WO2020218925A1

WO2020218925A1 - Processing of radar signals for fmcw radar

Info

Publication number: WO2020218925A1
Application number: PCT/NL2020/050262
Authority: WO
Inventors: Sharef Ahmed M NEEMAT; Faruk Uysal; Oleg Anatolyevich KRASNOV; Olexander YAROVYI
Original assignee: Technische Universiteit Delft
Priority date: 2019-04-23
Filing date: 2020-04-23
Publication date: 2020-10-29
Also published as: NL2022991B1

Abstract

The invention is related to a process to improve the range resolution and velocity estimation ambiguity of a radar, by concatenating received radar signals and applying corrections in time and/or time-frequency domain wherein the corrections are in the form of phase corrections or time-delay corrections, by concatenating beat-frequency slices to create concatenated beat frequency slices and applying a phase correction to each frequency slice. The invention further relates to a radar system with improved range resolution and velocity estimation ambiguity comprising a radar system including a transmitter to generate and transmit an FMCW radar signal, a receiver to receive two or more pulse and/or sweep returns of the transmitted signal, and a processing system including a fast Fourier transform processor to concatenate received radar signals and apply corrections in time and/or time-frequency domain wherein the corrections are in the form of phase corrections or time-delay corrections, by concatenating beat- frequency slices to create concatenated beat frequency slices and applying a phase correction to each frequency slice.

Description

PROCESSING OF RADAR SIGNALS FOR FMCW RADAR

Field of the Invention

The present invention relates to a process to improve the range resolution and to improve the velocity estimation ambiguity of a radar for detecting objects, by using radar systems and, more particularly, by using frequency modulated continuous wave (FMCW) radar systems.

Background of the Invention

Conventional radar systems transmit modulated or pulsed signals to determine properties of an object, such as range to the object or speed of the object. For example, in frequency modulated continuous wave (FMCW) radar the frequency of a radar signal is modulated, yielding information about range to an object when the radar signal is reflected from the object.

In deramping Frequency Modulated Continuous Wave (FMCW) radar, range is defined by frequency. A frequency estimation technique like the Fourier Transform (FT) is typically used to separate targets in the frequency domain. The FT frequency resolution is defined by the signal observation time. In FMCW, the observation time is limited by what is known as the 'transient' or 'fly-back' region between frequency sweeps. Targets' Doppler velocities are calculated across target range bins from multiple sweeps in a Coherent Processing Interval (CPI). The Doppler sampling frequency is the Pulse/sweep Repetition Frequency (PRF).

WO-A- 2018005070 describes systems and methods that are directed towards frequency jump burst-pulse-Doppler (FJB-PD) waveforms and processing that can be used to provide wideband, high range resolution (HRR) radar profiling capability in a clutter dense environment. A disadvantage of the method described therein is that to improve the range resolution more transmitted bandwidth is needed, and that it can an only evaluate one doppler velocity interval in one CPI.

Neemat, S. et al have published an article with the title "Simultaneous processing of time-shifted orthogonal LFMCW waveforms" (2017 Signal Processing Symposium, IEEE, 12 September 2017 (2017-09-12), pages 1-4), which describes processing with a phase correction, which is easily implementable in real-time. It describes the concatenation of half a signal from one sweep with half a signal from the next sweep, which totals one sweep.

The phase correction is done in the frequency domain only, with the purpose to

concatenate a signal from half a sweep with half a signal from the next sweep.

Hence there remains a need for a frequency modulated continuous wave (FCMW) radar that improves the range resolution without transmitting more bandwidth, and offers flexible range-velocity processing. The current invention proposes a new processing strategy to address these issues.

Summary of the Invention

It is an object of the present invention to provide a process for improving the range resolution and a better distinction between targets. It is a further object of the invention to provide a process that helps detecting targets that are very close in range. In a further aspect, the present invention relates to the implementation of staggered pulse repetition frequency algorithms for the purpose of target velocity disambiguation.

These and other objects are addressed by the process and apparatus of the present invention.

Accordingly, the present invention relates to a process to improve the range resolution and velocity estimation ambiguity of a radar, by concatenating two or more received radar signals and applying corrections in time and/or time-frequency domain wherein the corrections are in the form of phase corrections or time-delay corrections, by concatenating beat-frequency slices to create concatenated beat frequency slices and applying a phase correction to each frequency slice.

In a further aspect, the present invention related to a radar system with improved range resolution and velocity estimation ambiguity comprising a radar system including a transmitter to generate and transmit an FMCW radar signal, a receiver to receive two or more pulse and/or sweep returns of the transmitted signal, and a processing system including a fast Fourier transform processor to concatenate received radar signals and apply corrections in time and/or time-frequency domain wherein the corrections are in the form of phase corrections or time-delay corrections, by concatenating beat-frequency slices to create concatenated beat frequency slices and applying a phase correction to each frequency slice.

Detailed Description of the Invention

Embodiments of the invention are described hereinafter with reference to the accompanying drawings, wherein like letters and numerals refer to like parts, wherein the figures are approximately to scale, and wherein:

Fig. 1 illustrates in (a) a deramping FMCW radar simplified block diagram and in (b) a deramping operational overview, highlighting beat-frequency signals and the transient region.

Fig. 2 illustrates a simplified sine function spectral bandwidth illustration for signals with different durations. When coherently concatenating two sweeps, the sine function 3 dB width will reduce.

Fig. 3 illustrates a Reconfigurable range-Doppler processing permutations of fast- time slow-time received sweeps. The total CPI processing gain is maintained. Depending on the number of sweeps concatenated, there is a trade-off between range resolution and the maximum unambiguous Doppler velocity interval. Note that when d=N, only a range profile is provided because the matrix is then one dimensional. The following symbols in the figure represent:

x : Beat frequencies sweep

d : concatenation factor

k : number of samples

N : number of sweeps in the CPI

Fig. 4 illustrates examples for flexible CPI processing. Different values of the concatenation factor d are shown for sweep concatenation.

Fig. 5 illustrates phase matching in the STFT domain.

Fig. 6 illustrates examples for flexible CPI processing with transient region frames extrapolation. Different values of the concatenation factor d are shown for sweep concatenation.

Fig. 7 illustrates phase matching in the STFT domain after transient region frames extrapolation. Fig. 8 illustrates a simulation setup for the results presented in Fig. 9, where cases (a) to (e) correspond to Fig. 9 sub-figure labels.

Fig. 9 illustrates the simulation results for the scenario setup using the parameters in Table 2 and illustrated in Fig. 8. (a) Standard processing, PRF = 1 kHz. (b) Dropped sweeps to create PRF = 500 Hz. (c) Dropped sweeps to create PRF = 250 Hz. (d) Proposed processing with d = 2. (e) Proposed processing with d = 4.

Fig. 10 (a) illustrates the PARSAX FMCW radar situated at the top of the TU Delft building which was used for the experiments (b) illustrates the industrial chimney used as a stable target in the first experiment. (C) illustrates an automobile used as a moving target in the second experiment.

Fig. 11 illustrates simplified PARSAX radar block diagram with the configuration used for experiments. A waveform combining a 20 MHz and a 40 MHz sweeps is generated and combined by the Arbitrary Waveform Generator (AWG). Both FPGA receivers R-l and R-2 are Single Sideband (SSB) IQ ones, with the ability to reject either positive or negative frequencies. The shaded areas depict the receivers' upper and lower Low-pass filter (LPF) bounds.

Fig. 12 illustrates the Zero-Doppler cut zoom-in on the Chimney shown in Fig. 10 (a) and (b). The proposed processing of the 20 MHz channel - with a concatenation factor d=2 - closely matches that of the 40 MHz channel.

Fig. 13 illustrates range-velocity results maps for the automobile in the experiment: (a) As seen in the 40 MHz channel (b) As seen in the 20 MHz channel (c) Processing with manually discarding every other sweep of the20 MHz channel (d) Processing the 20 MHz waveform with a concatenation factor d = 2, the automobile's resolution closely match that of the 40 MHz waveform, in range, velocity and SNR.

In the figures the following abbreviations have been used, which represent the following:

Tx = transmitter (antenna)

Rx = Receiver (antenna)

ADC = Analogue to Digital Converter

Ch = channel LPF = Low Pass Filter

Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

The terms "radar" as used herein, includes a detection system that uses radio waves to determine the range, angle, or velocity of objects. It can be used to detect for example aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. A radar system generally consists of a transmitter producing electromagnetic waves in the radio or microwaves domain, a transmitting antenna, a receiving antenna (often the same antenna is used for transmitting and receiving) and a receiver and processor to determine properties of the object(s). Radio waves (pulsed or continuous) from the transmitter reflect off the object and return to the receiver, giving information about the object's location and speed.

The term "Continuous-Wave (CW) radar systems" as used herein, includes a type of radar system where a known stable frequency continuous wave radio energy is transmitted and then received from any reflecting objects. Continuous-wave (CW) radar uses Doppler, which renders the radar immune to interference from large stationary objects and slow- moving clutter.

The term "Frequency-modulated continuous-wave radar (FMCW)" - also called continuous-wave frequency-modulated (CWFM) radar as used herein, includes a range measuring radar set capable of determining distance. This increases reliability by providing distance measurement along with speed measurement, which is essential when there is more than one source of reflection arriving at the radar antenna.

The term "MIMO" or "MIMO radar" as used herein, includes an advanced type of phased array radar employing digital receivers and waveform generators distributed across the aperture. MIMO radar signals propagate in a fashion similar to Multistatic radar.

However, instead of distributing the radar elements throughout the surveillance area, antennas are closely located to obtain better spatial resolution, Doppler resolution, and dynamic range. MIMO radar systems transmit mutually orthogonal signals from multiple transmit antennas.

The term "dechirping" as used herein, is an alternative for stretch processing or deramping. These three terms are all used for reducing the sampling requirements of radar systems.

The term "uncoded" signal as used herein, includes a signal that has not been coded.

The term "signal generator" as used herein, includes means for generating frequency modulated continuous wave (FMCW) signal.

The term "modulator" as used herein, includes means of mixing phase coded signal with a carrier signal.

The term "transmitter" as used herein, includes means for transmitting modulated signals.

The term "receiver" as used herein includes means for receiving the return signal reflected target in every detection cycle.

The term "analog to digital converter" as used herein, includes means of digitizing analog signals.

The term "processor" as used herein, includes means of processing digital signal to extract range and velocity information of target.

The term "range" as used herein, includes referring to the object that is detected by the radar and the range is preferably related to the distance and the relative velocity of the object as calculated from the decoded signal. The relative velocity is a term generally used in radar technology and is advantageously the velocity in relation to the transmitter and / or receiver of the signals and / or reflected signals.

Deramping Frequency Modulated Continuous Wave (FMCW) radars operate by mixing a transmitted chirp signal with received returns, and filtering the resulting beat signal. For a single point-target, the time delay between the probing signal transmission and the scattered signal reception will result in a single-tone signal, known as a beat-frequency, whose frequency is proportional to that target's range. Range is therefore generally defined by frequency. The scaling between beat frequencies and range is defined by the transmitted bandwidth, and the signal observation time. A frequency estimation technique like the Fourier Transform (FT) is typically used to separate targets in range, by separating beat- frequency tones in the frequency domain. The radar's range resolution is determined by the transmitted bandwidth and the FT frequency spectrum resolution. Legacy computer architectures used in FMCW radars are highly compatible with the FT for its reduced computational requirements and predictable latency. The range resolution granularity defines the width of targets' range bins. In signal processing, the FT frequency resolution is defined by the signal observation time. Target velocities are calculated from Doppler processing - also typically using the FT - across targets' range bins from multiple sweeps. The radar Pulse/sweep Repetition Frequency (PRF) is generally the Doppler sampling frequency. The time spent to gather multiple sweeps for range and Doppler processing is typically known as a Coherent Processing Interval (CPI). Sweeps in a CPI are typically arranged in a fast-time slow-time matrix, where fast-time is the time within a sweep, and slow-time is the time across multiple sweeps. The total processing gain in a CPI is contributed to the matrix's 2-D FT processing gain. It is typical for radars to transmit at different PRF values, across multiple CPIs to unambiguously determine targets' ranges and velocities, in what is known as staggered-PRF techniques. In FMCW, the observation time is limited by what is known as the 'transient' or 'fly-back' region between frequency sweeps. The received signal is typically only sampled after the transient region, which causes discontinuities in received beat-frequencies (demarking the end of a received sweep), and puts a limit on the possibility of having a continuous observation time.

One of the problems our invention offers a solution for is the existence of the transient regions in received beat-frequency sweeps in a CPI, in the sense that: a) the existence of the transient regions does not allow for longer targets observations. A method to extend the observation time by coherently concatenating/processing beat-frequencies from more than one sweep at a time would result in a finer radar range resolution; b) such a concatenation method would give a tool to decouple the Doppler processing PRF from the transmitted signal PRF. This is in the sense that it becomes possible to - in parallel and from one CPI - create different lengths fast-time slow-time matrices, without compromising on the total processing gain in any of the created matrices, and therefore improves the velocity estimation ambiguity.

Advantageously, the whole process for measuring the range and velocity comprises the following steps: (a) transmitting an FMCW radar signal

(b) receiving two or more pulse and/or sweep returns

(c) deramping of the received signals to produce beat signals

(d) transforming the time-domain beat signals to the time-frequency domain to produce beat frequency slices in the time frequency domain

(e) concatenating beat-frequency slices to create concatenated beat frequency slices

(f) applying an inverse time-frequency transform to the concatenated beat

frequency slices to produce concatenated time-domain beat signals

(g) creating multiple data matrices

(h) applying range Doppler processing to obtain the range and velocity of the target.

We now found that by concatenating beat-frequency slices in the time-frequency domain using the Short-time Fourier Transform (STFT) for example, and applying a phase correction to each frequency slice as appropriate, followed by an Inverse STFT (ISTFT) the above problem is solved, better range resolution is obtained, and improved velocity estimation ambiguity is possible. Thus, advantageously, the concatenation of the beat frequency slices is performed in a coherent way by applying a phase correction to each frequency slice to produce coherently concatenated beat frequency slices. A second optional realization of this solution is to first extrapolate beat-frequency slices, to compensate for the observation time lost in the transient region, then concatenate the slices as aforementioned. Thus, advantageously, first extrapolation of each beat frequency slice is performed, followed by a phase correction to produce coherently concatenated beat frequency slices. The prior art is silent about this.

There are multiple advantages that come with this solution, of which a few are that: it is applicable to deramping processing, it relies on the FT (as opposed to more

computationally intensive or iterative frequency estimation algorithms), it does not improve the range resolution by stitches sweeps from multiple discontinuous bands, and therefore technically requiring more overall system bandwidth, it does not require target detection as a prerequisite, and it is applicable to extended-targets.

Our invention is novel in multiple ways. It is a first method for deramping FMCW radar sweeps coherent concatenation in the time-frequency domain. Furthermore, the method allows for range resolution improvement without transmitting additional bandwidth. It furthermore offers the ability to observe different range resolution granularities in parallel from one CPI. The method also offers the ability to - in parallel - generate different size fast-time slow-time matrices, and decouples the transmitted PRF from the Doppler processing PRF, without compromising on the total CPI processing gain. This offers the ability to observer different unambiguous Doppler velocity intervals - to perform staggered PRF velocity-disambiguation techniques for example - in one CPI.

Additionally, the method does not require target(s) detection as a prerequisite.

To explain it in more detail, a deramping FMCW radar - as in Fig. 1(a) - transmits bandwidth B over a sweep time T and observes a target at range r . The radar's Pulse Repetition Interval (PRI) is T . The observation time (ADC sampling interval),

T = (T— t ) where

the maximum transient time, which is selected based the desired system maximum range of interest. The antialiasing Low Pass Filter (LPF) defines . The observation time T is less than / because it is limited by the transient time region from the previous sweep. ADC sampling of the received signal typically begins after . The received beat signal from a point target can be expressed as

S_r(t) = A₀rec(t/T_o) cos( 2nf_bt + <p_Q) (1) for—T₀/2 < t < T₀/2, where Ao is the received amplitude,/_/, the target beat-frequency, and f₀ an arbitrary initial phase. As depicted in Fig. 1(b), the target range is defined as

where c is the speed of light and B_e the effective bandwidth. The effective bandwidth is related to the transmitted on by

This also expresses the degradation in the transmitted bandwidth due to the reduced observation time. From (2), the target beat-frequency is therefore 2 B r

f_b (4)

Tc

Spectral estimation techniques such as the FT are typically used to estimate the target frequency, and therefore its range. It is well known from FT signal processing that for a signal as in (1), the FT will result in an impulse function - assuming that f_b is on a frequency grid point - and a sine function, and that the frequency spectrum resolution is defined by the 3 dB width of that sine function centered at f_b. The 3 dB width of the sine function in the frequency domain is inversely proportional to the signal integration time T_e [2] as

This concept is depicted in Fig. 2. In FMCW radar, range resolution is proportional to the frequency spectrum resolution, and is defined by the 3 dB width of the sine function centered at f_b. From (2), (4) and (5), for two targets ri and r2 to be separable in the frequency domain, they need to meet the requirement

2 B r 2B r₇ 1

(6)

Tc Tc ^~ T which can be simplified to

It should be noted that in typical FMCW processing, T₀ = T_e, yielding

which is the classical form of FMCW range resolution. But as seen in (7), if there were a way to increase the integration time, it would be possible to improve the range resolution.

To improve the range resolution, the integration time in (5) and (7) is increased by coherently concatenating d sweeps. The improved range resolution is expressed as follows

where d is the concatenation factor as well as the range resolution improvement factor. It should be noted that the more coherently concatenated sweeps, the finer AR_d becomes, and therefore the larger the observed range migration is for moving targets. Range migration is sometimes a desirable phenomenon, where it is exploited for better performance of some detection algorithms. The value of d should therefore become a radar system parameter.

In classical FMCW radar processing, a CPI of a certain duration is selected as a system parameter. Received sweeps in the CPI are typically stored in a 2-D matrix (commonly named the fast-time slow-time matrix), after which, a 2-D FT is performed on that matrix to produce range-Doppler maps. The total processing gain in the CPI is the pulse compression gain - also known as the time-bandwidth product (BT) - multiplied by the number of sweeps in the CPI. Operationally, to maintain this processing gain, the total number of samples stored in a CPI is typically kept the same when changing the PRF, and a tradeoff is made between the unambiguous range and the unambiguous Doppler velocity interval. This is in the sense that more sweeps of shorter durations are received in High PRF (HPRF) mode, and less sweeps of longer duration in low PRF mode. If the radar operates in a HPRF mode, different unambiguous Doppler velocity intervals can be created by simply discarding every other sweep(s) in the fast-time slow-time matrix, but that would result in a total processing gain loss. The unambiguous velocity interval is related to the PRF as

A-PRF

v_u = ± (10)

4 where L is the radar wavelength. The creation of different lengths fast-time slow-time matrices is proposed by operating the radar in a HPRF mode, and concatenating sweeps for different values of d in parallel. This will allow the creation of different 'processing' PRF values from the operational HPRF, while maintaining the total processing gain. The created different processing PRF values will allow for the evaluation of multiple unambiguous Doppler velocity intervals, and multiple range resolution granularities, from the same CPI. The processing PRF can be expressed as

PRF

PRF a

d (11) This flexible processing concept is illustrated in Fig. 3, whereas the number of concatenated sweeps increase, the unambiguous Doppler velocity intervals is reduced, but all samples are still used and therefore the processing gain is maintained. A calculated example is furthermore given in Table 1. When d = 2 for instance, the processing PRF becomes 1 kHz, which is half the transmitted PRF of 2 kHz, but the range resolution is improved by a factor of two from 4.68 m to 2.34 m. All while maintaining the same total processing gain of 819200 in both cases because of not discarding any samples.

Table 1. Flexible CPI processing range resolution improvement versus maximum

unambiguous Doppler velocity trade-off example. Assumptions are: transmitted PRF = 2KHZ, T_s = 500 m$, T₀ = 400 m$, N = 64 sweeps in the CPI, CPI length = 32000 m$, B_e = 32 MHZ, wavelength l = 0.0905 m. Note that when d = 1, this is the case for conventional processing.

The limitations for improving the range resolution by coherently concatenating multiple sweeps are system non-linearities - in the transmitter and receiver - and

concatenation errors. Because of non-linearities, even a point-target will have a

certain 3 dB spectral width, dictated by the radar's nonlinearities. Any concatenation errors may also result in grating-lobes or spectral width widening.

The method of the invention is stepwise detailed below, with two preferred realizations. These are non-limiting examples provided to illustrate the invention, and to explain the theory in a more practical manner. In the first realization, beat-frequency slices are coherently concatenated using a phase-shift operation. In the second realization, the beat-frequency slices are first extrapolated to cover the transient region between sweeps, and then coherently concatenated using a phase-shift operation.

A depiction of the sweeps concatenation without extrapolation is presented in Fig. 4. The steps are:

1) Store digitally sampled beat-frequencies for sweeps from the output of the

deramping receiver. A sweep can be expressed as x_n[k], where n is the sweep number, and 2 < n ³ N. The number of sweeps in a conventional Coherent Processing Interval (CPI) is N, and N E Έ, and 1L denotes the set of all integers. The time domain sample index in a sweep is k , where k = 1, ..., K, and K = fT . The sampling frequency is /_s.

2) Take sweeps to the time-frequency domain by applying an STFT, where a sweep can be expressed in matrix form as

with Y rows and L columns, where l is the STFT frame index, l = 1,

and L = 1 + 1 {k— W) I Ah) J . The analysis window length is W. The STFT hop size is

Ah, and l-^'J denotes the floor operation. The frequency-slice index in the STFT frequency grid is y, where y = 0, ... , Y , and Y is the maximum beat-frequency index. The analysis window (for instance, Hamming) is w.

3) Form concatenated sweeps in matrix-form in the STFT domain as: the S matrices are of the form as in (12),’ °’ denotes the Hadamard product. The phase matching term C has L identical columns, and is defined as

where

Here f is the frequency value at frequency-slice index y, and the hop time t_h = Ah / . The phase matching is illustrated in Figure 5.

4) Select a concatenation factor d which indicates the desired number of sweeps to be concatenated in the CPI, where d e Q, and Q denotes the set of all rational numbers. The concatenated sweep number is N , where N = N / d , and N e .

5) Form concatenated sweeps in matrix-form in the STFT domain as

where m is the sweep number after concatenation, m = 1

.

6) Perform an ISTFT to form the new concatenated sweeps as:

J = ISTFT(S (17)

The concatenated sweep X_m will be of length dk.

7) Perform again from step 4 onwards in parallel for different values of d to create multiple fast-time slow-time matrices from the same CPI.

In the second realization, beat-frequency slices are first extrapolated to cover the transient region between sweeps, and then coherently concatenated using a phase-shift operation, as depicted in Fig. 6. The steps are:

1) Store digitally sampled beat-frequencies for sweeps from the output of the

deramping receiver. A sweep can be expressed as x_n[k\, where n is the sweep number, and 2 < n < N. The number of sweeps in a conventional Coherent Processing Interval (CPI) is N , and N E TL, and 1L denotes the set of all integers. The time domain sample index in a sweep is k, where k = 1, K, and K = f_sT₀. The sampling frequency is f_s.

with Y rows and L columns, where l is the STFT frame index, l = 1,

and L = 1 + 1 (k— W) I Ah) J . The analysis window length is W. The STFT hop size is

Ah, and i- ^denotes the floor operation. The frequency-slice index in the STFT frequency grid is y, where y = 0, ... , Y , and Y is the maximum beat-frequency index. The analysis window (for instance, Hamming) is w.

3) Using the Burg algorithm (as described in S. Kay, Modern Spectral Estimation: Theory and Application. Prentice Hall, 1999), estimate in-phase and quadrature (IQ) Linear Prediction (LP) coefficients [a]_r in matrix form for amplitudes of each frequency- slice y in each of the N sweeps. The prediction filter order is o, and o should be between 2 and |_ / 3j .

4) Extrapolate R frames for each y frequency-slice, for each of the N sweeps. Note that R = 1 +

W) / Ah) J , and the extrapolated frames can be written as

where r = 1,

After extrapolating for all y frequency-slices, an extrapolated sweep can then be written as

E. = [A. S ]„ (20)

where L = L + R .

5) Form concatenated sweeps in matrix-form in the STFT domain as:

the E matrices are of the form as in (20), o denotes the Hadamard product. The phase matching term C has L identical columns, and is defined as where

D , (/) = f,M, - <P, J O) + (^2p/A) (23)

Here f_y is the frequency value at frequency-slice index y, and the hop time t_h = D/i / f_s. The phase matching is illustrated in Fig. 7.

6) Select a concatenation factor d which indicates the desired number of sweeps to be concatenated in the CPI, where d E Q, and Q denotes the set of all rational numbers. The concatenated sweep number is N , where N = N / d , and N e .

7) Form concatenated sweeps in matrix-form in the STFT domain as

where m is the sweep number after concatenation, m = 1

.

8) Perform an Inverse STFT (ISTFT) to form the new concatenated beat-frequency

sweeps as

J = ISTFT(E (25)

The concatenated sweep X_m will be of length d - (k + ( f _r )) .

9) Perform again from step 6 onwards in parallel for different values of d to create multiple fast-time slow-time matrices from the same CPI.

The following, non-limiting examples are provided to illustrate the invention.

Example 1: Simulation results

To evaluate the flexible range-Doppler and range resolution improvement method, a simulation and processing scenario for five point-targets is setup using the parameters in Table 2 and illustrated in Fig. 8. On the one hand, the simulation compares 2-D FT results for the standard case with a PRF of 1 kHz (Fig. 8(a)), the creation of a second Doppler velocity ambiguity interval by manually discarding every other sweep from the CPI resulting in a Doppler sampling PRF of 500 Hz (Fig. 8(b)), and the creation of a third interval by manually using one sweep from every four sweeps from the CPI resulting in a Doppler sampling PRF of 250 Hz (Fig. 8(c)). On the other hand, this is compared with the proposed processing with d = 2 (Fig. 8(d)) and d = 4 (Fig. 8(e)) to create the same velocity ambiguity intervals, but with improving the range resolution. Hamming windowing was used for both the range and Doppler processing. The simulation results are presented in Fig. 9. Target G1 wraps around the unambiguous velocity intervals as expected, as it can be seen at a velocity of around -9 m/s in Fig. 9(b) and (d), and at around 3 m/s in Fig. 9(c) and (e). Targets G2 and G3 have a velocity which is always within the ambiguity intervals, and therefore do not fold. Since targets G2 and G3 are spaced 1.5 meters apart, they are only distinguishable when processing with d = 4, because the improved range resolution is then 0.73 m, as seen in Fig. 9(e). This resolvability is also the case for targets G4 and G5 which are at zero velocity.

Table 2. Simulation and experiment set up parameters

The flexible processing and range resolution improvement method is demonstrated experimentally using the Delft University of Technology (TU Delft) PARSAX FMCW radar shown in Fig. 10(a). The radar is mounted on the roof of the electrical engineering, mathematics and computer science (EEMCS) building at the TU Delft. It operates in S-band (3.1315 GHz) and uses an Intermediate Frequency (IF) of 125 MHz. A simplified PARSAX block diagram is depicted in Fig. 11 along with the experimental setup. On every receiver channel, transmitted and received signals are sampled at IF using a pair of Analog-to-Digital Converters (ADCs) on an Innovative Integrations X5-400M Xilinx Virtex5SX95T FPGA card. The ADCs are 14-bit devices with sampling rates up to 400 Mega Samples per Second (MSPS). Deramping Single Sideband (SSB) signal processing is performed digitally on the FPGAs. Beat-frequencies are transferred to a computer via the PCI-express bus for further processing. Experiments were conducted using the experiments-applicable configuration options shown in Table 2. The transmitted waveform from the AWG channel-1 was created by combining two frequency slopes of bandwidth 40 MHz and 20MHz respectively.

Receivers R1 and R-2 separate the received beat-frequencies from the 40 MHz and 20 MHz respectively. Both receivers are SSB IQ ones, with the ability to reject either positive or negative frequencies. The aim here is to demonstrate that the range resolution from processing the 20 MHz waveform can be improved to match that of the 40 MHz one, using the proposed method with a concatenation factor d = 2.

Example 2: A Stable Target

In this experiment we observed an industrial factory chimney as depicted in Fig. 10(a) and (b). The chimney was chosen as a stable target. The results are shown in Fig. 12. When processing the 20 MHz waveform with a concatenation factor d = 2, the chimney details are resolvable, and closely match that of the 40 MHz waveform.

Example 3: A Moving Target

In this experiment, we observed an automobile on a quiet road as depicted in Fig. 10(a) and (c). The automobile, driving at a velocity of around 19 m/s (70 kmh), will be unambiguous for the transmitted PRF of 2 kHz, and for when processing with a concatenation factor d = 2, which will reduce the processing PRF to 1 kHz. The results are shown in Fig. 13. The automobile appears to be of around 7 m in length in the 40 MHz channel, which is expected due to the range resolution being 3.74 m (as seen in Table 2), FT leakage, and typical automobile lengths of around 4 m. In the 20 MHz channel, the automobile appears to be of around 14 m in length, which is also expected due to the range resolution being 7.49 m. When processing with manually discarding every other sweep of the 20 MHz channel, similarly to what was done in the simulations section, the automobile appears to have the same velocity but with a slight SNR loss and a slight velocity displacement due to the FT leakage. When processing the 20 MHz waveform with a concatenation factor d = 2, the automobile's resolution closely matches that of the 40 MHz waveform, in range, velocity and SNR.

The experiments show that the method extends the observation time by using returns from more than one sweep at a time, which resulted in a finer range resolution without the need to transmit additional bandwidth. The method also made it possible to decouple the Doppler processing PRF from the transmitted signal PRF. This is in the sense that it became possible to - in parallel and from one CPI - create different lengths fast-time slow-time matrices, which allows the observation of different range resolution granularities, without compromising on the total processing gain in any of the created matrices. This therefore also allows for the observation of different unambiguous Doppler velocity intervals (to implement staggered-PRF velocity disambiguation techniques for example) in a single CPI.

Claims

1. Process to improve the range resolution and velocity estimation ambiguity of a radar, by concatenating two or more received radar signals and applying corrections in time and/or time-frequency domain wherein the corrections are in the form of phase corrections or time-delay corrections, by concatenating beat-frequency slices to create concatenated beat frequency slices and applying a phase correction to each frequency slice.

2. The process according to claim 1, wherein the range and velocity are measured by

(a) transmitting an FMCW radar signal

(b) receiving two or more pulse and/or sweep returns

(c) deramping of the received signals to produce beat signals

(f) applying an inverse time-frequency transform to the concatenated beat

frequency slices to produce concatenated time-domain beat signals

(g) creating multiple data matrices

3. The process according to claim 1 or 2, wherein the concatenation of the beat frequency slices is performed in a coherent way by applying a phase correction to each frequency slice to produce coherently concatenated beat frequency slices.

4. The process according to claim 1 or 2, wherein first extrapolation of each beat frequency slice is performed, followed by a phase correction to produce coherently concatenated beat frequency slices.

5. A radar system with improved range resolution and velocity estimation ambiguity

comprising a radar system including a transmitter to generate and transmit an FMCW radar signal, a receiver to receive two or more pulse and/or sweep returns of the transmitted signal, and a processing system including a fast Fourier transform processor to concatenate received radar signals and apply corrections in time and/or time- frequency domain wherein the corrections are in the form of phase corrections or time- delay corrections by concatenating beat-frequency slices to create concatenated beat frequency slices and applying a phase correction to each frequency slice.

6. The radar system according to claim 5, wherein the concatenation of the beat frequency slices is performed in a coherent way by applying a phase correction to each frequency slice to produce coherently concatenated beat frequency slices.

7. The radar system according to claim 5, wherein the first extrapolation of each beat frequency slice is performed, followed by a phase correction to produce coherently concatenated beat frequency slices.