The present invention relates to a method for correcting defects introduced by a
digitalization system. The present invention also relates to devices associated with th5 e
method. The present invention thus relates to an associated computer program product,
readable information medium, digitization system, digital acquisition chain, reception chain
and assembly.
Digital radiofrequency reception chains include digitalization systems generating
10 stray frequency components. For example, the stray components of the digitalization
system are introduced by an analog-digital converter and/or its input stage, for example
made up of an amplifier. The stray components correspond to defects introduced by the
digitalization system. These defects are primarily nonlinear distortions.
It is desirable to reduce the generated stray components in order to improve the
15 quality of the signals obtained at the output of the reception chains.
To that end, mathematical models are used describing the dynamic nonlinear
behavior of the digitalization converters. These mathematical models generally belong to
the family of Volterra models (Volterra, Hammerstein, Wiener-Hammerstein, RDD for
reduced dynamic deviation, etc.). Such mathematical models are even more complex
20 when they involve a large number of coefficients due to high nonlinearity orders and
depths of memory. Indeed, in the general cases, the defects depend on the value of the
excitation signal of the digitalization system at several moments.
Thus, the algorithms for estimating model coefficients by minimizing the modeling
error within the traditional least-squares meaning of the state of the art involve knowing
25 the ideal digital version of the analog input signal of the digitalization system, which is not
possible in practice. Furthermore, in the case of a real-time application, the complexity of
the mathematical models of the state of the art causes significant computing loads to
estimate the coefficients of the considered model.
There is therefore a need for a method for correcting defects introduced by a
30 digitization system that is easy to implement.
The present description describes a method for correcting defects introduced by a
digitalization system, the digitalization system digitizing an input signal to obtain an output
signal, the defects introduced by the digitalization system being able to be modeled by a
theoretical model linking an input signal of the digitalization system and the temporal drift
35 of the input signal to an output signal of the digitalization system, the theoretical model
being a nonlinear model with memory and discrete time, the theoretical model associating,
3
with each degree of nonlinearity, a set of several coefficients, the method comprising at
least the steps of obtaining the output signal of the digitalization system, calculating
coefficients of the theoretical model by minimizing the error between the output signal
calculated by the theoretical model and the obtained output signal, to obtain a calculated
theoretical model, applying the calculated theoretical model to the obtained output signa5 l
to determine the distortions introduced by the digitalization system and correcting the
output signal to obtain a corrected output signal by subtracting the determined distortions.
According to specific embodiments, the correction method includes one or more of
the following features, considered alone or according to any technically possible
10 combinations:
- the method further includes a step for determining a filter, applying the filter with
the output signal making it possible to obtain an approximation of the input signal.
- the method includes the step of determining a filter including estimating the
spectral power density of the distorted signal, detecting frequency components of
15 the spectral power density of the distorted signal having powers above a
predetermined threshold, establishing a bandpass filter from the detected
components, and calculating the impulse response of the filter from the established
bandpass filter.
- the calculating step includes the digital estimate of the temporal drift of the input
20 signal.
- the theoretical model has a maximum degree of nonlinearity and a depth of
memory.
- the theoretical model is a model obtained by expressing the output signal as a
function of a linear combination of products of samples of the input signal and the
25 temporal drift of the input signal at different moments, the model optionally being
reduced by considering the coefficients to be nil.
The present description also relates to a computer program product including a
readable information medium, on which a computer program is stored comprising program
instructions, the computer program being able to be loaded on a data processing unit and
30 suitable for driving the implementation of a method as previously described when the
computer program is implemented on the data processing unit.
The present description also relates to a readable information medium, storing a
computer program comprising program instructions, the computer program being able to
be loaded on a data processing unit and suitable for driving the implementation of a
35 method as previously described when the computer program is implemented on the data
processing unit.
4
The present description also relates to a digitalization system including an
integrated corrector, the corrector being suitable for carrying out a method for correcting
defects introduced by the digitalization system, the digitalization system digitizing an input
signal to obtain an output signal, the defects introduced by the digitalization system being
able to be modeled by a theoretical model linking an input signal of the digitalizatio5 n
system and the temporal drift of the input signal to an output signal of the digitalization
system, the theoretical model being a nonlinear model with memory and discrete time, the
theoretical model associating, with each degree of nonlinearity, a set of several
coefficients, the method comprising at least the steps of obtaining the output signal of the
10 digitalization system, calculating coefficients of the theoretical model by minimizing the
error between the output signal calculated by the theoretical model and the obtained
output signal, to obtain a calculated theoretical model, applying the calculated theoretical
model to the obtained output signal to determine the distortions introduced by the
digitalization system and correcting the output signal to obtain a corrected output signal by
15 subtracting the determined distortions.
The present description also describes a digital acquisition chain including a
digitalization system and a corrector separate from the digitalization system, the corrector
being suitable for carrying out a method for correcting defects introduced by the
digitalization system, the digitalization system digitizing an input signal to obtain an output
20 signal, the defects introduced by the digitalization system being able to be modeled by a
theoretical model linking an input signal of the digitalization system and the temporal drift
of the input signal to an output signal of the digitalization system, the theoretical model
being a nonlinear model with memory and discrete time, the theoretical model associating,
with each degree of nonlinearity, a set of several coefficients, the method comprising at
25 least the steps of obtaining the output signal of the digitalization system, calculating
coefficients of the theoretical model by minimizing the error between the output signal
calculated by the theoretical model and the obtained output signal, to obtain a calculated
theoretical model, applying the calculated theoretical model to the obtained output signal
to determine the distortions introduced by the digitalization system and correcting the
30 output signal to obtain a corrected output signal by subtracting the determined distortions.
The present description also relates to a reception chain including a digitalization
system as previously described or a digital acquisition chain as previously proposed.
The present description also relates to an assembly, in particular an aircraft, the
assembly including a reception chain as previously described.
5
Other features and advantages of the invention will appear upon reading the
following description of embodiments of the invention, the description being provided as
an example only and in reference to the drawings, which are:
- figure 1, a schematic view of an assembly including a reception chain,
- figure 2, a schematic view of the reception chain of figure 1, an5 d
- figure 3, a block diagram of the operations performed during the
implementation of an example of a method for correcting defects,
- figure 4, a block diagram of part of the operations carried out during the
implementation of an example of a method for correcting defects according to
10 claim 3,
- figure 5, a block diagram of another part of the operations carried out during
the implementation of an example of a method for correcting defects according
to claim 3, and
- figure 6, a block diagram of still another part of the operations carried out
15 during the implementation of an example of a method for correcting defects
according to claim 3.
An assembly 10 is shown schematically in figure 1.
The assembly 10 is for example a vehicle.
According to one particular case, the assembly 10 is an aircraft.
20 The assembly 10 includes systems 14 operating in real-time providing for the
operation of the assembly 10.
Three real-time systems 14 are shown in figure 1.
Hereinafter, it is assumed that one of the real-time systems 14 is a reception chain
16.
25 One example reception chain 16 is shown in figure 2.
The reception chain 16 includes an analog radiofrequency reception stage 18, a
digitalization system 20 and a corrector 22.
For example, according to the proposed example, the analog radiofrequency
reception stage 18 includes an antenna capable of receiving a radiofrequency signal and
30 converting it into an analog electrical signal. In a manner known in itself, the analog
radiofrequency reception stage 18 also comprises other components such as filters,
amplifiers or mixers.
The assembly made up of the analog radiofrequency reception stage 18, the
digitalization system 20 and the corrector 22 forms a digital acquisition chain.
35 The digitalization system 20 is capable of converting an analog signal into a digital
signal.
6
For example, the digitalization system 20 is an analog-digital converter (also
named an analog-to-digital converter), which is assumed in the rest of the description.
The analog-digital converter 20 introduces distortions into the analog signal.
This implies that the analog-to-digital converter 20 is a single-alternation analogdigital
converter, i.e. the analog-to-digital converter 20 is not an interleaved analog-digita5 l
converter.
In particular, the incompatibilities in time or gain (gain and time mismatches in the
English terminology) are not distortions from the analog-digital converter 20 but defects
arising from the presence of interleaving between at least two analog-to-digital converters.
10 The defects introduced by the analog-digital converter 20 can be modeled by a
theoretical model ] linking the input signal of the analog-digital converter 20 and the
temporal drift of the input signal to an output signal of the analog-digital converter 20.
The theoretical model ] is a nonlinear model with memory and discrete time.
The theoretical model ] associates, with each degree of nonlinearity, a set of
15 several coefficients.
In such a model ], by denoting ZVž the ideal digital version of the analog signal
denoted Z›Yœ applied at the input of the analog-digital converter 20, the following equation
1 is obtained:
[Vž ‘ #ZVž  # ˜ ˜ TrWž›ZVžœq –QZ
QY Vž—
r rbq
qc^
i
rc_
20 where:
’ [Vž the signal obtained at the output of the analog-digital converter 20,
’ P is an integer designating the maximum degree of nonlinearity,
’ for a given degree of nonlinearity X L M<*PN, the TrWž, for X L M;*PN,
designates the set of coefficients of order X.
25 Equation 1 can also be written in vectoral form as follows:
[Už ‘ ZVž  ’Zp]”jwhere:
’ Zp] is the regression vector associated with the model ] and defined by:
Zp] ‘ “ZVž*kt
ks Vž*Ÿkt
ks Vž¡‘ * ZVžkt
ks Vž*ZVž‘*,*Ÿkt
ks Vž¡i *,* ZVži•
j
,
30 and
’ \ is the vector gathering the coefficients of the model ] and written \ ‘
’T_;ž*T_<ž*T‘;ž*T‘<ž*T‘=ž*,*Ti;ž*,* TiPž”j+
7
The corrector 22 is able to correct the defects introduced by the analog-digital
converter 20.
"Correct" refers to an acceptable compensation in light of the desired performance
for the analog-digital converter 20.
For example, an acceptable compensation is a compensation making it possible t5 o
reduce the level of the stray components to the noise floor of the analog-digital converter
20 determined by the channel of the reception channel 16 to which the analog-digital
converter 20 belongs.
To that end, the corrector 22 is suitable for implementing a defect correction
10 method.
The corrector 22 is for example a programmable logic circuit.
The FPGA (field-programmable gate array) is one example of such a
programmable logic circuit.
The operation of the corrector 22 is now described in reference to an example
15 embodiment of a method for correcting defects introduced by the analog-digital converter
20. Such an example is illustrated by figures 3 to 6.
The correction method includes an obtaining step E100, a step for determining a
filter E110, a calculating step E120, an application step E130 and a correction step E140.
In the obtaining step E100, the output signal is obtained from the analog-digital
20 converter 20.
The output signal corresponds to the distorted signal.
The output signal is denoted [Vž hereinafter.
During the step for determining a filter, a filter is determined whereof the
application to the output signal makes it possible to obtain an approximation of the input
25 signal.
The application of the filter can be done by convolution in the temporal domain or
by product in the frequency domain.
The step for obtaining the filter E110 includes three sub-steps, which are a spectral
analysis sub-step SE111, a detection sub-step SE112 and a calculating sub-step SE113.
30 In the spectral analysis sub-step SE111, the spectral power density of the distorted
power signal [Vž is estimated. The obtained spectral power density is denoted .uWž.
The spectral power density is estimated by implementing a spectral analysis
algorithm.
For example, a Fast Fourier Transform (FFT) is used, applied to the distorted
35 signal [Vž.
8
In the detected sub-step SE112, the frequency components of the spectral power
density of the distorted signal are detected that have powers above a predetermined
threshold.
The predetermined threshold depends on the operating point of the analog-digital
converter 20 as well as its linearity performance. In fact, the predetermined threshold i5 s
chosen only to detect the non-stray components of higher power.
A bandpass filter gauge OWž is then chosen from the detected components.
According to one simple example, if a component is detected at a frequency, then
the gauge is equal to 1 at said frequency, and if no component is detected at a frequency,
10 the gauge is equal to 0 at said frequency.
In the calculating sub-step SE113, the impulse response of said filter having said
gauge OWž is calculated. The impulse response is denoted SVž+.
An example embodiment of the calculating sub-step SE113 is described
hereinafter.
15 In this example, as shown in figure 4, the calculating sub-step SE113 includes two
operations O1 and O2.
During the first operation O1, the inverse discrete Fourier transform (also referred
to using the acronym IDFT) of the gauge OWž is calculated.
For example, the inverse discrete Fourier transform is calculated using an inverse
20 fast Fourier transform (IFFT) algorithm.
During the operation O2, the impulse response obtained at the output of the first
operation O1 is truncated to the desired length.
Optionally, the impulse response is also weighted by an apodization window.
Thus, at the output of the step for obtaining the filter E110, the impulse response
25 of a bandpass filter adapted to the distorted signal obtained at the output of the analogdigital
converter 20 is obtained.
During the calculating step E120, the coefficients of the theoretical model ] are
calculated to obtain a theoretical model calculated from an approximation of the input
signal on the one hand and the output signal of the analog-digital converter 20 on the
30 other hand.
For example, the coefficients of the considered model ] are determined by
implementing an algorithm for minimizing the modeling error, in particular within the
meaning of least-squares.
More explicitly, on the one hand, the impulse response filter TVž is used to build a
35 rough approximation of the ideal digital signal ZVž of the analog excitation signal of the
digitalization system 20 by filtering the signal [Vž (the component(s) of stronger powers
9
are kept). On the other hand, the inverse of this filter is used (optionally) to eliminate the
components of stronger power from the signal [Vž. An alternative to this second filtering
consists of performing a subtraction between the signal [Vž filtered by TWž and the initial
signal [Vž (see figure 5). The algorithm for minimizing the modeling error within the
meaning of least-squares is then done with the rough approximation of the ideal digita5 l
signal ZVž and the signal resulting from the suppression of the components of higher
power from the signal [Vž.
In summary, the set of these coefficients is denoted \š in figure 3.
In still other words, the coefficients TrWž of the model ] are determined by using
10 the traditional linear optimization methods applied to the problem of the Wiener filter as it
is set out in Figure 5. Let RVž denote the estimating error defined such that
RVž ‘ [Vž  [™Vž ‘ [kVž  [™kVž
where:
’ [kVž is defined as [Vž  ZVž, and
15 ’ the signals denoted with a ~ are signals calculated using the model ].
The identification of the coefficients of the model ] then consists of minimizing
the mean quadratic estimating error or the quadratic sum of said error. For example, the
coefficients are then obtained using the Wiener-Hopf, block least square (BLS), recursive
least square algorithm, least mean square (LMS) algorithm or normalized least mean
20 square (NLMS) algorithm solutions.
In each of the preceding techniques, the estimate of the coefficients TrWž implies
knowing the samples ZVž associated with the excitation of the digitalization system 20. In
the case at hand, to replace the samples, a rough approximation of ZVž is used obtained
by filtering the signal [Vž distorted by the impulse response SVž previously designed.
25 The rough approximation of the signal is called ZGVž.
Furthermore, the calculating step includes the estimate of the temporal drift of the
input signal.
For example, this estimate can be done by digital filtering of its rough
approximation ZGVž.
30 During step E130, each coefficient of the considered model ] as well as the
model in question is used to obtain the associated defects.
Next, a correction step E140 is carried out by performing a subtraction from the
output signal of the obtained defects, to obtain a corrected output signal denoted Z™Vž.
More specifically, part of the model ] as well as a signal that is the output signal
35 [Vž, and not the ideal signal, is used.
;
The described method makes it possible to determine a specific defect without
knowing the ideal digital version of the analog signal to be obtained at the output of the
analog-digital converter 20. This makes it possible to use the method when an assembly
10 is operating under variable environmental conditions (temperature, frequency
components of the excitation signal, power of the excitation signal, etc.). The method i5 s
thus a correction method without calibration.
In other words, the method proposes to build an approximation of the signal ZVž
from the distorted signal [Vž to carry out an estimating algorithm based on a nonlinear
model with memory of the analog-digital converter 20 and which does not assume
10 knowing the ideal digital version of the input analog signal ZVž.
The applicant has shown, during testing, that the estimating method makes it
possible to determine, without calibration and effectively, the digitalization defects
introduced by the analog-digital converter 20.
The method applies to any type of theoretical model, such that the defects
15 introduced by the digitalization system 20 are able to be modeled by a theoretical model
linking an input signal of the digitalization system 20 and the temporal drift of the input
signal to an output signal of the digitalization system 20 and such that the theoretical
model has a maximum degree of nonlinearity and optionally a depth of memory.
As an example, the model is an alternative of the model described by equation 1
20 obtained by expressing the output signal as a function of a linear combination of products
of samples of the input signal and the temporal drift of the input signal at different
moments.
Furthermore, the calculating complexity of the implementation of these models can
be reduced by considering certain coefficients to be nil, in particular the even coefficients
25 or odd coefficients.
More generally, the method applies to any system or subsystem for the digital
acquisition of analog signals containing an analog-digital converter.
In particular, the method can be used in the context of multichannel digitalized
radiofrequency receivers, i.e., whereof the instantaneous band is wide enough to allow the
30 simultaneous processing of several communication signals.
Devices are also proposed allowing the implementation of the method.
For example, the interaction of a computer program product with a system makes
it possible to carry out the correction method.
The system is a computer.
35 More generally, the system is an electronic computer able to manipulate and/or
transform data represented as electronic or physical quantities in registers of the system
21
and/or memories into other similar data corresponding to physical data in the memories,
registers or other types of display, transmission or storage devices.
The system includes a processor comprising a data processing unit, memories and
an information medium reader. The system also comprises a keyboard and a display unit.
The computer program product includes a readable information medium5 .
A readable information medium is a medium readable by the system, usually by
the data processing unit. The readable information medium is a medium suitable for
storing electronic instructions and able to be coupled with a bus of a computer system.
As an example, the readable information medium is a floppy disk, an optical disc, a
10 CD-ROM, a magnetic-optical disc, a ROM memory, a RAM memory, an EPROM memory,
an EEPROM memory, a magnetic card or an optical card.
A computer program comprising program instructions is stored on the readable
information medium.
The computer program can be loaded on the data processing unit and is suitable
15 for driving the implementation of the correction method when the computer program is
implemented on the data processing unit.
More generally, a method is proposed resulting from any technically possible
combination of the embodiments previously described.

I/We Claim:
1.- A method for correcting defects introduced by a digitalization system (20), the
digitalization system (20) digitizing an input signal to obtain an output signal, the defects
introduced by the digitalization system (20) being able to be modeled by a theoretica5 l
model (]) linking an input signal of the digitalization system (20) and the temporal drift of
the input signal to an output signal of the digitalization system (20), the theoretical model
(]œ) being a nonlinear model with memory and discrete time, the theoretical model (])
associating, with each degree of nonlinearity, a set of several coefficients, the method
10 comprising at least the steps of:
- obtaining the output signal of the digitalization system (20),
- calculating coefficients of the theoretical model (]) by minimizing the error
between the output signal calculated by the theoretical model (]) and the
obtained output signal, to obtain a calculated theoretical model,
15 - applying the calculated theoretical model to the obtained output signal to
determine the distortions introduced by the digitalization system (20), and
- correcting the output signal to obtain a corrected output signal by subtracting the
determined distortions.
20 2.- The method according to claim 1, wherein the method further includes a step
for determining a filter, applying the filter with the output signal making it possible to obtain
an approximation of the input signal.
3.- The method according to claim 2, wherein the method includes the step for
25 determining a filter including:
- estimating the spectral power density of the distorted signal,
- detecting the frequency components of the spectral power density of the distorted
signal having powers above a predetermined threshold,
- establishing a bandpass filter from the detected components, and
30 - calculating the impulse response of the filter from the established bandpass filter.
4.- The method according to any one of claims 1 to 3, wherein the calculating step
includes the digital estimate of the temporal drift of the input signal.
35 5.- The method according to any one of claims 1 to 4, wherein the theoretical
model (]) has a maximum degree of nonlinearity and a depth of memory.
23
6.- The method according to any one of claims 1 to 5, wherein the theoretical
model (]) is a model obtained by expressing the output signal as a function of a linear
combination of products of samples of the input signal and the temporal drift of the input
signal at different moments, the model optionally being reduced by considering th5 e
coefficients to be nil.
7.- A computer program product including a readable information medium, on
which a computer program is stored comprising program instructions, the computer
10 program being able to be loaded on a data processing unit and suitable for driving the
implementation of a method according to any one of claims 1 to 6 when the computer
program is implemented on the data processing unit.
8.- A readable computer medium storing a computer program comprising program
15 instructions, the computer program being able to be loaded on a data processing unit and
suitable for driving the implementation of a method according to any one of claims 1 to 7
when the computer program is implemented on the data processing unit.
9.- A digitalization system (20) including an integrated corrector (22), the corrector
20 (22) being suitable for carrying out a method for correcting defects introduced by the
digitalization system (20), the digitalization system (20) digitizing an input signal to obtain
an output signal, the defects introduced by the digitalization system (20) being able to be
modeled by a theoretical model (]) linking an input signal of the digitalization system (20)
and the temporal drift of the input signal to an output signal of the digitalization system
25 (20), the theoretical model (]) being a nonlinear model with memory and discrete time,
the theoretical model (]) associating, with each degree of nonlinearity, a set of several
coefficients, the method comprising at least the steps of:
- obtaining the output signal of the digitalization system (20),
- calculating coefficients of the theoretical model (]) by minimizing the error
30 between the output signal calculated by the theoretical model (]) and the
obtained output signal, to obtain a calculated theoretical model,
- applying the calculated theoretical model to the obtained output signal to
determine the distortions introduced by the digitalization system (20), and
- correcting the output signal to obtain a corrected output signal by subtracting the
35 determined distortions.
24
10.- A digital acquisition chain including a digitalization chain (20) and a corrector
(22) separated from the digitalization system (20), the corrector (22) being suitable for
carrying out a method for correcting defects introduced by the digitalization system (20),
the digitalization system (20) digitizing an input signal to obtain an output signal, the
defects introduced by the digitalization system (20) being able to be modeled by 5 a
theoretical model (]) linking an input signal of the digitalization system (20) and the
temporal drift of the input signal to an output signal of the digitalization system (20), the
theoretical model (]) being a nonlinear model with memory and discrete time, the
theoretical model (]) associating, with each degree of nonlinearity, a set of several
10 coefficients, the method comprising at least the steps of:
- obtaining the output signal of the digitalization system (20),
- calculating coefficients of the theoretical model (]) by minimizing the error
between the output signal calculated by the theoretical model (]) and the
obtained output signal, to obtain a calculated theoretical model,
15 - applying the calculated theoretical model to the obtained output signal to
determine the distortions introduced by the digitalization system (20), and
- correcting the output signal to obtain a corrected output signal by subtracting the
determined distortions.
20 11.- A reception chain (16) including a digitalization system (20) according to claim
9 or a digital acquisition chain according to claim 10.
12.- An assembly (10), in particular an aircraft, the assembly (10) including a
reception chain (16) according to claim 11.