Method, system and computer program for estimating target range and / or radial velocity

Abstract

The present disclosure relates to methods and systems based on a new type of radar waveform, taking the form of a continuous aperiodic signal, effectively indistinguishable from white noise, though actually it is a signal allowing both accurate and ambiguity free range and radial velocity, i.e. Doppler, measurements.

Description

[0001] METHOD, SYSTEM AND COMPUTER PROGRAM FOR ESTIMATING TARGET RANGE AND / OR RADIAL VELOCITY

[0002] TECHNICAL FIELD

[0003] The present disclosure relates to target range and velocity estimation using radar technology.

[0004] BACKGROUND ART

[0005] As is well-known in the radar community, the Achilles heel of radar is just this fact that as an active sensor its operation is based on emission of signals. Such emissions are both obtrusive and revealing. Obtrusive in that they may interfere with other radars which well may operate in the same frequency band due to the general spectral congestion. Also, and this concerns especially military applications, they reveal the presence of the radar, whereupon this can be defeated, or the radar signal tampered with to disrupt the radar operation. There is a need in the art for improvements in radar technology addressing said issues.

[0006] SUMMARY OF THE INVENTION

[0007] The present disclosure relates to a method for estimating target range and / or radial velocity. The method comprises transmitting a radar signal. The radar signal comprises a plurality of linear frequency modulated signals, LFMs, separated by predetermined, though not necessarily equal, time shifts between their instantaneous frequencies. Each LFM has a predetermined amplitude with preferably constant modulus but phase randomly varying from one LFM to the next. Each LFM is configured to sweep linearly across a frequency band for a predetermined sweep time, Tsweep, the frequency band having a predetermined bandwidth, B, and predetermined centre frequency, fc, wherein the plurality of LFMs are configured to form a predetermined continuous aperiodic random signal, wherein the respective time shifts are shorter than the sweep time, Tsweep. The method further comprises receiving a radar signal reflection from any target to be detected by the radar. The radar signal reflection comprises the composite set of LFM signal reflections from the target. The method also comprises determining the range and / or the radial velocity based on the received radar signal reflection.

[0008] Determining the range and / or radial velocity further comprises downconverting the composite received signal set by one or several mixing devices, each adopting for the downconversion one of the transmitted LFM signals, and multiplying this with one or several received signals, it produce a beat signal, separable into frequency bands corresponding to the different LFMs, and within each band representing the target reflection, delayed by the time shifts of the plurality of LFM signals. Determining the range and / or radial velocity also comprises recording the composite received signal after analog to digital conversion.

[0009] In other words, determining the range and / or radial velocity further comprises downconverting the composite received signal set by one or several mixing devices, each mixing device adopting downconversion by multiplying one of the transmitted LFM signals with one or several received radar signal reflections, thereby producing beat signals, separable into frequency bands corresponding to the different LFMs, and within each band representing the target reflection, delayed by the time shifts of the plurality of LFM signals.

[0010] Stated differently, determining the range and / or radial velocity further comprises downconverting the composite received signal set by one or several mixing devices, each mixing device adopting for the downconversion one of the transmitted LFM signals, the downconversion consisting of multiplying the transmitted LFM signal with one or several received radar signal reflections, thereby producing beat signals, separable into frequency bands corresponding to the different LFMs, and within each band representing the target reflection, delayed by the time shifts of the plurality of LFM signals.

[0011] The method thereby enables the generation of a radar signal that is effectively indistinguishable from white noise, while simultaneously allowing both accurate and ambiguity-free range and radial velocity, i.e. Doppler, measurements. The continuous nature of the signal further prevents detection associated with periodic operation. Thus, the disclosed method offers a radar operation that provides sensitivity to small targets at the same level of performance as periodically operating radars with the added advantage of aperiodic operation emitting a noisesimilar transmit signal.

[0012] A further technical effect and advantage is found when the method is employed using array antennas. One of the main purposes of the disclosed method is to provide a radar with a radar signal that makes the radar unobtrusive, blending with thermal noise to the extent possible. The disclosed method eliminates the need for a physical radar beam, since beam forming may be performed as a post processing step. Additionally, the disclosed method enables simultaneous creation of multiple synthetic beams, thereby eliminating the need for any form of scanning - electronic or mechanical.

[0013] The method also enables taking advantage of the improved angular resolution due to increased phase diversity compared to traditional beam forming. Since increased resolution yields improved antenna gain, transmit power requirements and the level of interference caused by the radar is reduced, thereby further supporting the ambition of making the radar as unobtrusive as possible.

[0014] The disclosed method can be realized either in monostatic mode, wherein each transmit-receive, TR, module of the array antenna only receives the signal it transmits, or in multistatic mode of also receiving the transmission from the remaining TR-modules. An advantage of extending operation into a multistatic mode is increased receive sensitivity, further alleviating transmitpower needs.

[0015] According to some aspects, the predetermined sweep time, Tsweep, is configured to agree to the coherent integration time, i.e. the time available for the received signal to gain coherently during the signal return, limited to an upper bound on target scattering irregularities developing due to target motion in the course of time, preventing further signal gain.

[0016] Operating in either mono- or multistatic mode the proposed radar signal has the property that transmissions from the TR modules all occur at different generally fixed frequency separations, making the signals transmitted and received from the TR modules all orthogonal. Moreover, signals at any particular frequency will be transmitted / received at all TR-modules, albeit at different times, given by the set of time shifts adopted in the sweep aggregate. Compensating for the time shifts, it will therefore be possible to synthesize directional radar beams just as in the case of simultaneously fed TR-modules. Since all TR-modules remains active transmitting and receiving at all times, transmit duty cycle for each TR module is accordingly 100%.

[0017] According to some aspects, the respective predetermined time shifts of the LFM signals of the aggregate are configured to be no smaller than dictated by the signal return time from a predetermined range constraint and Doppler shift due to a predetermined radial velocity constraint. Preferably, the time shift is set to correspond to the order of twice the signal return time from the required radar maximum range thereby keeping separation of the weakest signal returns to adjacent transmitted LFM signals sufficiently large.

[0018] According to some aspects, the number, N, of linear frequency modulated signals within the sweep time of the sweep aggregate is set by sweep time divided by time shift.

[0019] With the different LFM signals ongoing in parallel, sweep time will be set by the time shift times the number TR modules, ensuring that the sweep time does not extend beyond the coherent integration time.

[0020] According to some aspects, Doppler shift of a target is measured as beat signal phase shift across the LFM signals of the sweep aggregate, with the phase shift proportional to target radial speed modulo an unknown number of full turns of phase, between the LFM signals, and where the unknown number of turns restricts target radial speed to be determined modulo velocity intervals set by this unknown number of turns.

[0021] This generates a set of precise equally likely velocity hypotheses, of which the false hypotheses can be eliminated by the downstream processes now described, thereby allowing for accurate radial velocity to be determined.

[0022] According to some aspects, determining the range and / or the radial velocity further comprises selecting sweep time, Tsweep, sufficiently long to spectrally resolve the change in LFM signal frequency shifts noticeable in the signal reflected by a moving target, as well as the Doppler shift variation, i.e. Doppler dispersion, during sweep time also occurring for such a target, to an accuracy better than that set by the modulo velocity ambiguity.

[0023] According to some aspects, the method further comprises selecting a set of radial velocity hypotheses, separated by the modulo velocity intervals. Doing so the method comprises, for each hypothesis, multiplying by a complex sinusoid compensating for the Doppler dispersion, beat frequency variation and phase growth due to Doppler between the aggregate LFM signals. The method further comprises, for each hypothesis, performing a Fourier transform of each beat signal of the aggregate, thereby obtaining the beat signals represented as beat frequency responses. The method further comprises, for each hypothesis and each beat frequency, performing a discrete Fourier transforms across the set of LFM thereby obtaining true Doppler and radial speed differences to each of the velocity hypotheses.

[0024] This enables eliminating erroneous velocity hypothesis and thereby, for targets detected, obtaining an accurate radial velocity estimate.

[0025] According to some aspects, the method further comprises, based on target response being weak or absent if hypothesis is untrue, selecting as corroborated velocity hypothesis the one providing maximum Doppler difference response, thus obtaining the true Doppler response from corroborated velocity hypothesis and Doppler difference and thereby also the true target radial velocity and range.

[0026] According to some aspects, the method further comprises transmitting each LFM signal in the set of LFM signals via a single transmit unit, the single transmit unit being one of the transmit units of an array antenna, and wherein the attribution of transmit units to LFM signals follows some random pattern. The method also comprises receiving each LFM signal in the set of LFM signals by the particular transmit unit from which it was transmitted. The method additionally comprises forming a set of target directional hypotheses by modifying the velocity hypotheses by linearly combining the LFM beat signals by a discrete Fourier transform, combined with a steering vector phase factor constructing a directive radar beam, for each target directional hypothesis, the steering vectors being separated by antenna angular resolution and representing a two- or three-dimensional search sector of the radar. The method further comprises selecting, as indicating a validated target, every case where the 2-dimensional Fourier beat-frequency- Doppler transform, weighted by compensation for Doppler dispersion, beat frequency drift, target Doppler, i.e. radial velocity, and target direction, reaches beyond a predetermined threshold value. According to some aspects, receiving the radar signal reflection further comprises receiving the LFM signal emanating from any of the transmit units in several, preferably all, transmit units of the array antenna.

[0027] The use of array antennas enables beam forming as a post processing effect, with the possibility of simultaneous creation of multiple synthetic beams, thereby eliminating the need for any form of scanning.

[0028] According to some aspects, determining the range and / or the radial velocity further comprises allowing the LFM signal time shifts of the aggregate to be smaller than the delays corresponding to far away range or high velocity targets, downconverting the overshooting range returns by the succeeding LFM signal, thereby falsely assigning transmit sources in the antenna array to the downconverted range returns, leading to false range, velocity and directional assignments, if these are overshooting returns, and superimposing echoes from transmission of one LFM signal to next the overshooting erroneous echo directions varies from transmission of one LFM signal to next, meaning that overshooting and thus falsely positioned echoes become weak and can be removed by thresholding.

[0029] According to some aspects, the centre frequency, fc, is configured to be in the range of eight to twelve gigahertz, GHz, and wherein the bandwidth is configured to be in the range 50 to 500 megahertz, MHz, preferably 100 MHz. According to some aspects, the ratio of the predetermined bandwidth, B, divided by the predetermined centre frequency, fc, B / fc, is one percent, and wherein the centre frequency, fc, is configured to be in the range of one GHz to thirty GHz.

[0030] The method is thereby adapted for radars in the established radar band regimes, enabling high radial velocity resolution for a majority of radar systems.

[0031] The disclosure further relates to a radar system for estimating target range and / or radial velocity. The radar system comprises an antenna array. The antenna array comprises at least one transmit-receive module, each transmit-receive module comprising a pair of transmit and receive units, such as a transceiver. Each transmit-receive module is configured to transmit and receive a radar signal as described above and below. The radar system further comprises processing circuitry configured to cause the radar system to carry out the method for estimating target range and / or radial velocity as described above and below. The radar system has all the technical effects and advantages of the disclosed method for estimating target range and / or radial velocity.

[0032] The disclosure also relates to a computer program for estimating target range and / or radial velocity. The computer program comprising computer program code which, when executed by processing circuitry of a radar system for estimating target range and / or radial velocity, causes the radar system to carry out the method for estimating target range and / or radial velocity.

[0033] The computer program has all the technical effects and advantages of the disclosed method for estimating target range and / or radial velocity.

[0034] BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figures 1a and 1b illustrate the method for estimating target range and / or radial velocity;

[0036] Figures 1c-e illustrate the disclosed radar signal and its usage in a radar system context;

[0037] Figure 1g illustrates examples of sweep aggregate waveforms for L-, X- and W-bands; and

[0038] Figures 2a-2c illustrates the system for estimating target range and / or radial velocity.

[0039] DETAILED DESCRIPTION

[0040] Figures 1a-1g illustrates aspects of the disclosed method. In particular figures 1a and 1b illustrate the method for estimating target range and / or radial velocity, figure 1 c illustrates the disclosed radar signal, figures 1d and 1e illustrate transmission and reception of the radar signal, as well as beam forming as a post processing step, and figure 1g illustrates examples of sweep aggregate waveforms for L-, X- and W-bands.

[0041] The present disclosure relates to a method 100 for estimating target range and / or radial velocity.

[0042] The main innovative step of the invention is a new type of radar waveform, herein to be termed sweep aggregate signal. Such a signal takes the form of a continuous aperiodic signal, effectively indistinguishable from white noise, though actually it is a signal allowing both accurate and ambiguity free range and velocity (i.e. Doppler) measurements.

[0043] By contrast, almost all conventional radar relies on periodic operation. That the operation is periodic is extremely revealing and makes the signal virtually impossible to hide in noise. It is feasible to scramble periodic operation to some extent (known as staggering), thus hiding the radar from the more simplistic methods of detecting the signal. However, staggering cannot occur randomly without significant penalty to radar performance, and thus must follow certain given patterns, again making the radar emissions revealing.

[0044] As for the possibility of abolishing periodic operation altogether and adopting a true white noise transmitted signal, this has quite inferior sidelobe performance and will thus do poorly in handling weak radar targets.

[0045] In summary, almost all radar is designed on the principle of basically periodic operation and the challenge of hiding such signals to avoid detection and interference remains. The invention offers here a solution, providing the sensitivity to small targets at the same level of performance as periodically operating radar with the added advantage of aperiodic operation emitting a noisesimilar transmit signal.

[0046] The sweep aggregate waveform is particularly advantageous in the setting of group or electronically steered radar antennas. This antenna technology has today entirely replaced the mechanically moving parabolic antenna, previously being the distinctive feature of a radar. Technically, the development means that the mechanical actuators of these antennas have been replaced by phase shifters distributed over the antenna aperture. Due to the revolutionary development of miniaturization of electronic circuits it is even possible to replace the central unit, creating the radar transmit signal and receiving and amplifying the radar echo, by miniature integrated transmit / receive units, distributed over the antenna aperture, each controlling the phase of the transmitted and received signal. With these novel techniques, significant enhancements are obtained, both as regards antenna patter adaptivity and in particular fast reaction time to changes in the scenery the radar is requested to survey.

[0047] The purpose of the disclosed sweep aggregate radar is to make the radar unobtrusive, blending with thermal noise to the extent possible. The disclosed sweep aggregate signals provide 1 ) a 100% duty cycle signal with a noise like envelope, 2) the need for a physical radar beam is eliminated, by pushing beam focusing into the signal processing domain, 3) simultaneous creation of multiple synthetic beams, eliminating the need for any form of scanning - electronic or mechanical. These technical effects and advantages contribute significantly to the overriding goal of unobtrusiveness.

[0048] The radar signals will be transmitted and received by one or more transmit-receive, TR, modules. Thus, each TR-module is configured to transmit and receive a radar signal. According to some aspects, at least one TR-module comprises a transmitter and a receiver. According to some aspects, at least one TR-module comprises a transceiver. The disclosed sweep aggregate radar can be realized either in a monostatic mode, where each TR-module only receives the signal it transmits, or in a multistatic mode of also receiving the transmission from the remaining TR-modules. The advantage of extending operation into a multistatic mode is increased receive sensitivity, further alleviating transmit power.

[0049] Figure 1c illustrates the sweep aggregate signal. The aggregate is formed by a set of linear frequency modulated, LFM, signals (LFMs) separated by known delays. Figure 1c illustrates the signal by its instantaneous frequency obtained as the signal phase derivative. This remains constant throughout the sweeps starting and stopping at the lowest and highest frequency in the band generated. Each LFM signal is thus determined by sweep time, Tsweep, bandwidth, B, and center frequency, fc. Both delays and the amplitude of each LFM signal, while having to be known in subsequent radar processing, may be set to vary from one LFM signal to the next. Characteristically delay is selected significantly shorter than sweep time. According to some preferred aspects for the LFM aggregate, sweep time is selected to agree with coherent integration time, T. Hence, multiple LFM signals are transmitted simultaneously, either by individual TR-modules or by one or several TR-modules transmitting superimposed LFM signals. For the aggregate the signal delays are set to be no smaller than the signal return, dotted lines, from maximum range, rmax. Rather, delays are suitably chosen to correspond to twice this range, to keep separation of the weakest signal returns to adjacent transmitted LFM signals sufficiently large.

[0050] Thus, the method comprises transmitting S100 a radar signal. The radar signal comprises a plurality of linear frequency modulated signals, LFMs, separated by predetermined, though not necessarily equal, time shifts between their instantaneous frequencies. Each LFM has a predetermined amplitude with preferably constant modulus but phase randomly varying from one LFM to the next. Each LFM is configured to sweep linearly across a frequency band for a predetermined sweep time, Tsweep, the frequency band having a predetermined bandwidth, B, and predetermined centre frequency, fc. The plurality of LFMs are configured to form a predetermined continuous aperiodic random signal. The respective time shifts are shorter than the sweep time, Tsweep.

[0051] The method further comprises receiving S200 a radar signal reflection from any target to be detected by the radar, the radar signal reflection comprising the composite set of LFM signal reflections from the target.

[0052] The method also comprises determining S300 the range and / or the radial velocity based on the received S200 radar signal reflection. The technique for processing LFM waveforms, starts by downconverting the echo signal to baseband, by mixing it with the transmit signal. The conversion forms the phase difference between the two signals. Moreover, the technique presupposes the signal reflected by a target to be the echo of the transmit signal delayed by the amount ST . Hence the phase difference is the phase of a complex sinusoid with frequency set by the delay S , according to where B is LFM signal bandwidth and T sweep time, which for sweep aggregate signals is preferably set to agree with coherent integration time but generally for radar adopting LFM radar waveforms is selected much shorter than T. The frequency is known as beat frequency. By applying a Fourier transform, in practice a Fast Fourier Transform, FFT, the echo becomes focused to a frequency peak at making a combination of range and velocity for the target determined. Unambiguous values for range and velocity is found by extending processing over multiple LFM sweeps for a period of time equaling T . Extending the beat frequency Fourier transform by a discrete Fourier transform across the sequence of sweeps, target echoes are focused to spectral peaks at frequency pairs in a beat frequency - Doppler spectral plane. Thus, the Doppler shift of the target is established and thereby target radial velocity, and subsequently range become determined (based on the frequency peak of the linear combination of range and linear velocity).

[0053] Thus, determining S300 the range and / or radial velocity further comprises downconverting S310 the composite received signal set by one or several mixing devices, each adopting for the downconversion one of the transmitted LFM signals, and multiplying this with one or several received signals, it produce a beat signal, separable into frequency bands corresponding to the different LFMs, and within each band representing the target reflection, delayed by the time shifts of the plurality of LFM signals.

[0054] In other words, determining S300 the range and / or radial velocity further comprises downconverting S310 the composite received signal set by one or several mixing devices, each mixing device adopting downconversion by multiplying one of the transmitted LFM signals with one or several received radar signal reflections, thereby producing beat signals, separable into frequency bands corresponding to the different LFMs, and within each band representing the target reflection, delayed by the time shifts of the plurality of LFM signals.

[0055] Stated differently, determining S300 the range and / or radial velocity further comprises downconverting S310 the composite received signal set by one or several mixing devices, each mixing device adopting for the downconversion one of the transmitted LFM signals, the downconversion consisting of multiplying the transmitted LFM signal with one or several received radar signal reflections, thereby producing beat signals, separable into frequency bands corresponding to the different LFMs, and within each band representing the target reflection, delayed by the time shifts of the plurality of LFM signals.

[0056] Determining S300 the range and / or radial velocity also comprises recording S320 the composite received signal after analog to digital conversion.

[0057] The sweep aggregate signal enables the possibility of a mode of operations suitable for high- resolution radar, wherein radar transmission continues during the entire period of receiving the radar echoes. In this case the orthogonality between delayed LFM signals is exploited to form an aggregate of delayed LFM waveforms, each with sweep time set equal to what will be referred to as coherent integration time, cf. Figure 1c. Coherent integration time upper bound is set by the condition that target motion remains predictable within the order of the wavelength during this time. With this condition satisfied echo amplitude can be filtered by analogue or digital means to reduce noise in proportion to the integration time. Typically, coherent integration time in microwave applications varies from a fraction of a millisecond to a fraction of a second, being magnitudes larger than the typical radar echo return times and thereby amounting to a very high processing gain. With sweep time selected as coherent integration time and LFM signal time separation by return time, many LFM signals will be ongoing in parallel, the number of such being coherent integration time divided by return time.

[0058] In the case where each such LFM signal is fed to an individual TR-module in a group radar antenna, there is the same number of TR-modules in the antenna as there is LFM signals in the sweep aggregate. It follows that at any moment of time each TR-module operates at a different frequency, making the signals transmitted and received from them all orthogonal. Moreover, signals at any particular frequency will be transmitted / received at all TR-modules, albeit at different times, corresponding to the set of delays adopted in the sweep aggregate. This is illustrated in figure 1 d, and will be described further below. Compensating for the delays, it will therefore be possible to synthesize directional radar beams, while having all TR-modules remaining active transmitting and receiving at all times. This is illustrated in figure 1e, and will be described further below. Transmit duty cycle for each TR-module is accordingly 100 %. For the sweep aggregate set of delayed LFM signals, the delay separating them is selected to be safely larger than the delay corresponding to the maximum intended radar range.

[0059] Thus, according to some aspects, the predetermined sweep time, Tsweep, is configured to agree to the time available for the received signal to gain coherently during the signal return, limited to an upper bound on target scattering irregularities developing due to target motion in the course of time, preventing further signal gain.

[0060] For illustrative purposes, the sweep time, Tsweep, will assumed to equal the coherent integration time, T, though this is not a strict requirement.

[0061] The echo from a moving target is in turn (approximately but not exactly, as will be analyzed below) a delayed copy of any of these transmitted LFM signals - the delay restricted to a maximum amount < set by maximum allowed radial speed vmaxand maximum allowed range rmax , while c is speed of light. Here, the Doppler term is generally smaller than the range term

[0062] The leakage diminishes with increased delay time separation , so a good design strategy is to keep the LFM signal transmitted next after the LFM signal causing the echo, at the same separation as that to the signal transmitted, hence selecting Since Doppler delay is comparatively small compared to range delay, it will have little effect on the net leakage occurring.

[0063] Thus, according to some aspects, the respective predetermined time shifts of the LFM signals of the aggregate are configured to be no smaller than dictated by the signal return time from a predetermined range constraint range and Doppler shift due to a predetermined radial velocity constraint, in all the time shift preferably is set to correspond to the order of twice the signal return time from the required radar maximum range.

[0064] As described above, determining range and radial velocity can be made from the peak amplitude at frequency 8f , determining the target parameter linear combination As mentioned above, extending the beat frequency Fourier transform by a discrete Fourier transform across the sequence of LFM signals, i.e. sweeps, target echoes are focused to spectral peaks at frequency pairs in a beat frequency - Doppler spectral plane, thus unambigoulsy determining both range rand velocity v.

[0065] This combined process of range and velocity determination can be adopted for any type of waveform. The method is endowed, however, with a difficulty as the radar must meet given requirements for unambiguous range and velocity also when range and velocity are large (the so termed range-Doppler ambiguity). Given radar range r the delay time is implying that for repeated transmissions the repetition interval A must satisfy Thereby velocity determination will rely on samples phase shifted by the amount For the phase shifted samples to be unambiguous, i.e. for the signal to be well-sampled, it is required that yielding the requirement for maximum unambiguous range and velocity.

[0066] Consider for instance long range L-band radar, assuming / max = 200km and Then This is clearly unacceptably low and in many applications, e.g. air surveillance or airborne radar, where significantly higher target speeds may have to be dealt with. Actual radar performance is even more restricted as designs reasons enforces significant margins on the inequality (as above in the case of sweep aggregate radar where was selected).

[0067] One adopted method of resolving the range-Doppler ambiguity is so-called staggering, i.e. of slightly varying the transmit repetition period. Doing so the false (i.e. folded) ranges or velocities arising due to the ambiguity will shift, whereas the true will stay the same and can be found.

[0068] There is an alternative way of resolving this range-Doppler ambiguity, noting that it is a true ambiguity only in its usual context of transmissions being of short duration and / or adopting small fractional bandwidth. In this case Doppler shift can be approximated as while generally it takes the form being instantaneous frequency. For an

[0069] LFM signal in the time span instantaneous frequency is

[0070] Doppler shift becomes For the second term - Doppler dispersion to be significant it is required that it results in a phase difference to the first term, detectable over integration time. Considering LFM signals across multiple sweeps such a phase difference does however not accumulate -the net phase accumulation is only the linear growth Hence the phase growth for only builds up within each single sweep. Upon integration across sweep time it becomes and to become significant the value must be larger than n . Speed resolution adopting this method thereby becomes . Here note that generally for the sweep aggregate radar. Thus, the pulse-Doppler method of determining velocity by center frequency Doppler phase accumulation is very much more precise than the method of discerning Doppler shift by its variation with in-band frequencies.

[0071] Though the resolution provided, adopting Doppler shift variation, is not high it may still be sufficient to suppress the pulse-Doppler ambiguity and thus eliminate the need for additional methods for its resolution, e.g. staggering. As discussed above, the pulse-Doppler ambiguity leaves velocities unresolved according to Hence the resolution required for Doppler shift variation velocity resolution is The requirement implied.

[0072] In this context the sweep aggregate exhibits a singular advantage in that in this case Thus, that delay time is much smaller than coherent integration time, and coherent integration time being equal to sweep time, becomes consistent with small fractional bandwidth. Assuming the choice being made, a requirement for suitable coherent integration time thereby arises, namely Satisfying this requirement unambiguous range and velocity resolution is achieved. Selecting equality in the requirement the number of orthogonal channels, and thus TR modules participating in coherent integration, becomes Increasing Tthe number of elements can be increased. Obviously, the number of channels can also be reduced by increasing AT , i.e. adopting a sparser set of LFM signals in the sweep aggregate. Doing so has the added advantage of further reducing the leakage between adjacent transmissions.

[0073] Thus, according to some aspects, the number, N, of linear frequency modulated signals within the sweep time of the sweep aggregate is set by sweep time divided by time shift.

[0074] There is an additional concern regarding the Doppler-shift impact for sweep aggregate signals. As stated above Doppler shift takes the form being instantaneous frequency. It has the obvious approximation Deviations from the approximation, i.e. Doppler dispersion, increases with velocity v, and beyond some velocity limit destroys the resonant behavior of Doppler shift in the beat frequency Fourier transform. The criterion for this happening is precisely the same as the velocity ambiguity limit above, i.e. the negative impact on beat frequency resonance occurs when

[0075] Summarizing this analysis of the impact of Doppler dispersion, the possibility emerges to obtain unambiguous Doppler by a 2-dimensional Fourier transforms, setting system parameters to yield equality (where N = T / AT is the number of LFM channels)

[0076] If the velocity difference is larger than set by (1.4.2), the target response will become non-resonant and thus poor or absent due to the Doppler dispersion.

[0077] Thus, according to some aspects, determining S300 the range and / or the radial velocity further comprises selecting S330 sweep time, Tsweep, sufficiently long to spectrally resolve the change in LFM signal frequency shifts noticeable in the signal reflected by a moving target, as well as the Doppler shift variation, i.e. Doppler dispersion, during sweep time also occurring for such a target, to an accuracy better than that set by the modulo velocity ambiguity.

[0078] Whilst sweep aggregate signals cannot be directly applied to radar, operating against reasonably fast targets, in a standard Fourier transform way, signal processing can be modified to establish a workable approach. The starting point is the insight that multiplying the beat signal with a complex sinusoid oscillating at a Doppler frequency set by some velocity VQ , the beat signal becomes dependent on the speed difference rather than target actual speed v. Performing a Fourier transform, for this to be resonant it is required that

[0079] If moreover the 2-dimensional Fourier transform technique could be applied to yield unambiguous Doppler in the sweep aggerate case.

[0080] This insight can be used to obtain highly accurate determination of target range, radial velocity and direction.

[0081] In short, according to some aspects, the method further comprises, selecting S340 a set of radial velocity hypotheses, separated by the modulo velocity intervals as described above and below. The method further comprises, for each hypothesis, multiplying S342 by a complex sinusoid compensating for the Doppler dispersion, beat frequency variation and phase growth due to Doppler between the aggregate LFM signals. The method also comprises, for each hypothesis, performing S344 a Fourier transform of each beat signal of the aggregate, thereby obtaining the beat signals represented as beat frequency responses. The method additionally comprises, for each hypothesis and each beat frequency, performing S346 a discrete Fourier transforms across the set of LFM, thereby testing for different true Doppler and radial speed differences to the each of velocity hypotheses. Details relating to these aspects will be described further below.

[0082] Consider the basic monostatic case i.e. each TR module processes just the echo of the LFM signal transmitted by that particular module. For aggregate channel n , denote the signal of a target with range and velocity r, v , while denoting the transmitted signal Hence, with he scattering amplitude

[0083] The downconversion product reads is an approximation of the conjugate product insofar that is neglects a phase term

[0084] This term will only be of importance if its maximum change during sweep time is of the order ^2 or larger. However, for the L- and X-band applications, the phase change is at worst 0.18K , so indeed the phase term can be disregarded.

[0085] Up to a range dependent phase factor (incorporated in can be rearranged

[0086] The first phase term is due to the Doppler dispersion occurring for each LFM signal. This is typically non-negligible for the slow sweeps of the disclosed sweep aggregate signal. The second term is beat frequency, shifting by a phase difference between neighboring LFM channels.

[0087] The third term is due to center frequency Doppler shift, manifested in a phase shift growth along the sweep aggregate LFM channels.

[0088] The basic signal processing strategy is to a perform a Fourier transform on by integration over time intervals representing the sweep aggregate

[0089] LFM signals. For Doppler dispersion to be negligible under such integration the net phase growth of the Doppler dispersion term accumulated over sweep time must obey

[0090] The same requirement is obtained considering the interval in which the Doppler dispersion exponent is non-zero. The interval is attained as

[0091] Letting At = T the requirement (3A.5) is demonstrated.

[0092] The Doppler velocity ambiguity is also suppressed by the shift in beat frequency. The shift is given by the difference from first to last sweep, i.e. from H The shift will be negligible only if being smaller than the spectral resolution 1 / T attainted for sweep time T . Beat frequency drift arising due to excessive speeds must not be larger than the width of the resolution bin, meaning that the span of allowed velocities must satisfy

[0093] Evidently the criteria for Doppler dispersion and beat frequency change are qualitatively similar though the Doppler dispersion criterium is twice as restrictive.

[0094] According to (3A.4), for a target with range r and radial velocity v , the nth LFM channel yields a peak at beat frequency The amplitude of the peak will however be disrupted by the Doppler dispersion unless v is sufficiently close to zero according to the analysis above To compensate for the mismatch let the Fourier transform be preceded by a phase factor multiplication with 8v = v-vtest. Note that Sv obeys (3A.5). For finding target beat frequency

[0095] , as well as a high-resolution estimate of v = 8v+vtest, form the Fourier transforms of (3A.8)

[0096] Using the time difference to as integration variable The expression will by approximations be factorized so that the integrand does not depend on

[0097] LFM number n. First, the exact expression can be recast in the form

[0098] Moreover, with bandwidth B significantly smaller than center frequency f£ whereby

[0099] Recall that Tand A T was selected according to A follows that (3A.11 ) unambiguously represents the Doppler shift and beat frequency by the 2-dimensional Fourier transform performed over the number of sweeps

[0100] Here the range dependence of varies from one LFM channel to the next depending on which particular position in the group antenna it represents, and consequently the varying range to the target following. Incorporate this effect by the slight notational change

[0101] C the vector from the group antenna center position, then the vector from antenna center position to any of the TR-modules. With this notation (3A.11) can be recast into the following 2-D Fourier transform

[0102] The integrand is seen to oscillate rapidly thus yielding a net zero outside the resonance In the resonant case (where also the expression becomes (also invoking (3A.5)

[0103] Generally, inclusion of some tapering function in Fourier transforms (as is the case in (3A.13)) acts to shorten the effective integration interval and will therefore, to some extent, reduce spectral resolution. The spectral broadening corresponds to a reduced amplitude in the case of resonance, impairing on the ideal coherent gain the integration may yield. The integrand in (3A.14) can be considered just as such a tapering function, thus having a deteriorative effect on what coherent gain may be achieved. Another deteriorative effect in (3A.14) is how the phase of the integral varies with n. With the phase variable the contribution to coherent gain from each term in (3A.14) is given by the integral value times the difference in phase of each integral in (3A.14) and their phase mean value.

[0104] Note that in (3A.13) both the velocity vand directional information m depends on the same index n. The issue arises whether this interdependence between v and m causes any ambiguities. To investigate, assume that (3A.13) would allow for velocity and directional errors respectively. It will be assumed that errors are small and m£orthogonal to m , keeping to unit length. For a false target, resonant to true target beat frequency, the following expression must be valid The implied relation is satisfied only if all TR-modules are equidistantly separated in order of appearance, i.e. For the half wavelength separation If

[0105] 0 = 0 , i.e. beam synthesis in the direction normal to the aperture, the condition agrees with that of avoiding any Doppler ambiguity, which above has been recognized as the limit for the allowed range speed variation At oblique beam directions vEshrinks but will never be small since the beam steering angle is limited - deviations of no more than 60° from the normal direction have been assumed.

[0106] Depending on the application, it might be sufficient to only consider Doppler, e.g. in the case of close targets, such as radars for cars in city traffic. Alternatively, as will be elaborated further below, lobes can be formed in postprocessing when processing the received signals in order to test all velocity hypotheses and directions.

[0107] Thus, according to some aspects, based on target response being weak or absent if hypothesis is untrue, selecting S350 as corroborated velocity hypothesis the one providing maximum Doppler difference response, thus obtaining the true Doppler response from corroborated velocity hypothesis and Doppler difference and thereby also the true target radial velocity and range.

[0108] In order to avoid the identified ambiguity, a linear map of LFM channels to an equidistant grid of TR modules must be avoided. Obviously to obtain an effective antenna an equidistant grid with half wavelength grid separation is suitable. Typically it would extend in two dimensions, but exact shape is of little concern. Assume array element ordering is by linear progression, say left to right row after row, going from +N / 2 to N / 2 . The crucial requirement is that the assignment of LFM channels to TR module number is randomized. Thus let perm(0,± l,...,±N / 2) be some arbitrary permutation of 0,+l,...,+Nl2 . The assignment is then

[0109] It follows that the summation in (3A.15) becomes a summation of N complex sinusoids, yielding a net mean modulus of The signal to sidelobe ratio for velocity (as well as indirectly range) and angular accuracy is thus 1 / N (i.e. -20 dB in the case N = 100 ).

[0110] Thus, according to some aspects, transmitting S110 each LFM signal in the set of LFM signals via a single transmit unit, the single transmit unit being one of the transmit units of an array antenna, and wherein the attribution of transmit units to LFM signals follows some random pattern. The method further comprises, receiving S210 each LFM signal in the set of LFM signals by the particular transmit unit from which it was transmitted.

[0111] Before going into detail, an illustration of some aspects of the method, from reception at a TR- module to determination of target range and / or radial velocity can be described as follows. A TR- module transmits a stored record of a particular LFM signal of the sweep aggregate signal. The TR-module then receives a signal reflection and filters out the LFM signal it transmitted by downconverting the received signal with the stored LFM signal, and then passing the mixed signal through an LFM bandpass filter. After analog direct current, DC, cancelling circuitry, the signal is converted from analog to digital. Processing of the digitally converted signal commences by multiplication with the cosine window. The subsequent step is removing the residual, though still strong, DC transmit signal leakage. The filtering is obtained by an FFT and then zeroing the lowest spectral components, after which an inverse FFT restores the signal to the time domain. Subsequent signal processing includes compensation for beat frequency drift and Doppler dispersion. Compensation is obtained by dividing processing into parallel threads, each of which is phase adjusted by 1) beat frequency alignment to n=0 LFM channel based on a speed hypothesis combined with 2) Doppler dispersion suppression for the same speed hypothesis and 3) Speed uncertainty reduction to speeds in the vicinity of vtest. Only if these factors are coherently matched to true target velocity, the target response will register as a focused beat frequency peak in subsequent Fourier transform. Stacking velocity / beat frequency response from the various speed hypotheses are made available at the output of each TR module.

[0112] The beat frequency response is phase shifted to a required beam direction by steering vector distributed across the beat frequency responses of all TR-modules of the radar. Targets are then detected by a performing an FFT across all LFM channels within each bin. Resulting Doppler frequency yields target velocity minus the value of the particular bin. In the obtained 2- dimensional beat frequency-velocity or equivalently range-velocity representation target are finally found by standard thresholding routines. This is also illustrated further in relation to figure 2.

[0113] Proceeding in the proposed manner, the overall processing task, even if large in its entire, is mapped into a number of parallel processes, each manageable. For the TR modules there is the task of applying an FFT taking the TB / N beat signal samples into the same number of beat frequency bins. For the velocity interval there are 20 such transforms to be conducted. The disclosed method can be realized either in monostatic mode, wherein each transmit-receive, TR, module of the array antenna only receives the signal it transmits, or in multistatic mode of also receiving the transmission from the remaining TR-modules.

[0114] Thus, according to some aspects, receiving S200 the radar signal reflection further comprises receiving S220 the LFM signal emanating from any of the transmit units in several, preferably all, transmit units of the array antenna.

[0115] Thus, consider operation in a multistatic mode, wherein each TR-module processes the full set of impinging LFM signal echoes. Downconverting as before the beat signals for each LFM signal will have bandwidth B / N , centered around frequency By analogue-to- digital, AD, conversion at full radar bandwidth, followed by bandpass filtering, the different beat signals are separated.

[0116] According to some aspects, the method further comprises forming S352 a set of target directional hypotheses by modifying the velocity hypotheses by linearly combining the LFM beat signals by a discrete Fourier transform, combined with a steering vector phase factor constructing a directive radar beam, for each target directional hypothesis, the steering vectors being separated by antenna angular resolution and representing a two- or three-dimensional scan sector of the radar.

[0117] Consider data restricted to a time interval With this time window restriction, the linear transmit sweep of each TR module n will in the downconversion process catch the linear sweeps from the rest of the aggregate to a more or less truncated extent. As above, shift beat signal time individually for each module n according to Thereby, receiving transmissions from TR-module k in TR-module n, when k < n the end of the sweep will be caught corresponding to an overlapping time interval Similarly, for a sweep k > n the beginning of the sweep is caught during an overlapping time interval In all

[0118] Note that available sweep time for each LFM signals is TR module n LFM signal k downconversion becomes

[0119] Here rk,n = r + Srn-3rk . The overall phase in (3A.19) is suitably re-expressed

[0120] Comparing (3A.2) and (3A.3) it follows, utilizing the notation of (3A.4)

[0121] The first phase term in expresses the expected shift to the center frequency for the downconverted LFM signal k in the n TR module. The second term is the phase shift between the k and n LFM signals. It depends on how time t = 0 is selected and LFM signals subsequently counted. As an additional complication to (3A.13) for the monostatic case, coherent summation of (3A.22) requires compensation for this phase factor. Center frequency shift is achieved by digital down-conversion, multiplying each phase factor The phase shift term, it is noted, can be restated in terms of the radar time-bandwidth product, i.e It follows that the phase shift assumes very large values, while correctly assessing this value modulo 2π is crucial for successful coherent summation. In the monostatic case any small frequency deviation in the transmit signal from radar specification cancels, as the transmit signal is used for downconversion. Since transmit and downconversion signals are different in the multistatic case, no such cancellation takes place and any lack of synchronism between the TR modules must be compensated for.

[0122] In the monostatic case transmit leakage into the receiver chain manifests itself after downconversion as a strong DC signal. Being a DC signal there are analogue methods for its attenuation, thus avoiding ADC saturation. Leakage from the remaining TR modules is outside the beat frequency band and can be removed by analogue filtering. In the multistatic case this leakage must be handled after ADC conversion. It is expected that it will be no stronger than the analogue attenuated internal transmit leakage, thus stressing ADC dynamic range no further than when handling this. Rather, good use can be made of the leakage residues, serving as a synchronization references, representing a radar echo with range and velocity zero and with complex amplitude is a non-important real value between zero and unity determining TR-module attenuation.

[0123] Measurement of beat frequency thus determines namely frequency and complex value of the beat frequency peak

[0124] It follows that the functions can be determined and be compensated for.

[0125] Since the k,n-dependent compensation in effect entails a reduction to the monostatic case the various dependencies handled in the subsequent processing steps of integrating and summing (3A4) can be largely copied from the monostatic case to (?) - the main difference is that summation can be conducted for both indices k,n in contrast to (3A.13).

[0126] Compare (3A.23) with (3A.4) and how (3A.11) follows from (3A.4). Consider for simplicity beam formation normal to the antenna aperture, i.e. Then for t

[0127] In the resonant case (where also the expression becomes (cf.

[0128] (3A.13) and (3A.14)) The approximation of the integral with can be verified numerically.

[0129] While (3A.25) pertains to the signal received in a single TR-module, the final processing stage is coherent summation of the signals across all TR-modules. Due to the small phase and amplitude variations of the totality of LFM signals such summation corresponds to summation with no further weighting than that given by the beam steering vector Beam direction in the resonant case corresponds to . Hence

[0130] From (3A.25) in the resonant case of target values for m, fy, fB

[0131] In (3A.14) integration was compared to a weighting function reducing spectral resolution, or equivalently making effective integration time smaller than T. In that case the approximation error in substituting the integral in (3A.14) with T was negligible. For the multistatic case (3A.25) the situation is more complex and now there are two factors combing in reducing coherent integration gain from its nominal TBN2value. For one, integration times for the suite of multistatic responses is and thus smaller than full integration time T to varying degrees

[0132] Secondly, approximating the integral in (3A.14) with the result is more variable than for substituting the (3A.4) integral with T. Similar to the monostatic case, while (3A.27) provides an analytic, albeit approximate, expression for coherent gain, coherent gain can be computed accurately in any particular example. As for (3A.14) this can be done either as a direct summation of the complex amplitudes, where the modulus determines the coherent gain, or preceded by a phase compensation, where the phase of the (3A.25) integral for each n,k are compensated for (amount to summation of the modulus of the n, k amplitudes).

[0133] The multistatic processing task, i.e. that of implementing (3A.24), follows correspondingly to monostatic (3A.11 ). There are two main differences. One is the difference is the extra processing step of digital downconversion of the frequency shifted LFM signals in each TR module. The other is summation over index pairs rather than a single index. As for the monostatic case, the beat frequency spectra are suitably computed for each TR module separately. The computation amounts to the task of applying FFTs taking for each of the N beat signals in the module the TB / N beat signal samples into the same number of beat frequency bins. There are N signals in each TR module.

[0134] Remaining processing steps is, according to (3A.27), to combine the beat signals of each TR module to form a Doppler processed signal for each beam direction. For each TR module the processing burden for forming Doppler spectra in one particular beam direction amounts to a FFT of length N for each of the beat frequency points.

[0135] Thus, the beat frequency response is phase shifted to a required beam direction by steering vector distributed across the beat frequency responses of all TR-modules.

[0136] Targets are then detected by a performing an FFT across all LFM channels within each bin.

[0137] Resulting Doppler frequency yields target velocity minus the value of the particular bin. In the obtained 2-dimensional beat frequency-velocity or equivalently range-velocity representation targets are finally found by standard thresholding routines.

[0138] Thus in all, according to some aspects, the method comprises selecting S354, as indicating a validated target, every case where the 2-dimensional Fourier beat-frequency-Doppler transform, weighted by compensation for Doppler dispersion, beat frequency drift, target Doppler, i.e. radial velocity, and target direction, reaches beyond a predetermined threshold value.

[0139] Having LFM signals repeated at intervals , slow time velocity determination will rely on echoes phase shifted by the amount For the phase shifted samples to be unambiguous, i.e. for the signal to be well-sampled, it is required that Assume that repetition rate agrees with that of LFM separation in a sweep aggregate, i.e. The requirement follows.

[0140] For certain radar applications, e.g. long range L-band radar, which can have an effective maximum range the restriction on vmaxmay become prohibitive.

[0141] As described above, TR module phase centers wander randomly from one LFM transmission to the next. This causes directional defocusing for targets at ranges r>cAr)2 when applying beam focusing to the LFM transmission. By consequence, these far-off targets will not be detected and will thus not cause false range target detections for the next sweep. Alternatively, the range limitations set by A can be overridden by continuing beam forming and processing data beyond r for the each LFM transmission, letting LFM channels overlap.

[0142] According to some aspects, determining S300 the range and / or the radial velocity further comprises allowing the LFM signal time shifts of the aggregate to be smaller than the signal return time from far away range or high velocity targets. According to some aspects, determining S300 the range and / or the radial velocity further comprises downconverting S360 the overshooting range returns by the succeeding LFM signal. According to some aspects, determining S300 the range and / or the radial velocity further comprises assigning S362 transmit sources in the antenna array to the downconverted range returns which will be false in both range, velocity and direction if these are overshooting returns. According to some aspects, determining S300 the range and / or the radial velocity further comprises superimposing S364 echoes from transmission of one LFM signal to next the overshooting erroneous echo directions varies from transmission of one LFM signal to next. According to some aspects, determining S300 the range and / or the radial velocity further comprises removing S366 overshooting and thus falsely positioned targets by thresholding, as these echoes having varying directional assignments will appear weak compared to the echoes of targets, falling within the predetermined range and velocity constraints.

[0143] Figure 1g illustrates technical effects of the method in different contexts. Specifically, figure 1g illustrates examples of sweep aggregate waveforms for L-band long range radar, for X-band medium range and W-band short range radar. The first two cases are set up with group antenna air surveillance in mind allowing very high targets speed (indeed 1000 m / s is no sharp upper limit). The W-band application is typically for automotive radar with the orthogonal LFM signals not considered to feed a large group antenna but rather allow for the possibility of different radars adopting different channels and thus avoiding mutual interference.

[0144] Consider the L- and X-band examples in Figure 1g. For these was found possible. Here, single channel reception is assumed for X band, and receiver bandwidth (agreeing with range frequency shift in Figure 1d) will be 500kHz . For the long range relatively narrow band L- band, receiver bandwidth is then preferably the full bandwidth of the radar, i.e. 1 MHz. For both cases bandwidths allow for 14 bit AD conversion, i.e. TR-module transmit receive isolation is largely determined by circulator performance. Circulators with 10% bandwidth providing 40 dB isolations are available. The isolation can be further improved upon since after downconversion the transmit signal is a DC signal, which is cancellable by e.g. an operational amplifier. Here, for L- and X band will be assumed achievable. As for TR-module antenna gain, this will be set by search solid angle. Assume for simplicity that the beam steering in the group antenna takes place in a cone normally directed to the antenna aperture. Assuming the cone 120° wide, the unit sphere area spanned is n . Sphere area 4n implies GRX = GTX = 4 . Inserting the Figure 1d values for B, T and maximum range, it can be shown that for the L- and X-band case respectively. With transmit power for both the L- and X-band cases (hence 71 / 1 / per TR-module), yields for the L- and X-band case respectively.

[0145] In the W-band example, it is suggested that the sweep aggregate is adopted for road vehicles in the vicinity of each other. The LFM signal orthogonality is in this case adopted to avoid interference between the radar of the different vehicles. With typical radar parameters for road vehicle applications, a sweep aggregate can consist of the order 1000 channels, as shown in figure 1f. Each vehicle basically exploits a single LFM of the sweep aggregate, implying that a collection of perhaps 1000 road vehicles can operate their radars in the immediate vicinity of each other without mutual interference. Signal processing, hardware design, price, complexity and indeed the very purpose of the radar is different for this application than for the present invention, which provides the technique and purpose of the full sweep aggregate exploited by an individual radar.

[0146] Consider one of the TR-modules in a sweep aggregate radar. The response of a point target at range r in the form of received power is determined from radar transmit power. Coherent signal processing can be conceived as a means of compressing received power into a bandwidth being the reciprocal of the coherent integration time 1 / T . The minimum radar cross section for detectability is that yielding equality between so processed received power (determined by the radar equation) and thermal noise within this bandwidth, i.e

[0147] .The module transmit power required for any particular noise equivalent cross section is thereby determined by

[0148] As described above, within each TR module the receive signal is downconverted and Fourier transformed. Applying the Fourier transform, transmit signals of the sweep aggregate will reveal themselves at beat frequency peaks while target echoes of the sweep aggregate transmissions, appear in each TR module receiver, spanning the full bandwidth, being stacked beside each other at frequencies - The echoes can thus be separated by bandpass filtering, keeping only the echo for n = 0 in the monostatic case. In the filtering process, it is recognized that the echoes being weak have to compete with leakage of the transmissions ongoing in the TR modules. Filtering to the required degree of fidelity can only be achieved digitally. In this there are two concerns. The first is to obtain sufficient ADC dynamic range (i.e. ADC number of bits) to keep AD conversion sensitive to the level of thermal noise, while not being saturated by transmit leakage. Secondly digital filtering sidelobe performance must not destroy the achievable sensitivity. Monostatic transmit leakage (appearing as a DC component after downconversion) is expected particularly strong and the dimensioning factor in TR module design. Monostatic transmit leakage will be reduced in amplitude compared to the level of the ongoing transmission - the reduction factor ^0 / will be set by circulator performance combined with whatever further attenuation is achieved by DC cancellation circuitry. Still, transmit leakage is expected to be many magnitudes larger than typical echo signal amplitudes. High performance AD conversion will be required so that this transmit signal residual corresponds (with some safety margin) to ADC most significant bit i.e exploting the full ADC dynamic range NAD. The level of the least significant ADC bit is required to agree with that of thermal noise. It follows that useful TM-module transmit power is

[0149] Typical assumptions for a noise / module for L- and X-band air surveillance radar and W-band automotive radar are given in figure 1f. Resulting values for number of bits are also provided.

[0150] To further illustrate the technical effects and advantages, the sweep aggregate signal is described in more detail below.

[0151] To analyze LFM signal orthogonality and in particular the impact of time and bandwidth truncation, a mathematical description of sweep functions (the mathematical generalization of LFM signals for infinite time and bandwidth), their properties and in particular the combination of such functions with the same sweep rate into sweep aggregates is provided. It will be seen that true orthogonality prevails in a sweep aggregate. Crucial to sweep aggregate radar is however that sweep rate may change due to Doppler shift - an effect here termed Doppler dispersion. The necessary modifications required to incorporate Doppler dispersion are described above and below. As a preliminary, the Fourier transform of the delta function will be required. Here the Fourier transform conventions will be as follows

[0152] The delta function Fourier transform follows immediately

[0153] Now consider functions given at a fixed sweep rate 2α , i.e. fixed linear frequency rise The associated phase function is consequently The Hilbert space basis functions to be exploited are (with t and r unbounded)

[0154] Any function can be expanded in functions computing the expansion coefficients as functional space scalar products in full analogy to the case of the Fourier transform

[0155] The map will be referred to as the sweep transform. It has many properties similar to the Fourier transform. Given the original function / (r) can be retrieved by computing

[0156] The reconstruction follows from

[0157] Thereby which was to be proved.

[0158] In the practical applications the sweep functions will be band and time limited. The limitations are imposed considering the time dependent instantaneous frequency given by

[0159] Require that sweep functions only are non-zero within a frequency band of width B and a time duration T . Thereby with the sweep aggregate LFM signals made up by sweep functions with a so selected, and continuously repeated at a sweep period T . For transmitted LFM signals the phase 0 may vary randomly from one sweep to the next. Select the number of LFM signals in the aggregate. Introduce sweep number notation The entire sweep aggregate transmit signal becomes, up to a scaling with transmit amplitude The individual LFM signals are thus delayed, phase shifted copies of the generic signal

[0160] Neglecting Doppler dispersion, target response of any of the sweep aggregate signals will consist of same aggregate LFM signal, though with the delay imposed (recall

[0161] ). The target response becomes (2A.10) modified into

[0162] Note that for t within any such an interval

[0163] The result is thus a time harmonic function (alternatively termed complex sinusoid) at the beat frequency Forming the conjugate products (2A.12) thus enables efficient signal processing, applying a finite Fourier transform across sweep time T . Normalization for a finite Fourier transform is different from the infinite case (2A.1 ). The finite Fourier and its Fourier series inverse are stated

[0164] Since Fourier transform of yields a frequency peak at it may be viewed as performing pulse compression of the radar echo. In the case of an unbounded sweep would result in a delta function but for finite times the peak formed function will have sidelobes. As will be demonstrated, the sidelobes become unacceptably large, unless weighting / tapering is introduced in the transform. Such an improved transform will be provided subsequently.

[0165] First however, analyze the un-tapered, i.e. rectangular transform. For simplicity regard the n = 0 sweep - the same results obviously pertain to the rest of the aggregate sweep functions.

[0166] Of relevance here is the sidelobe level for the zero beat frequency, representing the transmit signal. Thus consider

[0167] In particular, note that . The second expression is recognized as the scalar product between (normalized) received signal at delay Sr and transmit signal in functional space sense, and thus measures the orthogonality between these. With the transmit signal response normalized according to the first expression constitute the power ratio by which transmit leakage affects the echo signal and must be checked for the radar echo not to be overwhelmed.

[0168] A noteworthy observation is that according to (2.A.15), leakage is independent of T. In the sweep aggregate case but the same expression applies equally well in the opposite case, i.e. for leakage due to range sidelobes the normal setting of fast chirp or stretch pulsed transmissions. For these, leakage is partly reduced by an intermittently operating transmitter, though the intermittency of the gating may by itself be a further source of sidelobes, so a concern for transmit sidelobe leakage remains also for this case.

[0169] Sidelobes must not overwhelm target signals levels. These are set by hardware performance and signal processing gain. With the power leakage being effectively a condition for square weighting Fourier transform sidelobes can be shown to be

[0170] Common to the three application examples in Figure 1d the quantity NADBT (referred to as required FFT TX / RX ratio in Figure 1d) is found to be about 150 dB. By comparison the square window FFT TX / RX ratio is much inferior and far from making the inequality (2A.16) satisfied. A remedy might be to restrict surveillance range from the maximum allowed for the sweep aggregate i.e. whereby transmit power can be reduced to some value while the condition of coherent processing yielding thermal noise sensitivity remains. From (1A.2)

[0171] Clearly, even though sidelobe influence grows for smaller delay, i.e. shorter range, the radar return grows more rapidly. Consequently, there is indeed a range 'max i below which sidelobe influence will not overwhelm the radar echo. As implied by the target response

[0172] Values for in the three application cases, given in Figure 1 d, become 313 m, 31 m and 0,03 m respectively. Thus, reducing maximum range to achieve sufficient isolation makes the three radar examples quite useless for their respective application.

[0173] Just as (2A.14) may be viewed as (2A.4) with a square truncation imposed, any other window function W(t) can be adopted in the scalar product definition (2A.4). As it turns out the insertion of such a window will have a dramatic influence on resulting orthogonality in the sweep aggregate application. Allowing for the window function, (2A.4) assumes the form Though still with the requirement improved orthogonality will now be demonstrated. Indeed, it will reach the required levels of isolation. The particularly effective window to be adopted and analyzed will be termed full cosine tapering. The window is defined as

[0174] Here

[0175] (2A.24) is noted to have denominator zeros both for Sr=0 and 8T - 1 / B . In both cases also the numerator is zero so the actual function values are obtained as limit values

[0176] For radar applications In this case (2A.24) can be approximated

[0177] Since ust as for the square window yields transmit signal fractional power leakage. Hence, that the FFT TX / RX ratio must not overwhelm hardware limitations takes the form

[0178] The inequality is satisfied with ample margins for the cosine widow.

[0179] Processing so far yields a coherent gain TB i.e. of the order 60 dB in the L- and X-band cases of Figure 1d. It pertains to processing each LFM channel individually and will be significantly improved utilizing all channels, i.e. by synthetic beam formation as described above and below. As indicated in Figure 1d this step performs a discrete Fourier transform within velocity spans Av around each velocity hypothesis bin and each beam direction, i.e. steering vector assumption, Coherent gain NTB is thereby achieved.

[0180] Thus, according to some aspects, the centre frequency, fc, is configured to be in the range of eight to twelve gigahertz, GHz, and wherein the bandwidth is configured to be in the range of 50 to 500 megahertz, MHz, preferably 100 MHz. According to some aspects, the ratio of the predetermined bandwidth, B, divided by the predetermined centre frequency, fc, B / fc, is one percent, and wherein the centre frequency, fc, is configured to be in the range of one GHz to thirty GHz.

[0181] Figure 2 illustrates a radar system 200 for estimating target range and / or radial velocity. The radar system 200 comprises an antenna array 204. The antenna array comprises at least one transmit-receive, TR, module 210a, 210b. Each transmit-receive module comprising a pair of transmit and receive units 212a, 212b, such as a transceiver. Each transmit-receive module being configured to transmit and receive a radar signal as disclosed above and below.

[0182] The radar system 200 further comprises processing circuitry 220 configured to cause the radar system to carry out the method for estimating object range and / or radial velocity as described above and below. According to some aspects, the processing circuitry 220 comprises a processor 221 and a memory 222. The memory 222 is configured to store a computer program for estimating target range and / or radial velocity thereon. The computer program comprises computer program code which, when executed by processing circuitry, e.g. the processor 221 , of the radar system for estimating object range and / or radial velocity, causes the radar system to carry out the disclosed method for estimating object range and / or radial velocity.

[0183] According to some aspects, at least part of the processing circuitry is integrated into the antenna array 204.

[0184] According to some further aspects, at least part of the processing circuitry is integrated into each TR-module 210a, 210b, as will be described further below.

[0185] Illustrated is an example outline of signal route in sweep aggregate radar. The diagram tracks the processing flow from a particular TR-module 210a. Illustrated is an example wherein the TR- module 210a only receives the LFM signal transmitted from the TR-module, a situation achieved by the narrowness of band pass filter 235. Basic to the radar system is the stored record 231 of a particular LFM signal in the sweep aggregate, which is emitted by the TR unit antenna 212a. The echo is channeled to the receiver chain, while transmit leakage is attenuated by circulator 232. The received signal is downconverted by mixer 234 making the residual transmit signal appear as a DC signal. Standard analog DC cancelling circuitry (not shown) obtains further analog cancellation of this, beyond the circulator isolation. The resulting signal is AD converted

[0186] 236 at the rate set by single channel bandwidth (given by allowed range delays as explained above in relation to figures 1a-d).

[0187] Processing of the digitally converted signal commences by multiplication with a cosine window

[0188] 237 as described above. The subsequent step is removing the residual, though still strong, DC transmit signal leakage. The filtering is obtained by a Fast Fourier Transform, FFT, 238 and then zeroing the lowest spectral components 239, after which 240 an inverse FFT restores the signal to the time domain. Subsequent signal processing includes compensation 241 for beat frequency drift and Doppler dispersion. Compensation is obtained dividing processing into parallel threads, each of which is phase adjusted by 1) beat frequency alignment to n=0 LFM channel on speed hypothesise , followed by 2) Doppler dispersion suppression for speed hypothesis Only if these factors are coherently matched to true target velocity, the target response will register as a focused beat frequency peak in subsequent Fourier transform 242. Stacking velocity / beat frequency response from the various speed hypotheses are made available at the output of each TR-module 243. The beat frequency response is phase shifted to a required beam direction by steering vector distributed across the beat frequency responses of all TR-modules 244. Targets are then detected by a performing an FFT 245 across all LFM channels within each e bin. Resulting Doppler frequency yields target velocity minus the e value of the particular bin. In the obtained 2-dimensional beat frequency-velocity or equivalently range-velocity representation target are finally found by standard thresholding routines.

Claims

CLAIMS1. A method (100), performed in a radar system, for estimating target range and / or radial velocity, the method comprising transmitting (S100) a radar signal, the radar signal comprising a plurality of linear frequency modulated signals, LFMs, separated by predetermined, though not necessarily equal, time shifts between their instantaneous frequencies, each LFM having a predetermined amplitude with preferably constant modulus but phase randomly varying from one LFM to the next, each LFM being configured to sweep linearly across a frequency band for a predetermined sweep time (Tsweep), the frequency band having a predetermined bandwidth (B) and predetermined centre frequency (fc), wherein the plurality of LFMs are configured to form a predetermined continuous aperiodic random signal, wherein the respective time shifts are shorter than the sweep time (Tsweep), receiving (S200) a radar signal reflection from any target to be detected by the radar, the radar signal reflection comprising the composite set of LFM signal reflections from the target, and determining (S300) the range and / or the radial velocity based on the received (S200) radar signal reflection, wherein determining (S300) the range and / or radial velocity further comprises• downconverting (S310) the composite received signal set by one or several mixing devices, each mixing device adopting downconversion by multiplying one of the transmitted LFM signals with one or several received radar signal reflections, thereby producing beat signals, separable into frequency bands corresponding to the different LFMs, and within each band representing the target reflection, delayed by the time shifts of the plurality of LFM signals,• recording (S320) the composite received signal after analog to digital conversion.

2. The method according to claim 1 , wherein the predetermined sweep time (Tsweep) is configured to agree to the time available for the received signal to gain coherently during the signal return, limited to an upper bound on target scattering irregularities developing due to target motion in the course of time, preventing further signal gain.

3. The method according to claim 1 or 2, wherein the respective predetermined time shifts of the LFM signals of the aggregate are configured to be no smaller than dictated by thesignal return time from a predetermined range constraint range and Doppler shift due to a predetermined radial velocity constraint, in all the time shift preferably is set to correspond to the order of twice the signal return time from the required radar maximum range.

4. The method according to any of the preceding claims, wherein the number, N, of linear frequency modulated signals within the sweep time of the sweep aggregate is set by sweep time divided by time shift.

5. The method according to any of the preceding claims where Doppler shift of the target is measured as beat signal phase shift across the LFM signals of the sweep aggregate, with the phase shift proportional to target radial speed modulo an unknown number of full turns of phase, between the LFM signals, and where the unknown number of turns restricts target radial speed to be determined modulo velocity intervals set by this unknown number of turns.

6. The method according to claim 5, wherein determining (S300) the range and / or the radial velocity further comprises- selecting (S330) sweep time (Tsweep) sufficiently long to spectrally resolve the change in LFM signal frequency shifts noticeable in the signal reflected by a moving target, as well as the Doppler shift variation, i.e. Doppler dispersion, during sweep time also occurring for such an target, to an accuracy better than that set by the modulo velocity ambiguity.

7. The method according to claim 6, further comprising selecting (S340) a set of radial velocity hypotheses, separated by the modulo velocity intervals implied according to claim 5,- for each hypothesis, multiplying (S342) by a complex sinusoid compensating for the Doppler dispersion, beat frequency variation and phase growth due to Doppler between the aggregate LFM signals,- for each hypothesis, performing (S344) a Fourier transform of each beat signal of the aggregate, thereby obtaining the beat signals represented as beat frequency responses, andfor each hypothesis and each beat frequency, performing (S346) a discrete Fourier transforms across the set of LFM, thereby testing for different true Doppler and radial speed differences to the each of velocity hypotheses.

8. The method according to 7, further comprising based on target response being weak or absent if hypothesis is untrue, selecting (S350) as corroborated velocity hypothesis the one providing maximum Doppler difference response, thus obtaining the true Doppler response from corroborated velocity hypothesis and Doppler difference and thereby also the true target radial velocity and range.

9. The method according to any of the preceding claims, further comprising- transmitting (S110) each LFM signal in the set of LFM signals via a single transmit unit, the single transmit unit being one of the transmit units of an array antenna, and wherein the attribution of transmit units to LFM signals follows some random pattern, receiving (S210) each LFM signal in the set of LFM signals by the particular transmit unit from which it was transmitted,- forming (S352) a set of target directional hypotheses by modifying the velocity hypotheses by linearly combining the LFM beat signals by a discrete Fourier transform, combined with a steering vector phase factor constructing a directive radar beam, for each target directional hypothesis, the steering vectors being separated by antenna angular resolution and representing a two- or three-dimensional scan sector of the radar, and- selecting (S354), as indicating a validated target, every case where the 2-dimensional Fourier beat-frequency-Doppler transform, weighted by compensation for Doppler dispersion, beat frequency drift, target Doppler, i.e. radial velocity, and target direction, reaches beyond a predetermined threshold value.

10. The method according to claim 9, wherein receiving (S200) the radar signal reflection further comprises receiving (S220) the LFM signal emanating from any of the transmit units in several, preferably all, transmit units of the array antenna.

11. The method according to claim 9 or 10, wherein determining (S300) the range and / or the radial velocity further comprises- allowing the LFM signal time shifts of the aggregate to be smaller than the signal return time from far away range or high velocity targets,- downconverting (S360) the overshooting range returns by the succeeding LFM signal,- assigning (S362) transmit sources in the antenna array to the downconverted range returns which will be false in both range, velocity and direction if these are overshooting returns,- superimposing (S364) echoes from transmission of one LFM signal to next the overshooting erroneous echo directions varies from transmission of one LFM signal to next, and- removing (S366) overshooting and thus falsely positioned targets by thresholding, as these echoes having varying directional assignments will appear weak compared to the echoes of targets, falling within the predetermined range and velocity constraints.

12. The method according to any of the previous claims, wherein the centre frequency (fc) is configured to be in the range of eight to twelve gigahertz, GHz, and wherein the bandwidth is configured to be in the range of 50 to 500 megahertz, MHz, preferably 100 MHz.

13. The method according to any of the preceding claims, wherein the ratio of the predetermined bandwidth (B) divided by the predetermined centre frequency (fc), B / fc, is one percent, and wherein the centre frequency (fc) is configured to be in the range of one GHz to thirty GHz.

14. A radar system for estimating target range and / or radial velocity, the radar system comprising an antenna array, the antenna array comprising at least one transmit-receive module, each transmit-receive module comprising a pair of transmit and receive units, such as a transceiver, each transmit-receive module being configured to transmit and receive a radar signal according to any of claims 1-13, and- processing circuitry configured to cause the radar system to carry out the method for estimating object range and / or radial velocity according to any of claims 1-13.

15. A computer program for estimating target range and / or radial velocity, the computer program comprising computer program code which, when executed by processing circuitry of a radar system for estimating object range and / or radial velocity according to claim 14, causes the radar system to carry out the method for estimating object range and / or radial velocity according to any of claims 1 -13.

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