WO2007133083A1

WO2007133083A1 - Frequency modulated continuous wave radar and synthetic aperture radar

Info

Publication number: WO2007133083A1
Application number: PCT/NL2007/050229
Authority: WO
Inventors: Adriano Meta
Original assignee: Nederlandse Organisatie Voor Toegepast-Natuurwetenschappelijk Onderzoek Tno; Eonic B.V.
Priority date: 2006-05-16
Filing date: 2007-05-16
Publication date: 2007-11-22

Abstract

In a frequency modulated continuous wave radar received reflections are mixed down with the transmitted frequency modulated signal. A series of mixed down signals is obtained for successive frequency sweeps, said series defining a first time direction along each mixed down signal and a second time direction from one mixed down signal to another at corresponding time points along the first time direction. A phase correction is applied to the mixed series of mixed down signals, the phase correction for a first time value in the first time direction corresponding to the deviation at a scaled time value obtained by scaling the time value dependent on a frequency in the second time direction. A frequency dependent time scaling factor value is used that reduces smearing effect of a deviation from linear frequency modulation.

Description

Title: Frequency modulated continuous wave radar and synthetic aperture radar

The invention relates to a frequency modulated continuous wave (FMCW) radar and to a synthetic aperture radar (SAR) wherein such an FMCW is applied.

Frequency modulated continuous wave (FMCW) radar and synthetic aperture radar (SAR) are both techniques that increase resolution of radar signals in one dimension. An FMCW radar makes use of a frequency modulated signal, so that distance differences of reflecting targets are resolved into frequency differences in the reflected signal. SAR combines phase information from different reflections obtained after moving the antenna to different positions relative to the targets to simulate the effect of an antenna with a large extent along the line of flight. FMCW and SAR can be combined to realize high resolution in two-dimensions, FMCW providing high resolution for targets at different distances and SAR providing high resolution for targets at different positions along the line of flight.

Unfortunately the resolution of such a combined technique can deteriorate as the result of non-linearity of the frequency modulation of the FMCW signal. In the ideal linear FMCW the change of frequency of the transmitted signal during the time period needed for a signal to travel from the antenna to a reflecting target and back does not depend on time. As a result ideally at any time there is a constant frequency difference between the received reflection from a target and the transmitted signal at the time of reception of the reflection. Non-linearity of the frequency modulation has the effect of smearing this frequency difference, i.e. causing each target to produce mixed down signals of different frequencies, at the cost of resolution.

This smearing problem is known for FMCW per se and various solutions have been proposed in this context. WO2004/021042 and US patent application No 2005/0001761 describe examples of such corrections. US patent application No 2005/0001761, for example, describes prior art methods wherein the reflections are mixed with a signal obtained from a delay line to obtain a beat signal. US 2005/0001761 itself describes a method wherein a Taylor series expansion of the non-linearity is estimated using an iterative computation, wherein the reflected signal is also corrected iteratively.

WO2004/021042 describes a method wherein an undisclosed correction for non- linearity is applied to the result of residual video phase correction, which is conventionally used to remove a distance dependent effect of modulation rate on the phase of the reflections. Unfortunately, the smearing effect of non-linearity is more complicated when the antenna is moved relative to the targets, as in the case of the combination of SAR and FMCW. Therefore, the effects of non-linearity can be removed from the reflected signal only if the correction is the same for all targets that contribute to a reflected signal. But the movement of the antenna means that the time delay between transmission of the signal and reception of a reflection depends on time in different ways for objects at different positions. Thus, the way in which the non-linearity affects the signal is also different for objects at different positions. As a result no common correction is available for all targets. The known correction techniques do not result in complete removal of the effect of non-linearity from a mix of reflections of different targets.

Among others, it is an object to provide for a SAR system that uses FMCW signals, wherein the effect of non-linearity of frequency modulation can be eliminated.

According to one aspect a method according to claim 1 is provided. Herein a series of mixed down signals for successive frequency sweeps is used. The series define a first time direction along each mixed down signal and a second time direction from one mixed down signal to another at corresponding time points along the first time direction. A frequency modulation with a (typically unintentional) deviation from linear frequency modulation is used. A phase correction is applied to the series of mixed down signals. The phase correction for a first time value in the first time direction corresponds to the deviation at a scaled time value. The scaled time value is obtained by scaling the time value dependent on a frequency in the second time direction, using a scaling factor value that reduces a smearing effect of a deviation from linear frequency modulation, compared to correction without time scaling. It has been found that this makes it possible to reduce smearing for all targets together.

Approximately optimal phase correction is obtained when the scaled time value substantially equals said first time value minus said first time value times a ratio of the frequency in the second time direction divided by a transmission frequency of the frequency modulated signal. Preferably the transmission frequency of the transmitted signal at said first time value is used in the division. However, the smearing effect may already be reduced even if the time-scaling is not performed exactly in this way. Different time scalings may be tried and those that reduce smearing can be used.

In an embodiment the phase correction is applied by computing a Fourier transform of a further signal defined by said series the mixed down signals at the first time value as a function of the time in the second time direction, and multiplying the Fourier transform by a phase factor with a phase defined by the deviation at the scaled time value. In an alternative embodiment a corresponding convolution of the further signal may be used to apply the phase correction, but this may require more computational resources. In an embodiment the application of the phase correction is preceded by a preliminary phase factor defined by the deviation for at first time value to the series of mixed down signals at the first time value and applying a residual video phase correction to each of the series of mixed down signals, obtained by applying the preliminary phase factor. Thus further effects of non-linearity are removed. In an embodiment the deviation is determined from a result of mixing the transmitted signal with a time-delayed version of the transmitted signal. Thus a local calibration of the deviation is provided. In a further embodiment the deviation for respective different second time values in the second time direction is determined, and different corrections are applied corresponding to said deviation for different second time values. Thus time dependent drift of the deviation can be corrected for.

In an embodiment the method is implemented in a processing circuit of a radar system. For example by programming a programmable processor to perform steps of the method. In a further embodiment the radar system comprises a delay line to determine the deviation.

These and other targets and advantageous aspects will become apparent from a description of exemplary embodiments, using the following figures.

Figure 1 shows a radar system

Figure 2 illustrates a line of movement

Figure 3 shows a flow-chart of signal processing

Figure 4 shows a flow-chart of further signal processing Figure 5 shows a signal flow

Figure 1 shows a radar system comprising a signal source 10, a directional coupler 12, an antenna 14, a mixer 16, a calibration circuit 17 and a processing circuit 18. Signal source 10 is coupled to antenna 14 via directional coupler 12. Antenna 14 is coupled to a first input of mixer 16 via directional coupler 12. Signal source 10 is coupled to a second input of mixer 16 via directional coupler 12. Processing circuit 18 is coupled to signal source 10 and mixer 16.

Calibration circuit 17 comprises a delay line 170 and a further mixer 172. Signal source 10 is coupled to inputs of further mixer 172 via delay line 170 and directly respectively. An output of further mixer 172 is coupled to processing circuit 18.

In operation signal source 10 generates a frequency-modulated signal that contains successive frequency sweeps. Antenna 14 transmits the signal and receives back reflections. The reflection signal that results from the reflections is supplied to mixer 16, where the reflection is mixed with the frequency-modulated signal. The resulting low frequency beat signal is supplied to processing circuit 18.

The antenna is move along a line of movement during transmission and reception of signals. Figure 2 illustrates a line of movement 20 of the antenna 14. Antenna 14 transmits a beam 22 at an angle to line of movement 20. Targets lie substantially on a surface 26. By way of example a vertically directed beam is shown, but other angles may be used. Reflections occur from a target range 24 on surface 26. The mathematical background of operation can be explained in terms of the phase of the signals. As is well known in a constant frequency signal the phase increases proportional to time. When linear frequency modulation is used part of the phase increase is quadratic. In this case the transmitted signal at a time t has a phase proportional to

FO*t + A*t²/2

Herein FO is a base frequency and A expresses the modulation rate, i.e. rate of change of the frequency. The received signal at the antenna is a combination of contributions of targets at different distances (as used herein "target" refers to a hypothetical reflecting surface part of infinitesimal, but reflecting size, so that extensive physical objects like buildings may be said to be made up of a collection of reflecting "targets" as the term is used herein). The contribution of the reflection from a target at a certain distance has a phase corresponding to the phase of the transmitted signal at a time t'=t-dt, wherein dt is the travel time needed to travel from the radar to the target and back and is proportional to the distance. (In addition the phase may depend on a phase shift PO due to reflection by the target, but this does not affect frequency). When the target and the radar move relative to one another, dt itself is time dependent. As a result the phase of the contribution of reflection from the target to the beat signal in the reflected signal at time t, is proportional to

P0+F0*dt-A*dt²/2 + A*t*dt

In cases wherein the time dependence of dt can be neglected (such as stationary FMCW without SAR) the dependence of this phase on time t represents a reflection with constant beat frequency A*dt. In general the reflected signal is a combination of reflections from different targets at different distances, each with a phase determined by its own dt.

The amplitude of the Fourier transform of this combination as a function of frequency f represents the strength of different reflections as a function of distance. Thus in the case of a stationary antenna this provides high resolution for targets at different distances to the antenna, but of course it does not resolve targets at the same distance (e.g. in a circle on the ground in the case of an antenna that points vertically downward).

When SAR is used, the antenna is moved, and as a result dt depends on time and position of the target. The position dependence can be expressed in terms of To, the time delay at the point of minimum distance from the target to the line of flight (i.e. corresponding to the distance between the target and a point on the line of flight where the line of flight crosses a virtual plane through the target that is perpendicular to the line of flight). The delay dt depends on time t and To as a function of the difference of t and To. When a constant frequency is used (SAR without FMCW) each individual target contributes a basic time dependent response, multiplied by the reflection factor of the target and shifted in time according to the To of the target. The reflected signal is a sum of such contributions. After deconvoluting the basic time dependent response the reflected signal as a function of time represents the reflection factor of the targets as a function of To of the targets. In the combination of SAR and FMCW, TMCW is used to resolve objects at different distance to the antenna and SAR is used to resolve targets that have the same distance to the antenna. The frequency of the transmitted signal is swept in a series of successive sweeps while the antenna moves along the line of flight. In each sweep the reflected signal is received back and mixed with the transmitted signal. This results in a signal S(t, T) from mixer 16 that depends on the position of the antenna during the sweep, represented by a time T at a predetermine point relative to the start of the sweep and the time t difference between T and the time of receiving the reflection. In a very rough approximation, when linear frequency modulation is used, the dependence on t for a target during a sweep corresponds to a constant beat frequency within a sweep that depends on the To and T. By resolving different frequencies reflections from targets at different distances can be resolved and after deconvolution reflections from targets at different positions along the line of flight can be resolved as a function of time T. In combination this signal S(t, T) reflection strength as a function of target position can be resolved. Methods of doing this, assuming perfect linear frequency modulation, are known per se.

A problem occurs when the frequency modulation deviates from perfectly linear modulation. This effect can be described by adding a deviation term E(t) to the phase of the transmitted signal, which is now proportional to

FO*t + A*t²/2 +E(t)

As a result in the beat signal the phase of the contribution of the reflection from a target and the transmitted signal at the time of receiving the reflection becomes proportional to P0+F0*dt-A*dt²/2 + A*t*dt + E(t)-E(t-dt)

The effect of the last two terms is to smear the frequency of the contribution of reflection from a target to the beat signal. If one takes the Fourier transform of the beat signal as a function of time "t", the last to terms result in an error term that is convoluted with the sharp peak that is associated with the term A*t*dt.

It can be noted that, if the error E(t) is known, the term E(t) can easily be eliminated by shifting the phase of the beat signal by a corresponding amount. But the term E(t-dt) cannot so easily be eliminated, because the travel time dt is different for different targets that contribute reflections to the beat signal. This term still leads to smearing. If not corrected it reduces resolution of the radar. In one embodiment the effect of this term is eliminated with the aid of residual video phase correction (RVP correction), which is known per se. RVP correction is conventionally used to remove the effect of the term A*dt²/2 in the phase of the beat signal, which makes the time independent part of the phase different for targets at different distance (with different dt). RVP correction can be executed by computing the Fourier transform of the beat signal as a function of time "t", which results in a Fourier transform as a function of frequency "f" and shifting the phase of the Fourier transform by an amount proportional to f²/(2*A). However, other techniques, such as time domain convolution can be used as well to realize RVP correction. When a target produces an almost constant frequency beat signal, with frequency fr this has the effect of shifting the time dependence of the beat signal over fr/A and applying a phase shift of -fr²/(2*A). When the contribution of reflection from a target is located at a frequency fr=A*dt the RVP correction shifts time by dt. In the case of non-linear frequency modulation, RVP correction of a signal from which the term E(t) has been corrected by phase shifting has the additional effect that it removes the time dependence of the deviation term E(t-dt). Hence successive application of a phase shift to remove E(t) and RVP correction by shifting in proportion to f²/(2*A) has the compound effect that the phase of the contribution of reflection from a target becomes approximately

PO+FO*dt+ A*t*dt -E'(t)

(Herein E'(t) is a corrected version of E(t)). The important point to note is that this has the effect that the remaining term due to non linear frequency modulation can be removed from this signal by phase shifting, as this term in the signal is the same for the contributions from all objects, i.e. it does not depend on dt. Hence it has been found that by applying a phase shift correction for the non-linear frequency modulation twice, and applying RVP correction of the signal in between, the smearing effect of non-linearities in the frequency modulation can be approximately removed.

However, it has been found that this works well only when there is no relative movement of the target with respect to the antenna, i.e. when dt does not depend on time. This is because RVP correction produces a time independent shift, which cannot completely correct for a time dependent delay dt. This is relevant for the combination of SAR and FMCW. When SAR and FMCW are combined there is relative movement, so that dt depends on both the time T of a predetermined time point relative to the start of the sweep and the time difference t between T and the time of reception of the reflected signal: dt(t,T). The time shift TRVP due to RVP correction is the same for all times t along the sweep: TRVP(T). As a result, after RVP correction the nonlinear frequency modulation error term E(t-dt), which becomes

E(t-dt(t,T)+TRVP(T)) after RVP correction, still depends on target position through dt because RVP does not completely remove the effect of dt from the error.

In an embodiment this effect is corrected by applying a further Fourier transform a second time direction defined by T, to the signal obtained by phase shifting to remove the effect of E(t) and subsequent RVP correction. Thus, the signal that is Fourier transformed contains the contribution of reflection from a target wherein the remaining non-linearity effect is still partly present. The result of the further Fourier transform is a function of a frequency fD. This Fourier transform is corrected by shifting its phase over

E(t(l-fD/(FO+At))

That is, instead of the simple time dependent phase shift E(t) used at the beginning of the process, a phase shift for a scaled time value is used.

Different phase shifts are used for different Fourier transform frequency fD. In the correction time t is scaled (compressed or expanded) according to a factor l-fD/(FO+At).

This has been found to compensate for the effect of movement of the antenna. A mathematical explanation can be found as follows. The result of removal of the effect of E(t) and subsequent RVP correction is a signal wherein different targets contribute reflections with phase corresponding to

PO+FO*dt+ A*t*dt -E'(t-dt(t,T)+TRVP(T))

The difference dt(t, T)-TRVP(T) between the actual time delay dt and the time delay due to RVP correction is small, so that it may be approximated linearly.

dt(t,T)-TRVP(T)=t*dt^! (Herein dt' is the time derivative of dt with respect to t and it has been assumed that T is selected so that dt(0,T)-TRVP(T)=0). Hence each target approximately contributes a phase

P0+F0*dt+ A*t*dt -E'(t-t*dt')

This phase is a function of T and To through dt and dt¹. Thus, this phase co- defines a signal as a function of T. The Fourier transform of this signal is computed, to obtain a Fourier transform as a function of fD. This Fourier transform is a convolution of an ideal Fourier transformed signal (with phase corresponding to the first three terms) and a correction term corresponding to the last term.

This convolution can be replaced by a product if a stationary phase approximation can be used. This approximation says that the Fourier transform value is mainly determined by the function value near the time T of stationary phase, where the Fourier transform frequency equals the time derivative of the phase with respect to T, i.e. where a stationary phase condition is satisfied. However, dt depends on time as a function of t+T-To. Hence the derivative with respect to T is the same as the derivative dt' with respect to t. As a result, the Fourier transform value is mainly determined by the function value where the following stationary phase condition is satisfied:

(FO+A*t)*dt'=fD

From this an expression for dt' can be determined, which means that the correction term E'(t-t*dt') can be approximated by E(t'), wherein t' is a scaled time according to

t'=t-t*fD/(FO+A*t) The important point to note is that this correction is independent of target distance, because dt has been eliminated. Hence it can be applied in the same way to contributions of different targets in the received reflected signal. The next point to note is that the correction corresponds to a version of the non linearity error E(t) with a scaled time scale, the compression or expansion factor of this scaling depending on the Fourier transform frequency. Also it may be noted that F0+A*t is the instantaneous frequency fR of the transmitted signal at time t:

t'= t-t*fD/fR

In conclusion: the residual effect of non-linear frequency modulation can be removed by shifting according to the measured non-linearity at an expanded or compressed time scale. The resulting corrected signal may be subjected to an inverse of the further Fourier transform, to obtain a corrected signal that can be processed using conventional SAR+ FMCW processing for ideal linear frequency modulation.

Figures 3, 4 shows flow-charts of operation of processing circuit 18. Figure 3 shows a capture part of operation. In a first step 31 of the capture part a frequency sweep labelled with "n" is started. Preferably, signal processing circuit 18 signals signal source 10 to start the frequency sweep, but alternatively sweeps may be started in a different way, the start of the sweep being signalled to processing circuit 18. In a second step 32, signal processing circuit 18 samples values S(i, n) of a beat signal from mixer 16 at a series of time points t(i) (i=0,l,2...) after the start of sweep n. A third step 33 causes the process to be repeated a number of times from first step 31, at different times T indicated by "n" with the antenna at different positions. Thus, a first and second time direction are defined by i and n. The first time direction (indexed by "i") corresponds to time relative to a predetermined point in the sweep and the second time direction (indexed by "n") corresponds to the time of the predetermined point in the sweep (as used here "corresponding" includes equality of the corresponding elements, but also covers any relation by which one element can be determined from the other, such as a predetermined offset relation). Figure 4 shows a signal processing part of operation. In a first step

41 a phase correction is applied to correct for the instantaneous phase deviation E(t) from linear frequency modulation. An example of a method of determining E(t) will be described in the following. In a second step 42 a residual video phase correction is applied. By way of example this comprises a first sub-step 421 wherein for each value of "n" a Fourier transform is computed of the signal S(i,n) as a function of "i". This results in Fourier transformed signals T(f,n). In a second sub-step 422 each Fourier transformed signal T(f,n) is multiplied by a frequency dependent complex phase vector with phase angle equal to 360 degrees times f²/(2*A), where A corresponds to the rate of change of the frequency of signal source 10. This results in a phase corrected Fourier transform T'(f,n). In a third sub-step 423 an inverse Fourier transform of the phase corrected Fourier transform T'(f,n) is computed.

The resulting signal S'(i,n) is a version of the input signal with removed video phase. In a third step 43 the signal S'(i,n) for each value of "i" a Fourier transform is computed of the signal S'(i,n) for successive values of "n". This results in further Fourier transformed signals Q(i,fD). In a fourth step 44 the further transformed signal Q(i,fD) is multiplied by a correction signal C(i,fD), which shifts the phase according to a time-scaled non-linearity error. The correction signal C(i,fD) has a phase of E'(t'), where

t'=t*(l-fD/(FO+A*t))

Although a specific expression for the scaled time t' is used, it should be appreciated that even with slight deviations from this scale time some reduction of smearing due to non-linearity may already be realized. For example, instead a factor that is the inverse of l+fD/(F0+A*t) may be used, or in some cases the term A*t may be omitted. Several different factors can be easily tried and by comparing the resulting radar images with expected real target information it can be determined whether they reduce smearing In a fifth step 45 an inverse Fourier transform S"(i,n) of the product of Q and C is computed. This signal is substantially independent of the non- linearity E(t) of frequency modulation.

In a sixth step 46 conventional SAR and/or FMCW signal processing is applied to this signal S"(i,n). Such signal processing is known per se and will not be described in detail, except that it may be mentioned that for some forms of signal processing Fourier transforms may be used that can be eliminated by combining them with the inverse Fourier transforms of the flow chart of figure 4.

In the embodiment shown in figure 1 processing circuit 18 uses the output signal of calibration circuit 17 to compute the correction signals. This form of computing the correction signals provides a reliable and effective way of computing the corrections. However, it should be noted that other ways of determining the corrections (and in particular information that represents E(t)) may be used. The phase of the output of further mixer 172 is proportional to

F0*D+ A*D²/2+A*D*t+ E(t)-E(t-D)

In this expression D is the delay of delay line 170. When D is small this phase can be approximated by

F0*D+ D*(A*t + dE(t)/dt)

The deviation from the phase at ideal linear modulation is thus proportional to the time derivative of E(t) times D. D is known, because it is determined by delay line 170. Since D, A and FO are known processing circuit 18 is able to estimate E(t) from the phase of the output signal of further mixer 172. In the embodiment processing circuit 18 computes the estimated E(t) accordingly and uses the computed E(t) to perform the correction of first step 41. Furthermore processing circuit 18 uses the computed E(t) to compute the correction signal C(i,fD). This can be done by computing the scaled time t and inserting it in the E(t) value obtained by processing circuit 18. In this case E'=E may be used. In an embodiment processing circuit 18 processes the mixed signal obtained using delay line 170 in a similar way as the signal from the antenna. That is, the signal is multiplied by a phase factor to remove the effect of E(t) and subjected to RVP correction. This results in a signal with phase.

F0*D+A*D*t+ E'(t)

By removing the effect of F0*D+A*D*t another estimate for E'(t) can be obtained. In this embodiment the correction term E'(t) obtained in this way is used for determining the correction signal C(i,fD).

Figure 5 illustrates signal flow. An incoming signal from the antenna is subjected to a mixing process 50, followed by a first phase factor application process 52, an RVP correction process 54, a Fourier transform process 56 (with respect to second time T) and a first phase factor application process 58. This may be followed by an inverse Fourier transform process with respect to second time T (not shown). The RVP correction process itself may contain a Fourier transform process and an inverse Fourier transform process with respect to first time t, and a third phase factor process in between.

An incoming signal from the delay line 170 is subjected to a mixing process 51a and a correction extraction process 51b and a frequency fD time time-scaling process 57. The result of the correction extraction process 51b defines a first phase factor for first phase factor application process 52. The result of frequency fD dependent time-scaling process 57 defines a second phase factor for second phase factor application process 58.

Processing circuit 18 may be implemented as a programmable processing circuit, programmed with a program that causes the described processes to be performed, or with a circuit structured to perform these operations. Programs for such a processing circuit may be carried by in a computer program product such as a programmable memory (e.g. a flash memory, a PROM etc), a magnetic or optical disk, an Internet signal etc. In an embodiment processing circuit 18 contains different processing units for all or part of the processes of figure 5 (except mixing), but instead all processes may be performed by a single processor. As a programmable processing circuit a programmable signal processor circuit may be used for example, or a general purpose programmable computer. Furthermore, although an embodiment using sampled and preferably digitized signals has been used, it should be appreciated that alternatively time continuous and/or analogue signals may be processed at various stages instead.

The computation of the corrections may be performed for each sweep in the series of sweeps, the output signals from further mixer 172 for each sweep and the resulting phase corrections being applied to the reflection signals obtained with that sweep. In an embodiment the second time dependence of the correction is applied only to the first phase factor (prior to RVP correction), a single E(t') being used to determined the second phase vector (e.g. an E(t') obtained for a representative second time value T or an average). In a further embodiment also the second correction depends on T. Herein a measured E(t) obtained at a time value T is preferably used, wherein T is selected so that it causes the stationary phase condition for the relevant fD to be satisfied.

This has the advantage that the effect of time dependent fluctuations in non-linearity can be eliminated. Alternatively, calibration measurements may be performed at other times, for example in one or more additional sweeps between sweeps that are used to transmit signals, or once for a plurality of measurements of S(i,n). In the latter cases, a switching circuit may be used to enable mixer 16 to perform the function of further mixer 172 (further mixer 172 being omitted). This reduces system costs and eliminates effects due to phase mismatches between the mixers.

Although a specific embodiment of the signal processing operations has been described, it should be appreciated that different implementations can be used to obtain equivalent effects. The sequence of applying the various processes may changed, where such change does not significantly affect the result. Also such changes in sequence may be used in combination with appropriate modification of interchanged processes. As an example, sequential application of a Fourier transform and multiplication with any factor function may be replaced by sequential application of convolution with the Fourier transform of the factor function and a Fourier transform of the result. Also, of course, if this results in successive application of a Fourier transform and its inverse, both can be omitted, as their combination results in an identity transformation. Furthermore, in some cases part of the corrections may be omitted, for example if non-linearity is significant only during part of the sweep. Also of course instead of a single antenna for transmission and reception separate antennas may be used, or the directional coupler may be omitted, since the beat frequency of the frequency modulated signal with itself is fixed at zero. Furthermore of course various amplifiers delay lines filters etc may be used as convenient to facilitated operation.

Claims

1. A method of processing a radar signal, the method comprising

- generating a frequency modulated signal having a deviation from linear frequency modulation;

- transmitting the frequency modulated signal; - receiving back reflections of the frequency modulated signal;

- mixing the received reflections with the frequency modulated signal;

- defining a series of mixed down signals for successive frequency sweeps, said series defining a first time direction along each mixed down signal and a second time direction from one mixed down signal to another at corresponding first time values in the first time direction;

- applying a phase correction to the mixed series of mixed down signals, the phase correction at the first time value for respective signal components of the mixed down signal corresponding to the deviation at a scaled time value, obtained by scaling the first time value dependent on a frequency of the signal components in the second time direction, using a time scaling factor value that reduces a smearing effect of the deviation from linear frequency modulation.

2. A method according to Claim 1, wherein the time scaling factor for respective signal components of the mixed down signals is proportional to frequency of the components in the second time direction.

3. A method according to Claim 1, wherein the scaled time value substantially equals said first time value minus said first time value times a ratio of the frequency in the second time direction divided by a transmission frequency of the frequency modulated signal.

4. A method according to Claim 1, wherein the transmission frequency is a transmission frequency of the transmitted signal at said first time value.

5. A method according to any one of the preceding claims, wherein said applying step comprises computing a Fourier transform of a further signal defined by said series the mixed down signals at the first time value as a function of the time in the second time direction, and multiplying the Fourier transform by a phase factor with a phase defined by the deviation at the scaled time value.

6. A method according to any one of the preceding claims, the method comprising applying a preliminary phase factor defined by the deviation for at first time value to the series of mixed down signals at the first time value and applying a residual video phase correction to each of the series of mixed down signals, obtained by applying the preliminary phase factor, said applying step being applied to a result of the residual video phase correction.

7. A method according to any one of the preceding claims, comprising determining said deviation from a result of mixing the transmitted signal with a time delayed version of the transmitted signal.

8. A method according to claim 7, comprising determining said deviation for respective different second time values in the second time direction from a result of mixing the transmitted signal with a time delayed version of the transmitted signal, and applying different corrections corresponding to said deviation for different second time values.

9. A radar system comprising - an output for transmitting a signal;

- an input for receiving reflections of the signal;

- a frequency modulated signal source coupled to the output;

- a mixer coupled to the input and to the frequency modulated signal source, for mixing the received reflections with a frequency modulated signal from the frequency modulated signal source;

- a signal processing circuit coupled to an output of the mixer and configured to obtain a series of mixed down signals for successive frequency sweeps, said series defining a first time direction along each mixed down signal and a second time direction from one mixed down signal to another at corresponding time points along the first time direction; and to apply a phase correction to the mixed series of mixed down signals, the phase correction for a first time value for respective signal components of the mixed down signal in the first time direction corresponding to the deviation at a scaled time value obtained by scaling the time value dependent on a frequency of the signal components in the second time direction, using a time scaling factor value that reduces a smearing effect of a deviation from linear frequency modulation.

10. A radar system comprising a delay circuit coupled between the signal source and the mixer or a further mixer, the processing circuit being configured to perform the steps of claims 7 and/or 7.

11. A computer program product comprising a program of instructions for a programmable processor, which when executed by a programmable processor cause the programmable processor to

- receive reflections of a frequency modulated signal that have been mixed down with the frequency modulated signal; - define a series of mixed down signals for successive frequency sweeps, said series defining a first time direction along each mixed down signal and a second time direction from one mixed down signal to another at corresponding time points along the first time direction;

- apply a phase correction to the mixed series of mixed down signals, the phase correction for a first time value in the first time direction corresponding to the deviation at a scaled time value obtained by scaling the time value dependent on a frequency in the second time direction, using a time scaling factor value that reduces a smearing effect of a deviation from linear frequency modulation.