METHOD FOR DETERMINING THE ARRIVAL DIRECTION IN THE PRESENCE OF SPECTRAL FOLDING AND ASSOCIATED DEVI

专利摘要:
The invention relates to a method for determining the direction of arrival of radio signals in the presence of spectral folding, the method using an interferometric network (12) with four antennas (16) with identical diagrams, and sampling with two frequencies of separate sampling by antenna (16), the method also comprising, for all the useful signals detected: - the determination of the interference situation for each antenna (16), - for the other antennas (16) that the antenna (16) affected by the double interference, the extraction of the phase of the useful signal, and - for the possible antenna (16) affected by the double interference, the estimation of the phase of the useful signal.
公开号:FR3046250A1
申请号:FR1502685
申请日:2015-12-23
公开日:2017-06-30
发明作者:Meur Anne Le
申请人:Thales SA；
IPC主号:

专利说明:

Method for determining the arrival direction in the presence of spectral folding and associated device
The present invention relates to a method for determining the arrival direction in the presence of spectral aliasing and an associated device.
In general, the present invention relates to the field of broadband passive reception of electromagnetic signals (radar or communication signals).
It is particularly desirable to determine the direction of arrival (also referred to by the acronym "DOA" for the term "direction of arrivai").
For this, a phase direction finding interferometer for capturing electromagnetic signals and calculating their direction of arrival is used. The successive distances between antennas respect well-known known proportions in order to ensure a direction of arrival measurement of the unambiguous signal.
For technological reasons, in broadband listening of electromagnetic signals, it is generally not possible to perform sampling at a frequency greater than twice the width of the band occupied by all the analog signals (so-called broadband), that is to say to respect the Nyquist criterion. This requires indeed ultra-fast digital converters, which do not meet the constraints of weight / volume / consumption, when they are not completely inaccessible for the bandwidths that one seeks to treat.
When the Nyquist criterion is not respected, the signals from all Nyquist bands fall back into the first Nyquist band, and are likely to generate mixtures, which considerably reduces the performance of the receiver. In order to correctly estimate the parameters of these signals, and in particular the DOA, a receiver with M distinct sampling frequencies is used here, but does not respect the Nyquist criterion, M being an integer.
The judicious choice of the number M of sampling frequencies and their value makes it possible to remove the frequency ambiguities, that is to say to guarantee the existence of a one-to-one correspondence between an analog frequency in the total band ( called radio frequency or true frequency) and a M -uplet of frequencies taken from the first Nyquist band of each of the M samplings (called M-tuple of folded frequencies).
When a single signal is present in the wide band, it is possible to perform the detection using a conventional method of detection in the presence of thermal noise. It is also possible to calculate the direction of arrival of the signal.
The case where the complex spectrum of the signal is superimposed on one of its replicas must be treated in a particular way. For a real signal whose frequencies check
and for a sampling frequency / ", given, a sufficient condition for there to be no superposition is that there exists an integer k such that
and
For simplicity, it can be said that there is no overlap when the rest of the entire division of the carrier frequency of the signal by
is greater than the instantaneous band of the signal, or in other words, when the carrier frequency of the signal is "sufficiently far" from the multiples of the half sampling frequency.
However, in a passive system, the received signal is unknown and compliance with this condition is not guaranteed.
When several signals are simultaneously present in the wide band, the situation is further complicated because two signals simultaneous but separated frequency can be superimposed in time and frequency after folding. These mixtures are of a particular type: they occur for a sampling frequency, or even simultaneously for several sampling frequencies, but not for all, because of the uniqueness of the correspondence between all the radio frequencies and all the M-tuples of frequencies.
There is therefore a need for a method of determining the direction of arrival of signals emitted by a radio source to overcome the aforementioned drawbacks and in particular to deal with situations involving several signals.
For this purpose, the present description relates in particular to the method for determining the direction of arrival of radio signals in the presence of spectral folding, the method using an interferometric network with four antennas with identical diagrams, and sampling by two sampling frequencies. antenna, the spectral folding being such that in the time / frequency representation of a signal, the signal being said useful signal, at most one antenna is affected by a parasitic phenomenon on its two sampling frequencies, the phenomenon being due to a first external parasite, and a second parasite being either a second external parasite or an internal parasite. The method comprises receiving a signal from each antenna, sampling the signals received on each of the four antennas (16) at two sub-Nyquist frequencies forming the set
where /, Λ, / 3 and / 4 are four distinct sub Nyquist frequencies and perm is a permutation of the set {/ ^ / 2, / 3, / 4}, so that the signals received on two separate antennas are sampled by two distinct pairs of sampling frequency sub Nyquist. The method comprises the spectral analysis by applying, during a synchronous acquisition period on all the samplings, a discrete Fourier transform to obtain 2P time-frequency grids, each element of a grid containing a complex vector called measurement, detecting the presence or absence of a useful signal at a plurality of frequencies. The method also comprises, for all the useful signals detected, the determination of the interference situation for each antenna, for the other antennas that the antenna affected by the double interference, the extraction of the phase of the useful signal, and for the possible antenna affected by the double interference, the estimation of the phase of the useful signal, comprising the first estimation of a first pair of candidate phases ξ 1 and f 2, from the measurement z resulting from the mixing of the useful signal, of the first parasitic signal, and of noise, the second estimate of a second pair of candidate phases ξ 1 and ξ 1 from the measurement ζ resulting from the mixing of the useful signal, the second parasite, and noise, and the selection of phase values among the candidate phases to obtain an estimate of the phase of the useful signal on the antenna affected by the double interference.
According to particular embodiments, the method comprises one or more of the following characteristics, taken separately or in any technically possible combination: the plurality of frequencies of the detection are analog frequencies regularly spaced from a frequency interval inverse to the acquisition time. the first estimate of first candidate phases comprises the calculation of the following equations:
and or :
• a is the argument of the measure z, • p is the module of the measure z, • r is the module of the wanted signal, and •] is the module of the first parasitic signal. the second estimate of a second pair of candidate phases comprises the calculation of equations according to the nature of the second parasite, when the second parasite is an internal parasite, the equations being
and or:
• r is the module of the useful signal, and • y is the real part of the measurement ζ when the second parasite is an external parasite, the equations being
and or :
• a is the argument of the measure ζ, • p2 is the module of the measure ζ, • r is the module of the wanted signal, and • r2 is the module of the second parasitic signal. the selection of phase values comprises associating the candidate phases to determine the two phase values corresponding to a common value representing the true phase, to obtain two associated phase measurements, and estimating the phase by merging the two phases; associated phase measurements. the association of the phases is implemented with the aid of a rule, the rule being the following rule: ξ [and ξ] 2 are associated if the pair
) is the couple among the four couples
who checks
- the estimate of the phase includes the calculation of the following expression:
Where: • jc is the estimated phase of the wanted signal; • ξχ is equal to ξ [obtained in the association step; • ξ2 is equal to ξ {obtained in the association step;
• σ is the variance of ξλ, defined by and • σ2 is the variance of ξ2, defined: o when the second parasite is internal, by
or o when the second parasite is external, by
the method further comprises calculating differential phases and calculating the direction of arrival from the differential phases.
The present description also relates to a device for determining the direction of arrival of radio signals in the presence of a spectral folding, the device comprising an interferometric network with four identical diagram antennas and sampling by two separate sampling frequencies by antenna, each antenna being adapted to receive a signal said received signal, the spectral folding being such that in the time / frequency representation of a signal, the signal being said useful signal, at most one antenna is affected by a phenomenon of interference on its two sampling frequencies, the phenomenon being due to a first external parasite, and a second parasite being either a second external parasite, or an internal parasite, a controller adapted to implement sampling, spectral analysis, detection of the presence or absence of a useful signal, then, for each detected useful signal, the determination of the interference situation for each antenna, the extraction of the phase of the useful signal on the other antennas that the possible antenna affected by the double interference and the estimation of the phase of the affected antenna by the double interference of a method as previously described.
According to one embodiment, the controller comprises a sampling unit capable of carrying out the sampling of the method as previously described and a computer capable of implementing the spectral analysis, the detection of the presence or the absence of useful signal, then, for each detected useful signal, the determination of the interference situation for each antenna, the extraction of the phase of the useful signal for the other antennas that the antenna affected by the double interference and the estimate the phase of the useful signal for the possible antenna affected by the double interference of the method as previously described.
According to one embodiment, the sampling unit comprises two analog-to-digital converters per antenna. Other features and advantages of the invention will appear on reading the following description of embodiments of the invention, given by way of example only and with reference to the drawings which are: FIG. schematic of a device for determining the direction of arrival of radio signals in the presence of spectral folding, and - Figure 2, a schematic view of a portion of the device of Figure 1.
A device 10 for determining the direction of arrival of radio signals in the presence of spectral folding is illustrated in FIG.
The device 10 comprises an interferometric network 12 and a controller.
The interferometric network 12 is an array with P antennas 16 with identical diagrams.
The choice of P = M = 4 makes it possible to obtain an unambiguous interferometer angularly and frequently over the entire broadband.
Each antenna 16 is adapted to receive a signal said received signal.
In the following, each antenna 16 is also referred to as a "sensor".
The controller 14 is adapted to process each signal received by the antennas 16 to obtain the arrival direction in the presence of spectral aliasing.
For this, the controller 14 is adapted to implement a method of determining the direction of arrival of radio signals in the presence of spectral aliasing.
An example of a controller ^ is illustrated schematically in FIG.
The controller 14 comprises a sampling unit 18 and a calculator 20.
The sampling module 18 is able to sample at two distinct sub-Nyquist frequencies each signal received by an antenna 16, so that each antenna 16 comprises two measurement channels.
This provides two sets of sampling frequencies. The two sets are chosen so as to form two permutations of the same quadruplet of frequencies sub Nyquist, so that two separate antennas 16 are not associated with the same pair of sampling frequencies.
Otherwise formulated, the signals received on each of the 4 antennas are sampled according to two frequencies forming the set {f, pern (f); f2, penr (f2}, f3, pem (f1); f4, pern (f4)), where f, f2, f3, f4 are the four distinct sub Nyquist frequencies and perm is a permutation of the set {/ i, / 2, / 3, / 4}, so that the signals received on two separate antennas are sampled by two distinct pairs of sampling frequency sub Nyquist.
There are thus two measurement channels per antenna 16. Each of the four sampling frequencies is common to two measurement channels. It is called the sampling channel the two measurement channels sharing the same sampling frequency.
The sampling module 18 comprises two analog-digital converters 22 by measurement.
In the example of Figure 2, the first analog-digital converter 22 of the first antenna 16 is adapted to sample the signal at a first sampling frequency fx.
The second analog-to-digital converter 22 of the first antenna 16 is adapted to sample the signal at a second sampling frequency f2.
The first analog-to-digital converter 22 of the second antenna 16 is adapted to sample the signal at the second sampling frequency f2.
The second analog-to-digital converter 22 of the second antenna 16 is adapted to sample the signal at a third sampling frequency f3.
The first analog-to-digital converter 22 of the third antenna 16 is adapted to sample the signal at the third sampling frequency f3.
The second analog-to-digital converter 22 of the third antenna 16 is adapted to sample the signal at a fourth sampling frequency f4.
The first analog-to-digital converter 22 of the fourth antenna 16 is adapted to sample the signal at the fourth sampling frequency f4.
The second analog-to-digital converter 22 of the fourth antenna 16 is adapted to sample the signal at the first sampling frequency j .
It is assumed that the narrow-band nature and the density of the signals in the environment are such that in the time / frequency representation of a (so-called useful) signal, the most complex interference situation is a double interference situation. intervening on two distinct sampling frequencies (an internal parasite and an external parasite or two external parasites).
Therefore, for a given signal (considered to be the wanted signal), the parasitic situation is due either to an internal parasite or to an external parasite, or to an internal parasite and an external parasite on two sampling frequencies. two external parasites on two separate sampling frequencies. In the case of two parasites, the device 10 ensures that for any signal in the wideband, the double interference situation is present on an antenna at most.
The computer 20 is able to process each measurement channel to obtain the direction of arrival.
The computer 20 is, for example, a processor or a programmable logic circuit.
The operation of the arrival direction determining device in the presence of spectral folding mixtures is now described.
The method comprises a reception step, a sampling step, a spectral analysis step, a step of detecting the presence or absence of a useful signal at a plurality of frequencies, and then, for all the useful signals detected. , a step of determining the interference situation for each antenna, a step of extracting the phase of the useful signal on the antennas not affected by the double interference and a step of estimating the phase of the useful signal on the possible antenna affected by double interference. At the receiving step, a signal is received by each antenna.
The receiver is an interferometer with P (P = 4) sensors aligned with identical diagrams.
The signal measured at the output of the sensors forms a vector of dimension P = 4 whose component p is written according to the following equation 1:
Where: • Θ is the angle formed by the direction of propagation of the incident wave with respect to the axis of the sensors, • λ is the wavelength of the signal, • dp is the abscissa of the sensor p on the axis, • bp is the noise on the sensor p, and • s is the amplitude of the signal, assumed to be narrowband. At the sampling step, the received signal is sampled for each antenna at two distinct sub-Nyquist sampling frequencies to obtain two sub-Nyquist sampled signals.
As explained above, the sampling step is implemented by the sampling unit 18. The spectral analysis step makes it possible to obtain a time / frequency representation that achieves an average adaptation to the band of the signals of interest.
In this step, on each measurement channel, a time / frequency grid is obtained by sliding spectral analysis on the sampled signal. These spectral analyzes are carried out by moving in a regular step a temporal support of duration ATm, and by applying a bank of filters by Discrete Fourier Transform (DFT) on this support. The results constitute a two-dimensional grid in which the iTth column represents the result of the iTeme spectral analysis, and in which the box or element of index {iT, iF) contains a complex quantity called measurement, representing the iFeme channel of the iTeme spectral analysis. For simplicity, the double index in time and frequency is then replaced by a unique index n.
The model thus becomes the following equation 2, for a measurement n on a measurement channel v:
Where: • p (v) is the sensor on which the measurements of the channel v are made, • sn denotes the Discrete Fourier Transform of the Nm samples of s for the time interval and the frequency interval of the considered cell; stt is independent of the sensor, • wv> "denotes the Discrete Fourier Transform of the noise on the antenna
Piy) - • d (v) is the distance from the sensor p (v) to a sensor arbitrarily taken as a reference, • n is a double index that traverses time and frequency.
In all that follows, it is assumed that the signal to noise ratio is large.
Under these conditions, the representation of equation 2 can be replaced by a polar decomposition. In the general case (that is to say in the absence of parasites), it is shown that the zp modules are independent of a and are noisy by a noise that is independent of the phase noise. We conclude that the phases (modulo 2π arguments) of zv are sufficient for the estimation of a, which is the problem we are trying to solve.
For simplicity, we can rewrite equation 1 in:
What is written in equation 3: z = rea + w
The signals of interest are real high frequency and narrowband signals. They are characterized by the fact that their spectrum consists of two spectral patterns with disjoint support, respectively on R + and R-, and consisting of a limited number of consecutive intervals, typically two consecutive intervals.
In the general case, there is therefore no interaction between the two spectral patterns of the real analog signal. Nevertheless, after subsampling, this no longer holds true when the radio frequency is close to a multiple of the Nyquist frequency, because then there is a superposition, in the first Nyquist band, between a replica of the positive part. and a replica of the negative part of the spectrum. In the case where the number of points of the Fourier Transform is even, the resulting measure is the sum of the two spectral patterns, which are conjugated to each other. This phenomenon is called internal interference or intra signal.
When several signals are present simultaneously in the wide band, there can also be interaction, if at least two signals occupy frequencies whose rest of the Euclidean division by the sampled frequency band is identical. We then observe a superposition, in the first Nyquist band, of a replica of the positive part (or the negative part) of the spectrum of the first signal with a replica of the positive part (or the negative part) of the spectrum of the first signal. second signal. This phenomenon is called external interference or inter signals.
In order to obtain synchronous information of the same spectral resolution, a start and an end of acquisition common to all DFTs are imposed. Also, the sampling frequencies fm and the number of points Nm of each DFT verify the following equation 4: Where:
• Nm represents the number of sampling points at the frequency fm, • Tm represents the sampling period (inverse of the sampling frequency fm), and • AF represents the spectral resolution common to all measurement channels. Equation 4 implies that the number of points Nm is different from one sampling to another. This choice of sampling frequencies fm so that the sampling frequencies are multiples of the band AF allows that from one sampling to another, the spectra of the signals are shifted by an integer of multiples of fm, therefore an integer number of multiples of AF, that is, an integer number of discrete Fourier Transform filters.
Moreover, the fm frequencies are close to each other because they are chosen close to the limit reachable by the technology, in order to limit the folds.
The number of folds for a frequency fm, denoted rm, which is equal to is therefore close to the average value of the rm, which will simply be called the coefficient r.
.
Another consequence of equation 4 is that the true frequency of a signal can not be multiple of two different half-sampling frequencies.
Indeed, if there is a true frequency such that, for two sampling frequencies (for example, but without loss of generality, fx and f2):
Where ki and k2 are two integers.
It is then obtained kjx = k2f2.
Since NXTX = N2T2 it is obtained f2 = fxN2 / Nx, and thus: kxfx = k2fxN2 / Nx, hence: kx = k2N2! Nx.
Therefore :
For kx to be integer it is necessary that
be whole.
It can be assumed without loss of generality that N2> Nr
Therefore
is an integer greater than or equal to 1, since N2 - Nl h 0.
Therefore
Since the Nm are much greater than the number of folds r, and the Nm are close to each other (since the / "are close to one another), k2 is large in front of r, so the true frequencies likely to be multiples of two different half-sampling frequencies are out of the wide band.
From all this, it follows that, if, for a given radio frequency, an internal parasitic phenomenon occurs in a sampling channel, due to the superimposition of the spectrum on one of its own replicas, then the phenomenon occurs. produced in this sampling channel only.
In the same way, it can be shown that if a given radio frequency is superimposed, after folding, in a sampling channel, with another radio frequency, then this superposition occurs in this sampling channel only.
With regard to the mixtures of three signals, it is used that the signals are narrow band, and therefore parsimonious in frequency, which makes it possible to neglect the cases where, during the acquisition period AT, a signal is parasitized by more than two other signals simultaneously. It will also be neglected that during the acquisition period AT, a signal may be parasitized by two signals simultaneously on the same sampling frequency.
Thus, for all the antennas, only four situations are possible.
In a first situation, no sampling path contains an external parasite, and no sampling path contains an internal parasite.
According to a second situation, one of the sampling channels contains an external or internal parasite. Two antennas share this sampling frequency.
According to a third situation, one of the sampling channels (ie fml the corresponding sampling frequency) contains an external parasite, and a second sampling channel (ie fm2 the corresponding sampling frequency) contains an internal parasite, such as so that m2 Ψ perm (ml) and ml ψ perm (m2).
According to a fourth situation, one of the sampling channels (ie / œ) the corresponding sampling frequency) contains an external parasite, and a second sampling channel (ie fm2 the corresponding sampling frequency) contains an internal parasite or external, so that m2 = perm (m ^) oi mK = perm (m2). Therefore, for one of the antennas (or Λ this antenna), there is interference on the two measurement channels. For any given signal in the wideband, this double interference concerns a single antenna which will be called "antenna affected by the interference phenomenon for the two sampling frequencies" or "antenna affected by the double interference".
Whatever the situation, it is assumed that there is a detection step which determines whether, for any radio frequency of the wide band, defined at the resolution of the spectral analysis, there is presence or absence of useful signal.
Such a function is obtained for example by the method described in the patent "Digital detection method" FR 1400935).
This detection step is followed by a step of determining the interference situation. This step consists in examining the quadruplets of folded frequencies associated with each radio frequency for which the presence of signal has been detected, in order to know if certain quadruplets have common values.
When the presence of a useful signal has been detected for a given radio frequency, this makes it possible in particular to know whether, in the quadruple of folded frequencies associated with it, zero, one or more values are in common with another quadruplet of folded frequencies associated with other detected signals, and therefore, if zero, one or more sampling channels have external interference. In the extraction step, for the other antennas that the antenna affected by the double interference, the phase of the useful signal is extracted.
In fact, in the first situation, on each measurement channel, it is possible to extract the phase of the useful signal.
In the second situation, one of the sampling channels contains an external or internal parasite. Two antennas share this sampling frequency. The extraction step is, for example, implemented by exploiting, for each of the two antennas concerned, the sampling frequency which does not contain a parasite; and, for other antennas, which are not tainted by parasites, any of the two available measurements or both measurements available.
In the third situation, no antenna is parasitized twice so that the remarks for the second situation also apply.
As a reminder, the situation 4 is a situation of double interference (interference on the two measurement channels of the same antenna). The estimation step is implemented in situation 4. This step consists in estimating the phase of the useful signal on the antenna which is affected by the double interference.
In this case, a specific treatment is proposed.
For this, it is described in the following an embodiment and then it is shown that the proposed embodiment provides an estimate of the phase of the useful signal in the complex situation situation 4. The step estimation method comprises a sub-step of estimating the useful signal module, a sub-step of estimating the module of the spurious signal, a sub-step of first estimation of a first pair of candidate phases, a sub-step of second estimation of a second pair of candidate phases, a sub-step of association / selection of the candidate phases, a sub-step of merging the selected phases. In the substep of estimating the useful signal module, the useful signal module is estimated using the other antennas that the antenna affected by the double interference. For example, the estimation of the useful signal module using the other antennas that the antenna affected by the double interference is implemented, for example by calculating the module of a non-parasitic measurement (see equation 3), possibly applying filtering (smoothing), since several measurements are available. In the sub-step of estimating the module of the spurious signal, the module of the spurious signal is estimated using the other antennas that the antenna affected by the double interference. By way of example, the estimation of the module of the parasitic signal using the other antennas that the antenna affected by the double interference is implemented by calculating the module of a measurement of the parasitic signal (see equation 3) , possibly applying filtering (smoothing), because several measurements are available. Indeed the parasite itself is parasitized at most twice, and this, on two different frequencies. At the sub-step of first estimation of the candidate phases, the first pair of candidate phases (ξ , ξϊ) are obtained from the measurement, from the module of the wanted signal and from the module of the parasitic signal.
For example, the first estimate sub-step of a first pair of candidate phases {ζΐ, ξ ) Includes the calculation of the following equations:
and or :
• a is the argument of the measurement, • p is the measurement module, • r is the useful signal module, and • η is the parasitic signal module, and the second estimate sub-step of the candidate phases, a second pair of candidate phases (ξ , ξΐ) is obtained from the measurement, and the module of the useful signal.
For example, the sub-step of second estimation of a second pair of candidate phases {ξ , ξ ) comprises calculating the following equations:
and or :
• r is the module of the wanted signal, and • y is the real part of the measurement. In the sub-step of association / selection of the candidate phases, phase values are selected from among the candidate phases.
For this purpose, the association / selection sub-step comprises associating the candidate phases to determine the two phase values corresponding to a common value representing the true phase, and the selection of these two phase values. The combination of phases is, according to a particular case, implemented using a rule, the rule being the following rule: ξ {and are associated if the pair {ξ [, ξΙ) is the pair among the four couples
: I am checking
The two
associates are selected. At the melting sub-step of the selected phases, the estimation of the phase of the useful signal is implemented by performing the calculation of the following expression: Where:
• x denotes the estimate of the argument of the useful signal, • ξχ is equal to ξ [obtained in the association / selection step, • ξ2 is equal to the ξ2 obtained in the association / selection step; • of is the variance of ξχ, defined by
and • c is the variance of ξ2, defined by
As will be demonstrated, the sub-steps for estimating the useful signal module, estimation of the parasitic signal module, first estimation of a first pair of candidate phases, second estimation of a second pair of phases. Candidates, of association / selection of the candidate phases, of fusion of the selected phases, make it possible to obtain an estimate of the phase of the useful signal in the fourth situation.
Let r and x respectively be the module and the argument of the useful signal.
Let rx and x be the module and the argument of the spurious signal that comes with the sampling frequency fml.
On the antenna A, after sub-sampling at the fmi frequency, the measurement is expressed as a mixture of the wanted signal, the parasitic signal and the noise according to the following equation:
The other cases, namely: the mixing of the useful signal with the conjugate of the parasitic signal, the mixture of the conjugate of the useful signal with the parasitic signal, the mixture of the conjugate of the useful signal with the conjugate of the parasitic signal, are written and treat in a similar way.
On the antenna A, after subsampling at the frequency fm2, in the case of an internal interference, a mixture of the useful signal, its conjugate and noise is measured according to the following equation 6:
Where: w, vsare two independent samples of a complex, centric Gaussian random variable of covariance
It should be noted that strictly speaking, one is not exactly independent. Their correlation coefficient is equal to the inverse of the number of frequency ambiguities.
It is proposed to estimate the phase jc using the measures of equations 5 and 6 assuming that ret rx are known, replacing / - and rx by their estimate.
On the other hand, since the imaginary part of the signal ζ contains only noise, equation 6 is reduced to an equation 7:
As a result, the parameter west is therefore Gaussian, centered, and of variance σ2.
To have an estimator of the phase x good on average and this, whatever I ,, it is considered that the phase jc, is a random variable independent of the noises and equidistributed on the interval [θ, 2 # [.
In equation 5, "noise" is expressed by the mathematical term rxelx '+ w. This random variable has a probability density that is expressed in the form of equation 8: Where:
• p is the probability density of the phase jc, • wx is the modulus of the complex number rxeix '+ w, and • φ is the argument of the complex number rxeix' + w.
It is noted the independence between the module and the argument, the module following a modified Rayleigh law (Rice's law) and the argument being equidistributed.
When r2! 2σ2 »1 (strong signal-to-noise ratio), the function of Bessel / 0 (.) Is approximated by the expression
The result for equation 8 is that:
After simplifications and taking into account that w, = rx for r2! 2σ2 »1, it is then obtained:
This last expression indicates that the argument is equidistributed on the segment [θ, 2; τ [, while the module is approximately Gaussian, centered on η and of standard deviation σ.
Using equations 5 and 6, the probability density of the z measurements (in module and argument form) and y is written according to equation 9:
In a similar way, the following equation 9bis is obtained:
At first glance, to estimate x, the maximum likelihood estimator could be implemented. Such an estimator maximizes the expression of equation 9 in x for z, y, r, η given.
This is equivalent to finding the estimator of x noted x using the following equation 10:
However, equation 10 is very non-linear, and there is no analytic solution.
On the other hand, since the signal-to-noise ratio is very good, x must check the following approximations:
It is proposed to separately solve each of the two equations of equation 11 so as to first find approximate values of the estimator x.
For the following, the following equations 12a and 12b are posed from the system of equations 11:
The following equations 12a and 12b form a system to be solved whose solutions will be called ξχ and ξ2, respectively. The last stage of the processing is to "merge" £ and ξ2 to determine the x estimator.
It is now proposed to qualify the solutions ξχ and ξ2 in number (ambiguities), mean and variance.
We solve equation 12a, that is, we are looking for ξχ that solves the following equation:
Using the fact that this expression is equivalent to obtaining on the parasitic path the following equation 13:
Posons | z | = p, Argz = oc. Equation 13 is equivalent to 2ρτζο% {ξχ -a) = p1 + r2 -rx
So, provided that
there are two possible solutions for estimating the phase of the wanted signal in the parasitized path that are expressed by the system of equation 14:
Where: • "arccos" refers to the mathematical function arccosinus. • where p and a are respectively the module and the argument of z. Since one of these estimators is unbiased, the variance of the estimator is found as follows.
Let z = z0 + u (see equation 5),
This makes it possible to define the quantities Apet Aa by the equations p = p0 + Ap and a = a0 + Aa.
When
, the following property is verified: the quantities Ap and Aa are two independent random variables, Gaussian, centered, of variance respective σ2 and
From equation 14, another expression of the estimate of the phase of the wanted signal in the parasitized path is obtained, an expression called equation 15:
In addition, we have:
In writing the limited development of expression
-to the first order in
Ap, this expression is transformed into equation 16,
From equation 15, and using the fact that the function arccos (t) is differentiable over the interval] - l; l [and that its derivative is
:, it is deduced that:
What is written in the form of equation 17
To understand the behavior of the term in
, it is possible to return to z0 = re "+ re'x 'so that only r, i , x and I,
From which it results, on the one hand:
And on the other hand :
The result is:
From this is deduced equation 18 which is a limited expansion of ^ in kpet Δα expressed as a function of x and x:
The quantities Δa e1
are two Gaussian noises, independent, centered and of the same variance
One of the two determinations of ξλ is therefore unbiased and of variance:
In the last two terms of the numerator, all the power terms of 4 cancel each other out.
Only the double products remain, namely:
Taking into account the first term, the numerator is reduced to 4plrf.
By replacing the term p0 by the term p, the variance of the estimator ξλ is obtained with equation 19 which follows:
What can be rewritten according to xet x1 in the following form:
Let us solve equation 12b according to which G (y, ξ2) = y - 2r cos ξ2 = 0.
It's got two possible solutions for
where y = Re (ç). One of these estimators is unbiased and it is possible to find the variance of the estimator as before.
It is posed: y = + w <with Jo = 2rcosx
In the normal case where w / 2r "1, the solutions of equation 12b are written according to the following equation:
So the variance of ξ2 is expressed according to the following equation 21:
So there are two possible candidates for
and two possible candidates for
, four possible values for the pair (^,, £>). Of these four couples, in principle only one corresponds to two values close to ξχ and ξ2. The ambiguity on the possible values for x is thus raised by taking the couple minimizing the difference between
The couple selected
is the one who checks the following rule:
Where i, j, k, l g {1,2}
For simplicity, the retained torque is noted {ξλ, ξ2) in the following.
In addition, it is posed
It remains to find x from £ and ξ2.
For this, it is proposed to estimate x by αξχ + βξ2 with a + β = 1 so that x is unbiased and so as to minimize the variance of I:
The Lagrangian of this optimization problem is:
The solution in {a, fi) is given by:
a + β = 1 gives J
, is
The expressions of the parameters a and β are deduced according to the following equations:
Hence the expression of the sought estimate which corresponds to the following equation:
Similarly, it is deduced the expression of the variance of the estimate sought in the following equation 24:
Where, according to equations 19 and 21,
and
It has been shown that the sub-stages of first estimate, second estimate, and selection make it possible to obtain an estimate of the phase in the fourth situation.
It should be noted that this reasoning is easily transposed for the case where the sampling frequency / m2 is affected, no longer of an internal parasite, but of an external parasite, different from the first one.
The measure ζ is then written according to a different equation, namely the following equation 5bis:
where r2 and x2 are respectively the phase and the modulus of a second parasite, acting on a second sampling frequency.
The system of equations to be solved is then written according to the following equation 12bis:
The phase differences with respect to an antenna taken as a reference (differential phases) are then calculated.
The direction of arrival is then calculated from the differential phases.
For example, the calculation of the arrival direction is implemented by an interferometry technique.
The method thus makes it possible to determine the direction of arrival in the presence of spectral folding.
More precisely, the method described is based on the development of an explicit model of the measurements in the presence of parasites as well as on a processing of extraction of the phase of the useful signal from the parasitized measurements.
The method has the advantage of being easy to implement.

权利要求:
Claims (11)
[1" id="c-fr-0001]
1, - Method for determining the direction of arrival of radio signals in the presence of spectral folding, the method using an interferometric network (12) with four antennas (16) with identical diagrams, and sampling with two distinct sampling frequencies by antenna (16), the spectral folding being such that in the time / frequency representation of a signal, the signal being said useful signal, at most one antenna (16) is affected by a parasitic phenomenon on its two frequencies of sampling, the phenomenon being due to a first external parasite, and a second parasite being either a second external parasite, or an internal parasite, the method comprising: - the reception of a signal by each antenna (16), - the sampling the signals received on each of the four antennas (16) according to two sub-Nyquist frequencies forming the set {/. Perni. fl. pern (f2); /, pern {f,); /, pem {f ^)}, where /, /, / and / are four distinct sub Nyquist frequencies and perm is a permutation of the set {/, / 2, / 3, / 4}, so that the signals received on two separate antennas (16) are sampled by two distinct pairs of sub Nyquist sampling frequency. spectral analysis by applying, during a synchronous acquisition period on all the samplings, a discrete Fourier transform to obtain 2P time-frequency grids, each element of a grid containing a complex vector called measurement; detecting the presence or absence of a useful signal at a plurality of frequencies, the method also comprising, for all the useful signals detected: - the determination of the interference situation for each antenna (16), - for the other antennas (16) that the antenna (16) affected by the double interference, the extraction of the phase of the wanted signal, and - for the possible antenna (16) affected by the double interference, the estimate of the phase of the signal useful, comprising: - the first estimate of a first pair of candidate phases / and ξΐ from the measurement z resulting from the mixing of the useful signal, the first parasitic signal, and noise, - the second e estimation of a second pair of candidate phases ξ and

from the measurement ζ resulting from the mixing of the wanted signal, the second parasite, and noise, and - selection of phase values among the candidate phases to obtain an estimate of the phase of the wanted signal on the affected antenna (16) by double interference.
[2" id="c-fr-0002]
2. - Method according to claim 1, wherein the plurality of frequencies of the detection are analog frequencies regularly spaced from a frequency interval inverse to the acquisition time.
[3" id="c-fr-0003]
3. - Method according to claim 1 or 2, wherein the first estimate of first candidate phases comprises the calculation of the following equations:

Where: • a is the argument of the measure z, • p is the module of the measure z, • r is the module of the wanted signal, and • rx is the module of the first parasitic signal,
[4" id="c-fr-0004]
4. - Method according to any one of claims 1 to 3, wherein the second estimate of a second pair of candidate phases comprises the calculation of equations according to the nature of the second parasite, when the second parasite is a parasite internal, the equations being

and

Where: • r is the module of the wanted signal, and • y is the real part of the measurement ζ when the second parasite is an external parasite, the equations being

and or :

• a is the argument of the measure ζ, • p2 is the module of the measure ζ, • r is the module of the wanted signal, and • r2 is the module of the second parasitic signal.
[5" id="c-fr-0005]
5. - Method according to any one of claims 1 to 4, wherein the selection of phase values comprises: - the association of the candidate phases to determine the two phase values corresponding to a common value representing the true phase, for obtain two measurements of associated phases, and - estimation of the phase by merging the two associated phase measurements.
[6" id="c-fr-0006]
6. - Method according to claim 5, wherein the association of the phases is implemented using a rule, the rule being the following rule: ξ [and ξΐ are associated if the pair

is the couple among the four couples


[7" id="c-fr-0007]
The method of claim 5 or 6, wherein the estimate of the phase comprises calculating the following expression:

Where: • x is the estimated phase of the wanted signal; • ξχ is equal to ξ [obtained in the association step; • ξ2 is equal to the one obtained in the association step;

• σ2 is the variance of ξι, defined by and • σ2 is the variance of ξ2, defined: o when the second parasite is internal, by

or o when the second parasite is external, by


[8" id="c-fr-0008]
8. - Process according to any one of claims 1 to 7, wherein the method further comprises: - the calculation of differential phases, and - the calculation of the direction of arrival from the differential phases.
[9" id="c-fr-0009]
9. - Device (10) for determining the direction of arrival of radio signals in the presence of spectral folding, the device (10) comprising: - an interferometric network (12) with four antennas (16) with identical diagrams and for sampling by two distinct sampling frequencies per antenna (16), each antenna (16) being adapted to receive a signal said received signal, the spectral folding being such that in the time / frequency representation of a signal, the signal being said useful signal, at most one antenna (16) is affected by a parasitic phenomenon on its two sampling frequencies, the phenomenon being due to a first external parasite, and a second parasite being either a second external parasite or a internal parasite, - a controller (14) adapted to implement sampling, spectral analysis, detection of the presence or absence of a useful signal, then, for r each detected useful signal, the determination of the interference situation for each antenna, the extraction of the phase of the useful signal on the other antennas (16) that the possible antenna affected by the double interference (16) and the estimate the phase of the antenna (16) affected by the double interference of a method according to any one of claims 1 to 8.
[10" id="c-fr-0010]
10, - Device according to claim 9, wherein the controller (14) comprises a sampling unit (18) able to carry out the sampling of the method according to any one of claims 1 to 8 and a calculator (20 ) capable of implementing the spectral analysis, the detection of the presence or absence of a useful signal, then, for each detected useful signal, the determination of the parasitic situation for each antenna, the extraction of the phase of the signal useful for the other antennas (16) than the antenna affected by the double interference (16) and the estimation of the phase of the useful signal for the possible antenna (16) affected by the double interference of the method according to the any of claims 1 to 8.
[11" id="c-fr-0011]
11. - Device according to claim 10, wherein the sampling unit (18) comprises two analog-to-digital converters (22) per antenna (16).

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同族专利:

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公开号 | 公开日

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US20190004140A1|2019-01-03|

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ES2831710T3|2021-06-09|

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US10921415B2|2021-02-16|

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WO2017109219A1|2017-06-29|

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EP3394630A1|2018-10-31|

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FR3046250B1|2018-02-16|

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EP3394630B1|2020-10-07|

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法律状态:
2016-12-29| PLFP| Fee payment|Year of fee payment: 2 |

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2017-06-30| PLSC| Publication of the preliminary search report|Effective date: 20170630 |

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2018-01-02| PLFP| Fee payment|Year of fee payment: 3 |

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2019-12-30| PLFP| Fee payment|Year of fee payment: 5 |

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2020-12-28| PLFP| Fee payment|Year of fee payment: 6 |

优先权:

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申请号 | 申请日 | 专利标题

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FR1502685|2015-12-23|

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FR1502685A|FR3046250B1|2015-12-23|2015-12-23|METHOD FOR DETERMINING THE ARRIVAL DIRECTION IN THE PRESENCE OF SPECTRAL FOLDING AND ASSOCIATED DEVICE|FR1502685A| FR3046250B1|2015-12-23|2015-12-23|METHOD FOR DETERMINING THE ARRIVAL DIRECTION IN THE PRESENCE OF SPECTRAL FOLDING AND ASSOCIATED DEVICE|

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EP16822189.3A| EP3394630B1|2015-12-23|2016-12-23|Method for determining the direction of arrival in the presence of aliasing and associated device|

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ES16822189T| ES2831710T3|2015-12-23|2016-12-23|Procedure for determining the direction of arrival in the presence of spectral fallback and associated device|

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PCT/EP2016/082649| WO2017109219A1|2015-12-23|2016-12-23|Method for determining the direction of arrival in the presence of aliasing and associated device|

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US16/063,495| US10921415B2|2015-12-23|2016-12-23|Method for determining the direction of arrival in presence of aliasing and associated device|