FR2745639A1 - RADAR SYSTEM - Google Patents

Abstract

An optimum angular resolution is obtained by calculating means, for the dimensions of the aperture of a rotating transmitting / receiving directive antenna of a radar system, by the methods of linear estimation (adaptive signal filtering, filtering optimal linear unbiased, Wiener estimate). A possibly massive degradation of the signal to noise ratio is prevented by the choice of a complex aperture illumination in general, which gives during the convolution with itself a complex function of modulus as constant as possible. The invention can be used in conventional radar systems but also in a similar manner, for example in sonars, lidars etc.

Description

RADAR SYSTEM

  The invention relates to a radar system comprising a direction antenna rotating at azimuth p, to which a transmission signal is supplied to a transmission signal input and from which a reception signal is taken at an output of reception signal, an image of the radar scenario being obtained from the reception signal, the complex amplitude of the reception signal, which represents a raw information ue ((pa) for a reflectivity function r (p), being a product of convolution

+ O

  ue (pa) = a (pa, - (p) p) () d (p, depending on the angle (a of rotation

  of the directional antenna between a radiation characteristic

  complex effective a (pa- (p) of the directive antenna and the function of

reflectivity r (p).

  In a conventional monostatic radar system (location, navigation, representation) with rotary transmit / receive direction antenna, the angular resolution is determined by the width of the main lobe and the height of the sidelobes of the 2 (antenna pattern. For given dimensions of the aperture of the directional antenna, it is possible, as is known, to obtain, by appropriate illumination of the aperture, a narrow main lobe but with large side lobes, or a larger main lobe. while at the same time having weak or disappearing side lobes, a reduction in the height of the secondary lobes is always linked to an enlargement of the main lobe and thus to a degradation of the angular resolution. homogeneous radiation of the antenna, but in this case very large side lobes are obtained, in which case it is not known until now. to find a compromise that may be appropriate to the case of application considered between

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  width of the main lobe and height of the secondary lobes of the diagram

  of the antenna by special illumination of the opening.

  The aim of the invention is to find a solution which makes it possible to escape the dilemma between the requirements currently existing for a narrowest main lobe possible and for the smallest possible side lobes. This is achieved for a radar system of the type mentioned at the beginning of this specification by an estimation device for determining an estimated value r (p) of the reflectivity function r (p) from the raw information ue (( pa) by means of a linear estimation method, an illumination (F) of an aperture, which produces an illumination of aperture

  substantially homogeneous effective A (4) 1, being chosen for the directional antenna.

  The methods known per se of adaptive signal filtering, unbiased unbiased optimal estimation or Wiener estimation allow according to the invention to obtain the best angular aperture for the dimensions of the aperture of the directional antenna by computational means. A disadvantage that would be immediately feared when using these methods, namely a massive degradation of the signal-to-noise ratio is prevented by the fact that, when using the optimal linear unbiased estimate and for a width 2, max of given normed opening of the directional antenna, the illumination of the opening F (.), That is to say the distribution of the active complex electric field strength for the azimuthal plane of the 'opening of the directional antenna, is chosen so as to give as a result of a convolution with itself at least approximately one illumination

  homogeneous effective opening angle K A (t) |.

  If, in order to determine the complex illumination F (.) Of the aperture, the following steps are carried out in the following order: a) a constant curve of the effective illuminance modulus of [A (4) 1 of the opening between -2max and 2, max b) starting from the equation

  A (): = Re (A ()) + Ira (A (5)) = const.

  the imaginary part or the unknown real part is calculated from a prescribed curve of the real part or the imaginary part, in part or in whole, c) the radiation characteristic a (papa-p) complex complex is calculated by transform Fourier transform of the effective complex illumination A (4) of the aperture, d) the complex characteristic of radiation f ((p-qa) of the directional antenna is obtained from the function f2-aq) =% Pa (. (p), e) the complex illumination of the aperture F (R) of the directional antenna is calculated by Fourier transform of the complex radiation characteristic f (qP- 9a), an advantageous and appropriate means is obtained for determining an illumination F (,) of the opening, that is to say a distribution of the intensity of the complex electric field, effective for the azimuth plane, of the opening of the directional antenna, which makes it possible to prevent a degradation of the signal-to-noise ratio while achieving optimal angular resolution. It should be noted in this regard that an underlined letter always means that it is a

complex size.

  An advantageous variant of an appropriate complex illumination of the opening is what is called illumination Chirp, which is indicated by the fact that a selected illumination of the opening E () is the following 1 1 rect ( _ ___. exp <jn.) k. (2 24) the complex factor ko being a normative factor of the directional antenna pattern and 3 is a parameter, for which the relationship 4 1 1, 2max "1

must be verified.

  An improvement consists in that a selected illumination of the opening F2 () is obtained from the illumination of

The opening indicated.

  1o 1.rect (_ exp (jC_2) o the constant component of module 1 F - recte remains constant but o an argument of F2 (), which is obtained by splitting the argument of F1 (R) into sections and then gathering randomly

sections, is formed.

  Suitable measures for use in a pulse radar are that in the case of a pulsed radar for the resolution without gaps of the reflectivity function, the angular resolution A (p) and the angular velocity co of the antenna at a direction as well as the frequency of recurrence of the pulses verify the relation c / fi-A (p = (o4max / fi <1, in which 2, max is the standard wavelength width b / X of the antenna o directive, whose standard height is equal to 2ma, = h / X (b = width and h = height of the rectangular opening, illuminated by the electric field),

the directive antenna).

  Advantageous embodiments for producing the directional antenna as a reflector antenna are indicated by the fact that the power supply system of a directional antenna formed as a reflector antenna is defocused. Measurements influencing the phase for the reflector for example in the form of a dielectric coating are taken on the directional antenna formed as

as an antenna of reflector.

  A similar use of the principle indicated in cases where the reflectivity function is to be solved for a directional antenna not only in one dimension in one direction but in two dimensions in azimuth and elevation shows that the principle according to the invention can be

  used with the same success in this case.

  A similar use to radar in a sonar, lidar, intrusion protection device, medical ultrasound diagnosis or the like indicates that the principles of the radar system according to the invention can be used advantageous

  also in other areas of application.

  The invention is explained hereinafter with the aid of drawings, in which FIG. 1 is a view modeling a directional antenna, FIG. 2 represents a model scenario for a radar system according to the invention, FIG. structure of a correlator illustrating the obtaining of the function ue (Pa) of amplitude of the reception signal, which is complex and which depends on the angle (pa of rotation of the antenna, FIG. 4 represents a filter illustrating also the amplitude function Ue (Pa), Figure 5 represents the curve of the argument of a first advantageous illumination of the opening over the entire width of a directional antenna and Figure 6 represents the curve of the argument of a second illumination

  advantage of the opening over the entire width of a directional antenna.

  The problem of estimating as precisely as possible channel impulse responses to noise-influenced test signal forms is often apparent in the electrical art. Known ways of solving this identification problem are adaptive signal filtering, the so-called unbiased unbiased optimal estimation and Wiener estimation. The two estimation methods mentioned in the first place are, for example, known from the dissertation of the graduate engineer Tobias Felhauer: "Optimale erwartungstreue Algorithmen zur hochauflosenden Kanalschatzung mit Bandspreizsignalformen", Fortschritt-Berichte VDI, Volume 10, Informatik / Kommunikationtechnik N 278, 1994, VDI Edition, Dusseldorf, p. 56 and by the article by T. Felhauer, P. Voigt, PW Baier, A. Mammela "The Optimal Optimization of Vorteilhefte Alternative to Correlation in Radarsytemen with Expanding Impulsen" in the journal "AEU" ( 1992), volume 46, No. 1, pages 32 to 38. The so-called Wiener estimation is described, for example, in the work of AD Whalen: "Detection of Signals in Noise", Academic Press, New York and London, 1971, adaptive filtering of the signal has the advantage of maximizing the signal-to-noise ratio. On the other hand, the adaptive filtering of the signal has the disadvantage that the result of the estimation is distorted by the secondary correlation values when using test signal forms having non-ideal correlation properties. This error does not appear in the unbiased unbiased optimal estimate. However, in the unbiased unbiased optimal estimate, a smaller signal-to-noise ratio is obtained than in the adaptive signal filtering, that is, a signal-to-signal degradation is obtained.

noise.

  It is part of the invention that the principles of linear signal estimation methods, ie adaptive signal matching or unbiased unbiased optimal estimation, can also be applied when acts to obtain from the reception signal obtained in a rotational directional antenna representation radar system an image with

  highest possible angular resolution of the scenario.

  We first explain the mathematical concepts underlying the application according to the invention of methods for estimating linear signals, for example adaptive signal filtering or unbiased optimal estimation, and we In particular, it concerns the degradation of the signal-to-noise ratio of the unbiased unbiased optimal estimate with respect to the adaptive filtering of the signals. The theoretical knowledge will then be applied to a system whose directional antenna has a uniform aperture illumination but which does not prove to be particularly appropriate due to a degradation of the signal-to-noise ratio. Then we will indicate concrete opening accuracies for directional antennas, which are advantageous when applying the unbiased unbiased optimal estimate. In addition, a suitable and relatively simple systematic method for determining

  opening lumens that can be used advantageously.

  The directional antenna considered in Figure 1 can be modeled in case of emission as a rectangular opening 1 in which an electric field prevails and of width b and height h. For the antenna 1 are introduced the coordinates and i normalized and reported to the antenna, which are obtained from the corresponding geometric dimensions by dividing by the wavelength X, in the free space. The opening 1 therefore has the normalized width 2Ymax, = b /, (1) and the normalized height 2lma, = h / X (2). The complex illumination of the normalized electric field of the opening 1 is B (, q). , for which we have B (, q) = O for m> ermaxe I rl> rlmax (3) If B (r, q) represents for example the illumination of the electric field of the antenna 1, we obtain the illumination of the magnetic field corresponding to

  from B (,, r1) via the free space wave resistor.

  We will be interested in the following only in the plane r = 0. The illumination of the active electric field for this plane of the antenna 1, illumination of the opening in abbreviated form, is + xc F (,) =. B (, q) dq (4) -ox Because of the equation (3), for the illumination of the opening F () according to equation (4) F (,) = 0 for [> max. (5) We define by the angle oa in the plane q = 0 a direction relative to the normal at the opening at the point = 0, l = 0. At a certain distance from the directional antenna, we obtain in the plane i = 0 as a function of the angle at the complex amplitude E (a) of the intensity of the electric field. The illumination F (_) of the aperture is normed so as to obtain the complex characteristic of radiation f (ca) = E (ac) / E (0) (6) of the directional antenna from F () next + oc 3f (= j F (2) .exp2si na] d (7) -oc

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  For the calculation of the complex radiation characteristic f (a) from the illumination of the antenna F () according to equation (7), it is assumed that If (c) is only much greater than zero than for small angles OE. If this condition is fulfilled and it is assumed that this is the case in what follows, we can replace in equation (7) with a good approximation sin (a) by a and we thus obtain + xc f (a) = [ F (). exp [j27ra] d ". (8) -oo

  The complex radiation characteristic f (ca) according to the equation

  tion (8) is the Fourier transform of the illumination of the aperture F (,)

following equation (4).

  In the following, reference is made to FIG. 2, a two-dimensional model scenario that is to say a plane having the coordinates x, y. The x-axis corresponds to the azimuthal angle (p = 0, the y axis to the azimuthal angle (p = 90) and the distance R from the origin (x = 0, y = 0). , each distance R corresponding to a special barrier of separation, prevails the normalized function of reflectivity r (p, R) .In what follows we consider the barrier of separation R = Ro This alignment barrier corresponds to the circle 2 The reflectivity function depends only on (p on this circle 2, we write r (p) = r (p, Ro) (9) Obtaining an image of the scenario radar now returns to estimate r (qp) according to equation (9), r (q) is the answer

  channel impulse to estimate in the problem of channel estimation.

  r (q) is periodic with period 2i. To simplify the subsequent considerations, we assume, contrary to reality, that r (p) = 0 for (p> 7r (10) this assumption does not lead to a serious modeling error, since it does not distort the estimation of r (qp) only in a narrow zone around q (p = n) because of the directional antenna which is supposed to radiate in a

concentrated and narrow domain.

  The directional antenna modeled according to FIG. 1 is introduced in the scenario of the radar according to FIG. 2 so that the plane r = 0 of the coordinate system of the antenna coincides with the x, y plane of the scenario and that also the origins of the two coordinate systems coincide. The opening 1 can rotate around its axis nl. The opening 1

  turned of the angle (2a with respect to the x-axis is represented in FIG.

  The angle q (Pa is hereinafter referred to as angle of rotation of the antenna

1o directive.

  The directional antenna is operated at the same time as the transmitting antenna and as receiving antenna. If the transmission signal input of the directional antenna is supplied to the angle of rotation (Pa shown in FIG. 2 of the directional antenna) by a sinusoidal emission voltage of complex amplitude and of frequency f = co / X (co = speed of light) (11), a sinusoidal reception voltage of the same frequency f and of complex amplitude ue is obtained at the reception output of the directional antenna. depends on the angle of rotation (Pa of the directional antenna and is designated Ue (pa) .The problem considered in the present invention is the estimation of the reflectivity function r ((p) from the amplitude It is indicated at this point that transmission and reception voltages are considered to be in the continuous mode as follows: pulsed voltages, such as those appearing in FIGS.

  pulse radar systems, will be considered after this.

  The emission signal input of the directional antenna is fed by an alternating voltage in the continuous mode of complex amplitude us = 1. For a function r (() of normatively corresponding reflectivity, at the output of the reception signal of the directional antenna, a continuous AC voltage of complex amplitude depending on the angle of rotation (pa of the directional antenna + oc Ue ((Pa) = J f 2 (p- (pa) .r ((p) d (p) (12) -o0 since the complex radiation characteristic f (o) of the antenna

  directive see equation (6), is valid both in transmission and in reception.

  The magnitude a (o) = f2 (-o) (13) is designated by the effective complex radiation characteristic of the directional antenna. a (ca) is the form of test signal in the problem of channel estimation. We obtain by a (o) according to equation (13) from equation (12) + "C ue ((Pa) =. A ((p- (p) .r (p) d (p. (14) The integration bounds in equations (12) and (14) can be o + c since, as assumed in equation (10), r ((p) equals zero for | (p |> r) For sufficiently large module values of (Pa, the amplitude of ue ((pa) tends to zero due to equation (10).) Each zone in which one obtains a ( ) significantly different from zero from equation (14) is considered to be a deciding domain of (a) For highly directional antennas, the determining area of (Pa is given approximately by (Pa <7. (15) It is only for very directional antennas that we obtain from equations (12) and (14)! Ue ((Pa) r (pa) (16) The lower the directivity of the antenna, the less Ue (Pa) not restated according to equation (14) represents the reflectivity function to be estimated r ((p). how one can obtain from the amplitude ue (pa) of the received signal a best possible estimate of the

r ((q) reflectivity function.

  Ue (qPa) according to equation (14) is the convolution product of a ((p) according to equation (13) and r ((p) according to equations (9) and (10), the angle (Pa of rotation of the directional antenna appearing under the convulsion integral as an offset parameter Ue (Pa) is hereinafter denoted by raw information concerning the reflectivity function r ((p). of Ue (qpa) according to equation (14) can be illustrated by the correlator structure according to Figure 3, in which can be taken from a block 3 shown

  o schematically the effective complex characteristic of radiation a ((pa-

  (p) for an instantaneous angle of rotation (p, this radiation characteristic a () a- (p) is multiplied in a multiplication element 4 by a reflectivity function r ((p) and then is formed in a 5 I integrator mentioned in Figure 4. In this case, a (p) is introduced into a response filter 6.

  impulse r (q); at the output of this filter 6 ue (çp) is obtained.

  It is unusual for the telecommunication technician that in the device according to Figure 4, the independent variable is not time as is usually the case but the azimuthal angle (p. its axis j, so that the angle of rotation (pa depends on the time t in a system-specific way, but this dependence on time does not play any role in the equations (12) and (14). These equations assume that we consider ue (Pa) as a function of the angle q (a of rotation, without relating the path of the critical value zone of the angle of rotation (Pa, see for example

  condition (15), with a special dependence on time (pa (t).

  It is simply assumed that ue (Pa) is determined for all the values of the angle of rotation (Pa of rotation of the determining value zone, the succession in

  the time of the values (pa of angle of rotation being meaningless.

  It is only for very directional antennas that the condition (16) is valid, so that the raw information ue (it) is a direct measure of the reflectivity function r ((p) only in these cases In non-directive antennas, the raw information ((pa) according to equation (14) is a version of the reflectivity function r ((p) modified according to the representations according to FIGS. this change following the subsequent processing of the raw information ue (qpa), a loss more or

  less in angular resolution.

  To explain the subsequent processing of the signal, we introduce the Fourier transform + aC Ue (U) = X Ue (pa) .exp [j271 (Pa) dqa (17) -oo from ue (Pa) according to equation (12). ) and equation (14), + A A () = J a (o) .exp [-j2cLo] dcL (18) of a (oa) according to equation (13) and + oC R () = J r ((p) .exp [-j27cqp] d (p (19)

-O

  of r (qp) according to equations (9) and (10). The Fourier transform according to equation (18) is equal due to equation (13) to the convolution product F (-) * F (-) and is designated effective illumination of the opening. Due to the limitation of F () according to equation (5) we have A (R) = 0 for l> 2m ,,. (20) Because of equation (14), we have the relation Ue () = A () 'R (,). (21) between the Fourier transforms according to equations (17), (18) and (19). Because of equation (20) we have for Ue (,) according to equation (21) Ue () = 0 for l> 2Imax (22) Equation (22) means that the spectral components of R (, ) possibly present in the range ll> 2, max can not in fact be determined for the illumination of the opening indicated by equations (4) and (5). For an aperture illumination of this kind, it is possible to determine only a version of R (,) limited to the area l <2max and disappearing outside this domain. To this version of R (,) corresponds a variant that can be observed of the reflectivity function r ((p), which is

  o also denoted by observable reflectivity function.

  To obtain an estimate of R () from Ue (,) according to equation (17) and thus obtain an estimate of r (q) from ue_ (p) according to equation (14), we use the following the invention one of the three methods known per se, namely either the filtering adapted to the characteristic a (a) of complex complex I5 radiation according to equation (13), or the unbiased unbiased optimal estimation (LOS) , the so-called Wiener estimate. The filtering adapted to the characteristic a (a) of efficient complex radiation according to equation (13) corresponds to the adaptive filtering of signals (SF) during the identification of the system and is designated in the following by filtering (DF) adapted the

diagram.

  In a manner known per se during the filtering adapted to the diagram, k = 4: / | A (4) | d & (23) A. an estimate R () of R () (see for example the aforementioned dissertation of T. Felhauer) R (_) = k Ue (>). A * (E) ( 24) The choice of the constant k according to equation (23) is used for normation and ensures that the actual estimate and curve of the function of

  observable reflectivity coincide, when r (q) is a delta pulse.

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  A function a (p) of this kind would be obtained in the case of a reflector

  unique punctual to distance Ro.

  Due to equation (20) we obtain from equation (24), (E) = 0 for @ll> 2a ,,. (25) In the unbiased unbiased optimal estimate we obtain an estimate R ({) of R ({) in the manner known per se (see, for example,

  the aforementioned essay by T. Felhauer).

   ;) | U * (,) / A (,) for, I2E, (26) O s inon We obtain from R () according to equation (24) or (26) by inverse Fourier transformation the estimate i (I): f- exp [j2I * p} = P] _exp [j2 = - (p] d, (27) 20.-2

  for the desired reflectivity function ((p).

  The drawback of the filtering adapted to the diagram according to equation (24) lies in the fact that in general A (A) '* (A) varies with, so that the estimate R ({) according to the equation ( 24) deviates more or less from the version of R (,) limited to domain 2I <_2max. The problem posed by the unbiased unbiased optimal estimate according to equation (26) is that division by A () is permissible only if A (4) does not have zero in the area I 1 < 2 {max. If there is no zero, then R ({) coincides with the version limited to the area 1 I <2max of _R (), that is, the estimate has

  the advantageous property of not being biased.

  Due to the limitation of R ({) to the area l <_2max, the sampling theorem can be applied. This means that? ((P) according to equation (27) can be reconstructed from sampling values spaced from the angular difference

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4_ (28)

  Ap according to equation (28) is referred to as angular resolution of the directional antenna. In the case of a pulse radar, the angular velocity of the directional antenna and the frequency of recurrence of the pulses are tuned together so that by injecting A (> according to equation (28), we obtain

(D-4 ,,. <1

  f A'P f (29) If it is superimposed on the raw information ue (pa) according to equation (14), a perturbation x (9pa) additive depends in general on the angle (qa of rotation, the information available raw is now written e (qp) = ue (Pa) + X ((Pa) (30) Disturbance x (Pa) means that instead of a value ue (qa) following equation (14) a distorted value e (ga) of x (qa) It is unusual for the communications technician in the representation of equation (30) that the perturbation x (qPa) depends on the angle (a). of rotation and not of time x ((Pa) represents for each (Pa the complex amplitude of a sinusoidal voltage under steady state conditions The origin of the error x (pa) may lie, for example, in the fact that a function x_ (p) of perturbation is superimposed on the function r (p) of reflectivity, for example a parasitic function x (P) of this kind might appear by the fact that it appears in addition to the objects of interest. the radar scenario at the distance Ro from other undesirable reflective objects, or by the fact that the reflection properties of the objects of the scenario of interest indicated by r (qp) are disturbed. A disturbance of this kind would appear, for example, if a wall of a building which was at first homogeneous and which was partly reflective of a very absorbing material was coated. It is important in practice that the effect of the receiving thermal noise can be converted into an equivalent disturbance x ((pa) which will be discussed later.) The perturbation x (pa) is considered in the following as a typical function of a random process having the independent variable (Pa Si e (Pa) according to equation (30) is determined several times for one and the same reflectivity function r (q), another function of type x ((Pa) of io random process is contained each time in the functions e (pa) The random process determining the perturbation x (qa) is assumed to be slightly stationary and have the following properties E {ReLx & (a)]} = E {Im [x ( Pa)]} = O (31) E {ReLx (pa)] .lm [x (Pa)]} = 0 (32) 2E {Re2 [x (pa)]} = 2E {Im2 Lx (qa)}} = E {x ((pa) .X * (Qa)} = a2x (33) a2x according to equation (33) is the variance of the perturbation x (Pa) The bilateral spectral density of the perturbation x (qp) is X (4) = 4 rect ((34)

  X (R) corresponds to the power density of time signals.

  The perturbation X (Qa) makes that it is superimposed on the estimate r (p) according to the equation (27) also a perturbation which is designated by r (Pa). The estimate ((p) | (f e) - e2'd. + X (tp) is obtained instead of equation (27). (35)

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  The variance of Xr ((p) is obtained in the case of the estimation by a filtering adapted to the diagram (DF), see the equations (23) and (24) with X () according to the equation (34) by "D2 = r4, .. / | f A () I dF t X (,) ._ A () J2 d

-2R .. - 2g ,.

(36) 4-

= 4, .- C: / f | A () | d.

-2 t, ..

  in the case of the unbiased unbiased optimal estimate (LOS), see equation (26), we obtain for the variance of X r (p) with X () according to equation (31) 2: __ .. .21 De 'denotes by degradation of the unbiased unbiased optimal estimate with respect to the filtering adapted to the diagram the magnitude at 2 siat (6 2 determine from 2DF according to equation (36) and by a2LOS according to the equation (37)

2 2

NOT A WORD

  d / dB = 101g (OC / a'F) = 101 f 4j yA () | d- $ A (dj (38) we have always, see the aforementioned dissertation of T. Felhauer, d> 0, (39) the sign of equality being valid for the case A () I = const for l 2 1 <- 2max (40) For a width 2, max of normed opening given, it is necessary to strive if one wishes to obtain a small degradation d, to find illumination opening F () according to equation (4), which give according to equations (13) and (18) illumination A (,) of effective opening satisfying the best possible equation (40), the object of advantageous improvements

  of the invention is the determination of these advantageous F () illuminations.

  The filtering adapted to the diagram has the advantage of a low effective perturbation compared to an optimal estimate of the linear non-kissing, see condition (39) and the disadvantage that systematic errors of estimation occur due to of a bias. This is why it is preferable for a relatively weak disturbance, that is to say for a relatively low 2, see equation (33), the unbiased optimal linear filtering, for a relatively strong perturbation on the contrary adapted filtering. to the diagram, io and you have to look exactly in each case which of the two ways

  to proceed is the most advantageous.

  In the preceding configurations, it is implicitly assumed that there is at the transmission signal input of the directional antenna a steady-state alternating voltage of complex amplitude u = 1 and that i5 is obtained. at the receiving output of the directional antenna therefore also a steady-state alternating voltage, whose complex amplitude is designated ue, ue depending on the angle (pa of rotation of the directional antenna, see the equations ( 12) and (14) In pulse radar systems, the transmission signal is a periodic sequence of oscillations train, that is to say of pulse duration T and frequency of recurrence of pulses f, when the raw information ue (pa) for the whole value area of the angle of rotation q (P, see, for example, the equation) must be determined in a pulse radar system. (15), it is necessary that the angular resolution A (p and the angular velocity cO of the directional antenna ain if

  that the frequency of recurrence of the pulses satisfy equation (29).

  In what follows we consider a single transmission pulse. We have for its complex envelope (41) u. (T) = u.rect (t / T) (41) this emission pulse with energy Es = IuS 2.T / 2. (42)

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  For the complex envelope of the corresponding reception signal, we have, apart from a temporal delay which we are not interested in here, _ (t) = u (pw.) Rect (t / T) (43) The receive signal according to equation (43) has the energy E. = | u. (M.) | T / 2 (44) In addition to the reception signal at the output of the directional antenna receiving signal, there is a white noise n (t) having a bilateral spectral density of power No / 2. The complex envelope _ (t, p (.) = U. (T, (P.) + _ (t, q).) (45) of the reception signal consisting of the wanted signal and the spurious signal is sent for optimization of the signal-to-noise ratio to a filter adapted to a (t, (pa) according to equation (43) with the low-pass equivalent of the impulse response h () = 1 T.rect (-t / T ) (46) At the output of this filter at the instant of the maximum signal-to-noise ratio, the estimate _e (Pa) of the complex useful amplitude Ue (pa) plus a variance perturbation 2 No 1 (47) is obtained.

2 T

2 2

  This variant 2 must be used instead of the variance ax2 in equations (36) and (37), when the influence of the thermal noise has to be detected. For a uniform opening illumination

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  FWo (E,) = {/ () or r | j 5 (48) - 0 otherwise We obtain from equation (8) the complex characteristic of radiation f (a) = sinc (2ic {,. A) (49) io and from equation (13) the effective radiation characteristic a (ac) = sinc2 (2n = m, ua). (50) In the foregoing, it has been considered inter alia that when using the unbiased unbiased optimum estimate to increase the angular resolution it is valid that the illumination of the aperture of the directive antenna satisfies certain requirements. In the following one indicates on the one hand means to obtain advantageous opening illuminations when using the unbiased unbiased optimal estimation and on the other hand

  concretely indicates an opening illumination of this kind.

  When using the optimal linear unbiased estimation and for a given normed opening width 2mr, of the directional antenna, the illumination of opening F (,), that is to say the distribution of the field complex electrical power for the azimuthal plane, from the opening of the directional antenna, is advantageously selected so as to give as a result of a convolution with itself at least approximately one illumination

of opening | A_ () |.

  An advantageous possibility of determining the complex illumination of opening F () of a directional antenna consists in carrying out in the order the following steps: 1) starting from a constant curve of effective illumination of opening JA (4) I between -2max and 2max, 2) we calculate starting from the equation A (4) = / Re2 (A (,)) + Im2 (A ()) = const from a prescribed curve of the real part Re or the imaginary part Im in sections or in whole in one line the unknown imaginary part Im or the unknown real part Re, 3) is determined from the illumination Af () of efficient complex opening by transformation Fourier the characteristic a (pa-qp) of complex complex radiation, 4) the complex characteristic of radiation f ("p <-Pa) of the directional antenna is obtained from the function f ((P- (Pa ) = a? (Pa- <p), 5) the complex aperture illumination F (,) of the directional antenna is calculated by Fourier transformation of the complex characteristic of

radiation f (tp-pa).

  Hereinafter, appropriate aperture illuminations of a directional antenna are determined, which can be used when applying the unbiased unbiased optimal estimate to increase

  the angular resolution of directional antennas.

  It has already been explained that when the unbiased unbiased optimal estimate is applied, the effective aperture illumination A () should best satisfy the condition already indicated in equation (40) IA () | = const. for l <2 ma, (51) to increase the angular resolution of directional antennas. Better the equation (51) is verified plus the degradation of the signal to noise ratio is

low.

  The illumination of the particularly appropriate aperture has been determined according to: - (4) F - keitit x) e (52) k -Z & 2. 2 w The complex factor k 0 in equation (2) serves to standardize the

antenna diagram.

  The effective illumination of aperture A (4) is obtained from the following aperture illumination F (,)

A (4) = F (-) * F (-). (53)

In what follows, we have

412 1 (54)

  In this case F () results in equation (52) an effective opening illumination, which approximately satisfies the stated condition

  o in equation (51). This is shown in the following.

  If the condition (54) is satisfied, the inverse Fourier transform of _F () and thus the complex characteristic of radiation + max f (ao = f E (,) ei2CdO (55) rmax gives a good approximation f (a) = The complex characteristic of radiation f (o) has been defined so that f (a = O) = 1. This gives the complex factor _0 in the complex factor f (o). equations (52) and (56) L = 2j3j [.. expgn3). ] (57) or for the complex characteristic of radiation according to equation (56) f (cc) = rect (a) .ex {j] (58)

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  From f (a) the efficient complex characteristic of radiation 51 - is obtained. ex -j - (: 9) a (a) = f2 (-a) = rect2 eX [3a] (59) With max = 2mae (60) y '= [/ 2 (61) a (o) can be modified according to equation (59) as follows: a (a) = rect 2 -,) exp [-j δa 1 (62)

2% '5

  The Fourier transform of a (ca) according to equation (62) is then approximately A (t) = La (a) j2da -o (63) = .ji '-rect (2-) exp [ij 2 -j sgn () 4] A () according to equation (63) satisfies condition (51), since we have A (4) | = const. for ii <2Smax (64) and it therefore turns out that the opening illumination proposed in equation (52) according to an appropriate improvement of the invention is advantageous when using the unbiased unbiased optimal estimate because in this case, the effective illumination aperture A () approximately satisfies the condition (51). The way in which A () coincides precisely for an opening illumination according to equation (52) with A () 1 according to the equation

(51), depends on parameter 3.

  The following explains the approximation used.

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  In the work of MI Skolnick, "Radar Handbook", McGraw Hill, 1970, pages 3-18, is stated on the basis of the stationary phase principle an approximate expression for the Fourier transform of rectangular pulses with carrier and modulated linearly. in frequency (Chirp signals). The approximation applies to Chirp signals having a large bandwidth time product. This approximation is reproduced briefly below. We deduce moreover time and frequency functions, which are obtained from the time and frequency functions indicated in the mentioned work of Skolnick by exchange

  of the time or frequency domain.

  - The complex envelope of a rectangular linear frequency modulated carrier pulse is (t) 1 rect (t) .exp [jnPt] (67) According to Skolnick, it is hypothesised

1O 162>, 1 (68)

  for the Fourier transform of u (t) according to equation (67) the approximation 03 (f) = Ju (t) e- ftdt = rect ex [-jpf + jf2 + isgn (). (69) If we replace in frequency (69) the frequency by the time t, we obtain the temporal signal i- (70) 1 'rect) xp [-jt + jsgn (g)' 4] The signal temporal U (t) according to equation (70) to the Fourier transform jf u (f) = _U (t) e "tdt - / rect (71) = U (t) e- 2xftdt -rect (f) - e [jqt

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  The equation (52) indicates an appropriate illumination of aperture for a directional antenna. (72) In addition, a directional antenna with an aperture illumination EF2 (,), which has a constant modulus IF () () 1 = 1 F2 (t) 1 as FI () is considered. = k 1. r (2_ io but which unlike this one has an argument which is obtained by division of the argument of F () that is to say of a parabola, then by random gathering of 5 shows in an example the curve of the argument of the first advantageous illumination of opening Fi () over the entire relative width / m of a directive antenna comprising four successive sections A1, A2. , A3 and A4 These four sections of the argument of Fj () forming a parabola are cut off from each other then gathered in a random order and thus give the argument represented in FIG. 6 of an example of a function

  F_ () of opening illumination also advantageous.

  The principle according to the invention can equally well be applied to cases in which the reflectivity function must not be solved for a directional antenna only in one dimension in the direction

  azimuthal but in two dimensions according to azimuth and elevation.

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Claims (10)

  A radar system comprising an azimuth-rotating directive antenna (p, to which a transmission signal is supplied to a transmission signal input and from which a reception signal is taken at a reception signal output, an image of the radar scenario being obtained from the reception signal, the complex amplitude of the reception signal, which represents raw information Ue (q "a) for a reflectivity function r ((p), being a convolution product + M I1 () +   ue (Pa) = fJ (pa, - (p) r (p) d (p, depending on the angle Pa of rotation of the antenna di-   rectifying between a complex efficient radiation characteristic a (qPa) of the directive antenna and the reflectivity function r (qp), characterized by an estimation device for determining an estimated value r (qP) of the function r (q ) of reflectivity from the raw information Ue (9pa) by means of a linear estimation process, an illumination (F) of an aperture, which produces a fairly homogeneous effective illumination aperture _A (R ) being chosen for the directional antenna.   Radar system according to Claim 1, characterized in that in the case of a pulsed radar for the resolution without gaps of the reflectivity function, the angular resolution Aq and the angular velocity c 0 of the directional antenna as well as the frequency fi of recurrence of the pulses verify the relation co / fi'A (p = co'4, max / fi <1, in which 2, max is the standard width in wavelength b / X of the directional antenna, whose height 2745639   norm is equal to 2lrmax = h / X (b = width and h = height of the opening   rectangular, illuminated by the electric field, of the directional antenna).   3. Radar system according to claim 2, characterized in that when using the optimal linear unbiased estimate and for a width 2m, given normal opening of the directional antenna, the illumination of the opening F (), that is to say the distribution of the active complex electric field strength for the azimuthal plane of the opening of the directional antenna, is chosen so as to result in a convolution with o him -at least at least approximately an effective opening illumination homogeneous A (4).   4. Radar system according to claim 3, characterized in that to determine the complex illumination F (,) of the opening, the following steps are performed in the following order: a) starting from a constant curve of the effective illumination A (R) J of the opening between -2, max and 2, max, b) starting from the equation A () = / Re2 (A ()) + m2 (A ()) const is computed from a prescribed curve of the real part or the imaginary part, by piece or in whole, of a line the imaginary part or the unknown real part, c) the characteristic a (p, -qp) of complex radiation effective is calculated by Fourier transform of the effective complex illumination A (R) of the aperture, d) the complex radiation characteristic f (tp-p (a) of the directional antenna is obtained from the function f (p-pa,) = / a (qpa- (p), e) the complex illumination of the opening F (,) of the directional antenna is calculated by Fourier transform of the characteristic of complex radiation f (p-qpa).   Radar system according to Claim 3, characterized in that 2745639   a selected illumination of the opening F (,) is the following: F (): -ko 2. rect 2 -exp (j; z2) the complex factor ko being a normative factor of the directional antenna diagram and 3 being a parameter, for which the relation 4P31 2max> "1 must be checked.   Radar system according to Claim 5, characterized in that a selected illumination of the opening E2 () is obtained from the illumination of the opening indicated in Claim 5 FA1 rect / _ / À exp (j / - V ') -' (= ko 2 / - (, 2.) o the constant component of the module i F1,) = iF2 = J. i * rectf i remains constant but o an argument of F_2 (), which is obtained by cutting the argument of Fj (,) into sections and then randomly gathering the stretches, is form.   Radar system according to one of the preceding claims,   characterized in that the power supply system of a directional antenna formed as an antenna   reflector is disposed in a defocusing manner.   Radar system according to one of Claims 1 to 6,   characterized in that measurements influencing the phase for the reflector for example in the form of a dielectric coating are taken on the antenna   directive formed as a reflector antenna.   9. System according to one of the preceding claims, characterized by 29 2745639   a similar use of the principle indicated in cases where the reflectivity function has to be solved for a directional antenna not only in one dimension in one direction but in two dimensions in azimuth and elevation.   10. System according to one of the preceding claims,   characterized by radar-like use in a sonar, lidar, intrusion protection device, medical ultrasound diagnosis or similar.