GB2290188A

GB2290188A - Radar range processing

Info

Publication number: GB2290188A
Application number: GB9410164A
Authority: GB
Inventors: Brent Summers
Original assignee: Commonwealth of Australia; GEC Marconi Ltd; Marconi Co Ltd
Current assignee: Commonwealth of Australia; BAE Systems Electronics Ltd
Priority date: 1994-05-20
Filing date: 1994-05-20
Publication date: 1995-12-13
Also published as: AU2531095A; GB2291301A; GB9421466D0; GB9410164D0

Abstract

A method of radar range processing in which the Fourier transform of the received signal is correlated with the complex conjugate of the transmitted signal divided by the power spectrum of the transmitted signal. This method avoids the generation of excessive range cell sidelobes while not requiring an increase in processing which is often necessary in the prior art eg using oversampling. The method utilises a matched filtering technique wherein received signal digitised samples are processed in a super-fast correlator 5 along with a computed version of a single period of the transmitted reference signal 3. Re-sampling at a rate commensurate with the digital input rate 6, which rate can be independent of that rate, allows a time or frequency domain representation of the processed signals to be output The invention may be used to investigate range information from the backscatter of an FMCW radar. <IMAGE>

Description

SIGNAL PROCESSING This invention relates to a signal processing apparatus and method for performing a matched filtering or circular correlation process between a digitally represented bandlimited periodic input signal and a single period reference waveform to produce outputs spaced at intervals independent of the input signal sampling rate, and particularly to producing outputs spaced at intervals equivalent to the signals bandwidth to extract range cell information from radar backscatter of a radar utilising a repetitive frequency modulated continuous wave (FMCW) type waveform.

As is well known, radar systems operate by extracting the wanted signal from the unwanted clutter by receiving and processing the radar backscatter of a transmitted r.f. signal.

The process of identifying the wanted return signal in the output signal of the receiver is generally performed by processing the radar backscatter in three dimensions, i.e. range, azimuth and doppler. This invention is particularly useful for, but is not limited to, improvements in the apparatus and method of processing the range dimension.

The conventional method of range processing in a radar is to measure the time delay between the transmitted and received signal. Then from knowledge of the speed of electromagnetic wave propagation, the range of the reflecting object may be calculated.

However, since it is generally not known where the target or targets exist in range until the subsequent processing in azimuth and doppler has been completed, it is customary to divide the range axis into cells and process a number of cells simultaneously. The minimum size of the cell is generally termed the "range resolution" of the radar system and is inversely proportional to the bandwidth of the signal. The number of processed range cells multiplied by the range resolution is generally termed the "processed range-depth".

In order to extract range cell information in, for example, a radar employing a FMCW type of waveform, the technique known as "matched filtering" is utilised. Matched filtering is basically a cross-correlation process between the received signal and a reference signal equivalent to the complex-conjugate of a single waveform period of the transmitted signal.

The 'ideal' process would concentrate all of the received energy into one output when the received signal is in perfect time alignment with the reference waveform and produce a zero output elsewhere. However, practical systems cannot realize this theoretical ideal and timesidelobes result. The size of these time-sidelobes affects the radars ability to detect multiple targets or targets in the presence of clutter. Therefore it is essential that the time-sidelobe level is controlled.

Matched filtering is commonly employed by many other types of detection system.

One method of controlling the time-sidelobe level is by coding the waveform such that its natural circular correlation function is as near to the ideal as possible. Many such codes exist. For example, Barker, Lewis-Kretchemer P1, P2, P3 and P4 codes, and are well documented in the open literature.

For such systems

where,

= transform of range dimension output signal (single period)r(t).

= transform of return signal (single period)x(t).

= complex-conjugate of transform of transmit waveform (single period)g(t).

If the transmitted signal is a linear FMCW repetitive waveform arranged such that the time-bandwidth product (TB) is equal to an integer number, this is a necessary and sufficient condition to ensure that the waveform is periodic over the same interval as the waveform repetition, then (ignoring any doppler component on the return signal for simplicity) for a digital signal processing system.

where, A is some amplitude scaling factor.

td = nominal transit time quantised to the nearest sampling interval At = is the time misalignment between the return signal and quantised time axis.

From equation (2) it can be seen that in the range cell domain (time) the output signal is entirely determined by the circular correlation function (ccf) of the transmitted signal g(t) since by definition the inverse transform of the power spectrum G(f) 2 is the ccf.

Note that the ccf is the same as the auto-correlation function (acf) but performed on a circular axis because of the periodic assumption made in the digital signal processing of signals.

Thus the conventional matched filtering or range correlation technique has the disadvantage that the performance of the radar is compromised by the range cell side lobes generated by the ccf of the transmitted waveform and that the range of transmitted waveforms which can be employed is limited by the fact that waveforms whose cef would generate excessive range cell side lobes cannot be used regardless of how desirable they might be otherwise.

This invention was intended to provide improved signal processing apparatus and methods overcoming these disadvantages, at least in part.

For further improvements in time-sidelobe level a window function (e.g. Blackman Harris, Dolph-Chebyshev etc) can be applied in the frequency domain (although in the strict sense this is no longer a matched filter and is normally referred to as "range correlation").

In this case, the range-domain signal will be composed of the signals ccf convolved with the transform of the window. Since a coded waveforms ccf approximates an impulse function, the resultant time-sidelobe level will be dominated by the window functions sidelobe level, thus providing a pre-determined method of control at the expense of a slight degradation in range resolution and coherent processing gain.

In general in signal processing it is often desirable to take a signal sampled at a first sampling interval and convert it into output data corresponding to the signal being sampled at a second, different, sampling interval.

One example of this is found in radar range processing.

In a practical application of matched filtering or range correlation by means of digital signal processing apparatus there has to be an integer number of sample intervals within a waveform repetition interval (WRI). In order to correctly represent the radar signal it is frequently necessary to over-sample the signal to avoid the undesirable affects of aliasing.

However, from the point-of view of the range processing it is undesirable to over-sample since it will not improve the resolution of the system and increases the processing requirement by virtue of having more samples within the WRI. Furthermore, if the range axis is evaluated at the input sampling rate it implies an increased processing requirement on subsequent processing stages.

Consequently, it is a frequent requirement that the range cells are computed at a rate consistent with the signals bandwidth regardless of input over-sampling rate.

The present invention provides an apparatus and method for achieving this in a processing efficient manner.

In a first aspect, this invention provides a method of radar range processing in which the Fourier transform of the received signal is correlated with the complex conjugate of the transmitted signal divided by the power spectrum of the transmitted signal.

This gives the advantage that, for zero doppler, the range cell response of the radar is determined solely by the window function used and is independent of the autocorrelation function or circular correlation function of the transmitted signal.

In a second aspect this invention provides a method for use in matched filtering or circular correlation between a digitally represented bandlimited periodic input signal and a pre-determined single period reference waveform such that the outputs of the process are spaced at predetermined intervals independent of the input signal sampling rate, comprising the steps of;; i) accepting a digitised signal, such that the samples are a unique representation of the signal, and also represented by an appropriate level and number of quanta, ii) Collecting overlapped batches of a number of successive samples, and storing the batch samples for future use, iii) Computing a frequency or time domain representation of the reference waveform, iv) Simultaneously computing a number or batch of outputs by means of a two stage process of super-fast correlation and range (or time)-domain re-sampling respectively, v) outputting a time or frequency domain representation of the processed signals at a rate commensurate with the digitised signal input rate.

In a third aspect this invention provides signal processing apparatus for use in matched filtering or circular correlation process between a digitally represented bandlimited periodic input signal and a pre-determined single period reference waveform such that the outputs of the process are spaced at predetermined intervals independent of the input signal sampling rate and comprising means for accepting an already digitised signal such that the samples are a unique representation and also represented by an appropriate level and number of quanta, means for collecting (overlapped) batches of a number of successive samples, means for storing the batch of samples for future use, means for computing a frequency or time domain representation of the reference waveform, means for simultaneously computing a number or batch of outputs by means of a two stage process of super-fast correlation and range (or time)-domain resampling respectively, and means for outputting a time or frequency domain representation of the processed signals at a rate commensurate with the digitised signal input rate.

This invention is particularly advantageous in extracting range cell information from radar backscatter of a radar utilising repetitive FMCW type waveforms, but is not limited to this use.

The signal processing method or apparatus can be carried out in real time or non real time and can output its results continuously or in a burst manner. Preferably the outputs of the process are spaced at intervals equivalent to the signals bandwidth.

The signal processing method or apparatus can be advantageously employed for matched filtering in a radar system with the signal being provided by the radar receiver.

The invention will now be described by way of example only with reference to the attached Figures in which; Figure 1A shows the signal spectrum of a received waveform, Figure 1B shows the instantaneous frequency characteristic of the waveform of Figure 1A, Figure 1C shows the signal spectrum of a reference waveform incorporating a window function and used with the waveform of Figure 1A, Figure 1D shows the resultant obtained by an IDFT of the correlation of the waveforms of Figures 1A and 1C.

Figure 2 shows signal processing apparatus employing the invention, Figure 3 shows a re-sampling algorithm which can be employed in the invention in flow chart form, Figure 4 shows a first signal processing method according to the invention in flow chart form, and, Figure 5 shows a second signal processing method according to the invention in flow chart form.

This invention provides an improved method of performing the range correlation. This method is to use a reference waveform of the form Y69 = W(fl x G*z (3) IG(t)12 Then, Rt =X(') x Y

It will be noted that if equation (4) is compared with equation (2) the absolute values of the signal spectrum have been cancelled out (for no doppler) leaving only a scaled and shifted window function. Or, in other words, the output is independent of the signals selfcorrelation properties.

This is a significant result since it implies that so long as the waveform utilises the bandwidth in approximately uniform proportion (as in the case of linear FMCW) the output signal of the range processing is simply the transform of a window function. This allows considerable control over the time or range sidelobe levels and decouples some of the waveform design constraints from those of the range processing.

With reference to Figures 1, Figure 1A illustrates the signal spectrum X(f) for a conventional linear FMCW waveform generated from an instantaneous frequency characteristic illustrated in Figure 1B. The spectrum of the reference waveform Y(f), which incorporates a Blackman-Harris window, is illustrated by Figure 1C, and Figure 1D illustrates the resultant time (range) domain output signal r(t) obtained from the Inverse Discrete Fourier Transform (IDFT) of R(f).

Figure 1D will be recognised as the transform of a Blackman-Harris window function.

Figure 2 shows radar range processing apparatus 1 which takes in reference data and signal data sampled at intervals T along lines 2 and 3 respectively and outputs range cell data at a sampling interval proportional to the swept band width.

The apparatus 1 achieves this by providing means for accepting an already digitised signal, for example from a radar receiver, such that the samples are a 'unique representation' of the signal and are also represented by an appropriate level and number of quanta. The samples are a unique representation in the sampling theorem sense, i.e. taken at a rate appropriate to the signals bandwidth or the bandwidth of the receiver imposed on the signal.

The apparatus also includes means for collecting (overlapped) batches of a number of successive samples, means for storing the batch of samples for future use, means for computing a frequency or time domain representation of what has hereinbefore been termed a "reference waveform", a super fast correlator 5 and a range-domain re-sampler 6 for simultaneously computing a number or batch of range cells by a two stage process of what shall be termed "super-fast correlation" and "range (or time)-domain re-sampling" respectively, means for outputting processed range cell (or time)-domain samples in either a continuous or burst manner at a rate commensurate with the real-time (or non real-time) input batch rate.

The critical steps of the invention method are further explained by the following: Regarding the operation of the super fast correlator 5, consider the direct correlation sequence

where

such that N, = the number of over-sampled samples (of spacing T) in a WRL N2 = the number of over-sampled sample intervals T in the processed range-depth xk = the over-sampled signal samples starting at the range of interest relative to the transit time.

= = the reference waveform (over-sampled).

Often the number of samples within a WRI (N1) is much greater than the number of samples required to cover the range-depth (N2).

Consequently, the correlation can be performed in parts as follows: 1. Round N2 up to the next power of 2 (unless it is already a power of 2) and rename D.

2. Sub-divide the data into B, 50% overlapped blocks of size 2D, where B = Int (NIID)+l.

Note, in order to achieve this, extend the data array to M by appending (BD+D-C-N,) zeros such that M=(B+l).D. That is,

3. Sub-divide the reference waveform into 'B' non-overlapping blocks where the array is extended from Nl elements by appending (BD-N) zeros to the end of the array.

An example of this would be; suppose the original value of Nl and N2 were 23637 and 49 respectively. Then following the above steps: L 49 round up to 2" = 64 = D.

2. B = 370, hence append 58 zeros to x, in which case M = 23744.

3. Append 43 zeros to y*.

Having done this, equation (5) can now be rewritten for

That is to say, the summation of a set of partial correlation sequences for B-blocks.

Let the partial correlation sequence for the b-th block be

where

Which is in the same form as equation (5) except that the size of the correlation is D instead of N.

Equation (7) for each block can be computed using circular correlation. Each 50% overlapped data block can be correlated with a reference block, zero extended to size 2D.

Hence,

where

Note that the difference in the summation upper limit between equation (9) and (10) is because for a particular block

Hence the reason for sub-dividing the data into 50% overlapped blocks.

Substituting (8) back into (6) results in the desired output for

(II) However, it will be noted from equation (11) that in order to save many of the inverse transforms, the block summations could have been performed in the frequency domain, That is,

This changes equation (11) to

The method so far described consitutes what was hereinbefore termed the "super-fast correlation" process. The second part of the method, the "range domain re-sampling" carried out in the range domain re-sampler 6, stems from the important observation that equation (12) is recognised to be the 'transform of the range-domain'.

Consequently, suppose the actual interval desired between range cells is 1 whereas, the oversampled interval is T. Then in order to cover the range depth it would be necessary to have NR(? spaced) range-cells.

Therefore, the desired range cell sequence

In order to evalueate equation (14) advantage can be taken of Horner's rule as follows: Suppose we have a polynomial of the form

If N=4, equation (15) can be expanded to

which can be factored as follows:

It can be seen that instead of computing all the coefficients it is only necessary to compute the kernal thus removing a dimension from the calculation.

Having computed the kernal coefficient, the polynomial can be evaluated by the following simple algorithm: 1. Initialise:

2. Iterate:

3. Final Step:

This algorithm can be applied directly to the evaluation of equation (14):

Figure 3 illustrates the evaluation of equation (18) in flow chart form and Figure 4 illustrates the complete process method so far described in flow chart form.

However, the method of performing the range domain re-sampling can be further improved for computational efficiency by simply replacing the polynomial evaluation with the means to perform an inverse Fast Fourier Transform (IFFY), means to select the first N2 terms, i.e. those oversampled range cells equivalent to the desired range-depth, means to zero extend back to D, means to FFT and means to use Horner's rule to evaluate a D-term polynomial.

Mathematically, these steps can be expressed as follows: From equation (13)

Zero extend the oversampled data array

,III E( & o0D4erms, i-e-{r J * {rc ~ ] c o ot c*Ha Then FFT to obtain,

Set-up the polynomial

And finally, evaluate by means of Horners Rule:

The complete process is shown in Figure 5.

It will be noted that for many applications the reference waveform can be precomputed and stored as the two dimensional array

thus facilitiating further computational savings.

Furthermore, by simply changing the reference waveform the same process can be used for either matched filtering or range processing.

The above description is based on the example of radar range processing where oversampling is to be eliminated and an optimum range cell interval proportional to the signal bandwidth is desired. In general it is not essential for the output data sampling interval to be proportional to the signal bandwidth but this is generally the optimum in radar range processing because it avoids both aliasing and unnecessary processing of superfluous range cells.

Although this invention has been discussed in terms of radar signal processing it could be used in other signal processing applications such as sonar, seismic surveying or tomography for example.

Claims

1. A method of radar range processing in which the Fourier transform of the received signal is correlated with the complex conjugate of the transmitted signal divided by the power spectrum of the transmitted signal.

2. A method for use in matched filtering or circular correlation between a digitally represented bandlimited periodic input signal and a pre-determined single period reference waveform such that the outputs of the process are spaced at predetermined intervals independent of the input signal sampling rate, comprising the steps of;; i) accepting a digitised signal, such that the samples are a unique representation of the signal, and also represented by an appropriate level and number of quanta, ii) Collecting overlapped batches of a number of successive samples, and storing the batch samples for future use, iii) Computing a frequency or time domain representation of the reference waveform, iv) Simultaneously computing a number or batch of outputs by means of a two stage process of super-fast correlation and range (or time)-domain re-sampling respectively, v) outputting a time or frequency domain representation of the processed signals at a rate commensurate with the digitised signal input rate.

3. Method according to claim 2 wherein the reference waveform is of the form Y60 = W(fl x G*(fl 10(1)12

4. A method according to claims 2 and 3 wherein the super fast correlation includes the following steps i. Round N2 up to the next power of 2 (unless it is already) and rename D.

ii. Sub-divide the data into B, 50% overlapped blocks of size 2D, where B = Int (N,/D)+1.

iii. Sub-divide the reference waveform into 'B' non-overlapping blocks where the array is extended form N, elements by appending (BD-N,) zeros to the end of the array.

iv. Computation of

in parts.

5. A method according to any one of claims 2 to 4 wherein the range-domain re sampling comprises the steps of; i) performing an inverse Fast Fourier Transform (IFFr), ii) selecting the first N2 terms, i.e. those over-sampled range cells equivalent to the desired range-depth, iii) zero extending back to a vector length D, iv) performing a Fast Fourier Transform (FFT) and v) using Horner's rule to evaluate a D-term polynomial.

6. A method according to any one of claims 2 to 5 wherein the output is range-cells for radar application.

7. A method according to any one of claims 2 to 6 wherein the function is matched filtering.

8. A method according to any one of claims 2 to 7 wherein the method operates on the input signal in real time.

9. A mefliod according to any one of claims 2 to 8 wherein the outputs of the process are spaced at intervals equivalent to the signals bandwidth.

10. A method according to any one of claims 2 to 9 wherein the signal comes from a radar receiver.

11. A method according to any one of claims 2 to 10 wherein the time or frequency domain representation of the processed signal is output in a burst manner.

12. Signal processing apparatus for use in matched filtering or circular correlation process between a digitally represented bandlimited periodic input signal and a pre-determined single period reference waveform such that the outputs of the process are spaced at predetermined intervals independent of the input signal sampling rate and comprising means for accepting an already digitised signal such that the samples are a unique representation and also represented by an appropriate level and number of quanta, means for collecting (overlapped) batches of a number of successive samples, means for storing the batch of samples for future use, means for computing a frequency or time domain representation of the reference waveform, means for simultaneously computing a number or batch of outputs by means of a two stage process of super-fast correlation and range (or time)-domain resampling respectively, and means for outputting a time or frequency domain representation of the processed signals at a rate commensurate with the digitised signal input rate.

13. Apparatus according to claim 12 wherein the reference waveform is of the form

14. Apparatus according to claim 12 or claim 13 wherein the super-fast correlation comprises means for computing;

15. Apparatus according to claim 1 wherein the 'range-domain re-sampling' comprises means for performing an inverse Fast Fourier Transform (IFIlT), means to select the first N2 terms, i.e. those over-sampled range cells equivalent to the desired range depth, means to zero extend back to a vector length D, means to FFT and means to use Horner's rule to evaluate a D-term polynomial.

16. Apparatus according to any one of claims 12 to 15 wherein the output is range-cells for radar application.

17. Apparatus according to any one of claims 12 to 16 wherein the function is matched filtering.

18. Apparatus according to any one of claims 12 to 17 wherein the apparatus operates on the input signal in real time.

19. Apparatus according to any one of claims 12 to 18 wherein the outputs of the process are spaced at intervals equivalent to the signals bandwidth.

20. Apparatus according to any one of claims 12 to 19 wherein the signal comes from a radar receiver.

21. Apparatus according to any one of claims 12 to 20 wherein the time or frequency domain representation of the processed signal is output in a burst manner.

22. A method of matched filtering or circular correlation substantially as described with reference to the accompanying figures.

23. Signal processing apparatus for use in matched filtering or circular correlation processes as shown in or as described with reference to the accompanying figures.