METHOD FOR DETERMINING PARAMETERS OF A COMPRESSION FILTER AND ASSOCIATED MULTI-CHANNEL RADAR

Abstract

A method for determining parameters of a finite impulse response pulse compression filter, implemented by a multi-channel radar comprises: a step Etp10 of transmitting a calibration signal and of acquiring this calibration signal after propagation through the transmission channel, a step Etp20 of injecting the signal acquired, at the input of each of the reception channels, a step Etp30 of measuring the signal at the output of each reception channel, a step Etp40 of calculating the transfer function of the matched filters on the basis of the signals at the output of the reception channels, a step Etp50 of measuring the value of the average power at the output of the various reception channels and of calculating the relative gains between each of the reception channels and a predetermined reception channel on the basis of the measured values of average powers.

Claims

1. A method for determining parameters of a pulse compression filter, implemented by a multi-channel radar comprising a transmission channel and a plurality of reception channels, the signals arising from the reception channels being grouped together so as to form a sum channel and at least one difference channel, said filter being a finite impulse response filter and said parameters comprising matched filters and relative gains between reception channels, said method lacing comprising: a step Etp10 of transmitting a calibration signal and of acquiring this calibration signal after propagation through the transmission channel, a step Etp20 of injecting the signal acquired, at the input of each of the reception channels, a step Etp30 of measuring the signal at the output of each reception channel, a step Etp40 of calculating the transfer function of the matched filters on the basis of the signals at the output of the reception channels, a step Etp50 of measuring the value of the average power at the output of the various reception channels and of calculating the relative gains γ.sub.i between each of the reception channels and a predetermined reception channel on the basis of said measured values of average powers.

2. The method as claimed in claim 1, wherein the matched filters (H.sub.s, H.sub.d) are defined by: $\hspace{1em}\{\begin{array}{c}{H}_s\left(F\right)=\frac{W\left(F\right)}{C_s\left(F\right)}.Math.\sqrt{.Math.W\left(F\right).Math.{.Math.C_s\left(F\right).Math.}^2}\\ H_d\left(F\right)=\frac{W\left(F\right)}{C_d\left(F\right)}.Math.\sqrt{.Math.W\left(F\right).Math.{.Math.C_d\left(F\right).Math.}^2}\end{array}$ where W(F) represents a weighting law defined in the frequency domain; Cs(F) and Cd(F) represent respectively the spectrum of the calibration signal, after passing through the transmission and reception channels, for the sum channel and a difference channel.

3. The method as claimed in claim 1, wherein the method furthermore comprises a step Etp35 of averaging the signal acquired at the output of each reception channel so as to improve the signal-to-noise ratio.

4. The method as claimed in claim 2, wherein the weighting law W(F) is smoothed.

5. The method as claimed in claim 1, wherein the values of relative gains y.sub.i are integrated into the expression for the matched filters of the difference channels.

6. A method of pulse compression, implemented by a multi-channel radar comprising a transmission channel and a plurality of reception channels, the signals arising from the reception channels being grouped together so as to form a sum channel and at least one difference channel, said radar comprising at least one memory area in which are stored the parameters of a pulse compression filter determined by the method for determining parameters as claimed in claim 1, said method of pulse compression wherein said pulse compression is performed, for the sum channel, by multiplying the spectrum of the signal S(F) at the output of the sum channel by the transfer function of the matched filter H.sub.s(F) corresponding to the sum channel and for a difference channel, by multiplying the spectrum of the signal D(F) at the output of a difference channel by the transfer function of the matched filter H.sub.d(F) corresponding to the difference channel considered and by the value of the relative gain γ.sub.i corresponding to the difference channel considered.

7. The method as claimed in claim 6, in which the parameters of a pulse compression filter are determined such that the values of relative gains γ.sub.i are integrated into the expression for the matched filters of the difference channels, the pulse compression, for a difference channel, being performed by multiplying the spectrum of the signal D(F) at the output of a difference channel by the transfer function of the matched filter H.sub.d(F) corresponding to the difference channel considered.

8. A multi-channel radar comprising a transmission channel and a plurality of reception channels, said radar wherein the transmission channel comprises a coupler connected at the output of said transmission channel, said coupler being configured to tap off a part of the signal at the output of the transmission channel (Tx) and reinject it at the input of each reception channel and comprising at least one calculation module able to implement the method as claimed in claim 1 to calculate parameters of a pulse compression filter on the basis of the signal reinjected in the reception channels and at least one pulse compression module able to implement a method of pulse compression, implemented by the multi-channel radar comprising the transmission channel and the plurality of reception channels, the signals arising from the reception channels being grouped together so as to form a sum channel and at least one difference channel, said radar comprising at least one memory area in which are stored the parameters of a pulse compression filter determined by the method for determining parameters as claimed in claim 1, said method of pulse compression wherein said pulse compression is performed, for the sum channel, by multiplying the spectrum of the signal S(F) at the output of the sum channel by the transfer function of the matched filter H.sub.s(F) corresponding to the sum channel and for a difference channel, by multiplying the spectrum of the signal D(F) at the output of a difference channel by the transfer function of the matched filter H.sub.d(F) corresponding to the difference channel considered and by the value of the relative gain γ.sub.i corresponding to the difference channel considered.

Description

[0030] Other features and advantages of the present invention will be more clearly apparent on reading the description hereinafter, given by way of nonlimiting illustration with reference to the appended drawings, in which:

[0031] FIG. 1 represents a simplified schematic of a radar for a reception channel;

[0032] FIG. 2 represents possible steps of the method according to the invention;

[0033] FIGS. 3a and 4a represent two examples of carrying out the processing to determine the parameters of the pulse compression filter according to the invention;

[0034] FIGS. 3b and 4b represent two examples of modes of implementation of the pulse compression filter according to the invention;

[0035] FIG. 5 represents results obtained as pulse compression output with the aid of various filters;

[0036] FIG. 6 represents the temporal shapes of the matched filters used;

[0037] FIG. 7 represents examples of defects of variation of amplitude in the transmission pathway;

[0038] FIG. 8 represents the temporal shape of the matched filters used;

[0039] FIG. 9a represents the results obtained as pulse compression output with the filters of FIG. 8;

[0040] FIG. 9b represents a zoom of the curves of FIG. 9a.

[0041] FIG. 1 represents a simplified schematic of a radar. In order not to overload the figure, just one transmission and reception channel has been represented. This example is wholly non-limiting and can be generalized to the case of a multi-channel radar comprising a plurality of reception channels.

[0042] An antenna 10 is connected to a circulator 11 itself connected to a transmission channel Tx and a reception channel Rx. The transmission channel can comprise a waveform generator 12 generating baseband signals which will thereafter be modulated by way of a mixer 13, with the aid of carrier frequencies generated by the frequency source 14. The signal at the output of the mixer 13is thereafter amplified by an amplifier 14. A coupler 15, connected to the output of the amplifier 14, makes it possible to tap off a part of the amplified signal and to redirect the latter to a switch 16 placed at the input of the reception pathway Rx. In this example this switch 16 comprises two positions. A first position, referenced 1 in the figure, makes it possible to inject the signal at the output of the transmission channel, by way of the coupler 15, at the input of the reception pathway Rx. This position serves for the calibration of the radar and makes it possible to calculate the parameters of the pulse compression filter. The second position, referenced 2, serves for the normal use of the radar and makes it possible to direct the signal originating from the antenna 10 toward the reception pathway Rx. The reception pathway can comprise a mixer 13 making it possible to transpose the signal with the aid of the carrier generated by the frequency source 14. The signal is thereafter filtered through a filter 17 and is then demodulated and converted into a digital signal with the aid of an Amplitude Phase Demodulator and of an Analogic Digital Converter (or DAP/CAN) 18.

[0043] The signals arising from the reception channels (Rx) are grouped together according to recombining techniques known to the person skilled in the art, to form a sum channel and at least one difference channel.

[0044] The operational signals received by the antenna 10 can be modeled by the expressions:

[00002]$\hspace{1em}\{\begin{array}{c}S=K.Math.G_s\left(\theta \right).Math.\sqrt{\mathrm{RCS}}.Math.e^{i.Math..Math.{\varphi }_s}.Math.A_s\left(t\right).Math.p\left(t\right)\\ D=K.Math.G_d\left(\theta \right).Math.\sqrt{\mathrm{RCS}}.Math.e^{i.Math..Math.{\varphi }_d}.Math.A_d\left(t\right).Math.p\left(t\right)\end{array}$

[0045] Likewise the calibration signals can be modeled by:

[00003]$\hspace{1em}\{\begin{array}{c}{C}_s=B.Math.e^{i.Math..Math.{\varphi }_s}.Math.A_s\left(t\right).Math.p\left(t\right)\\ C_d=B.Math.e^{i.Math..Math.{\varphi }_d}.Math.A_d\left(t\right).Math.p\left(t\right)\end{array}$

where: [0046] B, represents the amplitude, assumed unknown, of the calibration signal; [0047] p(t), represents the radar pulse of duration T such that |p(t)|=1 for 0<t<T; [0048] A.sub.s(t), represents the impulse response of the pathway of the Sum channel of the radar; [0049] A.sub.d(t), represents the impulse response of the pathway of one of the Difference channels of the radar; [0050] K, represents a constant originating from the radar equation; [0051] Gs(θ) and Gd(θ), represents the complex gain, assumed independent of frequency, of the antenna in the direction θ; [0052] RCS, represents the Radar Cross Section of a target; [0053] φ.sub.s and φ.sub.d represent the phase errors of the pathway for the Sum and Difference channels; [0054] , represents the convolution operator.

[0055] By performing a Fourier transform on each of these signals, we obtain:

[00004]$\{\begin{array}{c}S\left(F\right)=K.Math.G_s\left(\theta \right).Math.\sqrt{\mathrm{RCS}}.Math.e^{i.Math..Math.{\varphi }_s}.Math.A_s\left(F\right).Math.P\left(F\right)\\ D\left(F\right)=K.Math.G_d\left(\theta \right).Math.\sqrt{\mathrm{RCS}}.Math.e^{i.Math..Math.{\varphi }_d}.Math.A_d\left(F\right).Math.P\left(F\right)\end{array}.Math..Math.\mathrm{and}.Math..Math.\hspace{1em}\{\begin{array}{c}{C}_s\left(F\right)=B.Math.e^{i.Math..Math.{\varphi }_s}.Math.A_s\left(F\right).Math.P\left(F\right)\\ C_d\left(F\right)=B.Math.e^{i.Math..Math.{\varphi }_d}.Math.A_d\left(F\right).Math.P\left(F\right)\end{array}$

where A.sub.S(F) and A.sub.D(F) respectively represent the complex gains of the Sum and Difference channels.

[0056] The weighted and normalized matched filters (independent of the calibration level B) for each of the channels can be defined by:

[00005]$\hspace{1em}\{\begin{array}{c}{H}_s\left(F\right)=\frac{W\left(F\right)}{C_s\left(F\right)}.Math.\sqrt{.Math.W\left(F\right).Math.{.Math.C_s\left(F\right).Math.}^2}\\ H_d\left(F\right)=\frac{W\left(F\right)}{C_d\left(F\right)}.Math.\sqrt{.Math.W\left(F\right).Math.{.Math.C_d\left(F\right).Math.}^2}\end{array}$

where W(f) is any weighting law defined in the spectral domain, such as for example a Blackman law, a Hanning law, a Hamming law, Taylor law or any other equivalent law as well as any combination of laws that are known to the person skilled in the art.

[0057] In order to limit the Gibbs phenomena, that is to say the temporal overshoots related to the abrupt truncation of the spectrum, this spectral weighting law can be smoothed so as to attenuate the discontinuity at the transition between the useful band and the off-band area. This smoothing can be obtained, for example, by applying, to the weighting W(f), a convolution with another weighting window, such as for example and in a nonlimiting manner, a Hanning window, but of much shorter length than W(f). This length can for example be of the order of 1/32.sup.nd or 1/64.sup.th of the length of W(f).

[0058] The relative gains y can be defined by:

[00006]$\gamma =\frac{\sqrt{.Math.W\left(F\right).Math.{.Math.C_s\left(F\right).Math.}^2}}{\sqrt{.Math.W\left(F\right).Math.{.Math.C_d\left(F\right).Math.}^2}}=\frac{\sqrt{.Math.W\left(F\right).Math.{.Math.A_s\left(F\right).Math.P\left(F\right).Math.}^2}}{\sqrt{.Math.W\left(F\right).Math.{.Math.A_d\left(F\right).Math.P\left(F\right).Math.}^2}}$

[0059] The pulse compression can be carried out, for the Sum channel, by performing:

[00007]${\mathrm{CI}}_s\left(F\right)=S\left(F\right).Math.H_s\left(F\right)=K.Math.G_s\left(\theta \right).Math.\sqrt{\mathrm{RCS}}.Math.W\left(F\right).Math.\frac{\sqrt{.Math.W\left(F\right).Math.{.Math.C_s\left(F\right).Math.}^2}}{B}{\mathrm{CI}}_s\left(F\right)=K.Math.G_s\left(\theta \right).Math.\sqrt{\mathrm{RCS}}.Math.W\left(F\right).Math.\sqrt{.Math.W\left(F\right).Math.{.Math.A_s\left(F\right).Math.P\left(F\right).Math.}^2}$

[0060] In the same manner, for the Difference channels, we can calculate:

CI.sub.d(F)=γ.Math.D(F).Math.H.sub.d(F)=K.Math.G.sub.d(θ).Math.√{square root over (RCS)}.Math.W(F).Math.√{square root over (ΣW(F).Math.|A.sub.s(F).Math.P(F)|.sup.2 )}

where Ci.sub.s(F) and Ci.sub.d(F) represent the spectrum of the compressed signal respectively for the Sum channel and for a Difference channel.

[0061] The compressed signal is obtained by performing the inverse Fourier transform on the signals CI.sub.s(F) and CI.sub.d(F).

[0062] As a function of the practical choices of implementation, a variant can consist in taking into account the relative gains y directly in the expression for the filter H.sub.d(F) thereby making it possible to simplify the expression for the pulse compression which becomes: CI.sub.d(F)=D(F).Math.Hd(F).

[0063] On completion of these operations, it may be noted that the sidelobes are controlled since it is the theoretical response which is yielded; CI.sub.s(F) and CI.sub.d(F) do not depend on the impulse responses A.sub.s(F), A.sub.d(F) of the pathway of the sum and difference channels of the radar.

[0064] Because a filter whose shape is 1/S(F), where S(F) represents the spectrum of the signal, is applied to the signal, the output produced is a spectral rectangle of width of the frequency band that is processed. The inverse transform of this signal is a cardinal sine signal. Applying a weighting in the filter produces a weighted cardinal sine. The choice of the weighting window will therefore make it possible to control the sidelobe levels.

[0065] It may also be noted that there is no differential gain between the Sum and Difference channels, to within the antenna gain, thereby making it possible to calculate the angular offset measurements (monopulse technique): the amplitude compensation is performed via the relative gains γ and the phase compensation being obtained naturally on principle since the phase of each channel is reduced to zero by applying the matched filters H.sub.s and H.sub.d.

[0066] FIG. 2 illustrates possible steps of the method for determining parameters of a pulse compression filter according to the invention.

[0067] The parameters of the compression filter can comprise the filter H.sub.s matched to the sum channel, the filters H.sub.d matched to the difference channel and the relative gains γ.sub.i between a predetermined reception channel chosen as reference channel and each of the other reception channels.

[0068] A calibration signal is transmitted by a generator of the transmission channel Tx in the course of a step Etp10. This signal is thereafter acquired at the output of the transmission channel Tx. This makes it possible to measure, in addition to the signal transmitted, all the defects related to the various components of the transmission pathway Tx.

[0069] The signal acquired is thereafter injected at the input of each reception channel Rx in the course of a step Etp20. After having passed through the reception pathway, the signals are thereafter measured at the output of each reception pathway Rx during a step Etp30.

[0070] In order to improve the signal-to-noise ratio, the method can comprise a step Etp35 of averaging the signal at the output of each reception channel.

[0071] The method thereafter comprises a step Etp40 of calculating the transfer function of the weighted and normalized matched filters H.sub.s, H.sub.d, for each of the channels on the basis of the signals measured at the outputs of each reception channel Rx. The transfer function of these matched filters for the sum channel H.sub.s and for a difference channel H.sub.d can be defined by:

[00008]$\hspace{1em}\{\begin{array}{c}{H}_s\left(F\right)=\frac{W\left(F\right)}{C_s\left(F\right)}.Math.\sqrt{.Math.W\left(F\right).Math.{.Math.C_s\left(F\right).Math.}^2}\\ H_d\left(F\right)=\frac{W\left(F\right)}{C_d\left(F\right)}.Math.\sqrt{.Math.W\left(F\right).Math.{.Math.C_d\left(F\right).Math.}^2}\end{array}$

[0072] where W(f) represents any weighting law defined in the frequency domain; [0073] Cs(F) and Cd(F) represent the calibration signal in the frequency domain, after passing through the transmission and reception channels, respectively for the sum channel and a difference channel.

[0074] In this expression for the pulse-matched filters H.sub.s, H.sub.d, it is noted that the shape of a Wiener filter is retrieved through the term

[00009]$\frac{1}{C_s\left(F\right)}$

which corresponds to the inverse of the calibration signal.

[0075] By expanding the expression for the filters, it may be shown that these filters H.sub.s, H.sub.d are independent of the level of the calibration signal.

[0076] In an advantageous manner, the choice of the weighting law makes it possible to control the sidelobes. Any dependency on the defects of the transmission and reception pathways being eliminated, the sidelobes will depend only on the choice of weighting law. This weighting law or weighting window is chosen as a function of the application and of the necessary level. By way of example, if lobes of −13 dB are tolerated, a rectangular window may be chosen. If lower levels are desired, it will be possible to choose for example a Hanning, Hamming or Taylor weighting or any other weighting law, or combination of laws, which is known to the person skilled in the art.

[0077] The pulse compression is carried out on a multi-channel radar. A problem is that each reception channel has different defects related to hardware dispersion. In order to be able to undertake multi-channel radar processings such as for example offset measurement, monopulse processings, it is necessary to inter-balance the various reception channels. The method therefore comprises a step of balancing the reception channels Rx so as to control the relative gains between channels.

[0078] For this purpose, the method comprises a step Etp50 of measuring the relative gains between the various reception channels Rx. A reception channel is taken as reference and, on the basis of the average power measured at the output of each reception channel, the value of the relative gains γ.sub.i between each reception channel Rx and the reception channel taken as reference channel is measured. These relative gains γ.sub.i are the gains of the reception channel Rx independently of the antenna 10 of the radar.

[0079] These various parameters of the pulse compression filter can, for example, be recorded in a memory area of the radar so that they can be reused.

[0080] In an advantageous manner, the calibration phase for a radar according to the invention does not require any means outside the radar (on-board or on-line calibration) and makes it possible to circumvent the temperature variations during the use of the radar or the replacement of a component electronic card of the radar pathway. This calibration can be carried out in a periodic or aperiodic manner.

[0081] The method for determining pulse compression filter parameters according to the invention can be implemented by one or more calculation modules of the radar. Likewise, the pulse compression can be implemented by a calculation module, for example a pulse compression module, dedicated or not. These modules may be one or more microprocessors, processors, computers or any other equivalent means programmed in an opportune manner.

[0082] FIGS. 3a and 4a represent two examples of carrying out the processing to determine parameters of the pulse compression filter according to the invention on the basis of the calibration signals of the sum channel Cal_S and of a difference channel Cal_D. The figure represents only one difference channel but the processing can be generalized to the case where several difference channels might be present.

[0083] In the processing illustrated in FIG. 3a, the pulse-matched filters H.sub.s and H.sub.d and the relative gains y are calculated separately.

[0084] FIG. 4a represents a variant embodiment in which the relative gains γ.sub.i are integrated directly into the expression for the matched filters of the difference channels H.sub.d.

[0085] In the two embodiments, a windowing operation 31 is applied to the pulse-matched filters H.sub.s and H.sub.d so that the filter is a finite-duration filter. This windowing operation 31 consists in performing a transposition of the signal into the time domain with the aid of an inverse Fourier transform, in multiplying the signal obtained by a time window and in retransposing the signal into the frequency domain.

[0086] FIGS. 3b and 4b represent two examples of modes of implementation of the pulse compression filters, the determination of whose parameters is illustrated respectively in FIGS. 3a and 4a.

[0087] In the embodiment of FIG. 3b, the temporal signal S arising from the sum channel undergoes a Fourier transform, is multiplied by the filter H.sub.s(F) and then undergoes an inverse Fourier transform to return to the time domain.

[0088] The temporal signal D arising from each difference channel is multiplied by the relative gain y corresponding to the difference channel considered, undergoes a Fourier transform, is multiplied by the matched filter H.sub.d(F) corresponding to the difference channel considered and is then transposed into the time domain by way of an inverse Fourier transform.

[0089] In the embodiment of FIG. 4b, the relative gain y corresponding to the difference channel considered being integrated into the expression for the matched filter of the difference channel H.sub.d(F), the temporal signal D arising from each difference channel is only multiplied by the matched filter H.sub.d(F) corresponding to the difference channel considered after having been transposed into the frequency domain by a Fourier transform. It will thereafter undergo an inverse Fourier transform to return to the time domain.

[0090] FIGS. 5 and 9a, 9b illustrate examples of results obtained by applying a compression filter according to the invention.

[0091] FIG. 5 represents the results obtained as pulse compression output with a conventional compression filter, a Wiener filter and the compression filter according to the invention in the case of a transmission Tx and reception Rx pathway not exhibiting any defect.

[0092] FIG. 6 represents the temporal shape of the filters used.

[0093] FIG. 7 is a graphical representation of defects of the transmission Tx and reception Rx channels. These defects are essentially variations of amplitude. FIG. 8 presents the temporal shape of the matched filters used.

[0094] As previously, FIG. 9a compares the results obtained as pulse compression output with the conventional and Wiener filters and that according to the invention. FIG. 9b is a zoom of FIG. 9a around the main lobe.

[0095] In FIG. 9b, it is noted that the use of the conventional matched filter amplifies the errors introduced by the transmission and reception pathways. FIG. 9a shows that if the Wiener filter is applied, an inherent main lobe is obtained but a tailoff with upswings is observed.

[0096] The use of the filter according to the invention makes it possible to obtain as pulse compression output at one and the same time control of the main lobe and control of the lobes of the pulse compression without having any tailoff. One obtains the levels that one would have with a conventional matched filter in the absence of spectral deformation by the reception pathway.

[0097] An advantage of the invention is in particular to make it possible to obtain a short temporal response allowing an embodiment of FIR type, an embodiment particularly well suited to implementation on a programmable logic circuit such as for example an FPGA.

[0098] Another advantage of the invention is that it uses a radar signal replica recorded during a radar calibration phase undertaken in an autonomous manner by the radar, without needing any means outside the radar and without needing to perform a specific factory calibration on each item of hardware.