Classifications

• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
  • H04B1/06—Receivers
  • H04B1/16—Circuits
  • H04B1/26—Circuits for superheterodyne receivers
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
  • G06F17/10—Complex mathematical operations
  • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
  • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
  • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
  • G01S7/021—Auxiliary means for detecting or identifying radar signals or the like, e.g. radar jamming signals
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
  • H04B1/69—Spread spectrum techniques
  • H04B1/7163—Spread spectrum techniques using impulse radio
  • H04B1/719—Interference-related aspects
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B7/00—Radio transmission systems, i.e. using radiation field
  • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
  • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
  • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
  • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
  • H04B7/0842—Weighted combining
  • H04B7/0848—Joint weighting
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
  • G06F17/10—Complex mathematical operations
  • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
  • G06F17/141—Discrete Fourier transforms

Definitions

• the present invention relates to the field of broadband passive reception (of the order of about 10 GigaHertz for example) of electromagnetic signals such as for example communication signals or radar signals.
• the present invention relates more particularly to a passive digital detection method.
• broadband listening of electromagnetic signals of the order of ten GigaHertz for example, it is generally not possible to perform sampling at a frequency meeting the Shannon criterion, nor to carry out the processing of the data resulting from this sampling. This requires sampling at frequencies lower than Shannon's frequency, which introduces spectral overlap or aliasing problems.
• a first category corresponds to very broadband receivers. These receivers permanently cover the entire analysis band and have a probability of interception (or POI for "Probability Of Intercept” according to the Anglo-Saxon terminology) very large for strong signals, but are characterized by low sensitivity and very limited ability to discriminate or analyze electromagnetic signals.
• a second group corresponds to narrow-band receivers called "superheterodynes". These receivers, after multibit sampling of this band by a conventional method, allow fine analysis of the signal (with a high sensitivity up to the search for the modulation after discrete Fourier transform), but obviously suffer from a degraded POI since out-of-band signals are not processed.
• sequencing functions which consist in determining the partial listening plan in bands and duration of listening but they only partially remedy this defect.
• An object of the invention is in particular to correct one or more of the disadvantages of the prior art by proposing a solution for detecting one or more useful signals while being robust to parasitic signals.
• the subject of the invention is a method for passive detection of electromagnetic signals that is robust to the folds implemented by a device comprising at least one antenna, said antenna comprising at least one sensor and said method comprising:
• a step of sampling the signals received on each sensor, during a common acquisition time ⁇ , using M different sampling frequency values f m not satisfying the Shannon criterion, the signals sampled at the same frequency forming a sampling channel, M representing an integer greater than or equal to 2 and m, the index of the sampling frequency lying between 1 and M, at least two sampling being carried out with sampling frequencies f m and numbers of sampling points N m different, the pair (N m , f m ) being chosen such that the ratio AT N m / f m remains constant whatever the index m,
• a step of transforming the sampled signals in the frequency domain by discrete Fourier transform on the N m sampling points of the received signal, sampled at f m over the common time interval ⁇ , the common spectral resolution for all the samplings being AF 1 / ⁇ ,
• the method furthermore comprises, for each time / frequency box of said discrete representation,
• ⁇ indicates the possible presence of a parasite on one of the samplings with ⁇
• the method further comprises a step of finding the highest power value among the sampling channels, the quadratic sum being calculated excluding said highest value power and summing the (M-1) remaining powers, said highest value power being considered as the power of a spurious signal.
• the signals are received over N time frequency boxes with N integer strictly greater than 1, the method further comprising the application of a non-linear function in each time / frequency box and a summation step the result obtained on the N time / frequency boxes.
• the threshold value is defined so as to ensure a predetermined false alarm probability.
• the invention also relates to a passive detection device comprising a reception module comprising at least one antenna and a calculation module configured to implement the method according to one of the previous variants, said receiving module being configured to receive surrounding electromagnetic signals and transmit them to the computing module for processing.
• the receiving module comprises an interferometric antenna array.
• FIG. 1a and 1b illustrate examples of implementation of the sampling step respectively in a single signal configuration and with two sampling channels;
• FIG. 2 represents an exemplary curve representative of the specific non-linearity of the multicase detector
• FIGS. 3 to 6 illustrate possible steps of the detection method according to the invention in different cases. It should be noted that the use of the terms "sampling" or
• Samling channel means all the signals received by the reception channels or measurement channels that are sampled with the same frequency.
• the principle of the invention is based on taking into account the spectrum aliasing phenomenon in the modeling and the processing of the received signal, that is to say in the mathematical resolution of the problem of broadband detection, in order to guarantee detection performance as close as possible to those that would be obtained without folding the spectrum.
• the passive digital detection method can mainly comprise a step of sampling the signal received on each sensor with several sub-Shannon frequency values, a step of filtering the signal by a bank of filters of the discrete Fourier transform type and for each time / frequency box, a step of calculating the normalized power in each sampling, a step of calculating the quadratic sum of the powers calculated taking into account the power of a possible parasite and a thresholding step using a predetermined threshold value.
• the threshold value can be set to ensure a predetermined false alarm probability (see Testing Statistical Hypothesis, El Lehmann, JP Romano, Springer 2005).
• the signal is received on an antenna or network of interferometric antennas. It will be assumed later that the reception device comprises P sensors where P represents a non-zero integer.
• the signals received on the different sensors are sampled with several different frequency values f m (with m natural integer varying from 1 to M where M is an integer greater than or equal to 2 representing the number of frequencies used) sub Shannon, that is to say not respecting the Shannon-Nyquist criterion.
• M must be sufficient to allow the removal of ambiguities in frequency and depends on the width of the analysis band.
• the signals sampled at the same sampling frequency f m form a sampling path of index m.
• each frequency f m is chosen so that its value is much lower than the intercept band B of the signals but greater than the band of the signals to be analyzed.
• each sampling preserves the spectrum of the useful signal to be analyzed in its form, but the translation of a possible quantity which depends on the value of the frequency f m .
• FIG. 1a illustrates the sampling method in a single signal configuration and with 2 sampling channels. This is a simplifying block diagram, where it is assumed that one deals with analytic signals whose spectrum has no component in the negative frequencies.
• a useful signal is at the frequency f 0
• the 2 M-tuples representing the frequencies f 0 and f 0 in the M sampling channels have a common value.
• a mixture of signals is measured in the sampling f m i, whereas there is no mixing in reality.
• the signal at the frequency f 0 although itself a useful signal, represents a parasite vis-à-vis the signal at the frequency f 0 .
• a parasitic signal folds into one of the M channels corresponding to the frequency f 0 , while no signal is present at the frequency f 0 , the presence of the parasite can generate a false alarm.
• the probability of presence of a parasite becomes significant, of the order of 10% or more, and incompatible with the performance required of most reception systems.
• a discrete Fourier transform is then applied to the N m sampling points of the received signal, sampled at f m over a common acquisition time ⁇ for each of the sensors.
• AF 1 / ⁇ is then the common spectral resolution for all samplings.
• N m represents the number of sample points at the frequency f m ;
• T m represents the sampling period at the frequency f m ;
• AF represents the frequency step of the DFTs (independent of m) This implies that the number of points N m is different from one sampling to another.
• This choice of sampling frequencies 1 / T m so that they are multiples of the AF band implies that from one sampling to the next, the signal spectra are shifted by an integer number of filters.
• the next phase is to model the received signal after DFT.
• R is chosen independent of m so as not to complicate the notations. This case is in no way limiting and we could consider a sensor structure with R dependent on m without modifying the reasoning that follows.
• Each sensor is therefore indexed by 2 indices, an index m for the type of sampling with m integer between 1 and M and an index r for the number of a sensor sampled at the frequency f m with r integer between 1 and R.
• the signal received in m, r can be written in the form:
• x mr ae iVmr + b ⁇ mr + w mr with ⁇ a ⁇ ⁇ 0, ⁇ b m ⁇ ⁇ 0 (equation 1)
• a complex, represents the contribution of the useful signal. If present,
• ⁇ ⁇ , ⁇ represents the interferometric phase shift of the index sensor (m, r) with respect to an unspecified sensor, for a plane wave (ie the useful signal), coming from a direction
• Equation 1 involves a large number of parameters. This makes it difficult to optimize the detection of the useful signal and to determine the interference situation. Since we can not take into account all the parameters, we consider a statistical type of modeling where the received signal measurements are samples of a random variable. We choose not to build a detector adapted for each direction of the useful signal and for each direction of the possible parasite. We limit our to good treatments on average with respect to the directions of arrival of the incident waves. Given the network intervening factors in interferometric phase shifts, we can show that this amounts to plunge the model of equation 1 in a family of models which consider the phase shifts ç mr as independent in m, r and equidistributed over the interval [o, 2 ⁇ [. This makes it possible to simplify the probability density of the measurements of equation 1.
• the density of probability is a mixture of the elementary densities; for Hi: p l0 ) and Pum 0 () ' ⁇ For H o: 00 ( ⁇ ) and Pote o O-
• the coefficients of the mixture are a (no parasite) and - ⁇ - (presence of parasite in m 0 ).
• the likelihood ratio which is the quotient of the probability density in Hi by the probability density in H 0 , can be written in the form:
• the optimal test to distinguish the hypothesis Hi from the hypothesis H 0 would be to compare L (y, .. ., y M 2 ) at a predetermined threshold value ⁇ L (y, ..., y M 2 )> or ⁇ threshold).
• equation 9 Given equations 5, 6, 8 and 10, the likelihood ratio of equation 9 can be written as:
• the signal-to-noise ratio ⁇ ' 2 1 ⁇ 2 is typically greater than 10 dB
• the test of equation 14 depends only on the parameter ⁇ , and can be optimized in Pd / Pfa (with Pd the probability of detection and Pfa the probability of false alarm) in the vicinity of a parasitic situation defined for and o I ⁇ 2 : it is enough to replace ⁇ by its expression in a and o I ⁇ 2 .
• the test is a symmetrical function of y 2 m (symmetry of interference situations).
• equation 14 can be written, after limited expansion of the exponential function and the logarithmic function, in the form: (equation 15)
• D yf, y 2 , ..., y M 2 ) e (yi + ) M such that l (y, y 2 , ..., y M 2 )> s) and Z) c SOn complementary in ( 3 ⁇ 4 + ).
• D contains the zone (s) where at least one y m 2 o is large (y ⁇ > 1) that is, the approximation of the test by equation16 for y m 2 large all about equal and by equation 17 for y 2 large among y m 2 , m ⁇ m 0 .
• x mrn a n e lVmr + b mn e ⁇ mrn + w mrn
• - a n is complex and represents the useful signal received in a reference sensor.
• R representing the set of measurements of the box n is written as in equation 2 of the monosource case (omitted here the index n not to complicate):
• Equation 19 the densities of Equations 22 and 23 are expressed as a function of / 2 ⁇ 2 that we will note y m 2 n thereafter.
• the likelihood ratio is expressed by the quotient of the densities
• the Neyman-Pearson optimal test to decide on the presence of the useful signal would be to compare this likelihood ratio with a threshold value.
• the terms of the likelihood ratio are evaluated to derive a substantially optimized test in the vicinity of the operating point of interest.
• equation 25 by: ⁇ (/ ")> or ⁇ threshold, reducing equation 26 to its
• the nonlinear function A (l) can then be defined by:
• Figures 3 and 4 represent the case of a monocase detection and Figures 5 and 6 the case of multicase detection.
• the signals received on each sensor of the receiver are sampled, on an acquisition time ⁇ , with frequencies f m of different value depending on the reception channels and do not meet the Shannon criterion.
• the sampling of the signals received on each sensor is carried out during each time interval.
• k integer.
• this implementation mode is in no way limiting and other time intervals ⁇ can be chosen as for example, [k.AT, (k + ⁇ ) ⁇ ].
• a discrete Fourier transform is then performed on the sampled signals.
• AF 11 AT is then the common spectral resolution for all the samplings.
• the reception channels are therefore synchronous with the period 1 / AF and have the same channel width. This gives a time / frequency representation of the signals.
• the next step consists in calculating, in each time / frequency box of said discrete representation corresponding to a tested frequency f 0 , the power standardized in each quadratic summation sampling of the powers of all the reception channels sharing the same sampling frequency. f m .
• This power can be calculated using the formula view
• the sum of the powers calculated on all the samplings in each time-frequency box is then calculated by taking into account the power of a possible parasite.
• the power of the possible parasite can be taken into account in different ways.
• FIG. 3 illustrates the optimal test of the detection method in the case where the signals are only received on a time / frequency box.
• the influence of the spurious signal is supported by subtracting the term
• the parameter ⁇ r 2 is supposed to be known (it can be obtained by calibration), the parameter a is computable from the density of the signals to be intercepted, and the parameter a is set to the minimum power of the parasites which one wants to protect, supposed to be of the same order of magnitude than the minimum power of the signals of interest.
• a thresholding step is then applied in each time / frequency box using a predetermined threshold value. This threshold value is determined so as to respect a given false alarm probability.
• Figure 4 shows a simplified version of the test.
• the detection algorithm assumes that the highest value power corresponds to the power of a spurious signal. Among the calculated power values, the highest is sought to exclude it. The quadratic sum of the powers is thus carried out with the remaining M-1 values.
• This simplified detection method systematically deletes a sampling channel, even if the signal power is low on all channels.
• the optimal method illustrated in FIG. 3 has a behavior which adapts to the power of the received signal, going from the deletion of the sampling channel having the strongest power, if this one is very largely preponderant by relative to others, to a behavior close to the quadratic detector on all the channels, if the power received on all the channels is substantially similar.
• FIG. 5 represents possible steps of the optimal detection method in the case where the signal is received over several time / frequency boxes. It is considered that the signal is received on a window of N time / frequency cells.
• the optimal multicase method calculates the normalized power in each channel sampling and in each time / frequency box, then the quadratic sum of the powers on all the samplings in each time / frequency box and subtract a term reflecting the power of the parasite.
• the process ends with a thresholding step using a predetermined threshold value.
• This threshold value can be determined so as to respect a given false alarm probability.
• Figure 6 illustrates the simplified version of the test of the detection method in the multicase case.
• the quadratic sum is computed by excluding the highest power value among the sampling channels.
• a nonlinear function ⁇ is then applied in each time / frequency box and then the result is summed over the N time / frequency boxes of the window on which the signals are analyzed.
• the process ends with a thresholding step using a predetermined threshold value.
• the sub Shannon sampling method according to the invention makes it possible to have a complete and instantaneous vision of the entire band of the signals.
• the detection test is robust to the presence of parasites, that is to say, one can, for a probability of false alarm fixed, find for this test a threshold value independent of the power of the parasite.
• the equation of the detector according to the invention contains an additional term.
• the detector behaves like a quadratic detector on all samplings, the parasitic sampling being excluded.
• the present invention also relates to a passive or receiver detection device.
• This device comprises at least one receiving module and a calculation module configured to implement the method described above.
• the receiving module is configured to receive surrounding electromagnetic signals and transmit them to the computing module for processing.
• the receiving module may comprise at least one antenna, or an array of interferometric antennas.
• the antenna comprises at least one sensor.
• the receiving module is configured to continuously receive electromagnetic signals over the entire analysis frequency band.
• the computation module is configured to at least be able to perform sub Shannon sampling on several bits.
• the computing module can be one or more microprocessors, processors, computers or any other equivalent means programmed in a timely manner.

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• 2014
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