The present invention claims the benefit of patent application FR 18 73917 filed on December 21, 2018 which is hereby incorporated by reference.
FIELD OF INVENTION
This invention relates to a signal interference determination method for determining the interference situation of a signal in a bipolar interferometer with undersampled digital reception. This invention also relates to a computer program product, an associated data carrier-storage medium and interferometer.
TECHNOLOGICAL BACKGROUND
The invention relates to the field of wide band reception of electromagnetic signals. More precisely, the present invention relates to a bipolar receiver with undersampled digital reception.
These devices are interferometers, that is to say goniometers based on the perception of an incident radio signal by a set of space diversity antennas.
Since the signals of interest for these devices happen to be at very different carrier frequencies, the frequency band to be received is very high.
Sampling this band in accordance with the Shannon sampling criterion proves to be difficult because it involves ultra-fast digital analogue conversion components, which do not satisfy weight/volume/consumption constraints, when these components are not completely inaccessible with current technologies for the bandwidths that it is sought to be processed. In addition, if such components existed, they would generate a digital data stream that would be incompatible with the data transfer bus speeds/rates and processing capabilities of the current computing units used to build the digital signal processing modules.
To solve this problem, use is made of a new type of digital receiver, which performs several sampling operations at sampling frequencies or rates far below the Nyquist frequency (equal to twice the frequency band for real signals).
This undersampling has the advantage of removing the constraints on the analogue-to-digital conversion, but causes the receiving band to fold back into the working Nyquist band. A frequency measured in this Nyquist zone is therefore ambiguous: a judicious selection of the number and values of sampling frequencies makes it possible to remove these ambiguities.

2
Another consequence of folding is that two (or more) signals present at the same time at different frequencies in the receiving band may happen to be at the same or close frequencies in the working Nyquist zone. This mixing situation is referred to as interference/noise. Figure 8 provides an illustration thereof problem. This occurs when two simultaneous signals have carrier frequencies whereof the difference or sum is a multiple of one of the sampling frequencies.
In the following sections, when a given frequency in the receiving band is examined, a signal of interest present at that frequency will be referred to as a useful/wanted signal. A possible simultaneous signal present at a frequency whereof the sum or difference with the frequency of the wanted signal is a multiple of one of the sampling frequencies will be referred to as a parasitic signal (interfering/spurious signal). When the frequency of the parasitic signal is examined in turn, the parasitic signal will become a useful signal, and the signal previously referred to as the useful signal will be considered as a parasitic signal.
These mixtures due to spectral folding make it difficult to develop a detection test (presence or absence of a useful signal), in respect whereof false alarms must be controlled. In addition, the signal resulting from the mixing of a wanted signal with an undetected undesired parasite will be poorly characterized, which could distort the expected paths/channels or even create false ones. These mixtures cannot be neglected, especially since they are far more frequent than the real mixtures in the receiving band.
SUMMARY OF THE INVENTION
There is therefore a need for an interference detection method for detecting interference situations in a digital undersampling receiver.
For this purpose, this description relates to an interference determination method for determining interference situations due to spectral folding in a wide band digital receiver, the method being operationally implemented by means of an interferometer having P antennas, where P is an integer that is greater than or equal to 1, each antenna being followed by an analogue reception chain and at least one digital reception module, the
number of digital reception modules being & , the method comprising at least one step of:
- sampling of the signals delivered by all the receiving chains, making use of M
different sampling frequencies fem, that are lower than the Nyquist-Shannon frequency,
m ranging from 1 to ** , and M being an integer greater than or equal to 4, the number of digital reception modules operating with a frequency fm being equal \oR-m, and the number
of digital reception modules for an antenna V being Qp , with R = Em=i^m =Y,p=iQP, the

said sampling frequencies fem providing integer numbers of samples Nm over a given time AT ;
- spectral analysis by means of synchronous and successive discrete Fourier
transforms, allowing for, on each of the ff digital reception modules, a time/frequency representation referred to as time resolution grid AT , and frequency resolution grid AF , each element of the grid being referred to as time/frequency cell and containing a complex quantity referred to as measurement;
- selection of a set of time/frequency domains (in the reception band), each
time/frequency domain being perceived in the ^ digital reception modules as ff
superimposed windows, each of the windows being composed of £ connected time/frequency cells;
- for each time/frequency domain, concatenation of the measurements taken from
each of the R windows in the form of 8 vectors of dimension £ x l denoted as Ypm _
where V is the sensor index and m is the sampling index;
- determination of the presence of possible parasites (interfering/spurious signals)
on each time/frequency domain, consisting in determining from among the following
hypotheses, based on the measurement vectors obtained, the hypothesis that maximizes
an approximation of the probability log-density of the A measurement vectors V:
- #D : absence of parasites;
- "«»• : presence of at least one parasite on the sample ™ a, with m0 e [1,M], and
- Hmt,mx: presence of at least one parasite on the sample ™ o and at least one parasite on the sample mi, with avec m1 e [l,M],m0 ^ mj) and m0 e [1,M].
According to particular embodiments, the method has one or more of the following characteristic features, taken into consideration in isolation or in accordance with all technically possible combinations:
- among the following three hypotheses:
• He: "absence of parasites" hypothesis;
• **i: hypothesis that maximizes an approximation of the log-density of probability, from among the hypotheses with one parasitized sampling frequency;
• H- ■ hypothesis that maximizes an approximation of the log-density of probability, from among the hypotheses with two parasitized sampling frequencies;
the hypothesis chosen is:

• f*n, if its approximated log-density is the one for which correspondence to its assumed Gaussian law distribution is maximum;
-otherwise, ffi, if its approximated log-density restricted to non-parasitized (no interference) channels is the one for which correspondence to its assumed Gaussian law distribution is maximum;
otherwise, ^:, if its approximated log-density restricted to non-parasitized (no interference) channels is the one for which correspondence to its assumed Gaussian law distribution is maximum;
otherwise, it is determined that there are more than two parasitized sampling frequencies.
- at least one of the following criteria is calculated:
- a criterion of non-variability of the *W with respect to their filtered value on the different sampling frequencies specific to the antenna p;
- a criterion of equality of the modules ^ filtered on the different sampling frequencies specific to the antenna p; and
- a criterion of collinearity of the modules ^ filtered on the different sampling frequencies of the antenna p.

- the one or more calculated criterion/criteria are used to obtain an approximation of the probability log-density of the measurements.
- the approximated probability log-density is calculated according to the following approximations:
- for the hypothesis ^D :
1 R
r ~,var < f~,mod < ~,colwhere:
vvar _ _y \\y II2 vmod _ (y „ M7 \\\ _ y „ M7 II2 vcol _ ny „ „ (\7f/ I _ \\Z IIIIZ lh
_QE ' aP R'
• Zp is the mean of the vectors *W on the reception modules associated with
the same antenna p: Zp = —YlTnYpm, and • Ypm is the deviation of a vector *pm from the mean ^p;

- for the hypotheses w^-n:
rmo = Rm0L\n [——J + rmo;
where c is an unknown constant representing the average power of the parasite on an axis, and where fmo is defined by:

p _ 1 ..var i R (..mod i vcolV mo — 2a2 Ym° 2o2^Ym° ™oi'
where:
? 2 . vvar — _ y IIy || vm«i _ fy n \\7 \Y\ _ V n ITTIQ Li P>m \\lp7n\\ ' YTTIQ \/-ipupmQ II pm0ll/ ^P Pmo IKpmoll
. vcol _ o y „ „ (\y* 7 | _ ||7 ||||7 ||V Ym0 u l-ipm || ipm|| ' Am0mi v^P pm^-m^ \\ pm^m^W)
7n^7nQlm1
V 11-7 II2
/-ip^pniQin-L W^pniQin-L \\ >
vcol — 9 V n n f| 7* 7 I _ II7 ||||7 IIV
/m0mi ^/-ip the said
sampling frequencies /e™ providing integer numbers of samples Nm over a given time period AT;
- a spectral analysis step by means of synchronous and successive discrete Fourier
transforms, allowing for, on each of the 2R digital reception modules, a time/frequency
representation referred to as time resolution grid AT , and frequency resolution grid AF ,
each element of the grid being referred to as time/frequency cell and containing a complex
quantity referred to as measurement;

- a domain selection step for selecting a set of time/frequency domains (in the
reception band), each time/frequency domain being perceived in the A digital reception
modules of the sub-array 1 and in the A digital reception modules of the sub-array 2 as 2R superposable windows, each of the windows being composed of L connected time/frequency cells;
- for each time/frequency domain, a concatenation step for concatenating the
measurements taken from each of the 2R windows in the form of R vectors of dimension i x 1 for the sub-array 1, denoted as ^pm, where P is the sensor index and m is the sampling index, and in the form of R vectors of dimension Lxi for the sub-array 2,
denoted as ^m, where V is the sensor index and m is the sampling index;
- for each time/frequency domain, a parasite (interference) determination step for
determining the presence of possible parasites (interfering/spurious signals), consisting in
choosing, from among the following hypotheses, based on the measurement vectors
obtained, the hypothesis that maximizes an approximation of the probability log-density of
the A vectors ^ip^ and the ff vectors *W™«*:
• #D : absence of parasites;
• ff*™«: presence of at least one parasite on the sample ™ a, with m« e \X. M] ■ and
. tfmlJmi: presence of at least one parasite on the sample mo and one parasite on the sample™i, with™i e [l,Af] m^m.) and ™D E[1,M]
According to one embodiment, the interference determination method for determining the interference situation is such that, among the following three hypotheses:
• HB : "absence of parasites" hypothesis;
• #i: hypothesis that maximizes an approximation of the log-density of probability, from among the hypotheses with one parasitized sampling frequency;
• ffa: hypothesis that maximizes an approximation of the log-density of probability, from among the hypotheses with two parasitized sampling frequencies;
the hypothesis chosen is:
- tf n, if its approximated log-density is the one for which correspondence to its assumed Gaussian law distribution is maximum;
- otherwise, ^i, if its approximated log-density restricted to non-parasitized (no interference) channels is the one for which correspondence to its assumed Gaussian law distribution is maximum;

- otherwise, ^s, if its approximated log-density restricted to non-parasitized (no
interference) channels is the one for which correspondence to its assumed Gaussian law
distribution is maximum;
otherwise, it is determined that there are more than two parasitized sampling frequencies.
According to one embodiment, the interference determination method for determining the interference situation includes:
- the calculation of the energy collected by the first sub-array;
- the calculation of the energy collected by the second sub-array;
the interference determination step being implemented for the sub-array that collects the maximum energy according to the single polarization algorithm.
According to one embodiment, the following criteria are calculated:
- for each sub-array, the single polarization criterion, and
- for the two sub-arrays taken together, the bipolar criterion.
According to one embodiment, the one or more calculated criterion/criteria are used to obtain an approximation of the probability log-density of the measurements.
According to one embodiment, the approximated probability log-density is calculated according to the following approximations:
- For the hypothesis wn (no parasites present), the quantity r0, also
denoted as rn :
^i = -^0, wherein ^D is the maximum eigenvalue of the quadratic expression in cf c2 :
FQ0 = -^ (K,Sr + KzT) + ^ (ci (r$ + y™d) + C2 Glo + Y?o°d) + fq0) Where /*?• is the quadratic expression:
Z
2 X""1 ii2 X""1
aq \\^2 q || — c2 7. °"P II 1-PII ^ ^C1C2 }aPai\ ^P 2lq p p,q
which can be interpreted as a bipolar criterion of module equality and co-linearity;
where Y±£r, 7iSD ,7ID1 , Y%£r, YTB" ,Y2B' are the single polarization criteria of non-variability, module equality and colinearity respectively for the sub-arrays for the "no parasites present" hypothesis defined in claim 4;

where ffp is the proportion of digital reception modules operating with the antenna with index p on the first sub-array; ap is the proportion of digital reception modules operating with the antenna with index q on the second sub-array; where z*p is the mean of the vectors ^ipm over all the samples of the antenna P of the first sub-array 1: Zp = —£m Ylpm and wherein ^=g is the
mean of the vectors **»«* over all samples of the antenna m* is the proportion of digital reception modules attached to the antenna
with index V on the first sub-array, which do not operate with the frequency fe^-a and ff?mD
is the proportion of digital reception modules attached to the antenna with index 1 on the
second sub-array, which do not operate with the frequency femu ;
i i
Wnere Z,-^pTn — — 2jm*ma 'lpm 3nCI ^2pma — — 2jm*ma *2pm>
where Qp.m, is the number of digital reception modules attached to the antenna with index P on the first sub-array, which do not operate with the frequency ^e^-D and Qq.^-a is the number of digital reception modules attached to the antenna with index Q on the second sub-array, which do not operate with the frequency fem,;
Where ^-a is the number of digital reception modules operating at the sampling frequency /*«■ on each sub-array;
where ci represents the gain of the first sub-array in the polarization of the incident signal;
where ci represents the gain of the second sub-array in the polarization of the incident signal.
- for the hypotheses ^m*.!**, the quantities

2na
t-7n07n1
c
lm0m1 ~ "iPm0m1 ~ '"mllra1'''111 r I T A;

where ^m.mi is the number of digital reception modules operating with the frequency fem, or with the frequency fe™-i in each of the two sub-arrays, and where jlm»fB, represents the approximated log-density restricted to non-parasitized (no interference) channels; it is equal to the maximum eigen value of the quadratic expression:
PO — fvvar 4- vvar rVm0m1 2(j2 \'l,m0m1 ^ Y2,m0m1J
R — R
j m0m1 r 2(-,col i vmod \ i r2(~,col i vmod ' j 2 V 1 \ 2-im^mr,,m-[ *±pm «"U ^j2pmr,pm-[ 7> 2-im^mr,,m-[ *2gmi
where Qp,m9,m1 is the number of digital reception modules attached to the antenna with index V that do not operate with either the sampling frequency fe™», or with the sampling frequency fe™.x on the first sub-array, and Qq,mm,m1 is the number of digital reception modules attached to the antenna with index q that do not operate with either the sampling frequency ^m, or the sampling frequency fe^-± on the second sub-array;
where ^™«mi is the number of digital reception modules operating at the sampling frequency fema or/emi on each sub-array;
where ci represents the gain of the first sub-array in the polarization of the incident signal;
where ca represents the gain of the second sub-array in the polarization of the incident signal;
A computer program product is also provided comprising a readable data carrier-storage medium, on which is saved and stored a computer program comprising of program instructions, the computer program being loadable on to a data processing unit and adapted so as to cause the operational implementation of a method as previously described when the computer program is deployed to run on the data processing unit.
A readable data carrier-storage medium is also provided on which is saved and stored a computer program comprising of program instructions, the computer program being loadable on to a data processing unit and adapted so as to cause the operational

implementation of a method as previously described when the computer program is deployed to run on the data processing unit.
Also provided is an interferometer with two single polarization sub-arrays having p antennas, where P is an integer that is greater than or equal to 2, each antenna being followed by an analogue reception chain and one or more digital reception modules, each digital reception module comprising an analogue-to-digital conversion system and a digital processing module, each analogue-to-digital conversion system being associated with a respective sampling frequency, an analogue-to-digital conversion system being associated with a sampling frequency when the analogue-to-digital conversion system is capable of performing sampling at the sampling frequency, each frequency being such that the sampling performed by the analogue-to-digital conversion system is a sampling that does not satisfy the Shannon criterion and with the interferometer being capable of operational implementation of a method as previously described.
BRIEF DESCRIPTION OF THE DRAWINGS
The characteristic features and advantages of the invention will become apparent upon reading the description that follows, given only as an non-exhaustive example, and made with reference to the attached drawings, for which:
- [Fig 1] Figure 1 is an illustration of the problem of the interference caused;
- [Fig 2] Figure 2 is a schematic view of an exemplary interferometer comprising a computer;
- [Fig 3] Figure 3 is a graphical representation of an example of a time/frequency grid;
- [Fig 4] Figure 4 is a representation of the wanted (useful) signal in a time/frequency grid;

- [Fig 5] Figure 5 is a schematic representation of two time/frequency grids associated with two different sampling frequencies, and containing the same incident signal;
- [Fig 6] Figure 6 is an illustration of an example of the operational implementation of one of the steps in the interference determination method for determining the interference situation;
- [Fig 7] Figure 7 is an illustration of an example of the operational implementation of the steps of the method;
- [Fig 8] Figure 8 is a schematic view of a bipolar interferometer comprising a computer;

- [Fig 9] Figure 9 is a graphical representation of the two time/frequency grids
associated with the antenna V in the two sub-arrays and the sampling frequency fem;
- [Fig 10] Figure 10 is a representation of a wanted signal in the two time/frequency
grids associated with the antenna V in the two sub-arrays and the sampling frequency fem . ■
- [Fig 11] Figure 11 is a schematic representation of the four time/frequency grids associated with the antenna P in the two subarrays and the two sampling frequencies fe™t and /e"iz _ containing the same incident signal; and
- [Fig 12] Figure 12 is an illustration of an example of the operational implementation of the steps of the method for the case of the bipolar interferometer shown in Figure 8.
DESCRIPTION OF THE EMBODIMENTS OF THE INVENTION The embodiments will be described according to two modalities, which are detailed below, namely a single polarization case and a bipolar case. Although there are many similarities between the two cases, to simplify reading, the two cases will be treated largely independently.
DESCRIPTION OF THE EMBODIMENTS THE INVENTION
The embodiments will be described according to two modalities, which are detailed below, namely a single polarization case and a bipolar case. Although there are many similarities between the two cases, to simplify reading, the two cases will be treated largely independently.
SINGLE POLARIZATION CASE
Before more precisely describing the several embodiments in detail, a brief explanation is provided of the inventive approach followed by the applicant, starting firstly from the existing need.
There is a need for an enhanced interference detection function, that provides the ability to determine not only the presence or absence of a wanted (useful) signal at a given frequency, but also to determine the specific interference situation prevailing (absence of parasites ie no interference, or presence of parasites ie interference, and which are the sampling frequencies), with the least possible error. In the case where the number of parasitized (interference) sampling frequencies is equal to M, and the number of sampling frequencies is strictly greater than M-2, it shall be sought only to ascertain that such is the

situation prevailing (without seeking to determine which are the parasitized (interference) channels), also with the least possible error.
This will allow for improving the performance with respect to the detection itself, as also the other functions of the processing chain (estimation of the direction of arrival, signal characterization). Another advantage is that it will allow the use of analogue-to-digital conversion components operating at frequencies lower than the Nyquist frequency, while minimizing the effects of spectral folding.
The literature on detection generally assumes that the received signal is alone in its environment, and does not address the problem of interference, i.e. interference between signals due to spectral folding.
It is proposed to use the receiver architecture shown in Figure 2, in the general case of several sampling frequencies per antenna.
This architecture is that of an instantaneous wide band interferometer with digital
reception and undersampling. The interferometer consists of P very wide band antennas; each of these antennas is connected to the input of an instantaneous wide band reception chain, designed and developed an analogue manner. Each analogue receiving chain outputs its signal to at least one digital reception module, consisting of an analogue-to-digital conversion module followed by a digital signal processing module capable of performing spectral analysis. The set of analogue-to-digital conversion modules
uses a set of M sampling frequencies that are different and lower than the Nyquist frequency. The same sampling frequency can be used multiple times, but necessarily in combination with analogue-to-digital conversion modules corresponding to different antennas.
The unit formed by a digital reception module and the analogue reception chain with which it is associated is referred to as the reception channel.
As explained above, the problem encountered with subsampling is that two signals that are temporally superimposed or overlapping can also, by way of spectral folding, be frequency superimposed in the working Nyquist zone, although this superimposition or overlap does not exist in the receiving band. With respect to one of the two signals, the term "interference of the the said signal due to spectral folding" may be used. The problem affects both signals by reciprocity.
It is not proposed to deal with signals of sufficiently close frequencies originally in the receiving band, which therefore are not frequency resolved in the receiving band (see real mixtures). However, this case is much less likely than the cases dealt with.

The purpose of the proposed method is to determine, on the basis of the measurements, the interference situation due to spectral folding (absence or presence of parasites (interfering/spurious signals), and, in case of presence of parasites, identify the frequencies that are the parasitized/interference sampling frequencies).
Since it is assumed that there are no more than two sampling frequencies among
M affected by signal interference, the number of possible interference situations amounts to —^— (1 for no interference frequency, ** for only one interference frequency and
M for two interference frequencies).
The applicant proposes to exploit the fact that the signals of interest are generally spread over a plurality of adjacent spectral analysis channels and present in multiple successive spectral analyses, and model the measurements extracted over a plurality of adjacent channels and multiple successive analyses in vectorial form.
One of the applicant's ideas is in particular to approximate, for each possible interference situation, the likelihood function of the measurement vectors by a computable majorant (function) that can only be calculated by means of square moduli, scalar products and filtering of measurement vectors taken from all reception channels, and can be interpreted as the sum of three criteria reflecting their variability, the equality of their modulus and their collinearity respectively.
The proposed method determines the interference situation (absence or presence of parasites, and in the event of interference, the sampling frequencies affected), while maximizing, over all possible interference situations, the approximation previously obtained, or maximizing the correspondence thereof to its assumed Gaussian law distribution.
As the interference situation is known, the method then eliminates the parasitized (interference) channels and only uses the non-sparitized (no interference) channels to decide whether or not there is a useful signal present by operationally implementing a conventional thermal noise detection method.
In short, it is possible to express the invention as an interference determination method for determining interference situations due to spectral folding and a signal detection method for detecting electromagnetic signals that are operationally implemented by means
of an array, with ? wide band antennas, where p is an integer that is greater than or equal to 1, each antenna being followed by an analogue reception chain and one or more digital
reception modules, the number of digital reception modules being ff in total, the said method comprising:

- a signal sampling step for sampling the signals delivered by all the receiving chains,
making use of ** different sampling frequencies /e™ , that are lower than the
Nyquist-Shannon frequency, m ranging from 1 to M, and M being an integer greater than or equal to 4, the number of digital reception modules operating with a sampling frequency
fem being equal to A™, and the number of digital reception modules for an antenna V
being .
For the hypotheses ^™« (one or more parasite(s) present on the sampling frequency
mn), the quantities
4io = Rm0Llnp^) + rmo, where r™« is defined by:
~ 1 R
p _ yvar . foment . yCt>l' 2(7 3 ■ 2(7 : ^ ■ fm*J-
where ■ vvar = -V nm HY II2 vmod = (Y a \\7 lh -V a 117 II2
WIICIC . ymo — /, p,m ||Ipm|| < Im0 V/jp upm0 ll^pmo ||J Zjp upm0 ll^pmo ||
Ymi = 25]ptt ■ vccl '»!% 2cr" fm"m* 2<75 vm*m± rmnm.±j where'
|2
2
vrar y My II vmod /'y a II 7 M^ Y /y II 7 II
YIUQIUI 2-I P>m ||*pm|| > YIUQIUI yLtp^-piUQini W^prnQiUiW) /-ip ^-pm^rn^ ^^pm^m^ >
7n^7nQ,m1
vcol _ir „ „ (\y* 7 I — 117 IIII7 IIV
Ym.Qm1 ^ 2-tp fmo, fmo,mi), then there are two parasitized sampling frequencies, and these frequencies are ™ n and ™i (hypothesis
- in a second embodiment, the method includes a step of calculation of:
f° = f° /\ = max (tL)
1 m0 = l MV m°J
r2 = max (fLm,)
1 m0 = l,...,Mv mom\J mx = l,...,M
where:
• T0 represents the "absence of parasites (no interference)" hypothesis. This hypothesis is referred to as Ha-

• r1 represents the best hypothesis with one parasitized sampling frequency ffm« , referred to as ^ 1, and
• r2 represents the best hypothesis with two parasitized sampling frequencies ^m,,™, _ referred to as ^i.
in this second embodiment, the method also includes the determination of the best hypothesis among H0 ,^i, # s, the one chosen being:
**D , if its approximated log-density ^n satisfies the test of correspondence to its supposed Gaussian law distribution (see single polarization case);
Otherwise, Hi, if its approximated log-density restricted to non-parasitized (no
interference) channels *"i satisfies the test of correspondence to its supposed Gaussian law distribution (see single polarization case);
Otherwise, H2 _ jf the approximated log-density restricted to non-parasitized (no
interference) channels ^3 satisfies the test of correspondence to its supposed Gaussian law distribution (see single polarization case);
Otherwise, there are more than two parasitized sampling frequencies.
- the calculations are limited to time/frequency domains assumed to contain more
than just noise, by applying a pre-detection algorithm consisting in comparing the quadratic
sum of the moduli of the ^ measurement vectors of each time/frequency domain with a predefined threshold, set for a fairly high false alarm probability.
- the total number of sampling frequencies ** is greater than or equal to 3, and the
method determines the interference situation from among all the hypotheses: no parasitized
sampling frequency, one parasitized sampling frequency, and so on, up to M — 2 parasitized sampling frequencies.
- the method uses all the partial criteria, or only one or two of the partial criteria, or any weighting of the partial criteria.
- the processed signals are real or complex.
- the method works in degraded mode if the resolution &F is not the same for all grids.
An more detailed example of operational implementation is now described. Figure 2 illustrates the general architecture of an interferometer 10 for which the invention is applicable.

The interferometer includes P antennas Ai> --AP very wide band, a priori identical,
followed each by a reception chain CRi' -,CRP. |n the general case p is an integer greater than or equal to 2. The invention also applies when P=1.
For the following sections, the index V of each antenna is an integer between 1 and P, also serving as a reference for all the elements attached to it, material means, measurements and various calculated quantities.
The phase centres of the antennas can be distributed spatially. The spatial
distribution of antennas Ai> — Ar _ js defined to ensure a specified accuracy and angular ambiguity ratio.
Behind each antenna, an analogue filter selects a very wide band Umin- fmax\j\. For a narrow band signal emitted from an infinite source, the signal delivered from
the antenna with index V has the following expression:
Spit) = ppa(t) cos (inft + O(t) + cpp(0,X)) + bp(t) where:
• f is the carrier frequency of the incident signal within the receiving band; f=c/A,
where c is the speed of light and X the wavelength.
• a(t) and O(t) are the modulations of the incident signal;
• pp is the modulus of the gain of the antenna V ; for an interferometer it can be
assumed that pp = 1;
. + .
These M sampling frequency values 24 are assigned to the analogue-to-digital conversion modules 22 that sample the signal provided by the receiving chains respectively
upstream, at the sampling frequency fem, m being an integer between 1 and M.
If a given sampling frequency is assigned to an analogue-to-digital conversion module associated with a given antenna, it is assigned only once.
The number of digital reception modules R is at most equal to P-M- . In practice,
for material reasons, the aim is to minimize P while maintaining the performance of the array.

tf m is the number of digital reception modules operating with the sampling frequency e;™.. It is also the number of antennas associated with this sampling frequency. It should be noted that R = £m=iRm>> that not all values of Km are necessarily identical and that
Qp is the number of digital reception modules operating with the antenna with index
QP a = —— p, p R is the proportion of these digital reception modules. It should be noted that
Qp - M , R = £p=i Qp and that not all values of Qp are necessarily identical.
^.m, is the number of digital reception modules attached to the antenna with index p, which do not operate with the frequency fe^t, a0m = ^m° is the proportion of these
digital reception modules.
Qp,mmmi is the number of digital reception modules attached to the antenna with index V that do not operate with the sampling frequency fem,> nor with the sampling frequency/^ _ apm m = P'1"0^1 JS the proportion of these digital reception modules.
v' °' 1 R-Rmo-Rmi
The digital signal processing modules 26 all perform a sliding DFT spectral analysis of the signal presented to them, in order to obtain a time/frequency representation that effects an average adaptation to the band of signals of interest.
The DFT of a digital reception module working with the sampling frequency /e™is carried out over a signal duration ±Tm wjth a number of samples Nm = A7*m./em.
In order to obtain synchronous information of the same spectral resolution on all
reception channels, a common acquisition start and end is imposed on the DFTs of each
reception channel. Thus for all values of m:
JV 1
—— = AT" = AT = — fem *'™ fli AF
The time intervals successively analyzed by DFT can be contiguous or overlapping. If r is the overlap rate, the time intervals are [J(l _ r)&T, i(2 - r)AT[ where i is the current
time index of the interval. For example, with a 50% overlap, these time intervals are
[.AT .AT A„r llT'lT + A7V
If the input signal of a DFT is real over M« points, the output is therefore a complex,
discrete useful spectrum over ^m points indexed by / ranging from 0 to Nm -1 _ at the step of AF. If the input signal is a complex signal obtained after double quadrature demodulation, then the spectrum of the analytical signal is obtained directly by a Fourier transform at ^?« points.

Each DFT thus delivers a time/frequency grid over time. Each cell of a grid contains a complex >>wuj indexed byj in frequency with a step AF, by i in time with a step 0- - r}AT , by p, sensor index, and by m, sampling frequency index. Figure 3 provides an illustration thereof.
Finally, all the A DFTs of the # digital reception modules deliverR time/frequency grids with the same temporal and frequency resolution. Each time/frequency grid is indexed
by p, and by m and denoted as Gp**..
The receiving band is assumed to be divided into K frequency intervals of width equal to the common resolution of the DFTs, AF Each interval is identified by an index k. The processing develops, off-line, a correspondence table that provides the index j of the frequency in the Nyquist band as a function of the index k of the frequency in the receiving
band and the index m of the sampling frequency, / = jOcm)
The duration of the time slot &T is generally shorter than that of the signals of interest, and therefore a useful signal appears on multiple successive spectral analyses over time.
It also appears in a plurality of adjacent frequency channels because its spectrum is not necessarily centered in one of the DFT channels, its spectral width may be greater than AF.
The result is that a useful signal is generally perceived, by successive spectral analyses over time, as a related set of several time/frequency cells. Figure 4 provides an illustration thereof.
This invention proposes to model and process the received signal on time/frequency domains, each corresponding to an interval limited in time (typically the duration of a few DFTs) and frequency (typically a few channels).
The band [fmin,fmax[ is divided into frequency intervals, either overlapping or not, of width £=AF i L2 being a natural number. Similarly, the time axis is divided into intervals, either overlapping or not, of duration £i(l —r)Ar i it being a natural number. For each time/frequency domain thus obtained, the correspondence table makes it possible to take a set of £ = W x L- connected time/frequency cells, referred to as a window, for each of
the A reception channels.
The processing then analyses all time/frequency domains independently of each other.
An order of reading of the cells is chosen arbitrarily and identically for all windows, for example, first in the frequency axis, then in the time axis. The set of L measurements of

each window forms a vector, referred to as a measurement vector, which can be indexed by p, the sensor number, m, the sampling frequency number, i' and j' where i' and j' are chosen from the indices i and j' of the window cells, arbitrarily but identically for all windows. For example, i' and jA' can be chosen to be equal to index i and index j in the upper left cell.
With the conventions used as examples, and with, for example, tt = a and i-3 = 3 the vector Li = 2 et Li = 3 is equal to:
'p,m,li,ji ~ yyp,m,i'',]' yp,m,i',]'+l yp,m,i',]'+2 yp,m,i'+l,]' yp,m,i'+ !,]'+! yp,m,i'+l,j'+2J
0-T u refers to the transposition operator.
To simplify the entries, a vector W will then simply be denoted as V, it being understood that the windows involved in the processing all correspond to the same time/frequency domain, and that all time/frequency domains are treated in the same way and independently of each other.
For two different sampling frequencies, the values of i' are different, and the frequency positions of the windows are therefore different. Figure 5 provides an illustration thereof.
In a variant processing embodiment, a pre-detection step enables reducing the amount of calculations by eliminating time/frequency domains that do not contain a useful signal. This pre-detection treatment consists, for example, in calculating for each
time/frequency domain, the quadratic sum of the moduli of the ^ vectors corresponding to
ii n2
this time/frequency domain, £p,m||*pm|| , then comparing the value obtained with a predefined threshold. The threshold in question is set for a fairly high false alarm rate, so as to ensure that no time/frequency domain containing useful signal is wrongly eliminated, the final false alarm probability being ensured by the detection step itself.
Within the framework of the radio reception device described above, the method includes a determination function for determining, for a given measurement vector, the interference situation (absence of parasites ie no interference, or presence of parasites ie interference, and which are the sampling frequencies that are affected):
This determination function considers the following cases of interference:
No sampling frequency is parasitized (interference), the hypothesis denoted as ^D ;
Presence of one (or more) parasite(s) on one of the sampling frequencies
Tnm(m0 e [M*D, i.e. W hypotheses denoted as H^-a (™D e [1,M]);
Presence of one (or more) parasite(s) on a second sampling frequency m 1, different from mo, i.e. M(M-l)/2h hypotheses denoted as:
Hmomi (rrio E [l,M],m1 £ [1,M], m0 gt m±).

It is proposed to model the measurement vectors as follows in H0 :
Y — Api(Pp 4- V
Ipm -^^ ^ vpm
Where:
• ^p is the interferometric phase shift of the signal received by an antenna, with respect to a reference;
• A Is a complex vector representing the useful signal;
• Vpm is the vector of thermal noise. *U are samples of a complex Gaussian vector
random variable. These samples are independent from one P to another and have a covariance assumed to be common and approximately equal to 2a2IL, where h is the
identity matrix of size £ x L . For the same V and for two different ™ we can also assume that there is independence of ^ because only the noise taken in the width of the DFT filter near the true frequency of the signal is common.
This model is valid for a plane wave (source assumed to be infinite) and for a useful narrow band signal.
The measurement vectors are therefore considered, under the hypothesis wn, as complex independent Gaussian vector random variables with mean Aelv + Ble^v + VpniQ \Ypmi = Ae^v + Bie^P + Vpm±
According to decision theory, the value taken by the probability densities representing each of the hypotheses for the observed measures should be calculated and

the hypothesis that maximizes this value should be chosen. This strategy minimizes the probability of error in the event that all situations are equally probable.
The difficulties are the number of unknown parameters (A, Bu B~ _ the ^p-^t-v^*?), and the resulting complexity of the calculations if it is sought to apply the conventional method, which consists in replacing the unknown parameters by their estimated maximum likelihood (Maximum Generalized Likelihood).
To reduce the number of unknown parameters of the above physical model, it is proposed to use a simplified statistical model to describe the parasitized measurement vectors. In this model, the parasitized measurement vectors are represented by complex vectors of dimension L. The real and imaginary parts of the components of these vectors are independent samples of a real random variable centred and uniformly distributed over
an interval of width *C So that the probability density of the measurement vectors will be (1/C)L. This model applies for any number of parasites per sampling frequency. The
determination of the coefficientc is explained in the appendix.
At the end of this simplification, in the event that only one sampling is parasitized (we will call this sampling ™D and this hypothesis ^), we can write the probability density as the product of the probability densities of the measurement vectors over the set of all sensors and sampling:
/ , 1 (2na2\Rm0L f 1 V ii • IIJ
Pm0 \lesYpm,A,les(pp,C)=- — l-^-l exp)J^ /^ "Ypm ~ Ael«, over all samples of the antenna p, except
on the supposedly parasitized (interference) sampling m0 :Zpmo = Yim*m0 Ypm >;
and where ^ is the deviation of the vector *W from its mean ^"i:
Y —7 A-Y
The term rm1 _ which comes from the channels assumed to be not parasitized (no interference), and which increases as a function offf •»«■ , favours the elimination of as many reception channels as possible. This is why the term RmoL In \^-\, which comes from the
parasitized (interference) channels, and which is negative or zero as soon as 2TTO": < C _ js necessary in order to choose the right hypothesis. This term acts as a penalty for the hypotheses where the receiving channels are eliminated.
In the following sections, the term r^o is referred to as restricted approximated log-density (i.e. restricted to the reception channels assumed to be not parasitized (no
interference)). The term r^o is interpreted as the sum of three terms or partial criteria:
The term ■■'■-■e' this term is less than or equal to zero, with equality if for any m * mD , *W = ^m,. This term constitutes a criterion of non-variability of *pmwith respect to their
filtered value on the different sampling frequencies of the antenna V (except the sampling frequency or frequencies assumed to be parasitized in the hypothesis considered)
The term ^, ; this term is less than or equal to zero, with equality if ||Zpmo|| is
independent of V . This term constitutes a criterion of equality of the moduli of the *p™
filtered on the different sampling frequencies of the antenna P (except the sampling frequency or frequencies assumed to be parasitized in the hypothesis considered)
The term ^,'; this term is less than or equal to zero, with equality if for any P < *? , *F- iS colinear to ^qmi' This term constitutes a colinearity criterion for the ^W-and ^m
filtered on the different sampling frequencies of the antenna P and the antenna "7 (except for the sampling frequency or frequencies assumed to be parasitized (interference) in the hypothesis considered)

In the case of hypotheses of type ^1 (one (or more) parasite(s) present on the sampling frequency m ■ and one (or more) parasite(s) present on the sampling frequency mi), the criterion becomes:

L^. „. — ru. „. Zi 111
where:

X C /

+r

• ^m,m, is the number of reception modules operating with the frequency fe™m
or with the frequency/e"i±: «mlJm1=«m1 +«m±
.f = _Lvvar I R-Rm0m1 mod , R-Rmgmx coj
Lm0m1 2c.2k = °'l-2 is greater than a threshold S chosen to adhere to a fixed error rate. The f*k and ^k can be calculated offline by simulation. Correspondence is defined as:
f~ \ ^ / i^k ~ Vk) P(Tk,Hk,ak) = exp --
Ho is decided if PCIQ, HO- op) is greater than -S .
If PCfV^D,(7D) is not greater than the threshold s ,Hx is decided if P(f i'Pi.'°i) is greater than the^ threshold.
If PC\'Mi*°i) is not greater than the threshold S , **: is decided if ?{? 2-Pi-^i)
is greater than the s threshold.
If PiT-.u-.o-) is not greater than the threshold-^ , it means that there are more than two sampling frequencies causing interference to the signal in question.

For practical reasons it is possible to operate with the opposite of the logarithm of correspondence:
-\nP(rk,nk, ak) = —2 + lnV27T(Tfc
LGk
Under these conditions, the tests of superiority of ^v fc-/V ak) in relation to S are transformed into tests of inferiority of _friP(fk'l^k- ^t) in relation to —1»S.
For the hypotheses ^ 1 and **a , the sampling frequencies causing interference are
determined by:
/_ (2no''
m0 = Argrnax) rmo+i?moL-lnl- Q
[Tma+RmaL-\n
m0 = l,...,M
and
(2na
(mo.mj = Argmax rm0jmi + i?mo,miL ■ In ■
m0 = l,...,M \ m1 = l, ...,M 7n0^7n1
In this embodiment, the method is freed from the dependence on c in order to select the best hypothesis.
In the case of the hypothesis ^D (no parasites present), the criterion becomes:
° ° 2a2 2a2 2c2
Where:
. yvar = - Xp,m||^pm|| where *W is the difference of each vector V from its mean ^v (criterion of non-variability from the mean);
,ymod_ (£pap||Zp||) -Epap||^P|| (moduli equality criterion), and . Ymod = (£p ap\\ZP ||) - £p ap\\ZP || (colinearity criterion).
In a first embodiment, we look for the maximum of
!()> ^m0,m0e[l,M]' '■m0,m1,m0e[l,M]m1e[l,M],m0*m1-
If r0 = max (r0,rTnoTnoe[1M],rTnoTniTnoe[1M]mie[1M]Tno^Tni), then there is no parasite (hypothesis Hn).
If there exists ™n such that f^o = max
((USm0,m0e[i,M}^m0,m^,m0e[i,M}m^[i,Mlm0*m^, then there is only one parasitized sampling frequency, and this sampling frequency is ™, (hypothesis "*»■).

If there exists a pairm ■, m 1 such that
F^, = max[T0,T^^e[i;kr],rV|^e[w]j^,6[i^j^ ** J.
then there are two parasitized sampling frequencies, and these frequencies are ™D and ™i (hypothesis Hmamiy
In a second embodiment, the method includes the calculation of the following three quantities. These calculations do not require knowledge ofc .
/\ = max (tL)
1 m0 = l MV m°J
~ m^.,M^m°m^
mx = \,...,M
Where:
• T0 represents the " absence of parasites" hypothesis. This hypothesis is referred
to as Ha.
• r1 represents the best of the hypotheses with one parasitized sampling frequency
w^e. This hypothesis is referred to as ^i.
• r2 represents the best of the hypotheses with two parasitized sampling
frequencies ^"ilJmi. This hypothesis is referred to as H:.
The proposed processing treatment is generalized to different material choices and different reception situations, by means of the following equations:
f0 = i(cmod>ccoi) = (1-0,1) if we consider that the measurements module can vary from one antenna to another without this being the consequence of interference. This may

occur, for example, due to couplings between antennas, or in the case of reception of a signal along different paths (direct and reflected on the carrier's structures or other external structures) or if the array used is not gain normalized (in the case of an amplitude goniometry/direction finding array);
• \fvar>^mod>^col) \±>i->v) IT ,
• (cvar, cmod, ccol) = (0,0,1) if there is only one sampling frequency per receiving chain and if the measurements module is made to vary from one antenna to another (for the reasons mentioned above);
• (cvar,cmod,ccoi) = (0,1,0) if there is only one sampling frequency per receiving chain and if L=1
• (cvar,cmod,ccoi) = (1,0,0) if the measurement modulus is made to vary from one
antenna to another (for the reasons mentioned above) and if £ = * .
The processing treatment then eliminates from the set of all ^ vectors *jwn, those whose sampling frequency index"1 corresponds to one parasitized (interference) sampling frequency. Over all of the vectors *W?i thus obtained, it is proceeded by the conventional process of detection to detect the signal in the presence of thermal noise.
This processing is repeated for all time/frequency domains, or, in the variant embodiment with pre-detection, for all time/frequency domains selected by pre-detection.
BIPOLAR CASE
Before more precisely describing the several embodiments in detail, a brief explanation is provided of the inventive approach followed by the applicant, starting firstly from the existing need.
There is a need for an enhanced interference detection function, that provides the ability to determine not only the presence or absence of a wanted (useful) signal at a given frequency, but also to determine the specific interference situation prevailing (absence of parasites ie no interference, or presence of parasites ie interference, and which are the sampling frequencies that are parasitized (interference)), with the least possible error. In
the case where the number of sampling frequencies is equal to & _ and the number of
parasitized sampling frequencies is strictly higher than ** - 2 , it shall be sought only to ascertain that such is the situation prevailing (without seeking to determine which are the parasitized (interference) channels), also with the least possible error.
This will improve the performance of the detection itself, but also of the other functions of the processing chain (estimation of the direction of arrival, signal

characterization). Another advantage is that it will allow the use of analogue-to-digital conversion components operating at frequencies lower than the Nyquist frequency, while minimizing the effects of spectral folding.
The literature on detection generally assumes that the received signal is alone in its environment, and does not address the problem of interference, i.e. interference between signals due to spectral folding.
It is proposed to use the receiver architecture shown in Figure 8, in the particular case of one sampling frequency per antenna.
This architecture is that of an instantaneous wide band bipolar interferometer with digital reception and sub-sampling. The interferometer consists of two subarrays, each with
the same numberp of very wide band antennas. Each sub-array has its own polarization.
Each of the ? antennas is connected to the input of an instantaneous wide band reception chain, designed and developed in an analogue way. Each analogue receiving chain outputs its signal to at least one digital reception module, consisting of an analogue-to-digital conversion module followed by a digital signal processing module capable of performing
spectral analysis. The set of analogue-to-digital conversion modules uses a set of M sampling frequencies that are different and lower than the Nyquist frequency. The same sampling frequency can be used multiple times, but necessarily in combination with analogue-to-digital conversion modules corresponding to different antennas.
It is referred to as the reception channel the whole assembly formed by a digital conversion reception module and the analogue reception chain with which it is associated, denoted as CRip for the sub-array 1 and CR2q for the sub-array 2.
As explained above, the technical problem encountered with subsampling is that two signals that are temporally superimposed or overlapping can also, by way of spectral folding, be frequency superimposed in the working Nyquist zone, although this superimposition or overlap does not exist in the receiving band. With respect to one of the two signals, the term "interference of the the said signal due to spectral folding" may be used. The problem affects both signals by reciprocity.
It is not proposed to deal with signals of sufficiently close frequencies originally in the receiving band, which are therefore not frequency resolved in the receiving band (see real mixtures). However, this case is much less likely than the cases dealt with.
The purpose of the proposed method is to determine, on the basis of the measurements, the interference situation due to spectral folding (absence or presence of parasites (interfering/spurious signals), and, in case of presence of parasites, identify the frequencies that are the parasitized/interference sampling frequencies).

Since it is assumed that there are no more than two sampling frequencies among M affected by signal interference, the number of possible interference situations amounts to —^— (1 for no interference frequency, ** for only one interference frequency and
M for two interference frequencies).
The applicant proposes to exploit the fact that signals of interest are generally spread over a plurality of adjacent spectral analysis channels and present in multiple successive spectral analyses, and model the measurements extracted over a plurality of adjacent channels and multiple successive analyses in vectorial form.
One of the applicant's ideas is in particular to approximate, for each possible interference situation, the likelihood function of the measurement vectors by a computable majorant (function) that can only be calculated by means of square moduli, scalar products and filtering of measurement vectors taken from all reception channels, and can be interpreted as the sum of criteria reflecting their variability, the equality of their modulus and their collinearity respectively, calculated on the two arrays together.
The proposed method determines the interference situation (absence or presence of parasites, and, in the case of interference, the sampling frequencies affected), maximizing, on all possible interference situations, the approximation previously obtained, or maximizing the correspondence thereof to its assumed Gaussian law distribution.
As the interference situation is known, the method then eliminates the parasitized (interference) channels and only uses the non-sparitized (no interference) channels to decide whether or not there is a useful signal present by operationally implementing a conventional thermal noise detection method.
In a summarizing manner, it is possible to express what has just been disclosed as an interference determination method for determining interference situations due to spectral folding and a signal detection method for detecting electromagnetic signals that are operationally implemented by means of an interferometric array, composed of two single
polarization sub-arrays with p wide band antennas, P being an integer greater than or equal to 1, each antenna being followed by one or more digital reception modules, the
number of digital reception modules being A on each sub-array, distributed in an identical manner over the two sub-arrays, the said method comprising:
- A signal sampling step for sampling the signals delivered by all the receiving
chains, making use of ** different sampling frequencies /e™ , that are lower than the
Nyquist-Shannon frequency, ™ ranging from 1 to M , and M being an integer greater than or equal to 4, the number of digital reception modules operating with a sampling

frequency fem being identical on each array and being equal to Rm , the number of digital reception modules for an antenna V of the sub-array 1 being Q? , and the number of digital reception modules for an antenna of the sub-array 2 being *?g , with R = £m=i Rm = Ep=i Qp
- On each reception module, a spectral analysis step by means of synchronous and
successive discrete Fourier transforms on all the 2# reception modules, of the Nm
samples obtained by sampling at the frequency fem during possibly overlapping time intervals of duration AJ" , making it possible to obtain, on each of the 2# reception modules, a time/frequency representation referred to as a time-resolution grid AT that is common to all the digital reception modules, and a frequency resolution grid AF that is common to all the digital reception modules, each element of the grid being referred to as a time/frequency cell and containing a complex quantity referred to as a measurement.
- A step, that may be performed offline, of mapping of the frequencies in the receiving band at the resolution A^ to the Nyquist band frequencies of each of the 2ff digital reception modules.
- A step of dividing the time/frequency space (in the reception band) by a set of
possibly overlapping time/frequency domains, perceived in the A reception modules of the sub-array 1 and in the K reception modules of the sub-array 2 as 2ff overlapping windows,
each of the windows being composed of£ time/frequency cells.
- Possibly, a step of selecting the time and frequency domains presumed to contain more than noise, by applying a pre-detection algorithm consisting in comparing the quadratic sum of the moduli of the 2# measurement vectors of each time and frequency domain, to a predefined threshold, set for a fairly high false alarm probability.
- For each time/frequency domain, or for the selected domains, a measurement transformation step for transforming the measurements taken from each of the 2S windows
into the form of ^ vectors of dimension Lxi for the sub-array 1, denoted as ^p™, where
V is the sensor index and m is the sampling index, and into R vectors of dimension £ x *
for the sub-array 2, denoted as *W™», where ^ is the sensor index and ™ is the sampling index.
- For each time/frequency domain, or for the selected domains, a parasite
(interference) determination step for determining the presence of possible parasites
(interfering/spurious signals) consists in choosing, from among the following hypothesis:
• Hn : absence of parasites;

• "ram : presence of one (or more) parasite(s) on the sample mo, with mo e [1*M]
(that is to say ** hypotheses);
•Hmt,mi ■ presence of one (or more) parasite(s) on the sample ™ o and one (or more)
M(M - 1) parasite(s) on the sample ™ i, with ™i e [1, M] _ m^O * m4l) mD E [1, M] (j.e. 2
hypotheses);
the hypothesis that maximizes a computable approximation of the probability density
of the A measurements ^f"" and the R measurements **p««, this approximation resulting from:
• a modeling of the measurements *VP»™ and **P>» assumed to be not parasitized
(no interference) by independent samples of a complex vector random variable of
dimension £ , mean Gaussian probability density ^eiip-; and covariance 2a~h, where ^ is
the complex vector of dimension £ representing the wanted signal, *V the interferometric
phase shift, 2crIthe noise power in a time/frequency cell, and h the identity matrix of
dimension LxL
• a modelling of the measurements ^p^and J':?m assumed to be parasitized
(interference) by complex vectors of dimension £ , where the components of these vectors are independent samples of a centred complex random variable with independent real and
imaginary components that are uniformly distributed over a width interval *C so that the probability density of the measurements will be (1/C)L.
• then an increase in the probability density of the 2ff measurement vectors ^pm
and ^
yprno Vqm0
where Qp,m, is the number of digital reception modules attached to the antenna with index V on sub-array 1, which do not operate with the frequency fe^-a and ^.mi is the number of digital reception modules attached to the antenna with index 1 on sub-array 2, which do not operate with the frequency fe^m;
ou ff^-B is the number of digital reception modules operating at the sampling frequency fe™, on each sub-array;
where ci (resp c:) represents the gain of the sub-array 1 (resp 2) in the polarization of the incident signal.
The vector L1 J is then estimated by the eigenvector associated with ^™«.
• For the hypotheses^W^-i (one (or more) parasite(s) present on the sampling frequency ™D and one (or more) parasite(s) present on the sampling frequency mi), the quantities:
+ ,
'2JTO3'
c
rLj* = In ?«.» = 2FL, m L\sn.
where RnVat is the number of digital reception modules operating with the frequency femm with the frequency fe™*. in each of the two sub-arrays, and where ^,m, is the maximum eigen value of the quadratic expression:

PO — fvvar 4- vvar rVm0m1 2(j2 \'l,m0m1 ^ Y2,m0m1)
R-R
J m0m1 r if col , mod \, 2(vcol , mod \ , f T j 2 V 1 Ul,m0nii T Y\,mamx) T c2 \Y2,m0m1 T f2,m(miJ T 7 Hmamx)
,2
^-pm^m-i W^lpm^m^
q p
T LC-^C2 7 ttpm0m1&qm0m1\^'lpm0m1^'2qm0m1\ PA
Where fqmomi\s the quadratic expression:
z- 2 \ My 11^ 2 \ My
JHm^m-i C± 7 ®-qm§m-± \\^J2qmQm1 \\ 2 / pm^m-^ ||-^1

which can be interpreted as a bipolar criterion of moduli equality and co-linearity;
where Timi^i, Tim,?^ yim,m,, Ksm^mi _ ^m.m, _ fjm^, are the single polarization criteria of non-variability, moduli equality and co-linearity respectively for sub-arrays 1 and 2 for the hypotheses with "two parasitized (interference) sampling frequencies, defined in the method described in the single polarization case;
where at^va1 \s the proportion of digital reception modules attached to the antenna with index V of the sub-array 1 that do not operate with either the sampling frequency /*"*■ or the sampling frequency fe^-a, and where 1J9mi",i is the proportion of digital reception modules attached to the 3 antenna with index of the sub-array 2 that do not operate with either the sampling frequency fe^-a or the sampling frequency /em±;
wnere i'X-pm.c.m.-. = ~ lJm.*mr,,m-i 'lpm 3^10 ^2pmnpm„ ~ 7j 2jm^mn,m-i *2qm-
Vpm0m1 1 Vqmo.m!
where Qp,mm,m1 is the number of digital reception modules attached to the antenna with index V that do not operate with either the sampling frequency fe^t or the sampling frequency/em± on sub-array 1, and Qg,mMJm1 is the number of digital reception modules attached to the Q -antenna with index that do not operate with either the sampling frequency fe™% or the sampling frequency ^«i on sub-array 2;
where fim,w*i is the number of digital reception modules operating at the sampling frequency /em, or /em± on each sub-array;
where ci (resp ci) represents the gain of the sub-array 1 (resp 2) in the polarization of the incident signal.
The vector L1 J is then estimated by the eigenvector associated with ^m.
In a first embodiment, the method includes the following deductions: if f0 = max (f0,fmo,fmo;mi)„ then there is no parasite (hypothesis ff»). If there exists in0 such that f0= max (f0,fmo,fmo;mi), then there is only one parasitized sampling frequency, and this sampling frequency is in0 (hypothesis H^J.

If there exists a pair fh0, in1 such that tfh0,m±= max (fo>fm0>fm0,m1)> tnen there are two parasitized sampling frequencies, and these frequencies are in0 and in1 (hypothesis
''fh0fh1/-
In a second embodiment, the method includes a calculation step of:
f° = f° /\ = max (tL)
1 m0 = l MV m°J
r2 = max f/t,„mi)
1 m0 = l,...,Mv m°mi;
Tn^l,...^ 7770*777!
where:
• T0 represents the "absence of parasites" hypothesis. This hypothesis is referred
to as ^ a ;
• r1 represents the best of the hypotheses with one parasitized sampling frequency
w^e, referred to as ^i, and
• r2represents the best of the hypotheses with two parasitized sampling frequencies
ff™i.% , referred to as H~.
in this second embodiment, the method also includes the determination of the best hypothesis among H0 ,^i, H~, the one chosen being:
Ho, if its approximated log-density ^n satisfies the test of correspondence to its supposed Gaussian law distribution (see single polarization case);
Otherwise, Hi, if its approximated log-density restricted to non-parasitized (no
interference) channels f\ satisfies the test of correspondence to its supposed Gaussian law distribution (see single polarization case);
Otherwise, Hi, if the approximated log-density restricted to non-parasitized (no
interference) channels ^i satisfies the test of correspondence to its supposed Gaussian law distribution (see single polarization case);
Otherwise, there are more than two parasitized sampling frequencies.
- The total number of sampling frequencies M is greater than or equal to 3, and the method determines the interference situation from among all the hypotheses: no parasitized sampling frequency, one parasitized sampling frequency, and so on, up to
M -2 parasitized sampling frequencies.
- The processed signals are real or complex.
- The method works in degraded mode if the &F resolution is not the same for all grids.

An example of a more detailed implementation is now described. Figure 8 illustrates the architecture of an interferometer 10 in the particular case of one sampling frequency per antenna.
Sub-array 1 includes P antennas AXX-~AI,P , very wide band, each followed by a receiving chain c* M.--CJ? M> . Sub-array 2 includes P antennas A%X-'AI>P , very wide band, each followed by a receiving chain CR2,i,-- CR2,p. In the general case P is an integer greater than or equal to 2 .
The proposed method also applies to the case P = l .
We assume that the antennas of the two sub-arrays have identical two by two patterns, to the nearest polarization. The two sub-arrays can be either co-located or not.
For the following, the index V (respectively the index R ) of each antenna of the
sub-array 1 (respectively of the sub-array 2) is an integer between 1 and P , also serving
as a reference for all the elements attached to it, material means, measurements and
various calculated quantities.
The phase centres of the antennas can be distributed spatially. The spatial
distribution of antennas A*,*,--AUP and A2,I,--A2,P, is defined to ensure a specified
accuracy and angular ambiguity ratio.
Behind each antenna, an analogue filter selects a very wide band [fmin,fmax]-For a narrow band signal emitted from an infinite source, the signal delivered by the
antenna with index V of the sub-array 1 has the following expression:
sip(0 = clpa(t) cos (in ft + X) js the sum of the interferometric phase shift of the incident signal at the MP phase centre of the antenna considered with respect to a reference point ° , (plp(9,X) = -^-OMD ■ u(0) where UCT is the unit vector directed in the direction of arrival of the incident

signal 0 , the main object of the interferometer, and the complex gain phase of the antenna in the direction of the incident signal;
. bip(£) js the thermal noise of the receiving chains, assumed to be Gaussian and independent between receiving chains, and of uniform and identical spectral density for all receiving chains;
Similarly on sub-array 2:
s2q(t) = c2qa(t) cos (2nft + dtp) + 2q(9,X) =—0Mq -u(9)
where UC#) is the unit vector directed in the direction of arrival of the incident signal 0, the main object of the interferometer;
• b2q(t) is the thermal noise of the receiving chains, assumed to be Gaussian and
independent between receiving chains, and of uniform and identical spectral density for all
receiving chains;
Each receiving chain CRlt , CR1P (respectively CR21 , CR2P) consists of a strictly analogue part which is followed by at least one digital reception module 20 comprising an analogue-to-digital conversion module 22 associated with a sampling frequency 24 followed by a digital signal processing module 26.
The analogue-to-digital conversion module 22 is capable of performing a sampling of the signal at sampling frequency 24.
The sampling frequency 24 is such that the reception band of the analogue signal is not contained in a single Nyquist zone. The sampling frequency 24 is lower or even much lower than the Nyquist frequency, but it is still much higher than the spectral spread of the signals of interest. Thus the spectrum of signals of interest is preserved, but it is translated by a possible quantity that depends on the sampling frequency.
A digital signal processing module 26 is capable of performing a spectral analysis of the signal converted to digital, with a weighted discrete Fourier transform (DFT).
The interferometer 10 also includes a computing unit 28 collecting the measurements obtained at the output of each digital signal processing module 26, and capable of obtaining the direction of arrival of the incident signal on all the antennas

A%i,...> AI,P and A2,I,-'A2,P- This computing unit 28 is also capable of implementing an interference determination method for determining signal interference situations in the Nyquist zone analysed by DFT.
The interferometer 10 has a total of M values of different sampling frequencies 24 in order to remove frequency ambiguities when moving from the frequency measured in the
Nyquist zone used (a priori the first) by the DFT to the frequency in the receiving band, M being an integer greater than or equal to 3.
One of the characteristic features of the invention is to minimize the interference effects due to spectral folding on detection performance aspects, and to improve the performance aspects of other functions in the processing chain (estimation of direction of arrival, signal characterization) when:
-1 sampling frequency is parasitized (interference), if M equals to 3
-1 or 2 sampling frequencies are parasitized (interference), if M equals to 4
-1,2, ...M — 2 sampling frequencies are parasitized (interference), if M > 4.
These M sampling frequency values 24 are assigned to the analogue-to-digital conversion modules 22 that sample the signal provided by the receiving chains respectively upstream, at the sampling frequency fem, m being an integer between 1 and M. The sampling frequencies are distributed identically over the two sub-arrays.
If a given sampling frequency is assigned to an analogue-to-digital conversion module associated with a given antenna in a sub-array, it is assigned only once.
On each sub-array, the number of digital reception modules is identical and takes an R value is at most equal to P ■ M. In practice, for material reasons, the aim is to minimize R while maintaining the interferometer's goniometry performance.
Rm is the number of digital reception modules operating at the sampling frequency >e™zi on each sub-array. It is also the number of antennas associated with this sampling frequency. It should be noted that que # = £m=i#m, that not all values of ^m are necessarily identical and that Rm< P.
Qp is the number of digital reception modules operating with the antenna with index P on sub-array ^,av=— is the proportion of these digital reception modules. It should be
noted that Qp < M„ R = Y,p=i Qp and that not a" values of Qp are necessarily identical.
Qp,mois the number of digital reception modules attached to the antenna with index
V on sub-array 1, which do not operate with the frequency femo , aPiJrio = ^,m° is the
proportion of these digital reception modules.

Qp,m0,m1 is the number of digital reception modules attached to the antenna with index V that do not operate with the sampling frequency femo, or with the sampling frequency fem on sub-array 1, apm m =—p,m°,mi is the proportion of these digital
reception modules.
The same is introduced for the sub-array 2: Qq,aq,Qqmo,aqmo,Qqmom±aqmom±..
The digital signal processing modules 26 all perform a sliding DFT spectral analysis of the signal presented to them, in order to obtain a time/frequency representation that effects an average adaptation to the band of signals of interest.
The DFT of a digital reception module working with the sampling frequency ferm is carried out over a signal duration A?*m with a number of samples Nm = ATm.fem..
In order to obtain synchronous information of the same spectral resolution on all reception channels, a common acquisition start and end is imposed on the DFTs of each
reception channel. Thus for all values of"1 :
The time intervals successively analyzed by DFT can be contiguous or overlapping.
Ifr is the rate of overlap, the time intervals are [i(l - r)AT, i(2 - r)AT[ where ! is the
current time index of the interval. For example, with a 50% overlap, these time intervals are
[.AT .AT A„r llT'lT + A7T
If the input signal of a DFT is real over ^m points, the output is therefore a complex, discrete useful spectrum over Nm points indexed by j ranging from ° to Nm -1 , at the step of AF . |f the input signal is a complex signal obtained after double quadrature demodulation, then the spectrum of the analytical signal is obtained directly by a Fourier transform at ^™ points.
Each DFT thus delivers a time/frequency grid over time.
Each DFT thus delivers a time/frequency grid over time. Each cell of a grid contains
a complex 3%p.w».vi indexed by j in frequency with a step W , by i in time with a step
(1 -r)ATbyp, index of the sensor, and by™ , sampling frequency index. Figure 3 provides an illustration thereof.
Finally, all of the ff DFTs of the ff digital reception modules associated with
sub-array 1 (respectively sub-array 2) deliver R time/frequency grids with the same temporal and frequency resolution. Each of the time/frequency grids associated with
sub-array 1 (respectively sub-array 2) is indexed by V , and by ™ (respectively by Q , and

by m ) and denoted as Gi^w« (respectively Gz,?>,™.). Thus there are 2R grids, with the same temporal and frequency resolution available.
The receiving band is assumed to be divided into K frequency intervals of width equal to the common resolution of the DFTs, AF . Each interval is identified by an index * . The processing develops, off-line, a correspondence table that provides the index / of the frequency in the Nyquist band as a function of the index * of the frequency in the receiving band and the index m of the sampling frequency, j = j(k, ni).
The duration of the time slot A7* jS generally shorter than that of the signals of interest, and therefore a useful signal appears on multiple successive spectral analyses over time.
It also appears in a plurality of adjacent frequency channels because its spectrum is not necessarily centered in one of the channels of the DFT, its spectral width may be greater than AF.
The result is that a useful signal is generally perceived, by successive spectral analyses over time, in the form of a connected set of several time/frequency cells. Figure 10 provides an illustration thereof.
The present invention proposes to model and process the received signal on time/frequency domains, each corresponding to an interval limited in time (typically the duration of a few DFTs) and frequency (typically a few channels).
The band [fmin,fmax[iS divided into frequency intervals, either overlapping or not, of width ij^F , L- being a natural number. Similarly, the time axis is divided into intervals, either overlapping or not, of duration /^(l -r)AT, Lt being a natural number. For each time/frequency domain thus obtained, the correspondence table makes it possible to take a set of L = Lt x L2 connected time/frequency cells, referred to as a window, for each of the
R reception channels of the sub-array 1 and for each of the A reception channels of the sub-array 2.
The processing then analyses all the time/frequency domains independently of each other.
An order of reading of the cells is chosen arbitrarily and identically for all windows,
for example, first in the frequency axis, then in the time axis. The set of £ measurements of each window forms a vector, referred to as a measurement vector, which can be indexed
by the sub-array index (1 or 2), by V , the sensor number, ™ , the sampling frequency
number, * and /' where i and /' are chosen from the indices ' and / of the window

cells, arbitrarily but identically for all windows. For example, * and /* can be chosen to be
y
equal to index! and index I in the upper left cell. This vector is denoted as 'ipmi'j' for the
v
sub-array 1, and ^.amt'/ for the sub-array 2.
With the conventions used as examples, and with, for example, ^i = 2 and i-3 = 3
y
, the vector zu>mi'i' is equal to:
rw,-6w w w w., ;w w.,Jr
Where T is the transposition operator.
To simplify the entries, a vector Ylpmi,j, (respectively Y2qmi,jr) will then simply be
y denoted as lfm (respectively ^aqm), it being understood that the windows involved in the
processing all correspond to the same time/frequency domain, and that all time/frequency
domains are treated in the same way and independently of each other.
For two different sampling frequencies, the values of ; are different, and the frequency positions of the windows are therefore different. Figure 11 provides an illustration thereof.
In a processing variant, a pre-detection step enables reducing the amount of calculations by eliminating time/frequency domains that do not contain a useful signal. This pre-detection treatment consists, for example, in calculating for each time/frequency domain, the quadratic sum of the moduli of the 2fl vectors corresponding to this
time/frequency domain, Ep,m (||*ipm|| + ll^pmll ).tnen comparing the value obtained to a predefined threshold. The threshold in question is set for a fairly high false alarm rate, so as to ensure that no time/frequency domain containing useful signal is wrongly eliminated, the final false alarm probability being ensured by the detection step itself.
Within the framework of the radio reception device described above, it is worth noting the role played by a determination function, for two measurement vectors given on
the two sub-arrays (Yklpn*. Y{2qm\ 0f the interference situation (absence of parasites, or presence of parasites, and which are the parasitized sampling frequencies):
This determination function considers the following cases of interference:
• No sampling frequency is parasitized (interference), the hypothesis denoted as ^D ;
• Presence of one (or more) parasite(s) on one of the sampling frequencies
m„(m0 6 [l,M])t i.e. Af hypotheses denoted as Hm. (™D e [l,Af]);

• Presence of one (or more) parasite(s) on a second sampling frequency7" 1, different
M(M - 1) from rrtm, that is to say 2 hypotheses denoted as Hmo7ni (m0 e [1, M], m1 e
[l,M],m0 *mj).
It is proposed to model the measurements as follows in ^D :
Y2qm = c2Aei(p^ + V2qm Where the two sub-arrays are referred to as index 1 and 2 respectively. Where 'Pip is the interferometric phase shift of the signal received by the antenna v , with respect to a reference, on sub-array 1, and *$•% is the interferometric phase shift of
the signal received by the antenna 9 , with respect to a reference, on sub-array 2.
Where ci (resp ci) is a dimensionless coefficient referred to as sub-array 1 (resp 2) gain in the polarization of the incident signal. It can be assumed that ci and ci are positive and real, which means integrating their phase into the interferometric phases Pp and V n lpm° -ctAei,pv\\2 x exp -1 V II
— > y,
2ff2 /_, »'2"m" - c2Aei,p"i\\2
Pm0 (Zip,Z2q,A, les cplp, les and ^*i, the applicant proposes to replace the probability density with a majorant and to select the hypothesis for which the majorant of the probability density is maximum.
The method thus proposes to select the hypothesis for which the increase in
probability density is maximum. After applying the logarithm function, then removing the
term 2RLln&iztr*) which is common to all hypotheses, the criterion to be maximized is
obtained:
(2na2\ rmo = 2RmoL In I —— I + Xmo
*™* is the maximum eigen value of the matrix associated with the quadratic form under constraint cl + cl = 1 :
m0f 1 1 FQ™o =J^2K0,m0 "i ^2 {Khm0cl + K2,m0c2 + K12,m0clc2)
whose coefficients ^i, Ki.m,, ^m.^i^m.are given by:
i7 — ~,var I ^.var
ft0,m0 — Yl,m0 "•" Y2,m0
2
is — vmod I vcol _ \ ~ II7 ||
n2,m0 ~ r2,m0 T r2,m0 / t "pm0 \\^lpm0 \V ^12^ = ^12m0 = ^Zj^^pl^a^a^l
PA ,var ..mod ~,col ~,var ..mod ~,col
Where YXmr0,Y™^Yim0 YI^YTX.Y^ > are the sin9|e Polarization criteria of non-variability, moduli equality and collinearity, for the sub-array 1 and sub-array 2 respectively.

And where zv^m represents the mean of *VF™« , on all sampling of the antenna V , except on the supposedly parasitized sampling m0: ZlprUo = —^— £m*mo Ylpm ,;
The same applies to sub-array 2: Z2qmo = -^Im*mo Y2qm.
The vector L1 J is then estimated by the eigen vector associated with ^™*
FQm, can be rewritten as
1 , , R-R
FQm0 = ^2 te„ + «0) + -^ (ci(ncX + y££) + ^22(r£% + rlX) + finj
Where /Tm, is the quadratic expression:
/lm0 = —cl /^ aqm0 \\^2qm0 \\ ~ c2 ?. Smo \\^lpm0 \\ "•" ^clc2 /^ apm0aqm0 \^lpm0^2
-,2qrriQ \ PA
The term /*?™« can be interpreted as a bipolar criterion of moduli equality and co-linearity.
The term *™» which comes from the channels assumed to be not parasitized (no interference), and which increases as a function of fi™« , favours the elimination of as many reception channels as possible. It is the majorant sought for the probability log-density of
measurements from non parasitized channels. The term RmoL In \^-\, which comes from
parasitized channels, and which is negative or nil as soon as 2na2 < C,, is necessary in order to choose the right hypothesis. This term acts as a penalty for hypotheses where
receiving channels are eliminated. The determination of the C coefficient is explained above.
In the case of hypotheses of type ^i^i (one (or more) parasite(s) present on the sampling frequency mo and one (or more) parasite(s) present on the sampling frequency
mi), the criterion becomes: rmoTni = 2RmoTniL In{—) +
where fl"ii^i is the number of reception modules operating with the frequency f*™* or with the frequency femi {Rmo,mi=Rmo + Rmi)
where ^m,™,. is the maximum eigen value of the quadratic form in (Pi- cs) under the constraint Ci +c| = 1:
rQ-mom-L = ~2 0,™omi "" n~Z2 (/VL,m0m1cl "•" "2,m0m1c2 "•" "12,m0m1clc2J
The coefficients of which are defined by:
i7 — vvar I vvar
I^0,m.0m1 Yl,m0m.i ' r2,m0m1

ZT - v™"1 + vcci - V r/ II7 t
4
K = y™*1 + y'r"; -Yff ||z |f
t pr =v = ?V iT iT 17* 7
J'fl
where rf^^, y^?^, Yim^m, Y2m0mv YzXm,. ylm0mx are the single polarization criteria of non-variability, moduli equality and collinearity respectively for sub-arrays 1 and 2 for hypotheses with "two parasitized (interference) sampling frequencies (see previous section).
Where ^f™!!™! is the average of ^ip™ over all samples of the antenna V of the sub-array 1, except on samples assumed to be parasitized (interference): Zlpmo =

V V Cknrl 7_ ic fho moon r»f fho *^
£m*mo *ipm. and ^2qm0 mjstne mean of the r**m over all samples of antenna V of the
Qpm0
sub-array 2, except on samples assumed to be parasitized (interference): Z2qmoPm
T. 2jm*m0,m-, *2qm-
The vector L1 J is then estimated by the eigen vector associated with ^i»i.
FQm0m1can De rewritten as:

PO — fvvar 4- vvar rVm0m1 2(j2 \'l,m0m1 ^ Y2,m0m1)
R — R
J m0m1 f 2( col .mod \ + r2( col , mod \ , f -yn2 V 1 l'l,niomi Y\,mamx) T c2 \Y2,m0m1 T J^.mom,!^ T 7 l(m0i?iJ
Where fqmomi\s the quadratic expression:
z- 2 \ My 11^ 2 \ My
lpm.Qm11
JHm^m-i ^-1 / ®-qm§m-± \\^J2qmQm1 || 2 / pm^m-^ ||-^:
-(- Z.C1C2 7 ^■pm^m^-qm^m^X^lpm^m^.
2^7710^71!
PA

The term /flm,*^ can be interpreted as a bipolar criterion bipolar of moduli equality and co-linearity.
The term Amo7ni which comes from the channels assumed to be not parasitized (no
interference), and which increases as a function of flm,m,, favours the elimination of as many reception channels as possible. It is the majorant sought for the probability log-density

of measurements from non parasitized channels. The term 2RmoTniL In \^-\, which comes
from parasitized channels, and which is negative or zero as soon as 2na2 < C, is necessary in order to choose the right hypothesis. This term acts as a penalty for hypotheses where
receiving channels are eliminated. The determination of the c coefficient is explained above.
In the case of hypothesis sm (no parasites present), the criterion becomes: f0 = A0 where A0 is the maximum eigen value of the quadratic form in (ct,c2) under the constraint c\ + cf = 1:
_ l R , .
The coefficients of which are defined by:
A0,0 — Ylfi "•" Y2,0
p
Ptf
Where y™r, Ywod Y2ood,Y2.ol are tne single polarization criteria of non-variability, moduli equality and colinearity for sub-arrays 1 and 2 respectively for the hypothesis "no parasites present" (see single polarization case).
And where z*p is the mean of the vectors *Vp™ over all samples of the antenna V
of the sub-array 1: Zlp = —Y,m±maYipm,, and where z*v is the mean of the vectors ^^
over all samples of the antenna 9 of the sub-array 2: Z2q = —Y*m±mQ ^2qmQq
The vector L1 J is then estimated by the eigenvector associated with ^m. FQo can be rewritten as:
FQ0 = 2^2 (r™r + r%r) + ^ {cl (K# + Y?Sd) + c22 Gltf + 72mood) + / ttpttq |ZlpZ2q |
V,1
The term /*?■ can be interpreted as a bipolar criterion of moduli equality and co-linearity.
In a first embodiment, the maximum is searched for fo.fmo,mo6[i,Af]^m0,m1,moG[i,M]m16[i,Af],mo*m1> then the parasitized sampling frequencies are determined as described in the single polarization case.
if f0 = max (f0, Tmo, fmo,mi ) , then there is no parasite (hypothesis ^D ).
If there exists ™o such that tfho= max (f0,fmo,fmo;mi), then there is only one
/\ parasitized sampling frequency, and this sampling frequency is ° (hypothesis ™B).
If there exists a pair ™D , **i such that f^0;^l= max (f0, Tmo, fmo;Tril), then there are two parasitized sampling frequencies, and these frequencies are ™a and ™i (hypothesis
In a second embodiment, as described in the single polarization case, the following three quantities are calculated:
r0 = r0,r1 = max (rmn),r2 = max (rmnm')
u u l m0 = l,...,M °J m0 = l,...,MK m°miJ
mx = l,...,M
Fa represents the "absence of parasites" hypothesis (hypothesis ^o).
'"I represents the best of the hypotheses with one parasitized sampling frequency **»»•. This hypothesis is referred to as **i.
ra represents the best of the hypotheses with two parasitized sampling frequencies ffm„™,. This hypothesis is referred to as H-i.
Then, in this embodiment, as in the case of single polarization, we successively
examine the ^^=0,1.1 and select the first rk whose correspondence to its supposed Gaussian law distribution is above a chosen threshold. The hypothesis sought is the corresponding "* hypothesis. If none of them are in compliance with its law, it means that the number of parasitized sampling frequencies is greater than two.
For hypotheses ^ 1 and ffa, the sampling frequencies causing interference are determined by:
m0 = Argmax(Amo + RmoL ■ In(——) I
m0 = l M V V L //
and

(%,%) = ArgmaxfAm0jmi+flm0jmiL-lnf—— jj
m1 = l,...,M 7n0^7n1
The processing treatment then eliminates from all # vectors YLp,m and Y*um those whose sampling frequency index™ corresponds to one parasitized (interference) sampling frequency. On all vectors ¥ij>,™ and **I.TO thus obtained, the signal is detected conventionally in the presence of thermal noise.
This processing is repeated for all time/frequency domains, or, in the variant with pre-detection, for all time/frequency domains selected by pre-detection.
A variant of the processing consists, for each selected time/frequency domain, of:
• Calculating the energy collected by sub-array 1, that is to say the quadratic sum of
the moduli of the ff vectors constituting the time/frequency domain, Ep,m||*ip,m||
• Calculating the energy collected by sub-array 2, that is to say the quadratic sum of the moduli of the ff vectors constituting the time/frequency domain, Ep.mll^mll
• Selecting the maximum energy sub-array;
• Applying the single polarization algorithm described in the single polarization case to measurements in this sub-array alone.

CLAIMS

1. An interference identification method for identifying interference situations due to spectral folding in a wide band digital receiver, the method being operationally implemented by means of an interferometric array, composed of two single polarization sub-arrays with
P wide band antennas, where P is an integer that is greater than or equal to 1, each antenna being followed by an analogue reception chain and one or more digital reception
modules, the number of digital reception modules being R on each sub-array, distributed in an identical manner over the two sub-arrays, the said method comprising:
- a signal sampling step for sampling the signals delivered by all the receiving chains,
making use of M different sampling frequencies fem , that are lower than the
Nyquist-Shannon frequency, ™ ranging from 1 to M _ and M being an integer greater than or equal to 4, the number of digital reception modules operating with a sampling
frequency fem being identical on each array and being equal to ff m, the number of digital reception modules for an antenna V of the sub-array 1 being *2p , and the number of digital reception modules for an antenna of the sub-array 2 being QQ , with # = £m=i#m = £p=i Qp> the said sampling frequencies fem providing integer numbers of samples Nm over a given time A?" ,
- a spectral analysis step by means of synchronous and successive discrete Fourier transforms, allowing for, on each of the 2R digital reception modules, a time/frequency representation referred to as time resolution grid AJ* , and frequency resolution grid AF , each element of the grid being referred to as time/frequency cell and containing a complex quantity referred to as measurement;
- a domain selection step for selecting a set of time/frequency domains (in the reception
band), each time/frequency domain being perceived in the A digital reception modules of
the first sub-array 1 and in the ff digital reception modules of the second sub-array as 2R
superposable windows, each of the windows being composed of £ connected time/frequency cells;
- for each time/frequency domain, a concatenation step for concatenating the
measurements taken from each of the 2R windows in the form of R vectors of dimension L x 1 for the sub-array 1, denoted as *VP»™ , where V is the sensor index and m is the

sampling index, and in the form of ^ vectors of dimension L x 1 for the sub-array 2, denoted
as *W™», where V is the sensor index and m is the sampling index;
- for each time/frequency domain, a parasite (interference) determination step for
determining the presence of possible parasites (interfering/spurious signals) consisting in
choosing, from among the following hypotheses, based on the measurement vectors
obtained, the hypothesis that maximizes an approximation of the probability log-density of
the R vectors ^pm and the ff vectors Y-p™.:
• ^D : absence of parasites;
•^i: presence of at least one parasite on the sample ™ ■->, with m0 e [1,M], and •Hrn+mt; presence of at least one parasite on the sample mo and one parasite on the sample ™L, with m1 e [l,M],m0 ^ m^ andm0 6 [1,M] an.
2. An interference determination method for determining the interference situation
according to claim 1, in which, among the following three hypotheses:
• tf n: "absence of parasites " hypothesis;
• f i: hypothesis that maximizes an approximation of the log-density of probability, from among the hypotheses with one parasitized sampling frequency;
• **s: hypothesis that maximizes an approximation of the log-density of probability, from among the hypotheses with two parasitized sampling frequencies;
the hypothesis chosen is:
• ^a, if its approximated log-density is the one for which correspondence to its assumed
Gaussian law distribution is maximum;
- otherwise, Hi, if its approximated log-density restricted to non-parasitized (no interference) channels is the one for which correspondence to its assumed Gaussian law distribution is maximum;
- otherwise, **J , if its approximated log-density restricted to non-parasitized (no interference) channels is the one for which correspondence to its assumed Gaussian law distribution is maximum;
otherwise, it is determined that there are more than two parasitized sampling frequencies.
3. An interference determination method for determining the interference situation
according to claim 1 or 2, wherein the method comprises:
- the calculation of the energy collected by the first sub-array;
- the calculation of the energy collected by the second sub-array;

the interference determination step being implemented for the sub-array that collects the maximum energy according to the single polarization algorithm.
4. An interference determination method for determining the interference situation
according to claim 1 or 2, in which the following criteria are calculated:
- for each sub-array, the single polarization criterion, and
- for the two sub-arrays taken together, the bipolar criterion.

5. An interference determination method for determining the interference situation according to claim 4, wherein the one or more calculated criterion/criteria are used to obtain an approximation of the probability log-density of the measurements.
6. An interference determination method for determining the interference situation according to any of claims 1 to 5, in which the approximated probability log-density is calculated according to the following approximations:
- For the hypothesis Hn (no parasites present), the quantity f0 , also denoted as f0::
f0 = A0, wherein A0 is the maximum eigen value of the quadratic expression in ei-c::
FQ0 = ^ (/iT + rlf) + ^ (ci (/$ + r™d) + 4 (/$ + r2Td) + fio)
Where /■?• is the quadratic expression:
fio = ~cl / aq \\^2q\\ ~ c2 / ap ll^lpH + £-c\c2 / apaq\^lp^2qq p p,q
which can be interpreted as a bipolar criterion of moduli equality and co-linearity;
where Timr, 'KID0 .'KID1 , YW, YW Jit1 are the single polarization criteria of non-variability, moduli equality and colinearity respectively for the sub-arrays for the hypothesis "no parasites present" defined in claim 4;
where av is the proportion of digital reception modules operating with the V -antenna with index on the first sub-array;
ai is the proportion of digital reception modules operating with the antenna with index q on the second sub-array;
where z*f is the mean of the vectors KLpm over all samples of the antenna p of the first sub-array 1: zp = — £m rlpmand where z*q is the mean of the vectors v*i™ over all samples
of the antenna 9 of the second sub-array: zq = —TimY2qm',

where Qv is the number of digital reception modules operating with the antenna with index
P on the first sub-array, and *2p is the number of digital reception modules operating with
the antenna with index V on the first sub-array;
where ci represents the gain of the first sub-array in the polarization of the incident signal;
where ci represents the gain of the second sub-array in the polarization of the incident
signal;
- for the hypotheses H^a (one (or more) parasite(s) present on the sampling frequency ™n
), the quantities , Pmo = 2RmoLlnC^-) +Amo, wherein Rmo is the number of digital
reception modules operating at frequency f™a in each of the two sub-arrays, and where
■^o represents the approximated log-density restricted to non-interference channels; it is
equal to the maximum eigen value of the quadratic expression in ci' ci:
1
cr> — (vvar J- ,,var f^m0 ~ 2(J2 \Yl,m0 + Y2,m0J
Where fQtr.a is the quadratic expression:
f - - 2V \\7 II2- 2V \\7 II2
q p
+ ZC-^C2 7 apm0aqm0\^'lpm0^'2qm0\ P.Q
which can be interpreted as a bipolar criterion of moduli equality and co-linearity;
Where Yim"a-Yimu •Ylma,Yzm"a-Yima 'C', are the single polarization criteria of non-variability, moduli equality and co-linearity, for the first sub-array and the second sub-array respectively, for the hypothesis of "one parasitized (interference) sampling frequency", defined in claim 4;
Where af™„ is the proportion of digital reception modules attached to the antenna with index
V on the first sub-array, which do not operate with the frequency ^S and ff?mD is the
proportion of digital reception modules attached to the antenna with index 1 on the second
sub-array, which do not operate with the frequency /ffm, ;
vvnere zlpmo = - zjm*m0 'ipm ana z2pmo = - zjm*m0 '2pm 1
Where Qnma is the number of digital reception modules attached to the antenna with index
V on the first sub-array, which do not operate with the frequency fe™% and QQ.^IB is the

number of digital reception modules attached to the antenna with index Q on the second
sub-array, which do not operate with the frequency fem,;
Where s»i, is the number of digital reception modules operating at the sampling frequency
fe~,a on each sub-array;
where ci represents the gain of the first sub-array in the polarization of the incident signal;
where c: represents the gain of the second sub-array in the polarization of the incident
signal.
for the hypotheses H^a.^t, the quantities

_ _ (2na-
c
l7riQ7n1
lm0m1 = 'n Pm0m1 = '"m0m1','l11 "p. I ' A

where Rmonil is the number of digital reception modules operating with the frequency fe™a
or with the frequency f0™± in each of the two sub-arrays, and where ^"h represents the approximated log-density restricted to non-parasitized (no interference) channels; it is equal to the maximum eigen value of the quadratic expression:
1 ,
pr\ fvvar -i- vvar rVm0m1 2(j2 \'l,m0m1 """ r2,m0m1J
D D
j m0m1 (7 (..col , ..mod \ , r2(.,col , ..mod jn2 Vcl \Yl,m0m1 ' Yl,m0m1J ' L2 \Y2,m0m1 ' f2,m0m1)
' J<1m0m1)
Where ftt»imi is the quadratic expression:
2 \~" II II2 2\~l II II2
JtJm0m1 ~ ~cl / aqm0m1 \\^2qm0m1\\ ~ c2 / apm0m1 \\^'lpm0m1 \q p
+ LC]C-2 J apm0m1aqm0m1\^'lpm0m1^'2qm0m1\ P.Q
which can be interpreted as a bipolar criterion of moduli equality and co-linearity;
where ^mi, Yim.tm.x t Yi.mtmx t Kim^m,, Yim.tm.x t Yimumx are the single polarization criteria of non-variability, moduli equality and co-linearity respectively for the sub-arrays for the hypotheses with "two parasitized (interference) sampling frequencies, as defined in claim 4;
where avavni is the proportion of digital reception modules attached to the antenna with index p of the first sub-array that do not operate with either the sampling frequency ^ , or with the sampling frequency fs^i, and
where "'"i"1! is the proportion of digital reception modules attached to the antenna with index q of the second sub-array that do not operate with either the frequency of echantillonnage fg™* or the sampling frequency of fB™±;

wnere Zlpm m — im*m0,ni, 'I™ 3nQ ^2pmnpm„ ~ n 2jm^mn,m-i *2qm>
Qpm0,mi u f uf 1 QqmQ,mx u. i i
where Qv.m,^^ is the number of digital reception modules attached to the antenna with
index P that do not operate with either the sampling frequency fs^a or the sampling
frequency /9^i on the first sub-array, and Qq,m^,m1 is the number of digital reception
modules attached to the antenna with index q that do not operate with either the sampling
frequency fe™a or the sampling frequency fe^x on the second sub-array;
where Rmum± is the number of digital reception modules operating at the sampling
frequency f6™* or/s"n on each sub-array;
where ci represents the gain of the first sub-array in the polarization of the incident signal;
where C2 represents the gain of the second sub-array in the polarization of the incident
signal;
7. A computer program product comprising a computer program comprising of program instructions saved and stored on a data carrier-storage medium that is readable by a computer comprising a data processing unit, the computer program being adapted so as to cause the operational implementation of a method according to any one of claims 1 to 6 when the computer programme is deployed to run on the data processing unit.
8. A readable data carrier-storage medium on which is saved and stored a computer programme comprising of program instructions, the computer program being loadable on to a data processing unit and adapted so as to cause the operational implementation of a method according to any one of claims 1 to 6 when the computer program is deployed to run on the data processing unit.
9. An interferometer with two single polarization sub-arrays with p antennas, where P is an integer that is greater than or equal to 2, each antenna being followed by an analogue reception chain and one or more digital reception modules, each digital reception module comprising an analogue-to-digital conversion system and a digital processing module, each analogue-to-digital conversion system being associated with a respective sampling frequency, an analogue-to-digital conversion system being associated with a sampling frequency when the analogue-to-digital conversion system is capable of performing sampling at the sampling frequency, each frequency being such that the sampling performed by the analogue-to-digital conversion system is a sampling that does not satisfy

the Shannon criterion and the interferometer being capable of operational implementation of a method according to any of claims 1 to6.