METHOD FOR CHARACTERIZING TREATMENT VARIATIONS BETWEEN SEVERAL ANALOGUE WAYS
A method for characterizing and compensating processing differences in analog channels using periodic signals and digital circuitry addresses residual errors by aligning signals, enhancing system accuracy.
Patent Information
- Application Number
- FR2021010082
- Authority / Receiving Office
- FR · FR
- Patent Type
- Patents
- Current Assignee / Owner
- Filing Date
- 2021-09-27
- Publication Date
- 2024-12-20
- Estimated Expiration
- 2041-09-27
AI Technical Summary
Existing systems with multiple analog channels often exhibit residual processing differences that can cause errors downstream, despite using identical components, necessitating a method to characterize and compensate for these differences effectively.
A method involving the injection of specific periodic signals into each channel, digitization, and parameter estimation using least squares methods to determine amplitude and phase shifts, followed by compensation using digital circuitry to align signals.
Effectively characterizes and compensates for processing differences between analog channels, reducing errors by aligning signals based on estimated parameters, thereby improving system accuracy.
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Abstract
Description
Title of the invention: method for characterizing processing differences between several analog channels FIELD OF THE INVENTION
[0001] The present invention relates to a method for characterizing processing deviations between several analog channels. STATE OF THE ART
[0002] There are many systems comprising several analog channels arranged in parallel, and through which analog signals pass.
[0003] Such analog channels are often made with the same electronic components, so that each one applies a processing that is supposed to be the same.
[0004] However, there may be residual differences between the processing carried out by different analog channels of such a system. In certain applications, these residual differences may generate errors downstream of the analog channels. Statement of the invention
[0005] An aim of the invention is to characterize processing differences between several analog channels in a simple and efficient manner.
[0006] This aim is achieved by a method for characterizing processing differences between a first analog channel and a second analog channel, the method comprising steps of: - injection of a first analog signal at the input of the first analog channel, of a second analog signal at the input of the second analog channel, and of a third signal at the input of the second analog channel, the first analog signal being a periodic signal, the second analog signal being a periodic signal of the same amplitude, of the same period and of the same shape as the first analog signal, and the third analog signal being a periodic signal in phase quadrature with the second analog signal and of the same amplitude and of the same period as the second analog signal, - digitizing the first analog signal at the output of the first analog channel, so as to obtain a first digital signal having N samples, digitizing the second signal at the output of the second analog channel, so as to obtain a second digital signal xi having N samples, and digitizing the third analog signal at the output of the second analog channel so as to obtain a third digital signal ^'i having N samples, - estimation of parameters Vk i and ôk; from the first digital signal, the second digital signal and the third digital signal, where: - Vf, i is a ratio between an amplitude of the first analog signal at the output of the first analog channel and an amplitude of the second analog signal at the output of the second analog channel, - 5k J is a difference between a phase shift induced by the first analog channel on the first analog signal and a phase shift induced by the second analog channel on the second analog signal, the estimation comprising the application of a least squares method to determine values of the parameters; and dk z minimizing the following quantity: E j (xk (n)' rk { ( cos ( ôk} ) x( ( n ) - sin ( <5* 1 ) y{ ( n ) ) )2in which - xk(n) denotes the nth sample of the first digital signal, - x^n) denotes the nth sample of the second digital signal, - yz(?J) denotes the nth sample of the third digital signal.
[0007] The proposed method may also include the following optional features, taken alone or combined with each other whenever this makes sense.
[0008] Preferably, the first analog signal is sinusoidal.
[0009] Preferably, the application of the least squares method comprises the resolution of a system of equations assuming that COS (¾ / ) = 1 and / or that cos (2¾ = 1 and / or that sin (¾ / ) — Sk z and / or that sin (2¾ = 2¾^.
[0010] Preferably, at least one of the first analog signal, the second analog signal and the third analog signal comes from a digital signal generated by a digital circuit implementing the estimation of the parameters z and Ôk k
[0011] Preferably, the third analog signal is injected at the input of the second analog channel after the second analog signal.
[0012] Also provided is a method for compensating for processing deviations between a first analog channel and a second analog channel, the method comprising steps of - characterization of deviations between a first analog channel and a second analog channel of an analog signal receiver, by implementing the method defined previously, - correction of a digital signal from the second analog channel on the basis of the parameters { and 5k k so as to compensate for a phase difference and an amplitude difference induced by the second analog channel compared to the first analog channel.
[0013] The aim defined above is also achieved by a system comprising: - a first analog channel capable of receiving a first analog signal, the first signal being a periodic signal, - a second analog channel capable of receiving a second analog signal and a third analog signal, the second analog signal being a periodic signal of the same amplitude, the same period and the same shape as the first analog signal, and the third analog signal being a periodic signal of the same amplitude and the same period as the second analog signal and in phase quadrature with the second analog signal, - an analog-digital conversion stage capable of: digitizing the first analog signal at the output of the first analog channel, so as to obtain a first digital signal xk having N samples; digitizing the second signal at the output of the second analog channel, so as to obtain a second digital signal xi having N samples; and digitizing the third analog signal at the output of the second analog channel so as to obtain a third digital signal 3 / having N samples, - a digital circuit configured to estimate parameters Vk; and 5k;from the first digital signal, the second digital signal and the third digital signal, where Vk t is a ratio between an amplitude of the first analog signal at the output of the first analog channel and an amplitude of the second analog signal at the output of the second analog channel, and where dk {is a difference between a phase shift induced by the first analog channel on the first analog signal and a phase shift induced by the second analog channel on the second analog signal, the estimation implemented by the digital circuit U comprising the application of a least squares method to determine values of the parameters yk t and ôk ( minimizing the following quantity; E *=i(xk(n) -^(cos (¾^(n) - sin (5k ^(n)) )2OR - xk(n) denotes the nth sample of the first digital signal, - Xj{n) denotes the nth sample of the second digital signal, - denotes the nth sample of the third digital signal.
[0014] This system may also include the optional features of the characterization method defined above.
[0015] In particular, this system may comprise a digital-to-analog conversion stage configured to generate at least one of the first analog signal, the second analog signal and the third analog signal, from a digital signal provided by the digital circuit.
[0016] The digital-to-analog conversion stage may include a first digital-to-analog converter configured to generate the first analog signal, and a second digital-to-analog converter configured to generate the second analog signal and the third analog signal. DESCRIPTION OF FIGURES
[0017] Other characteristics, aims and advantages of the invention will emerge from the following description, which is purely illustrative and non-limiting, and which must be read in conjunction with the appended drawings in which:
[0018] [Fig.l] schematically illustrates a system comprising analog channels according to one embodiment.
[0019] [Fig.2] is a flowchart of steps in a characterization method according to a embodiment of the invention.
[0020] [Fig.3] shows examples of signals injected during the implementation of the characterization process of the [Fig.2]
[0021] [Fig.4] is a flowchart of steps of a compensation method according to a embodiment of the invention.
[0022] Throughout the figures, similar elements bear identical references. DETAILED DESCRIPTION OF THE INVENTION
[0023] 1) Description of a system comprising analog channels
[0024] [Fig.l] shows an example of a system comprising analog channels. This system is an analog signal receiver comprising a radio antenna system Al-A4, a plurality of analog channels RF1-RF4, an analog-digital conversion stage C, and a digital circuit U.
[0025] The plurality of radio antennas comprises any number M of antennas, with M greater than or equal to 2, for example M=4 in the example shown in [Fig.l].
[0026] The plurality of analog channels is connected to the antenna system and to the analog-to-digital conversion stage.
[0027] Each analog channel RFi of index i comprises an input and an output. The input of each analog channel RFi of index i is connected to the radio antenna Ai of index i as well. In other words, there are as many antennas as there are analog channels.
[0028] Each analog channel RFi typically comprises an RF input block (“RF front end” in English) arranged downstream of the radio antenna Ai associated with it. In a manner known per se, an RF input block may comprise the following components known to those skilled in the art: a bandpass filter, an amplifier, a local oscillator, a mixer, etc.
[0029] In the embodiment of [Fig.l], the analog-digital conversion stage C comprises M analog-digital converters CAN1-CAN4, each converter CANi being connected to the output of an analog channel RFi which is specific to it. In other embodiments, the analog-digital conversion stage C could comprise a different number of CAN converters, for example a single one which would be connected to the respective outputs of all the analog-digital channels.
[0030] The analog-to-digital converters CAN1-CAN4 are configured to digitize analog signals at a sampling frequency Fs.
[0031] The digital circuit U is arranged at the output of the analog-digital conversion stage C, so as to be able to process digital signals which have been digitized by the analog-digital conversion stage C.
[0032] The digital circuit U is for example or is part of a system on chip.
[0033] The system further comprises a digital-to-analog conversion stage C'. The digital-to-analog conversion stage C' is arranged at the output of the digital circuit U, and is furthermore connected to the respective inputs of the analog channels RF1-RF4. In this way, it is possible to inject into the analog channels analog signals generated by the stage C' from digital signals generated by the digital circuit U.
[0034] In the embodiment of [Fig.l], the digital-to-analog conversion stage C' comprises M digital-to-analog converters CNA1-CNA4, each converter CNAi being connected to the input of an analog channel RFi which is specific to it. Thus, a converter CNAi makes it possible to inject an analog signal into the analog channel RFi alone. In other embodiments, the digital-to-analog conversion stage C' could comprise a different number of converters CNA, for example a single one which would be connected to the respective inputs of all the analog-to-digital channels.
[0035] The conversion stages C and C' may be part of the same system-on-chip as the digital circuit U.
[0036] 2) Method for characterizing processing differences between analog channels
[0037] With reference to [Fig.2], a method 100 for characterizing processing deviations between an analog channel of index k (RFk) and an analog channel of index 1 (RFI) of the system presented above comprises the following steps.
[0038] In an injection step 102, three analog signals described below are injected.
[0039] It is assumed that the internal signal modifying functions possibly included in the analog channels of indices k and 1 are deactivated during the injection 102, so that the analog channels behave like simple transmission lines. In this way, if the channels of indices k and 1 were perfect, the same signals would be found at the output of these channels as at the input.
[0040] In step 102, a first analog signal is injected at the input of the analog channel of index k. The first analog signal is a periodic signal, characterized by an amplitude, a signal shape, and a period (i.e. the duration of an elementary periodic pattern of the signal).
[0041] For example, the first analog signal is produced by the conversion stage digital-analog C', based on a digital signal provided by the digital circuit U.
[0042] The first analog signal propagates in the analog channel of index k, from its input to its output. During this propagation, the analog channel of index k alters the first analog signal; the analog channel is in particular capable of residually modifying the amplitude and the phase of the first analog signal which passes through it.
[0043] Furthermore, a second analog signal is injected at the input of the analog channel of index 1. The second analog signal is identical to the first analog signal: it has the same amplitude, the same period and the same shape as the first analog signal.
[0044] For example, the second analog signal is produced by the digital-to-analog conversion stage C', on the basis of a digital signal provided by the digital circuit U.
[0045] The second analog signal propagates in the analog channel of index 1, from its input to its output. During this propagation, the analog channel of index 1 alters the second analog signal; the analog channel of index 1 is thus likely to residually modify the amplitude and the phase of the second analog signal which passes through it. However, the alteration caused by the second analog channel may be different from the alteration caused by the first analog channel. It is this processing difference that the method 100 aims to characterize.
[0046] Furthermore, a third analog signal is injected at the input of the analog channel of index 1. The third analog signal is a periodic signal of the same amplitude and period as the second analog signal. However, the third analog signal is in quadrature with the second signal. This means that the third signal differs from the second signal only by a phase shift of 90° with respect to the latter (all other things being equal).
[0047] For example, the third analog signal is produced by the digital-to-analog conversion stage C', on the basis of a digital signal provided by the digital circuit U.
[0048] The third analog signal propagates in the analog channel of index 1, from its input to its output. During this propagation, the analog channel of index 1 alters the third analog signal; the analog channel of index 1 is thus likely to residually modify the amplitude and the phase of the third analog signal which passes through it in the same proportions as the second analog signal.
[0049] In a digitization step 104, the analog signals are digitized by the analog-digital conversion stage in order to obtain digital signals:
[0050] • The first analog signal is digitized by the ADC of index k, so as to produce a first digital signal xk comprising N samples. We denote xk ( n ) the nth sample of the digital signal xk thus produced. • The second analog signal is digitized by the ADC of index 1, so as to produce a second digital signal xt comprising N samples. We denote by X / (n) the nth sample of the digital signal X1 thus produced. • The third analog signal is subsequently digitized by the ADC of index 1, so as to produce a third digital signal yi comprising N samples. We denote y {( n ) the nth sample of the digital signal yi thus produced.
[0051] The injections of the first analog signal, the second analog signal and the third analog signal can be implemented in any order, and the same applies to obtaining the digital signals xi and 3' / by digitization.
[0052] In particular, the injection of the second signal can be implemented before, during or after the injection of the first signal. It is in particular possible to have these two signals routed simultaneously to the analog channels of respective indices k and 1; alternatively, it can be arranged to inject these two signals one after the other. In particular, the three analog signals can be injected sequentially.
[0053] Furthermore, although the digitization step 104 is shown as being subsequent to step 102 in the flowchart of [Fig.2], it is of course possible for these two steps to be interleaved (for example, the first analog signal is injected and digitized, then the second signal is injected and digitized, then the third analog signal is injected and digitized).
[0054] In an estimation step 106, the digital circuit U estimates two parameters j and 5k j indicative of differences between the analog channels of indices k and 1, from the digital signals xy xt and 3 / obtained in the digitization step 104.
[0055] On the one hand, the parameter ( is a ratio between an amplitude of the first analog signal at the output of the first analog channel and an amplitude of the second analog signal at the output of the second analog channel.
[0056] On the other hand, the parameter 5k s is a difference between a phase shift induced by the first analog channel on the first analog signal and a phase shift induced by the second analog channel on the second analog signal.
[0057] The estimation carried out in step 106 applies the least squares method to determine values of the parameters Vk [ and 5k ; minimizing the following quantity Ck ;, consisting of a sum of squared residues: = E ^(x^n)-ykJcos (¾ z)xz( n) - sin ) )2lc1'
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[0069] the least squares method is applied by considering as a residue a difference between the first digital signal xk (left term of the residual) and a model of this first signal (right term of the residual). Notably, this model depends on the two parameters that we seek to estimate; and Ôk as well as the digital signals xi and Obtaining the values of the parameters y^ ; and ; which minimize the sum of residues Ck j can typically be implemented by the digital circuit U in solving the following system of equations: ac ___- () / 'k, l The parameters ( and 5k ; estimated in step 106 characterize deviations of the track analog channel of index 1 relative to the analog channel of index k. The partial derivatives of the quantity Ck t to be minimized are rewritten as follows: dLf. ; / -> 0 \ ÿy ' = 24 / [ ( cos ( dk t ) ) Sj + ( sin ( 5k ; - sin ( 2¾ ; ) + 2 ( -cos ( Ôlt t + sin ( 5^ { ) 2 sh1 ( 2( V)Xr 5 V cos ( 2 ^)^ +si " (WW™ k. I 1 | 1 2} " ' I \ \ \ >1 / / With : EVT—> NOT—1 TV n= i(xl(n) )Sv2= E^WV")) S = E n = lxl(n)yl(ri) s = L ^^(nyx^nts = E ^4( / 1)) (n) ■x / ài Ultimately, the values of ; and dk ( are obtained by solving the system of following equations, in this embodiment: W ( C°S (¾. 1 HX? + ( Sin ( Sk. I ) ) \ 1 / l1 l / \ • K-' / / ' h, / ( 2 sin ( 2ôt 1 ) ( ' W + cos ( 25k, 1 ) XV / j + sin ( 3k, 1 ) s.vl + cos ( \ 1 ) S,l;Vi = 0 This simplified system of equations can be solved with a reasonable computational load, for example by applying the Newton-Raphson method known to those skilled in the art. The parameters and ôk are stored in a memory, for example in a memory integrated in the digital circuit U. The preceding steps can be applied multiple times Ml times for different pairs of channels (k, 1), varying 1 so as to cover any channel other than the channel with index k. For example, if k=l is chosen, these steps are implemented for the following pairs of analog channels: (1, 2), (1, 3), (1, M). Of course, it it is then not necessary to re-inject the first analog signal several times.
[0070] 2.1) Use of sinusoidal analog signals
[0071] In the following, an embodiment of the method 100 will be described which is advantageous due to its simplicity. In this embodiment, the first analog signal injected is a sinusoidal signal.
[0072] If the first sinusoidal analog signal were digitized without alteration at the sampling frequency Fs, the first analog signal would be written in the following form:
[0073] A'o (n) = A cos (wn + <p )
[0074] With:
[0075] o ~ f F
[0076] where A denotes the amplitude, v the reduced frequency, the initial phase and f the frequency of the first analog signal.
[0077] In order to simplify the description of the process, we choose by convention (p = 0 (which has no impact on the process itself).
[0078] We can then model the first digital signal which results from the passage of the first analog signal through the analog channel of index k and its subsequent digitization, in the following manner:
[0079] xk (n) = pk cos (m + Bk), n = 1 ...N
[0080] where Bk denotes the phase difference induced by the passage of the first analog signal to through the analog channel of index k, and Pk denotes an amplitude of the first analog signal at the output of the analog channel of index k.
[0081] It is further recalled that the second analog signal is identical to the second analog signal. Under these conditions, the second digital signal xi, which results from the passage of the second analog signal through the analog channel of index 1 and its subsequent digitization, can be modeled in the following manner:
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[0083] where denotes the phase difference induced by the passage of the second analog signal through the analog channel of index 1 and Pi denotes the amplitude of the second analog signal at the output of the analog channel of index 1.
[0084] Finally, it is recalled that the third analog signal is in quadrature with the second analog signal; the third analog signal is therefore also sinusoidal. [Fig.3] shows an example of the realization of the second analog signal and the third analog signal, when these are sinusoidal and they are injected one after the other on the analog channel of index 1.
[0085] If the third analog signal were digitized without alteration to the frequency sampling the third analog signal would be written in the following form:
[0086] y0 (n) = A sin (mi)
[0087] Under these conditions, we can model the third digital signal y^ which results from the passage of the third analog signal through the analog channel of index 1 and its subsequent digitization, in the following manner:
[0088] y(n)=p, sin (nvz + fy), n = N + K ... 2N + K - i
[0089] where K denotes a time difference which temporally separates the third digital signal from the second digital signal.
[0090] The digital circuit U can easily align the third digital signal with the second digital signal xi, so as to obtain:
[0091] xl(n)=p / cos (am +, n= 1 ... N y ( n ) = p} sin ( tvn + 6; ), n = 1 ...N
[0092] In this embodiment, the two parameters i and ôk t that the digital circuit U estimates in step 106 can be written as follows:
[0093] ôkl=6k-el Pk 2.2) Possible approximations
[0094] In particularly advantageous embodiments, the digital circuit U is configured to solve the above system of equations by making certain approximations.
[0095] A first approximation consists of making the assumption that COS ( ôk = 1. This approximation can perhaps be seen as a limited development (LD) of order zero of the cosine function at zero (or of order 1, since there is no term in "5^. ( " in this LD).
[0096] A second approximation, analogous to the first, consists of making the hypothesis that COS ( 25k t ) = 1.
[0097] A third approximation consists of making the assumption that sin ( Ôk = ôk k This second approximation can be seen as a limited development (DL) of order one of the sine function at zero.
[0098] A fourth approximation, analogous to the third approximation, consists of making the hypothesis that sin (20^^ = 2ôkl.
[0099] Each of these four approximations is particularly good when the parameter dk ( is close to zero, which is a reasonable assumption. They both contribute to simplifying the resolution by the digital circuit U of the system of equations posed above.
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[0114] The digital circuit can apply any combination of these four approximations, in particular apply all four of them. When the four approximations mentioned above are applied, the system of equations to be solved simplifies as follows: y, JS 2-25, ,S \ + (-S + 5.S \=0 L / xf k, / x[Vj J [ xkxi k, l Xky / | - y I ôk , / S 2 ~ S \ + S \ + Ô. S + S — 0 M LH xf „qv kj XkXt \ ' '7 / / Note that this system of equations can be resolved formally, unlike the general case explained above in section 2.2), which is particularly advantageous. 2.3) Use of other types of periodic signals The method 100 can be generalized to other periodic analog signals. Indeed, any periodic analog signal can be written as a Fourier series, that is, as a weighted sum of cosine / sine functions. 3) Method for compensating for processing differences between analog channels A method 200 for compensating for processing deviations between analog channels of the system comprises the following steps. This method 200 comprises the implementation of the characterization method 100 described previously, so as to obtain at least one pair of parameters z and 5k / associated with the pair of analog channels of indices k and 1. Now suppose that a radio signal is received by the antenna connected to the analog channel of index k, and by the antenna connected to the analog channel of index 1. On the one hand, this radio signal passes through the analog channel of index k before being digitized into a digital signal which is conventionally called the digital reference signal. On the other hand, this radio signal passes through the analog channel of index 1 before being digitized into a digital signal which is conventionally called a digital signal to be corrected of index 1. In a compensation step 202, the digital circuit U corrects the digital signal to be corrected of index 1 to be compensated on the basis of the parameters ; and 5^. z, so as to compensate for the phase difference and an amplitude difference induced by the second analog channel compared to the first analog channel. Thus, this compensation “erases” the processing differences between the channels of indices k and 1, taking the channel of index k as reference. This compensation typically consists of multiplying the signal to be corrected with index 1 by the scalar l, when this signal is in baseband. f The preceding compensation step 202 can be implemented for any other 1 than k, that is to say for any channel other than the channel of index k taken as reference.
Claims
Claims
1. A method (100) of characterizing processing deviations between a first analog channel and a second analog channel, the method comprising steps of: - injection (102) of a first analog signal at the input of the first analog channel, of a second analog signal at the input of the second analog channel, and of a third signal at the input of the second analog channel, the first analog signal being a periodic signal, the second analog signal being a periodic signal of the same amplitude, of the same period and of the same shape as the first analog signal, and the third analog signal being a periodic signal in phase quadrature with the second analog signal and of the same amplitude and of the same period as the second analog signal, - digitization (104) of the first analog signal at the output of the first analog channel, so as to obtain a first digital signal xk having N samples, digitization of the second signal at the output of the second analog channel, so as to obtain a second digital signal xi having N samples, and digitization of the third analog signal at the output of the second analog channel so as to obtain a third digital signal V / having N samples, - estimation (106) of parameters; and ôk t from the first digital signal, the second digital signal and the third digital signal, where: - / is a ratio between an amplitude of the first analog signal in output of the first analog channel and an amplitude of the second analog signal at the output of the second analog channel, - t is a difference between a phase shift induced by the first analog channel on the first analog signal and a phase shift induced by the second analog channel on the second analog signal, the estimation comprising the application of a least squares method to determine values of the parameters [ and s minimizing the following quantity: E (“) - Yk l ( cos ( ôk t ) x} (n ) - sin (ôk, t(n))}2 in which - xk(n) denotes the nth sample of the first digital signal, - Xi(n) denotes the nth sample of the second digital signal, - V,(«) denotes the nth sample of the third digital signal.
2. The method of claim 1, wherein the first analog signal is sinusoidal.
3. Method according to one of the preceding claims, in which the application of the least squares method comprises the resolution of a system of equations assuming that COS = 1 and / or that COS ( 2ÔÀ. z ) = 1.
4. A method according to one of the preceding claims, wherein the application of the least squares method comprises solving a system of equations assuming that sin ( 5k = 5k f and / or that sin ( 2ôk ; ) = 2ôk k
5. Method according to one of the preceding claims, in which at least one of the first analog signal, the second analog signal and the third analog signal comes from a digital signal generated by a digital circuit implementing the estimation (106) of the parameters Vk [ and dk k
6. Method according to one of the preceding claims, in which the third analog signal is injected at the input of the second analog channel after the second analog signal.
7. Method (200) for compensating for processing deviations between a first analog channel and a second analog channel, the method comprising steps of: - characterizing (100) deviations between a first analog channel and a second analog channel of an analog signal receiver, by implementing the method according to one of claims 1 to 6, - correcting (202) a digital signal from the second analog channel on the basis of the parameters [ and 5k h so as to compensate for a phase deviation and an amplitude deviation induced by the second analog channel relative to the first analog channel.
8. System comprising: - a first analog channel (RFI) capable of receiving a first analog signal, the first signal being a periodic signal, - a second analog channel (RF2) capable of receiving a second analog signal and a third analog signal, the second analog signal being a periodic signal of the same amplitude, the same period and the same shape as the first analog signal, and the
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10. third analog signal being a periodic signal of the same amplitude and period as the second analog signal and in phase quadrature with the second analog signal, - an analog-digital conversion stage (C) capable of: digitizing the first analog signal at the output of the first analog channel, so as to obtain a first digital signal xk having N samples; digitizing the second signal at the output of the second analog channel, so as to obtain a second digital signal xi having N samples; and digitizing the third analog signal at the output of the second analog channel so as to obtain a third digital signal having N samples, - a digital circuit (U) configured to estimate parameters j and ôk f from the first digital signal, the second digital signal and the third digital signal, where Ÿk / is a ratio between an amplitude of the first analog signal at the output of the first analog channel and an amplitude of the second analog signal at the output of the second analog channel, and where 5k / is a difference between a phase shift induced by the first analog channel on the first analog signal and a phase shift induced by the second analog channel on the second analog signal, the estimation implemented by the digital circuit U comprising the application of a least squares method to determine values of the parameters Vk / and Ôk ; minimizing the following quantity yi zV 9 L n = ! (Xk(n) -}(cos (dk ^(n) - sin (<5*})y((n) ) y Or - xk(n) denotes the nth sample of the first digital signal, - Xi(n) denotes the nth sample of the second digital signal, ' ^z(n) denotes the nth sample of the third digital signal. System according to the preceding claim, comprising a digital-to-analog conversion stage (C') configured to generate at least one of the first analog signal, the second analog signal and the third analog signal, from a digital signal provided by the digital circuit (U). System according to the preceding claim, in which the digital-to-analog conversion stage (C') comprises a first digital-to-analog converter (CNA1) configured to generate the first analog signal, and a second digital-to-analog converter (DAC2) configured to generate the second analog signal and the third analog signal.