mention may be made of the CLEAN algorithm, also referred to as Anglo-Saxon

"Matching Pursuit" and described in the article by C. Buccella, M. Feliziani and G. Manzi entitled Detection and localization of defects in time-domain measurements with uwb pulse injection and clean algorithm postprocessing, IEEE Transactions on Electromagnetic Compatibility , 46 (4), pages 597-605, November 2004. L1 deconvolution algorithms such as the IST algorithm from the Iterative Soft Thresholding expression or the rapid IST algorithm may also be mentioned.

also called Fast-IST and whose descriptions and comparisons can be found in article del. Loris, M. Bertero, C. De Mol, R. Zanella and L. Zanni entitled

Accelerating Gradient Projection Methods for I1-Constrained Signal Recovery

by steplength selection rules, Applied and Computational Harmonic Analysis, 27 (2), pp. 247-254, 2009. Instead of taking the test signal directly as a deconvolution kernel, taking into account the distortion in this kernel makes it possible to

significantly improve the results provided in terms of resolution. This taking into account of the distortion makes it possible to obtain a relatively smooth core in

the time domain due to the low-pass nature of the distortion. This (4) last is indeed intended for forms of steeper signal, which was the case of the triangular core previously studied. As a preliminary remark, in the remainder of the description, a notation of the type x denotes a vector, that is to say a set of values organized in a matrix comprising a single column. In general, in the description, a vector x corresponds to a set of discrete elements representative of a function x (t). In addition, a matrix denoted X is a circulating matrix corresponding to the convolution operation with the vector x. For example, in the context of the method, an L1 type deconvolution is used for estimating a vector h representative of the function h (t). This amounts to minimizing a JLI function (h) that can be expressed, for example, by using the expression: Jla (h) = y - Gh z + uh (5) in which: h 1 = In, where hn is the h L1 standard, the use of this standard favors parsimonious h solutions; 20, u is a real constant that makes it possible to introduce a compromise between the fidelity of the estimate to the measure and its adequacy to the model, the latter being able to be adjusted empirically; G is a circulating matrix corresponding to the convolution operation with the core represented by the vector g corresponding to the function g (t), said core corresponding to the convolution product of the test signal s (t) with the distortion function ( t). The matrix G can be written using the expression: G = SE (6) in which: S represents a circulating matrix corresponding to the convolution operation with s, representative vector of the function s (t); represents a circulating matrix corresponding to the convolution operation with vector representative of the distortion function (t).

It is therefore in the matrix G that the distortion is taken into account. In the case where the distortion is ignored we have G = S. FIG. 2 gives an example of a reflectogram obtained by simulation with and without taking into account the distortion. This figure makes it possible to illustrate the performance gain induced by the taking into account of the distortion in an example of a chosen configuration. In this example, the distortion function is assumed to be known as long as it is created

artificially in a simulator. The latter here corresponds to five first order filters 1 o ordered in cascade. Its Laplace transform, E (jw), can be described using the following expression: ## EQU1 ## in which: w represents the n-th cutoff pulse. The choice of this model is linked to the fact that most of the phenomena

observed experimentally in the signal path are similar to a first-order filter. Figure 2 shows the actual response h (t) 200 of

20 simulated network, the function rsy (t) 201 representing the intercorrelation function between the signals s (t) and y (t), the response of the network 202 obtained after a conventional deconvolution without taking into account the distortion in the core , and the response of the grating 203 obtained after a deconvolution whose core takes into account the distortion which is here known. It appears that the taking into account of the distortion clearly improves the quality of the result. The resolution of the peaks is improved, which will notably have the effect of

facilitate the location of network faults. The estimation of h without the knowledge of a vector representative of the function (t) constitutes a myopic deconvolution problem insofar as only the deconvolution nucleus corresponding to the function g (t) = s (t) is known. ) * (t). Several powerful methods exist to solve this type of problem. They are usually based on statistical simulation methods such as the Markov chain Monte-Carlo method (7) designated by the acronym MCMC from the Anglo-Saxon "Markov Chain Monte-Calo". However, the latter are not conceivable for integration into an embedded system due to their complexity.

An approach similar to that of deconvolution-L1 and corresponding to a joint estimate of h and g is proposed in the article by S. Gautier, J. Idier, F. Champagnat, A. Mohammad-Djafari and B. Lavayssière. Entitled Treatment of ultrasonic echograms by blind deconvolution, GRETSI, 1997.

It consists in optimizing a cost function of the type: JI (11, g) = Y-C (ga + μ ~ hl + μz Qg z + μ3g z (8) in which: the sign 11-L refers to the norm L1, the sign - 2 refers to the norm L2, ul ,, u2 and, u3 are regularization parameters, Q is a matrix allowing to favor soft solutions of g, On the other hand, the second term associated with parameter, u , favors the parsimonious solutions of h Lastly, the last term limits the energy of g and thus improves the conditioning of the estimator In practice, the minimization of JI (h, g) can be done by alternating the variations This type of approach is used for image deconvolution, but the disadvantage of this method is that it can be slow to converge. u2 are strongly dependent which can make their adjustment difficult in practice.The method proposed in the context of the invention uses a st innovative strategy of approaching the two unknown functions h and successive approximations. Thus, a first deconvolution without taking into account the distortion is carried out resulting in an estimation denoted h "of the impulse response.Using this first result, the distortion function can be in turn estimated by least squares. a function J2 () defined below can be minimized, it can be determined using the following expression: JZ ~~ = Y - HSg z (9) in which: H is a circulating matrix representative of the operation The convolution vector with the vector h i is the vector corresponding to the newly acquired distortion function and can be introduced into the deconvolution nucleus and obtain a new estimate h (of the impulse response, the process being iterative. Iterations are applied in order to converge towards an acceptable approximation of the two functions h and this strategy works in cases where we have several to different with the same distortion or if the signal has enough well separable peaks. However, in the case of the diagnosis of cables, there is not enough data to be processed and there are too many cases where the method is very long to converge or else diverges. The method according to the invention is particularly intended to estimate in order to avoid having to apply too many iterations or trap convergence in erroneous solutions. This is done by introducing assumptions about the nature of. A hypothesis that can be chosen and used is to consider that most of the energy in the time domain is concentrated around the moment t = 0. This hypothesis comes from the fact that it is not possible to estimate the group delay of the distortion filter. It is therefore assumed that this function is centered around the instant t = 0, called the origin of the times in the following description. It is therefore considered that energy is concentrated around this point. The method according to the invention seeks here to penalize in a cost function the important values of which appear, in the time domain, on samples distant from the origin. In other words, solutions whose time-domain derivative does not exceed a chosen level are favored. Considering the Fourier transform, this results in rapid variations in certain points. Indeed, the points farther and farther from the origin in the time domain correspond to more and more rapid variations of the Fourier transform. This error can therefore be reduced by applying a smoothing constraint on the discrete Fourier transform Gn of the estimate of g, which amounts to penalizing the derivative through a cost function to be minimized.

In discrete values, the derivative AG ,, of the discrete Fourier transform TFD can be represented using the expression: AG ,, -Gn -Gn-1 (10) 1 o wherein: Gn and Gn_I represent the samples of the transformed TFD of g of respective indices n and n-1. The estimation can then be done by minimizing a function J (): J (Gn) - ~ [(Yn -HnGn) 2 + ~ IGn + ~ 2 (aGn) Zl (11) n = 0 in which:, u, and, u2 are adjustment parameters that can be set

Manually depending on the noise level and the spectral characteristics of the signals; the most important parameter is, u2 because it

conditions the action of the derivative and is essentially related to the spectrum width of the test signal s. Expression (11) can be written in matrix form:

J (g) -Y -Hg z + gl g z + μ2 DFg 2 (12) in which: D = -dN-2 dN-2 -dN-1 dN-1

the elements of this matrix being defined below; F represents the unit Fourier matrix and can be written as: 1 1 1 1 1 WN WN 2 WNN-1 1 WN-1 W2 (N-1) W (N-1) (N-1) NNN g represents the function searched in the time domain, corresponding to the core of deconvolution. The use of the matrix F makes it possible to express the Fourier transform, thus DFg corresponds to the derivative of the Fourier transform of the nucleus In general, the derivative constraint will be applied to the whole signal except of the continuous component, therefore do = 0 and tin = 1 for n> O. This cost function corresponds to a regularization of

15 Tychonoff as described in AN Tychonoff and VY Arsenin entitled Solution of Ill-posed Problems, Washington: Winston & Sons, 1977. By posing, N: = xH x we can obtain the expression of its derivative: aJ - 2 [(WH + U1i + u2FHDHDF) g-HHY]. (13) ag This derivative vanishes for: g - (HHH +, u I +, u2FHDHDF) -1 HH y. (14) F = 1 N / TV-j2cN, with: WN = e The minimization of the function J (g) can therefore be done by direct calculation. The inversion can be done in the Fourier base in order to diagonalize the circulating matrices, as it is the case for the spectral division, it then comes the following expression: g = FH (FHHHFH +, u1I + du2DHD) 1 FHHy . (15) It is then necessary to determine a forward DFT transform and a reverse DFT after inversion. The matrix to be inverted becomes here tridiagonal. The following expression is then obtained: ## STR5 ## u2 (d7, + d +1),

the coefficients Hn correspond to the DFT transform of the vector h, T (Ho ..., HN-1) = Fh. The resolution of a tridiagonal system such as that presented in the expression (15) can be done with a complexity of order N, that is to say

20 with a calculation number proportional to the number of samples N of the measurement vector. For this, one can for example use the Thomas algorithm usually designated by the acronym TDMA from the Anglo-Saxon expression "TriDiagonal Matrix Algorithm". Thomas' algorithm is described in the work of Pierre Borne and Frédéric Rotella entitled

25 Theory and Practice of Matrix Calculation, TECHNIP Editions, 1995. The extra cost in terms of computing power required by the addition of the derivative with respect to a spectral division therefore remains reasonable.

In summary, the myopic deconvolution process can be decomposed into three stages as illustrated in FIG.

A first step 300 corresponds to a first estimate of h by the CLEAN algorithm using the test signal s (t) as the core. A second step 301 corresponds to an estimate of g. The kernel is calculated in the frequency domain by the resolution of the tridiagonal system as that of the expression (15). This second step can be implemented using three main operations. A first operation corresponds to the application of a discrete Fourier transform TFD, for example on N points. Advantageously, a value of N allowing the use of a fast Fourier transform algorithm 1 o such as Radix-2 is chosen in the case where N is a power of 2. A second operation corresponds to the construction of the tridiagonal system of N / 2 dimension. A third operation corresponds to the resolution of the tridiagonal system of dimension N / 2. A third step 302 of the method corresponds to a final estimate of h by deconvolution-L1 by minimizing a function JLI (h). Advantageously, the fixed-point integration in an electronic circuit of this method described above is conceivable. The visible curves in FIG. 4 give an example of simulation result of the myopic deconvolution according to the invention. This figure shows the real network response h (t) 400, the function rsy (t) 401 representing the intercorrelation function between the signals s (t) and y (t), the response of the network 402 obtained after a deconvolution conventional without taking into account the distortion in the nucleus, and the response of the network 403 obtained after a deconvolution whose core takes into account the estimated distortion. The result obtained is slightly worse than in the example of FIG. 2 when the distortion function is known, but there is undeniably a clear improvement over the case where the distortion is ignored. FIG. 5 gives an example of a reflectogram obtained by applying the method according to the invention.

In this figure, the function rsy (t) measured 500 representing the intercorrelation function between the signals s (t) and y (t), the response of the network 501 obtained after a conventional deconvolution without taking into account the distortion in the nucleus, and the response of the grating 502 obtained after myopic deconvolution embodying the invention. In this example, the method is applied to the test of a Y grating. When the wave reaches the central junction 503 of the grating, a negative polarity wave is reflected, and when it reaches each of the two branch ends 12 and 13 which are in open circuit, a positive wave is reflected. A residual fraction of the wave then continues to propagate in the network giving rise to secondary echoes. In order to make the connection between the signals obtained and the propagation of the reflected waves, the distance and the time are linked by the expression: (17) in which: x represents the distance in meters; z represents the round trip time of the wave in seconds; V represents the propagation speed, in the case of the cables used for the experiment, this is worth v = 2.105km.s-1. In the case of this network, the lengths of the two branches l2 and l3 are very close, so it is difficult to distinguish 504 the two ends. It can be seen here that the proposed high resolution method makes it possible to make this distinction in contrast to a conventional deconvolution which does not take into account the distortion.

Claims (9)

CLAIMS 1- A method for estimating the impulse response h (t) of a cable network by myopic deconvolution, a test signal s (t) being introduced at an input point of the network and a signal y (t) being measured at a point of exit from the network, the entry point and the exit point being preferably the same, characterized in that it comprises: a step (300) of initial estimation of the impulse response h (t) deconvoluting the signal y (t) with a kernel corresponding to the test signal s (t); a step (301) for estimating a deconvolution kernel g (t) by using the result of the initial estimation of the impulse response h (t), said kernel taking into account the distortions f (t) introduced by the network ; A step (302) of refined estimation of h (t) by deconvolution using the core g (t). 2. Method according to claim 1, characterized in that the initial estimate (300) of the impulse response h (t) is obtained by applying the CLEAN algorithm. 3. Process according to any one of the preceding claims, characterized in that the refined estimate of h (t) (302) is obtained by deconvolution L1. 4. Process according to any one of the preceding claims, characterized in that it is assumed in the step (301) for estimating the deconvolution nucleus g (t) that the function (t) is centered around the moment t = 0. 5. Process according to claim 4, characterized in that the deconvolution nucleus g (t) is obtained by contruction and resolution of a tridiagonal system, this system corresponding to the expression: g = FH (FHHHFH +, uII + , u2DHD) 1 FHHy.in which: g is a vector corresponding to the deconvolution nucleus; , u1 and, u2 are actual setting parameters; I represents the identity matrix of dimension NxN; H is a circulating matrix representative of the convolution operation with the vector h representative of the initial estimate of the impulse response h (t); F represents the unitary Fourier matrix of dimension NxN; D represents a diagonal matrix of dimension NxN arranged in the following way: do -d1 d1 D = -dN-2 dN-2 -dN-1 dN-1 the elements of D having do = 0 and dn = 1 for n> 0 ; HH, FH and DH represent the conjugated transposed matrices of the matrices H, F and D. 6. The method of claim 5 characterized in that N is chosen so as to implement a fast Fourier transform algorithm such as Radix-2. 7- Method according to any one of claims 5 or 6 characterized in that the tridiagonal system is solved using the algorithm of Thomas. 25 8- Method according to any one of the preceding claims, characterized in that after the initial estimation (300) of the impulse response h (t), the estimation steps of the core g (t) (301) and of refined estimate (302) of hW are applied successively and iteratively. 20 30 9- Reflectrometry device comprising means for generating a test signal s (t), transmitting it in a test network, measuring a signal y (t) resulting from the course of s (t) in the network, analyzing the signal y (t), characterized in that it comprises means for implementing the method according to any one of the preceding claims.