CA2069979C - Method of generating a reference function for a pulse compression of frequency; phase and/or amplitude-modulated signals - Google Patents
Method of generating a reference function for a pulse compression of frequency; phase and/or amplitude-modulated signalsInfo
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- CA2069979C CA2069979C CA002069979A CA2069979A CA2069979C CA 2069979 C CA2069979 C CA 2069979C CA 002069979 A CA002069979 A CA 002069979A CA 2069979 A CA2069979 A CA 2069979A CA 2069979 C CA2069979 C CA 2069979C
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- 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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
- G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
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- 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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/06—Systems determining position data of a target
- G01S13/08—Systems for measuring distance only
- G01S13/10—Systems for measuring distance only using transmission of interrupted, pulse modulated waves
- G01S13/26—Systems for measuring distance only using transmission of interrupted, pulse modulated waves wherein the transmitted pulses use a frequency- or phase-modulated carrier wave
- G01S13/28—Systems for measuring distance only using transmission of interrupted, pulse modulated waves wherein the transmitted pulses use a frequency- or phase-modulated carrier wave with time compression of received pulses
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- Computer Networks & Wireless Communication (AREA)
- General Physics & Mathematics (AREA)
- Electromagnetism (AREA)
- Radar Systems Or Details Thereof (AREA)
- Magnetic Resonance Imaging Apparatus (AREA)
- Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)
Abstract
In a method of generating a reference function for pulse compression of frequency, phase and/or amplitude-modulated signals, a reference signal (ho(t)) corresponding to a conjugated complex function of an error-free frequency-modulated signal (so(t)) and a signal (sf(t)) containing phase and amplitude errors are generated in two following FFT units by a Fourier transformation in the form of signals (Ho, Sf) present at the outputs thereof.
Thereupon, the signal (¦Ho¦2) is generated from the output signal (Ho) of the one FFT unit by means of an intensity-forming unit and the signal (1/Sf) is generated from the output signal (Sf) of the other FFT unit by means of a reciprocal-forming unit and said two signals (¦Ho¦2, 1/Ff) are multiplied together in a following multiplying member;
finally, the output signal (Hi) of the multiplying member is subjected in an IFFT unit to an inverse transformation for generating the reference function (hi(t)) in the time domain.
For performing a pulse compression in the time domain a pulse response (fo(t)) corresponding to the function (sin(x)/x) is then formed from the signal (sf(t)) and the generated reference function (hi(t)) in a convolution unit (3).
Thereupon, the signal (¦Ho¦2) is generated from the output signal (Ho) of the one FFT unit by means of an intensity-forming unit and the signal (1/Sf) is generated from the output signal (Sf) of the other FFT unit by means of a reciprocal-forming unit and said two signals (¦Ho¦2, 1/Ff) are multiplied together in a following multiplying member;
finally, the output signal (Hi) of the multiplying member is subjected in an IFFT unit to an inverse transformation for generating the reference function (hi(t)) in the time domain.
For performing a pulse compression in the time domain a pulse response (fo(t)) corresponding to the function (sin(x)/x) is then formed from the signal (sf(t)) and the generated reference function (hi(t)) in a convolution unit (3).
Description
Method of generating a reference function for a pulse compression of frequency, phase and/or amplitude-modulated signals BACKGROUND OF THE INVENTION
1. Field of the Invention The invention relates to a method of generating a reference function for a pulse compression of frequency, phase and/or amplitude-modulated signals and relates in addition to a method for carrying out a pulse compression by means of a reference function.
1. Field of the Invention The invention relates to a method of generating a reference function for a pulse compression of frequency, phase and/or amplitude-modulated signals and relates in addition to a method for carrying out a pulse compression by means of a reference function.
2. Description of the Prior Art Pulse compressions are carried out in many areas of signal processing, for example in radar technology or in communications technology. Below, a pulse compression of frequency-modulated signals will be explained for example in radar systems.
Radar systems work by the echo principal. A transmitter emits electromagnetic waves which are partially absorbed and partially reflected by the target area. The signals received by the radar apparatus are used for locating and surveying objects or also for determining the velocity of moving targets. For this purpose the pulse method is usually employed. In this method a pulse of short duration is periodically transmitted; the backscattered signal is received and after conversion to a base band digitized. By reducing a pulse duration Te a high range resolution is obtained and by increasing the transmission peak power PO
the range is increased and the signal/noise ratio improved.
1 The pulse duration and the transmission peak power are decisive for the performance of the radar system; however, they represent contradicting requirements because a high transmission peak power cannot be produced in a short time:-To overcome these problems, pulse compression is employed.
Instead of a time-compressed pulse a time-expanded signal with frequency modulation is employed. Usually, linear frequency modulation is employed here and can be generated either with analog components or with a digital circuit having a following digital/analog (D/A) converter. When employing analog components a delay or SAW (Surface Acoustic Wave) network is used. Such a time-expanded frequency-modulated signal is denoted by the English term "chirp".
Now, with regard to the range resolution there is no limitation due to frequency modulation of a time-expanded signal because said resolution depends on the bandwidth of the frequency modulation. If the bandwidth Be of the frequency modulation is increased so that the same bandwidth (1/Te) of the time-compressed signal is achieved, after pulse compression of the time-expanded signal the same range resolution is obtained as with a pulse of short duration.
By employing the time-expanded signal the contradicting requirements, i.e. high transmission power and short pulse duration, are obviated so that a high range resolution can be achieved and at the same time a high signal/noise ratio.
On receiving backscattered radar data a pulse compression of the time-expanded signal is then performed and can be achieved likewise either with analog components (SAW) or, after A/D conversion of the signal, by means of a digital circuit. In the ideal case in which no phase and amplitude l errors occur in the transmitting and receiving operation with a linearly frequency-modulated signal, after a compression of the radar signal of a single point target a sin(x)/x function is obtained. This function is referred to as pulse response and the highest side lobe lies at 13.6 dB beneath the maximum of this function. In most cases an amplitude weighting is additionally carried out in the pulse compression so that the side lobes of the pulse response are suppressed to a greater extent. For a Hamming weighting a suppression of the highest side lobe of 43 dB
is obtained. This impairs the geometrical resolution by 46 % because the effective bandwidth in the pulse compression is reduced by the insertion of the amplitude weighting.
In a real case however phase and amplitude errors are present in a received signal. These errors can occur in the generation of the phase modulation of the time-expanded signallin the transmitting and receiving unit of the radar system, in the transmission and receiving of the electromagnetic waves by the antenna and in the A/D
conversion of received backscattered radar signals.
As a result, a pulse response is obtained which does not correspond to the ideal case. This causes a deterioration of the properties of the pulse response and this can greatly impair the quality of the radar image. The properties of the pulse response are described by a geometrical resolution, by the side lobe ratio and by the amplitude loss.
Pulse compression can be employed also in a radar with synthetic aperture (SAR) both in the range direction as in the azimuth direction (flight direction). An SAR system comprises a carrier, for example an aircraft, a helicopter, a satellite, and the like, which moves with a constant 1 velocity, an antenna with a viewing direction transversely of the movement direction, i.e. to the right or left, and a coherent radar system which transmits electromagnetic pulses, receives the backscattered radar echoes and quadrature demodulates them in the I and Q channel and thereafter digitizes them. For generating a two-dimensional image a pulse compression is carried out in the range and azimuth direction. With conventional pulse radar with pulse compression as has been described above, the range resolution is governed by the bandwidth of the transmitted pulse.
The azimuth resolution of a radar can be very much improved by the synthetic aperture method compared with a real aperture method. With an SAR system an antenna with wide directive pattern in the azimuth direction is employed and a coherent imaging carried out. A specific target is illuminated by the antenna during several pulses and each echo is received coherently. A long synthetic antenna can be formed thereby so that the phase history in the azimuth direction caused by the range variation from the carrier to the target during the illumination time can be corrected.
With this artificial increase of the antenna length a narrow bundling in the azimuth direction and a high azimuth resolution are achieved. The phase history in the azimuth direction leads to a frequency modulation, the bandwidth of which is referred to as Doppler bandwidth.
The data processing in the azimuth direction for a high geometrical resolution then consists of a pulse compression of the received azimuth signal because the latter also has a time-expanded frequency-modulated profile. Since the target illumination time in the azimuth direction increases linearly with the range, the length of the synthetic aperture becomes greater with the range and the 20i69979 l corresponding synthetic bundling narrower; as a result, the azimuth resolution becomes independent of the range.
Hereinafter various imaging geometries of an SAR system in which no linear frequency modulation occurs in the azimuth direction will be described. The frequency modulation in an SAR system in the azimuth direction can deviate from the linear case if the aperture angle ~a of the antenna in the azimuth direction is greater than about 20. For an antenna aperture angle ~a of 180 for example a cosinusoidal frequency profile is obtained and the angular variation of the cosine function extends from 90 to -90.
In this case, after the pulse compression instead of a sin(x)/x function a Bessel function of the first type of zero order is obtained, the side lobe r~tio being reduced to 7.8 dB. This impairs the image quality and that is undesirable.
With a large squint angle of the SAR carrier or in the case where the antenna alignment deviates more than 20 from the direction orthogonal to the flight direction, a linear frequency profile is also not obtained.
The hitherto most frequently employed method for pulse compression is the method of the socalled optimum filter ("matched filter"). Here, a convolution of the received signal is carried out with a conjugated complex time-inverted replica of the transmitted modulated pulse (cf.
for example Klauder, J.R. et al: "The Theory and Design of Chirp Radars". The Bell System Technical Journal, July 1960, p. 745 to 808, or Skolnik, M.I.: Radar Handbook, McGraw-Hill Inc., 1970, p.20-1 to 20-37, or Wehner, D.R.:
High Resolution Radar, Artech House, 1987, p. 65-69 and Davenport, W.B. and Root, W.L.: An Introduction to the Theory of Random Signals and Noise, McGraw-Hill Inc., 1958, p.244-247). This function calculated from the replica is 1 referred to as reference function. In the pulse compression in the azimuth direction of an SAR system the replica can be calculated from the imaging geometry. The replica contains all the phase and amplitude errors which can occur through the sending and transmission in the hardware. Furthermore, the replica also contains the deviation from the linear frequency modulation which can occur through the imaging geometry in an SAR system.
If phase and amplitude errors are present and if they are ignored in the pulse compression, the properties of the pulse response are impaired. This impairment can be reduced if said errors are taken into account when determining the reference function, i.e. if the reference function is generated from the replica of the transmitted pulse. The reference function according to the method of the matched filter consists of the conjugated complex time-inverted replica of the faulty frequency-modulated signal.
For a pulse compression in the azimuth direction with a nonlinear frequency profile the reference function according to the method of the matched filter also has a nonlinear phase profile and the pulse response may have very high side lobes which cannot be efficiently reduced by employing an amplitude weighting.
Instead of a convolution, frequently a fast Fourier transformed (FFT) algorithm is used for pulse compression (cf. US 4,379,295 - Abstract and US 4,912,472, col. 1, line 50 to col. 2, line 60). This algorithm is based on the fact that a convolution in the time domain corresponds to a multiplication in the frequency domain.
The received signal and the reference function are first Fourier transformed, then multiplied with each other and finally transformed back to the time domain by the inverse 1 Fourier transformation (IFFT). This processing can be carried out substantially faster than the convolution in the time domain and is therefore usually employed in the digital pulse compression of frequency-modulated signals.
By using pulse compression with a socalled matched filter, although the properties and the signal/noise ratio of the pulse response are improved when the phase and amplitude errors in the received signals are known it is not possible with this method to effect a correction of the phase and amplitude errors in such a manner than an ideal pulse response is achieved, i.e. a sin(x)/x function.
It is only on variation of the modulation rate of a signal with linear frequency modulation, corresponding to a square phase error, that the ideal pulse response is obtained with the matched filter and a reference function generated from the replica. All other cases of phase and amplitude errors lead to pulse responses which do not correspond to a sin(x)/x function.
SUMMARY OF THE INVENTION
It is therefore the object of the invention to optimize a method for generating a reference function for a pulse compression with frequency, phase and/or amplitude-modulated signals in such a manner that all phase and amplitude errors in pulse compression are eliminated and consequently, in spite of the phase and amplitude errors present in the received signal an ideal pulse is achieved, this also being independent of the strength and form of said errors.
The invention therefore proposes in a method of generating a reference function for a pulse compression of modulated signals the improvement in which an error-free frequency-1 modulated signal (so(t)), a signal (Sf(t)) containing phaseand amplitude errors, a reference signal (ho(t)) corresponding to a conjugated complex time-inverted function of the error-free signal (s(t)) and a reference signal (hf(t)) corresponding to the conjugated complex time-inverted input signal (Sf(t)) are each Fourier transformed in respective FFT units, thereby generating signals (SO' Sf, Ho and Hf);
output signals (Sf; Hf) from two of the FFT units are respectively multiplied by each other in a first multiplying member and output signals (SO' Ho) from the two other FFT units in a second multiplying member;
the reciprocal (1/Ff) of the output signal (Ff) of the first multiplying member is formed in a unit forming a reciprocal value and is multiplied in a third multiplying member by the output signal (Fo) of the second multiplying member;
the output signal (Fo/Ff) of the third multiplying member is multiplied by the signal (Hf), i.e. the fast Fourier transformation of the signal (hf(t)) at the output of the FFT unit in a fourth multiplying member and the output signal (Hi) of the fourth multiplying member is subjected in a following IFFT unit to an inverse Fourier transformation to generate the reference function (hi(t)) in the time domain.
Thus, when employing a reference function generated in accordance with the aforementioned method in a method for carrying out a pulse compression a pulse response is obtained which has a form and properties which remain independent of the phase and amplitude errors present in the signal received. The method according to the invention 1 for generating a reference function for a pulse compression of frequency, phase and/or amplitude-modulated signals can be referred to as ideal filter as regards its effect.
Due to the method according to the invention, the reference function determined from the replica of the faulty received signal or from the imaging geometry of an SAR system contains not only the adaptation to the signal as in the usual matching filter but also an additional term which eliminates completely the phase and amplitude errors of the received signal. Thus, according to the invention an ideal pulse response is always achieved, the geometrical resolution of which depends only on the bandwidth of the frequency-modulated signal and the form and properties of which are independent of the nature of the frequency modulation and of the errors present in the received signal.
By inserting an amplitude weighting into the reference function generated according to the method of the invention the side lobes of the sin(x)/x function can also be reduced. The method according to the invention acting as ideal filter is of great significance for many technical fields in which a pulse compression is employed. It is thereby possible to make a hardware specification regarding phase and amplitude errors less stringent without impairing the properties of the pulse response. Once the reference function according to the invention has been determined the pulse compression can be carried out as in usual methods and consequently the ideal filter operating in accordance with the method of the invention can be implemented without great hardware expenditure.
In the case that the replica of the transmitted signal is not available, the phase and amplitude errors can be determined from the processed image, which is obtained by 206~979 1 the conventional matched filter approach. The pulse response of a strong point target can be used in order to calculate a correction function of the ideal filter according to the invention. The correction function is then convolved with the processed image, whereby the amplitude and phase errors are eliminated.
BRIEF DESCRIPTION OF THE DRAWINCrS
The invention will be explained in detail hereinafter with the aid of preferred embodiments and reference to the attached drawings, wherein:
Fig. 1 is a block diagram of a pulse compression in the time domain of a linear frequency-modulated signal, a conventional method with a matched filter being employed;
Fig. 2 is a block diagram of a pulse compression using a matched filter as in Fig. 1 for a frequency-modulated signal with phase and amplitude errors;
Fig. 3 is a block diagram of a pulse compression in the time domain using the method according to the invention for obtaining an ideal pulse response in spite of a faulty frequency-modulated input signal;
Fig. 4 shows an example of embodiment for obtaining an ideal pulse response, a pulse compression being carried out in the frequency domain when processing in the frequency domain;
Fig. 5 shows an example of embodiment for implementing the method according to the invention for generating a reference function, and 1 Fig. 6 shows a preferred embodiment for implementing the method according to the invention for generating the reference function.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
In Fig. 1 an error-free received frequency-modulated signal so(t) is illustrated, the duration of which is Te. To simplify the illustration of the signal profiles in Figs. 1 to 4 only the backscattering of a single point target is taken into account and consequently a received signal corresponds to the replica of the transmitted pulse. The signal so(t) is assumed to be complex, i.e. it contains a real and an imaginary component. The same applies to all the signals in Fig. 1 to Fig. 6.
By means of a convolution unit 1 in Fig. 1 a pulse compression of the frequency-modulated signal so(t) present at the input is carried out. For this purpose, in the time domain a convolution of the frequency-modulated input signal so(t) is carried out with a reference function ho(t) applied from outside. In accordance with the theory of the matched filter, the reference function ho(t) is determined from the conjugated complex time-inverted replica of the transmitted frequency-modulated pulse.
Since as explained above to simplify the illustration of the signal profiles only the backscattering of a single point object is taken into account, the transmitted pulse has the same form as that of the received signal so(t).
The output signal fo(t) present at the output of the convolution unit 1 has, without use of an amplitude weighting, the form of a sin(x)/x function, the geometrical resolution being the better the greater the signal bandwidth.
12 2û69979 1 In Fig. 2 a pulse compression of a frequency-modulated signal Sf(t) is illustrated in which amplitude and phase errors are present. The reference function hf(t) formed in accordance with the theory of the matched filter consists of the conjugated complex time-inverted input signal Sf(t).
After a pulse compression by a convolution unit 2, at the output thereof a pulse response ff(t) is obtained which has a poorer geometrical resolution and greater side lobes.
Although by using the reference function hf(t) the maximum signal/noise ratio for the pulse response is achieved, the form of the pulse response may deviate very greatly from the sin(x)/x function.
Instead of the reference function hf(t) in Fig. 2 the error-free reference function ho(t) may also be employed for a convolution. In this case the properties of the pulse response are greatly impaired with large phase errors and the signal/noise ratio of the pulse response is reduced. However, with large amplitude errors the use of the reference function ho(t) is advantageous because the reference function hf(t) enhances the amplitude errors in the convolution. This is due to the multiplication of the reference function hf(t) by the input signal Sf(t) taking place in the convolution which leads to the amplitude errors being squared.
On the other hand, with large phase errors the use of the reference function hf(t) is more advantageous because during the convolution the phase of the reference function hf(t) is added to the phase of the received signal sf(t).
Since the reference function hf(t) is a conjugated complex time-inverted function of the received signal sf(t)l the phase of hf(t) has a sign opposite to the phase of the input signal Sf(t). As a result of this the phase error is 35 eliminated by the convolution unit 2 in the area of the main lobe of the pulse response and consequently with large 1 phase errors and when using the reference function hf(t) the pulse response has better properties than when using the reference function ho(t).
In all cases in which phase and amplitude errors (except for a quadratic phase error in which by using the reference function hf(t) the reference error is completely eliminated) occur, the matched filter is not able to correct the amplitude and phase errors in such a manner that a sin(x)/x function is achieved.
Employing the method according to the invention, acting as an ideal filter, it is possible to obtain an sin(x)/x function independently of the phase and amplitude errors present in the signal received. The received signal Sf(t) containing phase and amplitude errors is convoluted in a convolution unit 3 with the aid of a reference function hi(t) generated by the method according to the invention, as will be described hereinafter. The pulse response fo(t) present at the output of the convolution unit 3 in Fig. 3 then has the form of a sin(x)/x function if no additional amplitude weighting is carried out to suppress side lobes.
In Fig. 4 an embodiment is shown of an apparatus for implementing a method for carrying out a pulsed compression, the latter being illustrated in the frequency domain by means of a reference function generated by the method according to the invention. This example of embodiment is particularly well suited to hardware implementation with digital components because the hardware expenditure is considerably less than in an implementation in the time domain. A received signal Sf(t) and the reference function hi(t) determined by means of the method according to the invention, as will be explained in further 35 detail hereinafter with the aid of Fig. 5 or 6, are Fourier transformed by respective FFT units 4.1 and 4.3, the 1 spectra Sf and Hi present at the output of the FFT units 4.1 and 4.3 thereby being obtained. The two spectra Sf and Hi are multiplied together in a multiplying member 4.2 and thereafter subjected to an inverse Fourier transformation (IFFT) by an IFFT unit 4.4, thereby being transformed to the time domain. The pulse response fo(t) present at the output of the IFFT unit 4.4 has the form of a sin(x)/x function as in the pulse compression in the time domain (see Fig. 3).
To enable a pulse compression to be carried out, according to the invention the reference function hi(t) must be determined. In Fig. 5, in the form of a block diagram an embodiment is illustrated for determining the reference function hi(t~ with the aid of a fast Fourier transformation (FFT). By FFT units 5.1 to 5.4 the signals Sf(t), so(t), hf(t) and ho(t) present at the inputs thereof are transformed by a Fourier transformation to a frequency domain. As mentioned at the beginning, the two signals so(t) and Sf(t) refer to the backscattering of only a single point target. The signal Sf(t) corresponds to the replica of the transmitted pulse and is measured directly on reception whilst the signal so(t), whlch can be determined from parameters such as the modulation rate and duration of the frequency modulation, contains no phase and amplitude errors and has a linear frequency modulation. The reference functions hf(t), ho(t) are determined from conjugated complex time-interval functions of the signal Sf(t) an~ so(t) respectively.
By a unit 5.7 forming the reciprocal~the reciprocal value 1/Ff of the signal Ff is formed and is multiplied in a further multiplying member 5.8 by the output signal Fo of the multiplying member 5.6 so that at the output of the multiplying member 5.8 the signal Fo/Ff is present which plays the part of a correction signal. By means of this 2~6~979 1 correction signal phase and amplitude errors can be eliminated in the pulse compression. In a further multiplying member 5.9 the correction signal Fo/Ff is multiplied by the Fourier transformed output signal Hf of the FFT unit 5.3 so that at the output of the multiplying member 5.9 a signal Hi is obtained which corresponds to the Fourier transformed reference function according to the invention. The Fourier transformed reference function Hi thus consists of a correction term (Fo/Ff) and the Fourier transformed reference function Hf of the socalled matched filter (see Fig. 2).
If a pulse compression is carried out in the frequency domain, the output signal Hi of the multiplying member 5.9 may be taken for a multiplication by the output signal Sf of the multiplying member 4.1 or 5.1. As illustrated in Fig. 4, such a multiplication is carried out by the multiplying member 4.2. If a pulse compression is to be made in the time domain as well, an inverse Fourier transformation is necessary and is carried out by an IFFT
unit 5.10 so that at the output thereof the reference function hi(t) is obtained.
A preferred embodiment for generating the reference function hi(t) of the ideal filter is shown in Fig. 6.
Here, the signal Sf(t) corresponds to the replica of the transmitted pulse and thus contains all the phase and amplitude errors which occur during transmission and reception. The signal ho(t) corresponds to the error-free reference function so(t) with a linear frequency modulation. By means of FFT units 6.1 and 6.2 provided for forming Fourier transformations, the signals Ho and Sf respectively at the outputs thereof are generated. The signal Ho is then supplied to an intensity-forming unit 6.3, the signal IHol 2 thereby being obtained.
1 The signal Sf is applied to the reciprocal-forming unit 6.4 in order to form a reciprocal value. Thereafter the signals IHol 2 and the signal 1/Ff are multiplied together in a further multiplying member 6.5, thereby then generating a Fourier transformed reference function Hi of the ideal filter. An inverse Fourier transformation can then be performed by an IFFT unit 6.6, thereby generating at the output of the IFFT unit 6.6 the reference function hi(t) of the ideal filter for pulse compression in the time domaln .
Hereinafter the embodiment according to Fig. 6 will be compared in detail with the embodiment according to Fig. 5.
In Fig. 5 the signal Hi is equal to the product of the signals Hf and Fo/Ff, Fo being the Fourier transformed pulse response of the error-free signal so(t) and the signal Ff being the Fourier transformed pulse response of the faulty modulated signal Sf(t) (replica). The spectra Fo and Ff result from the multiplication of the output signals SO and Ho of the two FFT units 5.2 and 5.4 and of the output signals Sf and Hf of the FFT units 5.3 and 5.1 respectively. This gives by applying the laws of spectral transformation (i.e. the law of conjugated complex function) and using the relationship to form the intensity value of a complex signal by conjugation:
F = So Ho - Ho* Ho ~ ol 2 where Ho* is the conjugated complex signal of the signal Ho~ This gives for the output signal Hi in Fig. 5:
H = H F~ _ H I HO ~ ~O I I HO I
1 The last term IHol 2 /Sf in the above equation corresponds to the result for the output signal Hi in Fig. 6 whilst the second term from the left, i.e. Hf.Fo/Ff in the above equation, corresponds to the result for the output signal Hi in Fig. 5. This means that with the examples of embodiment in Fig. 5 and 6 the same results are obtained as regards the generation of the signal Hi. The embodiment according to Fig. 6 is more advantageous because the generation of the signal Hi or hi(t) can be carried out with less hardware expenditure.
The concept of the ideal filter can be also used for removing the azimuth ambiguities of point targets in SAR
images. Azimuth ambiguities appear in SAR images due to the discrete sampling of the Doppler signal which is weighted by the two-way azimuth antenna diagram. Doppler frequencies higher than the pulse repetition frequency are folded into the central part of the azimuth spectrum so that aliased signals are produced. Since the aliased signals are displaced in range and azimuth directions, the reference function of the ideal filter is a two dimensional one. This reference function provides, in addition to the matched filtering for the unaliased part of the received signal, the deconvolution of the azimuth ambiguities. The suppression of the azimuth ambiguities has substantial significance in enabling the PFR constraints in the SAR system design to be relaxed and also for improving SAR image quality and interpretation.
The ideal filter created by the invention can however be used not only for pulse compression in radar technology but also in other technical fields, for example in communications technology or in time measuring technology.
In these cases the pulse compression serves to increase the time resolution or to improve the signal/noise ratio. The ideal filter created by the invention can also be employed 1 with pseudocoded amplitude or phase-modulated signals, the use thereof being found very advantageous in these cases as well because the properties of the pulse response remain unchanged.
Radar systems work by the echo principal. A transmitter emits electromagnetic waves which are partially absorbed and partially reflected by the target area. The signals received by the radar apparatus are used for locating and surveying objects or also for determining the velocity of moving targets. For this purpose the pulse method is usually employed. In this method a pulse of short duration is periodically transmitted; the backscattered signal is received and after conversion to a base band digitized. By reducing a pulse duration Te a high range resolution is obtained and by increasing the transmission peak power PO
the range is increased and the signal/noise ratio improved.
1 The pulse duration and the transmission peak power are decisive for the performance of the radar system; however, they represent contradicting requirements because a high transmission peak power cannot be produced in a short time:-To overcome these problems, pulse compression is employed.
Instead of a time-compressed pulse a time-expanded signal with frequency modulation is employed. Usually, linear frequency modulation is employed here and can be generated either with analog components or with a digital circuit having a following digital/analog (D/A) converter. When employing analog components a delay or SAW (Surface Acoustic Wave) network is used. Such a time-expanded frequency-modulated signal is denoted by the English term "chirp".
Now, with regard to the range resolution there is no limitation due to frequency modulation of a time-expanded signal because said resolution depends on the bandwidth of the frequency modulation. If the bandwidth Be of the frequency modulation is increased so that the same bandwidth (1/Te) of the time-compressed signal is achieved, after pulse compression of the time-expanded signal the same range resolution is obtained as with a pulse of short duration.
By employing the time-expanded signal the contradicting requirements, i.e. high transmission power and short pulse duration, are obviated so that a high range resolution can be achieved and at the same time a high signal/noise ratio.
On receiving backscattered radar data a pulse compression of the time-expanded signal is then performed and can be achieved likewise either with analog components (SAW) or, after A/D conversion of the signal, by means of a digital circuit. In the ideal case in which no phase and amplitude l errors occur in the transmitting and receiving operation with a linearly frequency-modulated signal, after a compression of the radar signal of a single point target a sin(x)/x function is obtained. This function is referred to as pulse response and the highest side lobe lies at 13.6 dB beneath the maximum of this function. In most cases an amplitude weighting is additionally carried out in the pulse compression so that the side lobes of the pulse response are suppressed to a greater extent. For a Hamming weighting a suppression of the highest side lobe of 43 dB
is obtained. This impairs the geometrical resolution by 46 % because the effective bandwidth in the pulse compression is reduced by the insertion of the amplitude weighting.
In a real case however phase and amplitude errors are present in a received signal. These errors can occur in the generation of the phase modulation of the time-expanded signallin the transmitting and receiving unit of the radar system, in the transmission and receiving of the electromagnetic waves by the antenna and in the A/D
conversion of received backscattered radar signals.
As a result, a pulse response is obtained which does not correspond to the ideal case. This causes a deterioration of the properties of the pulse response and this can greatly impair the quality of the radar image. The properties of the pulse response are described by a geometrical resolution, by the side lobe ratio and by the amplitude loss.
Pulse compression can be employed also in a radar with synthetic aperture (SAR) both in the range direction as in the azimuth direction (flight direction). An SAR system comprises a carrier, for example an aircraft, a helicopter, a satellite, and the like, which moves with a constant 1 velocity, an antenna with a viewing direction transversely of the movement direction, i.e. to the right or left, and a coherent radar system which transmits electromagnetic pulses, receives the backscattered radar echoes and quadrature demodulates them in the I and Q channel and thereafter digitizes them. For generating a two-dimensional image a pulse compression is carried out in the range and azimuth direction. With conventional pulse radar with pulse compression as has been described above, the range resolution is governed by the bandwidth of the transmitted pulse.
The azimuth resolution of a radar can be very much improved by the synthetic aperture method compared with a real aperture method. With an SAR system an antenna with wide directive pattern in the azimuth direction is employed and a coherent imaging carried out. A specific target is illuminated by the antenna during several pulses and each echo is received coherently. A long synthetic antenna can be formed thereby so that the phase history in the azimuth direction caused by the range variation from the carrier to the target during the illumination time can be corrected.
With this artificial increase of the antenna length a narrow bundling in the azimuth direction and a high azimuth resolution are achieved. The phase history in the azimuth direction leads to a frequency modulation, the bandwidth of which is referred to as Doppler bandwidth.
The data processing in the azimuth direction for a high geometrical resolution then consists of a pulse compression of the received azimuth signal because the latter also has a time-expanded frequency-modulated profile. Since the target illumination time in the azimuth direction increases linearly with the range, the length of the synthetic aperture becomes greater with the range and the 20i69979 l corresponding synthetic bundling narrower; as a result, the azimuth resolution becomes independent of the range.
Hereinafter various imaging geometries of an SAR system in which no linear frequency modulation occurs in the azimuth direction will be described. The frequency modulation in an SAR system in the azimuth direction can deviate from the linear case if the aperture angle ~a of the antenna in the azimuth direction is greater than about 20. For an antenna aperture angle ~a of 180 for example a cosinusoidal frequency profile is obtained and the angular variation of the cosine function extends from 90 to -90.
In this case, after the pulse compression instead of a sin(x)/x function a Bessel function of the first type of zero order is obtained, the side lobe r~tio being reduced to 7.8 dB. This impairs the image quality and that is undesirable.
With a large squint angle of the SAR carrier or in the case where the antenna alignment deviates more than 20 from the direction orthogonal to the flight direction, a linear frequency profile is also not obtained.
The hitherto most frequently employed method for pulse compression is the method of the socalled optimum filter ("matched filter"). Here, a convolution of the received signal is carried out with a conjugated complex time-inverted replica of the transmitted modulated pulse (cf.
for example Klauder, J.R. et al: "The Theory and Design of Chirp Radars". The Bell System Technical Journal, July 1960, p. 745 to 808, or Skolnik, M.I.: Radar Handbook, McGraw-Hill Inc., 1970, p.20-1 to 20-37, or Wehner, D.R.:
High Resolution Radar, Artech House, 1987, p. 65-69 and Davenport, W.B. and Root, W.L.: An Introduction to the Theory of Random Signals and Noise, McGraw-Hill Inc., 1958, p.244-247). This function calculated from the replica is 1 referred to as reference function. In the pulse compression in the azimuth direction of an SAR system the replica can be calculated from the imaging geometry. The replica contains all the phase and amplitude errors which can occur through the sending and transmission in the hardware. Furthermore, the replica also contains the deviation from the linear frequency modulation which can occur through the imaging geometry in an SAR system.
If phase and amplitude errors are present and if they are ignored in the pulse compression, the properties of the pulse response are impaired. This impairment can be reduced if said errors are taken into account when determining the reference function, i.e. if the reference function is generated from the replica of the transmitted pulse. The reference function according to the method of the matched filter consists of the conjugated complex time-inverted replica of the faulty frequency-modulated signal.
For a pulse compression in the azimuth direction with a nonlinear frequency profile the reference function according to the method of the matched filter also has a nonlinear phase profile and the pulse response may have very high side lobes which cannot be efficiently reduced by employing an amplitude weighting.
Instead of a convolution, frequently a fast Fourier transformed (FFT) algorithm is used for pulse compression (cf. US 4,379,295 - Abstract and US 4,912,472, col. 1, line 50 to col. 2, line 60). This algorithm is based on the fact that a convolution in the time domain corresponds to a multiplication in the frequency domain.
The received signal and the reference function are first Fourier transformed, then multiplied with each other and finally transformed back to the time domain by the inverse 1 Fourier transformation (IFFT). This processing can be carried out substantially faster than the convolution in the time domain and is therefore usually employed in the digital pulse compression of frequency-modulated signals.
By using pulse compression with a socalled matched filter, although the properties and the signal/noise ratio of the pulse response are improved when the phase and amplitude errors in the received signals are known it is not possible with this method to effect a correction of the phase and amplitude errors in such a manner than an ideal pulse response is achieved, i.e. a sin(x)/x function.
It is only on variation of the modulation rate of a signal with linear frequency modulation, corresponding to a square phase error, that the ideal pulse response is obtained with the matched filter and a reference function generated from the replica. All other cases of phase and amplitude errors lead to pulse responses which do not correspond to a sin(x)/x function.
SUMMARY OF THE INVENTION
It is therefore the object of the invention to optimize a method for generating a reference function for a pulse compression with frequency, phase and/or amplitude-modulated signals in such a manner that all phase and amplitude errors in pulse compression are eliminated and consequently, in spite of the phase and amplitude errors present in the received signal an ideal pulse is achieved, this also being independent of the strength and form of said errors.
The invention therefore proposes in a method of generating a reference function for a pulse compression of modulated signals the improvement in which an error-free frequency-1 modulated signal (so(t)), a signal (Sf(t)) containing phaseand amplitude errors, a reference signal (ho(t)) corresponding to a conjugated complex time-inverted function of the error-free signal (s(t)) and a reference signal (hf(t)) corresponding to the conjugated complex time-inverted input signal (Sf(t)) are each Fourier transformed in respective FFT units, thereby generating signals (SO' Sf, Ho and Hf);
output signals (Sf; Hf) from two of the FFT units are respectively multiplied by each other in a first multiplying member and output signals (SO' Ho) from the two other FFT units in a second multiplying member;
the reciprocal (1/Ff) of the output signal (Ff) of the first multiplying member is formed in a unit forming a reciprocal value and is multiplied in a third multiplying member by the output signal (Fo) of the second multiplying member;
the output signal (Fo/Ff) of the third multiplying member is multiplied by the signal (Hf), i.e. the fast Fourier transformation of the signal (hf(t)) at the output of the FFT unit in a fourth multiplying member and the output signal (Hi) of the fourth multiplying member is subjected in a following IFFT unit to an inverse Fourier transformation to generate the reference function (hi(t)) in the time domain.
Thus, when employing a reference function generated in accordance with the aforementioned method in a method for carrying out a pulse compression a pulse response is obtained which has a form and properties which remain independent of the phase and amplitude errors present in the signal received. The method according to the invention 1 for generating a reference function for a pulse compression of frequency, phase and/or amplitude-modulated signals can be referred to as ideal filter as regards its effect.
Due to the method according to the invention, the reference function determined from the replica of the faulty received signal or from the imaging geometry of an SAR system contains not only the adaptation to the signal as in the usual matching filter but also an additional term which eliminates completely the phase and amplitude errors of the received signal. Thus, according to the invention an ideal pulse response is always achieved, the geometrical resolution of which depends only on the bandwidth of the frequency-modulated signal and the form and properties of which are independent of the nature of the frequency modulation and of the errors present in the received signal.
By inserting an amplitude weighting into the reference function generated according to the method of the invention the side lobes of the sin(x)/x function can also be reduced. The method according to the invention acting as ideal filter is of great significance for many technical fields in which a pulse compression is employed. It is thereby possible to make a hardware specification regarding phase and amplitude errors less stringent without impairing the properties of the pulse response. Once the reference function according to the invention has been determined the pulse compression can be carried out as in usual methods and consequently the ideal filter operating in accordance with the method of the invention can be implemented without great hardware expenditure.
In the case that the replica of the transmitted signal is not available, the phase and amplitude errors can be determined from the processed image, which is obtained by 206~979 1 the conventional matched filter approach. The pulse response of a strong point target can be used in order to calculate a correction function of the ideal filter according to the invention. The correction function is then convolved with the processed image, whereby the amplitude and phase errors are eliminated.
BRIEF DESCRIPTION OF THE DRAWINCrS
The invention will be explained in detail hereinafter with the aid of preferred embodiments and reference to the attached drawings, wherein:
Fig. 1 is a block diagram of a pulse compression in the time domain of a linear frequency-modulated signal, a conventional method with a matched filter being employed;
Fig. 2 is a block diagram of a pulse compression using a matched filter as in Fig. 1 for a frequency-modulated signal with phase and amplitude errors;
Fig. 3 is a block diagram of a pulse compression in the time domain using the method according to the invention for obtaining an ideal pulse response in spite of a faulty frequency-modulated input signal;
Fig. 4 shows an example of embodiment for obtaining an ideal pulse response, a pulse compression being carried out in the frequency domain when processing in the frequency domain;
Fig. 5 shows an example of embodiment for implementing the method according to the invention for generating a reference function, and 1 Fig. 6 shows a preferred embodiment for implementing the method according to the invention for generating the reference function.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
In Fig. 1 an error-free received frequency-modulated signal so(t) is illustrated, the duration of which is Te. To simplify the illustration of the signal profiles in Figs. 1 to 4 only the backscattering of a single point target is taken into account and consequently a received signal corresponds to the replica of the transmitted pulse. The signal so(t) is assumed to be complex, i.e. it contains a real and an imaginary component. The same applies to all the signals in Fig. 1 to Fig. 6.
By means of a convolution unit 1 in Fig. 1 a pulse compression of the frequency-modulated signal so(t) present at the input is carried out. For this purpose, in the time domain a convolution of the frequency-modulated input signal so(t) is carried out with a reference function ho(t) applied from outside. In accordance with the theory of the matched filter, the reference function ho(t) is determined from the conjugated complex time-inverted replica of the transmitted frequency-modulated pulse.
Since as explained above to simplify the illustration of the signal profiles only the backscattering of a single point object is taken into account, the transmitted pulse has the same form as that of the received signal so(t).
The output signal fo(t) present at the output of the convolution unit 1 has, without use of an amplitude weighting, the form of a sin(x)/x function, the geometrical resolution being the better the greater the signal bandwidth.
12 2û69979 1 In Fig. 2 a pulse compression of a frequency-modulated signal Sf(t) is illustrated in which amplitude and phase errors are present. The reference function hf(t) formed in accordance with the theory of the matched filter consists of the conjugated complex time-inverted input signal Sf(t).
After a pulse compression by a convolution unit 2, at the output thereof a pulse response ff(t) is obtained which has a poorer geometrical resolution and greater side lobes.
Although by using the reference function hf(t) the maximum signal/noise ratio for the pulse response is achieved, the form of the pulse response may deviate very greatly from the sin(x)/x function.
Instead of the reference function hf(t) in Fig. 2 the error-free reference function ho(t) may also be employed for a convolution. In this case the properties of the pulse response are greatly impaired with large phase errors and the signal/noise ratio of the pulse response is reduced. However, with large amplitude errors the use of the reference function ho(t) is advantageous because the reference function hf(t) enhances the amplitude errors in the convolution. This is due to the multiplication of the reference function hf(t) by the input signal Sf(t) taking place in the convolution which leads to the amplitude errors being squared.
On the other hand, with large phase errors the use of the reference function hf(t) is more advantageous because during the convolution the phase of the reference function hf(t) is added to the phase of the received signal sf(t).
Since the reference function hf(t) is a conjugated complex time-inverted function of the received signal sf(t)l the phase of hf(t) has a sign opposite to the phase of the input signal Sf(t). As a result of this the phase error is 35 eliminated by the convolution unit 2 in the area of the main lobe of the pulse response and consequently with large 1 phase errors and when using the reference function hf(t) the pulse response has better properties than when using the reference function ho(t).
In all cases in which phase and amplitude errors (except for a quadratic phase error in which by using the reference function hf(t) the reference error is completely eliminated) occur, the matched filter is not able to correct the amplitude and phase errors in such a manner that a sin(x)/x function is achieved.
Employing the method according to the invention, acting as an ideal filter, it is possible to obtain an sin(x)/x function independently of the phase and amplitude errors present in the signal received. The received signal Sf(t) containing phase and amplitude errors is convoluted in a convolution unit 3 with the aid of a reference function hi(t) generated by the method according to the invention, as will be described hereinafter. The pulse response fo(t) present at the output of the convolution unit 3 in Fig. 3 then has the form of a sin(x)/x function if no additional amplitude weighting is carried out to suppress side lobes.
In Fig. 4 an embodiment is shown of an apparatus for implementing a method for carrying out a pulsed compression, the latter being illustrated in the frequency domain by means of a reference function generated by the method according to the invention. This example of embodiment is particularly well suited to hardware implementation with digital components because the hardware expenditure is considerably less than in an implementation in the time domain. A received signal Sf(t) and the reference function hi(t) determined by means of the method according to the invention, as will be explained in further 35 detail hereinafter with the aid of Fig. 5 or 6, are Fourier transformed by respective FFT units 4.1 and 4.3, the 1 spectra Sf and Hi present at the output of the FFT units 4.1 and 4.3 thereby being obtained. The two spectra Sf and Hi are multiplied together in a multiplying member 4.2 and thereafter subjected to an inverse Fourier transformation (IFFT) by an IFFT unit 4.4, thereby being transformed to the time domain. The pulse response fo(t) present at the output of the IFFT unit 4.4 has the form of a sin(x)/x function as in the pulse compression in the time domain (see Fig. 3).
To enable a pulse compression to be carried out, according to the invention the reference function hi(t) must be determined. In Fig. 5, in the form of a block diagram an embodiment is illustrated for determining the reference function hi(t~ with the aid of a fast Fourier transformation (FFT). By FFT units 5.1 to 5.4 the signals Sf(t), so(t), hf(t) and ho(t) present at the inputs thereof are transformed by a Fourier transformation to a frequency domain. As mentioned at the beginning, the two signals so(t) and Sf(t) refer to the backscattering of only a single point target. The signal Sf(t) corresponds to the replica of the transmitted pulse and is measured directly on reception whilst the signal so(t), whlch can be determined from parameters such as the modulation rate and duration of the frequency modulation, contains no phase and amplitude errors and has a linear frequency modulation. The reference functions hf(t), ho(t) are determined from conjugated complex time-interval functions of the signal Sf(t) an~ so(t) respectively.
By a unit 5.7 forming the reciprocal~the reciprocal value 1/Ff of the signal Ff is formed and is multiplied in a further multiplying member 5.8 by the output signal Fo of the multiplying member 5.6 so that at the output of the multiplying member 5.8 the signal Fo/Ff is present which plays the part of a correction signal. By means of this 2~6~979 1 correction signal phase and amplitude errors can be eliminated in the pulse compression. In a further multiplying member 5.9 the correction signal Fo/Ff is multiplied by the Fourier transformed output signal Hf of the FFT unit 5.3 so that at the output of the multiplying member 5.9 a signal Hi is obtained which corresponds to the Fourier transformed reference function according to the invention. The Fourier transformed reference function Hi thus consists of a correction term (Fo/Ff) and the Fourier transformed reference function Hf of the socalled matched filter (see Fig. 2).
If a pulse compression is carried out in the frequency domain, the output signal Hi of the multiplying member 5.9 may be taken for a multiplication by the output signal Sf of the multiplying member 4.1 or 5.1. As illustrated in Fig. 4, such a multiplication is carried out by the multiplying member 4.2. If a pulse compression is to be made in the time domain as well, an inverse Fourier transformation is necessary and is carried out by an IFFT
unit 5.10 so that at the output thereof the reference function hi(t) is obtained.
A preferred embodiment for generating the reference function hi(t) of the ideal filter is shown in Fig. 6.
Here, the signal Sf(t) corresponds to the replica of the transmitted pulse and thus contains all the phase and amplitude errors which occur during transmission and reception. The signal ho(t) corresponds to the error-free reference function so(t) with a linear frequency modulation. By means of FFT units 6.1 and 6.2 provided for forming Fourier transformations, the signals Ho and Sf respectively at the outputs thereof are generated. The signal Ho is then supplied to an intensity-forming unit 6.3, the signal IHol 2 thereby being obtained.
1 The signal Sf is applied to the reciprocal-forming unit 6.4 in order to form a reciprocal value. Thereafter the signals IHol 2 and the signal 1/Ff are multiplied together in a further multiplying member 6.5, thereby then generating a Fourier transformed reference function Hi of the ideal filter. An inverse Fourier transformation can then be performed by an IFFT unit 6.6, thereby generating at the output of the IFFT unit 6.6 the reference function hi(t) of the ideal filter for pulse compression in the time domaln .
Hereinafter the embodiment according to Fig. 6 will be compared in detail with the embodiment according to Fig. 5.
In Fig. 5 the signal Hi is equal to the product of the signals Hf and Fo/Ff, Fo being the Fourier transformed pulse response of the error-free signal so(t) and the signal Ff being the Fourier transformed pulse response of the faulty modulated signal Sf(t) (replica). The spectra Fo and Ff result from the multiplication of the output signals SO and Ho of the two FFT units 5.2 and 5.4 and of the output signals Sf and Hf of the FFT units 5.3 and 5.1 respectively. This gives by applying the laws of spectral transformation (i.e. the law of conjugated complex function) and using the relationship to form the intensity value of a complex signal by conjugation:
F = So Ho - Ho* Ho ~ ol 2 where Ho* is the conjugated complex signal of the signal Ho~ This gives for the output signal Hi in Fig. 5:
H = H F~ _ H I HO ~ ~O I I HO I
1 The last term IHol 2 /Sf in the above equation corresponds to the result for the output signal Hi in Fig. 6 whilst the second term from the left, i.e. Hf.Fo/Ff in the above equation, corresponds to the result for the output signal Hi in Fig. 5. This means that with the examples of embodiment in Fig. 5 and 6 the same results are obtained as regards the generation of the signal Hi. The embodiment according to Fig. 6 is more advantageous because the generation of the signal Hi or hi(t) can be carried out with less hardware expenditure.
The concept of the ideal filter can be also used for removing the azimuth ambiguities of point targets in SAR
images. Azimuth ambiguities appear in SAR images due to the discrete sampling of the Doppler signal which is weighted by the two-way azimuth antenna diagram. Doppler frequencies higher than the pulse repetition frequency are folded into the central part of the azimuth spectrum so that aliased signals are produced. Since the aliased signals are displaced in range and azimuth directions, the reference function of the ideal filter is a two dimensional one. This reference function provides, in addition to the matched filtering for the unaliased part of the received signal, the deconvolution of the azimuth ambiguities. The suppression of the azimuth ambiguities has substantial significance in enabling the PFR constraints in the SAR system design to be relaxed and also for improving SAR image quality and interpretation.
The ideal filter created by the invention can however be used not only for pulse compression in radar technology but also in other technical fields, for example in communications technology or in time measuring technology.
In these cases the pulse compression serves to increase the time resolution or to improve the signal/noise ratio. The ideal filter created by the invention can also be employed 1 with pseudocoded amplitude or phase-modulated signals, the use thereof being found very advantageous in these cases as well because the properties of the pulse response remain unchanged.
Claims (4)
1. A method of generating a reference function for pulse compression of frequency, phase and/or amplitude-modulated signals, wherein an error-free frequency-modulated signal (so(t)), a signal (sf(t)) containing phase and amplitude errors, a reference signal (ho(t)) corresponding to a conjugated complex time-inverted function of an error-free signal (s(t)) and a reference signal (hf(t)) corresponding to the conjugated complex time-inverted input signal (sf(t)) are each Fourier transformed in respective FFT units, thereby generating signals (So, Sf, Ho and Hf);
output signals (Sf; Hf) from two of the FFT units are respectively multiplied by each other in a first multiplying member to produce an output signal (Ff) and output signals (So, Ho) from the two other FFT units are respectively multiplied by each other in a second multiplying member to produce an output signal (Fo);
the reciprocal (1/Ff) of the output signal (Ff) of the first multiplying member is formed in a unit forming a reciprocal value and is multiplied in a third multiplying member by an output signal (Fo) of the second multiplying member to produce an output signal (Fo/Ff);
the output signal (Fo/Ff) of the third multiplying member is multiplied by the signal (Hf), i.e. the fast Fourier transformation of the signal (hf(t)) at the output of the FFT unit in a fourth multiplying member to produce an output signal (Hi) and the output signal (Hi) of the fourth multiplying member is subjected in a following IFFT unit to an inverse Fourier transformation to generate the reference function (hi(t)) in the time domain.
output signals (Sf; Hf) from two of the FFT units are respectively multiplied by each other in a first multiplying member to produce an output signal (Ff) and output signals (So, Ho) from the two other FFT units are respectively multiplied by each other in a second multiplying member to produce an output signal (Fo);
the reciprocal (1/Ff) of the output signal (Ff) of the first multiplying member is formed in a unit forming a reciprocal value and is multiplied in a third multiplying member by an output signal (Fo) of the second multiplying member to produce an output signal (Fo/Ff);
the output signal (Fo/Ff) of the third multiplying member is multiplied by the signal (Hf), i.e. the fast Fourier transformation of the signal (hf(t)) at the output of the FFT unit in a fourth multiplying member to produce an output signal (Hi) and the output signal (Hi) of the fourth multiplying member is subjected in a following IFFT unit to an inverse Fourier transformation to generate the reference function (hi(t)) in the time domain.
2. A method of generating a reference function for pulse compression of frequency, phase and/or amplitude-modulated signals, wherein a reference signal (ho(t)) corresponding to a conjugated complex time-inverted function of an error-free frequency-modulated signal (so(t)) and a signal (sf(t)) containing phase and amplitude errors are generated in two respective following FFT units by a Fourier transformation in the form of signals (Ho, Sf respectively) present at the outputs thereof and corresponding to the Fourier transformation of the signals (ho(t) and Sf(t)) respectively;
a signal (?Ho?2) is formed from the output signal (Ho) by means of an intensity-forming unit, a signal (1/Sf) is formed from the output signal (Sf) of the other FFT unit by a reciprocal-forming unit, and these two signals (?Ho?2, 1/Ff) are multiplied together in a following multiplying member, and the output signal (Hi) of the multiplying member is subjected in an IFFT unit to an inverse transformation for generating the reference function (hi(t)) in the time domain.
a signal (?Ho?2) is formed from the output signal (Ho) by means of an intensity-forming unit, a signal (1/Sf) is formed from the output signal (Sf) of the other FFT unit by a reciprocal-forming unit, and these two signals (?Ho?2, 1/Ff) are multiplied together in a following multiplying member, and the output signal (Hi) of the multiplying member is subjected in an IFFT unit to an inverse transformation for generating the reference function (hi(t)) in the time domain.
3. A method of performing a pulse compression in the time domain employing a reference function (hi(t)) generated by the method of claim 1 or 2, wherein a pulse response (fo(t)) to a point target is generated in a convolution unit corresponding to the function (sin(x)/x) from a signal (sf(t)) containing phase and amplitude errors and from the generated reference function (hi(t)) and no amplitude weighting is additionally carried out to suppress side lobes.
4. A method of performing a pulse compression in the frequency domain using an FIT algorithm by means of a reference function (hi(t)) generated in accordance with the method of claim 1 or 2, wherein a signal (sf(t)) containing phase and amplitude errors and the reference function (hi(t)) are Fourier transformed in respective FFT units, the output signals (Sf and Ho) of the two FFT units multiplied together in a multiplying member and the output signal (Sf . Hi) of the multiplying member inversely Fourier transformed and transformed to the time domain, thereby forming the pulse response (fo(t)) to a point target corresponding to the function (sin(x)/x), and no additional amplitude weighting to suppress side lobes is performed.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| DE4117849A DE4117849C2 (en) | 1991-05-31 | 1991-05-31 | Method for generating a reference function for pulse compression of frequency, phase and / or amplitude modulated signals |
| DEP4117849.1 | 1991-05-31 |
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| Publication Number | Publication Date |
|---|---|
| CA2069979A1 CA2069979A1 (en) | 1992-12-01 |
| CA2069979C true CA2069979C (en) | 1996-10-01 |
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| CA002069979A Expired - Fee Related CA2069979C (en) | 1991-05-31 | 1992-05-29 | Method of generating a reference function for a pulse compression of frequency; phase and/or amplitude-modulated signals |
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| CA (1) | CA2069979C (en) |
| DE (1) | DE4117849C2 (en) |
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| DE4240225C2 (en) * | 1991-05-31 | 1995-09-07 | Deutsche Forsch Luft Raumfahrt | Method for generating a correction function for eliminating phase and amplitude errors of a compressed signal |
| US7245250B1 (en) * | 2005-08-16 | 2007-07-17 | Itt Manufacturing Enterprises, Inc. | Synthetic aperture radar image compression |
| CN204495995U (en) | 2011-10-26 | 2015-07-22 | 菲力尔系统公司 | Broadband sonar transmitter, broadband sonar and sonar |
| WO2013063531A2 (en) | 2011-10-26 | 2013-05-02 | Flir Systems, Inc. | Wideband sonar receiver and sonar signal processing algorithms |
| US10444354B2 (en) | 2011-10-26 | 2019-10-15 | Flir Systems, Inc. | Sonar data enhancement systems and methods |
| CN108267723A (en) * | 2017-01-04 | 2018-07-10 | 南京智慧魔方电子科技有限公司 | The offline online amplitude and phase error correction method of continental rise short distance K-band radar |
| US11415663B2 (en) * | 2017-06-08 | 2022-08-16 | Mitsubishi Electric Corporation | Radar device |
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| US4379295A (en) * | 1981-02-03 | 1983-04-05 | The United States Of America As Represented By The Secretary Of The Navy | Low sidelobe pulse compressor |
| NL8702342A (en) * | 1987-10-01 | 1989-05-01 | Hollandse Signaalapparaten Bv | FM-CW RADAR DEVICE. |
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| CA2069979A1 (en) | 1992-12-01 |
| IT1259396B (en) | 1996-03-13 |
| DE4117849C2 (en) | 1994-05-05 |
| ITTO920465A0 (en) | 1992-05-29 |
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