WO2023172129A1

WO2023172129A1 - Frequency modulated continuous wave receiver, transceiver and associated methods

Info

Publication number: WO2023172129A1
Application number: PCT/NL2023/050106
Authority: WO
Inventors: Nikita Petrov; Olexander YAROVYI
Original assignee: Technische Universiteit Delft
Priority date: 2022-03-08
Filing date: 2023-03-04
Publication date: 2023-09-14
Also published as: NL2031184B1

Abstract

A frequency modulated continuous wave receiver, comprising: an antenna input (110) arranged for receiving an antenna signal from a receiving antenna arranged for receiving a frequency modulated continuous wave; a receiver mixer (120) arranged for providing a mixed received signal based on mixing the received antenna signal of the antenna and a wide band continuous wave chirp; a digitizer (130) arranged for providing a digitized mixed received signal based on digitizing the mixed received signal; and a fractional correlator (140) arranged for determining a range profile signal indicative of the path length traversed by the frequency modulated continuous wave, wherein the range profile signal is based on correlating in a fractional Fourier transform domain the digitized mixed received signal with a narrow band modulation signal; and wherein the frequency modulated continuous wave is based on mixing the wide band continuous wave chirp with the narrow band modulation signal.

Description

FREQUENCY MODULATED CONTINUOUS WAVE RECEIVER, TRANSCEIVER AND ASSOCIATED METHODS

FIELD OF THE INVENTION

The invention relates to a frequency modulated continuous wave receiver. The invention further relates to a frequency modulated continuous wave transmitter, a frequency modulated continuous wave transceiver, a range finder, a method for receiving a frequency modulated continuous wave, a method for transmitting a frequency modulated continuous wave, a method for a frequency modulated continuous wave transceiver, and a computer program product.

BACKGROUND OF THE INVENTION

A linearly frequency modulated (LFM) waveform is used in various radar applications. The simplicity of the hardware with low requirements on analog to digital converter (ADC) sampling frequency, constant peak-to-average power ratio (PAPR) and good Doppler tolerance are advantages of the LFM waveform.

These advantages come with the cost of the limited flexibility of LFM signals, crucial for the realization of multipleinput multiple output (MIMO) radars and interference mitigation between different radars. To associate the received signals with the proper transmit channel, different multiplexing schemes are used in MIMO radars. They imply that the transmitted signals are different in time, frequency, chirp slope or code domains, but at the same time lead to the degradation of radar performance by shortening the unambiguous Doppler velocity, degrading the range resolution or increasing the sidelobe level.

A promising approach to address the aforementioned limitations consists of applying information-carrying modulation to chirps. In that way, the received waveform can be processed after mixing with the reference LFM signal (known as dechirping, deramping and stretch processing) - preserving all the advantages of LFM signal, mentioned above and adding to them the ability to discriminate different signals, essential for MIMO beam-forming, interference mitigation between different radars and realization of joint communication and sensing.

Current receivers of modulated chirps are realized via a filter bank and have the computational complexity of digital Fourier transform (DFT) i.e. O(N²), where N is the number of ADC samples per chirp. That is significantly larger than that of the standard dechirping realized via the fast Fourier transform (FFT): O(N log2(N)). Thus, high computational complexity of the compensated stretch processing makes challenging its realization on a radar chip, such as an automotive radar chip.

The state-of-the-art approach or architecture to process phase-modulated FMCW waveforms use the group delay filter in the receiver to align the responses from all the ranges before decoding, followed by FFT for range extraction. The original idea of such delay compensation comes from the correction of non-linearity of chirp slope for stretch processing. This receiver design, derived with an assumption of a narrow-band deviation of the signal from the linear frequency modulation (LFM), significantly degrades for long codes, which are of the main interest in applications mentioned above. An appropriate predistortion of the transmit signal to compensate this effect has been proposed, which leads, however, to the increase of the PAPR of the transmitted signal, undesirable for the transmitting chain.

A conceptually similar approach or architecture is with application to chirps modulated by an orthogonal frequency division multiplexing (OFDM) waveform. Instead of the group delay filter, a certain rearrangement of the OFDM sub-carriers is done to realize a symbol cancelling receiver. This, however, imposes multiple constraints on the selection of the waveform parameters.

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 69, NO. 1 , JANUARY 2020 discloses a frequency-modulated continuous-wave (FMCW) radarthat takes advantage of stretch processing (dechirping, deramping) to reduce the sampling requirements of radar systems such as automotive radars. When applying phase coding into FMCW radar systems for interference mitigation or joint communication, preservation of this benefit is impossible, due to the nature of this process. The current invention proposes a phase coded FMCW system as well as a processing strategy based on a group-delay filter to deal with unaligned phase-coded radar return signals. Moreover, the current invention proposes an interference mitigation method based on a phase-coded linear-frequency-modulated (LFM) continuous waveform.

Proposed is a novel receiver design for modulated LFM signals, which demonstrates the ability to recover the range profile accurately, similar to the compensated stretch processing and does it in the computational complexity of FFT. In order to do that, presented below is the signal model and derived is the matched filter receiver, which coincides with compensated stretch processing. It is further shown that due to the linear relation between the time delay and the beat frequency, the matched filter can be realized via the fractional correlation, which can be computed efficiently using the fractional Fourier transforms (FrFT) with the computational complexity of FFT. The receiver based on fractional correlation is also shown below. The performance of the proposed receiver is evaluated and compared to the other state-of-the-art solutions. Finally, the conclusions are drawn basically confirming that the above mentioned disadvantages are overcome.

SUMMARY OF THE INVENTION

An object of the invention is to overcome one or more of the disadvantages mentioned above.

According to a first aspect of the invention, a frequency modulated continuous wave receiver, comprising: an antenna input arranged for receiving an antenna signal from a receiving antenna arranged for receiving a frequency modulated continuous wave; a receiver mixer arranged for providing a mixed received signal based on mixing the received antenna signal of the antenna and a wide band continuous wave chirp; a digitizer arranged for providing a digitized mixed received signal based on digitizing the mixed received signal; and a fractional correlator arranged for determining a range profile signal indicative of the path length traversed by the frequency modulated continuous wave, wherein the range profile signal is based on correlating in a fractional Fourier transform domain the digitized mixed received signal with a narrow band modulation signal; and wherein the frequency modulated continuous wave is based on mixing the wide band continuous wave chirp with the narrow band modulation signal. The antenna input is arranged for receiving an antenna signal from a receiving antenna arranged for receiving a frequency modulated continuous wave. The antenna input is typically arranged for receiving and optionally amplifying the antenna signal. The antenna input may comprise filtering and/or conditioning of the antenna signal.

The receiver mixer is arranged for providing the mixed received signal. The mixed received signal is based on mixing the received frequency modulated continuous wave of the antenna and the wide band continuous wave chirp. The wide band continuous wave chirp is typically generated by a wide band continuous wave chirp generator shared with a frequency modulated continuous wave transmitter or part of a frequency modulated continuous wave transmitter. The wide band continuous wave chirp may be generated locally if the receiver and transmitter share the parameters of the chirp as well as the timing of the chirp.

The digitizer is arranged for providing the digitized mixed received signal. The digitized mixed received signal is based on digitizing the mixed received signal. Digitizing may comprise signal conditioning. Digitizing comprises transforming the signal to the digital domain, typically from the analogue domain.

The fractional correlator is arranged for determining a range profile signal. The range profile signal is indicative of the path length traversed by the frequency modulated continuous wave. The range profile signal is based on correlating in the fractional Fourier transform domain the digitized mixed received signal with the narrow band modulation signal. Correlation is performed in any fractional domain, such as a fractional domain between the frequency domain and the time domain.

Further, a correlation signal is based on a narrow band modulation signal. And further, the frequency modulated continuous wave is based on mixing the wide band continuous wave chirp with the narrow band modulation signal.

The receiver, based on Fractional Fourier Transform (FrFT), has demonstrated the technical effect of a comparable performance over the state-of-the-art solutions with lower computational complexity and/or a considerable improved performance over other state-of-the-art solutions with limited increase of computational complexity. Furthermore, the receiver has this technical effect, particularly the second part of the technical effect, for moderate-to-large bandwidth of the narrow band modulation signal relative to the ADC sampling frequency.

According to another aspect of the invention, a frequency modulated continuous wave transmitter, the transmitter comprises: a chirp generator arranged for generating a wide band continuous wave chirp; a signal generator arranged for generating a narrow band modulation signal; a transmitter mixer arranged for providing a mixed transmission signal based on mixing the wide band continuous wave chirp and the narrow band modulation signal; and an antenna output arranged for providing an antenna signal to a transmitting antenna based on the mixed transmission signal for the transmitting antenna transmitting a frequency modulated continuous wave. The transmitter provides the same advantages as mentioned for the receiver.

According to another aspect of the invention, a frequency modulated continuous wave transceiver, comprising: one or more frequency modulated continuous wave receivers according to any of the mentioned embodiments; and one or more frequency modulated continuous wave transmitters according to any of the mentioned embodiments. The transceiver provides the same advantages as mentioned for the receiver.

According to another aspect of the invention, a range finder comprising a frequency modulated continuous wave transceiver according to any of the embodiments, arranged as radar, preferably MIMO radar, or sonar, preferably MIMO sonar. The range finder provides the same advantages as mentioned for the receiver.

According to another aspect of the invention, a method for receiving a frequency modulated continuous wave, comprising: providing a digitized mixed received signal based on digitizing the mixed received signal which is based on: receiving an antenna signal from a receiving antenna arranged for receiving a frequency modulated continuous wave; and providing a mixed received signal based on mixing the received antenna signal of the antenna and a wide band continuous wave chirp; and determining a range profile signal indicative of the path length traversed by the frequency modulated continuous wave, wherein the range profile signal is based on correlating in a fractional Fourier transform domain the digitized mixed received signal with a narrow band modulation signal; and wherein the frequency modulated continuous wave is based on mixing the wide band continuous wave chirp with the narrow band modulation signal. The method for receiving provides the same advantages as mentioned for the receiver.

According to another aspect of the invention, a method for transmitting a frequency modulated continuous wave, comprising: configuring a chirp generator for generating a wide band continuous wave chirp; and configuring a signal generator for generating a narrow band modulation signal; wherein the configuring steps are performed for: providing a mixed transmission signal based on mixing the wide band continuous wave chirp and the narrow band modulation signal; and providing an antenna signal to a transmitting antenna based on the mixed transmission signal for the transmitting antenna transmitting a frequency modulated continuous wave. The method for transmitting provides the same advantages as mentioned for the receiver.

According to another aspect of the invention, a method for a frequency modulated continuous wave transceiver, comprising: one or more instances of the receiving method according to any of the embodiments; and one or more instances of the transmitting method according to any of the embodiments. The method for a transceiver provides the same advantages as mentioned for the receiver.

According to another aspect of the invention, a computer program product comprising instructions which, when the program is executed by a suitable processor, cause the processor to carry out any of the method embodiments. The computer program product provides the same advantages as mentioned for the receiver.

According to another aspect of the invention, a frequency modulated continuous wave receiver, comprising: an antenna input arranged for receiving an antenna signal from a receiving antenna arranged for receiving a frequency modulated continuous wave; a receiver mixer arranged for providing a mixed received signal based on mixing the received antenna signal of the antenna and a wide band continuous wave chirp; an optical converter arranged for providing an optical mixed received signal based on optical converting the mixed received signal; and a fractional correlator arranged for determining a range profile signal indicative of the path length traversed by the frequency modulated continuous wave based on correlating in a fractional Fourier transform domain the digitized mixed received signal with a narrow band modulation signal; and wherein the frequency modulated continuous wave is based on mixing the wide band continuous wave chirp with the narrow band modulation signal. The receiver provides the same advantages as mentioned for the other receiver.

According to another aspect of the invention, a frequency modulated continuous wave receiver, comprising: an antenna input arranged for receiving an antenna signal from a receiving antenna arranged for receiving a frequency modulated continuous wave; a receiver mixer arranged for providing a mixed received signal based on mixing the received antenna signal of the antenna and a wide band continuous wave chirp; and a fractional correlator arranged for determining a range profile signal indicative of the path length traversed by the frequency modulated continuous wave based on correlating in a fractional Fourier transform domain the digitized mixed received signal with a narrow band modulation signal ; and wherein the frequency modulated continuous wave is based on mixing the wide band continuous wave chirp with the narrow band modulation signal. The receiver provides the same advantages as mentioned for the other receiver.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

In an embodiment of the frequency modulated continuous wave receiver, the fractional correlator comprises: a fractional Fourier receiver transformer arranged for generating a received fractional Fourier signal based on fractional Fourier transforming the digitized mixed received signal; a fractional Fourier mixer arranged for providing a mixed fractional Fourier signal based on mixing the received fractional Fourier signal and a correlation signal based on the narrow band modulation signal; and an inverse Fourier transformer arranged for providing the range profile signal based on inverse Fourier transforming the mixed fractional Fourier signal. This embodiment advantageously provides an implementation of the fractional correlator.

In a further embodiment of the frequency modulated continuous wave receiver, the fractional Fourier transformer transforms over an angle <p based on one or more predetermined parameters, such as one or more predetermined parameters of the frequency modulated continuous wave and/or the receiver, preferably only one or more predetermined frequency modulated continuous wave and/or receiver parameters, more preferably an oversampling factor y_r, a bandwidth of the frequency modulated continuous wave B, and/or a sample frequency f_s. Differently formulated, in an embodiment, the fractional Fourier transformer transforms over an angle <p, wherein angle <p is independent of the path traversed by the frequency modulated continuous wave. As the angle <p is independent of the path traversed by the frequency modulated continuous wave, the angle <p may advantageously be a design parameter instead of a parameter that needs adjustment during operation or use. The angle <p may advantageously be selected or set in advance such that the receiver may be adapted also in advance to the selected or set angle <p. The adaptation may advantageously comprise pre-calculating data or intermediate values used in the receiver, such as the correlation signal.

In an embodiment of the frequency modulated continuous wave receiver, the correlation signal or a constituent part of the correlation signal is precalculated; and the receiver comprises a memory for storing the precalculated correlation signal or a precalculated constituent part of the correlation signal. The memory advantageously allows to reuse precalculated data, more specifically the memory and the pre-calculating reduce energy usage of the receiver, response time of the receiver and/or a processor load, if a processor is part of the receiver or at least partly implementing the receiver.

In an embodiment of the frequency modulated continuous wave receiver, the fractional correlator comprises: a fractional Fourier modulation transformer arranged for generating a fractional Fourier modulation signal based on fractional Fourier transforming the narrow band modulation signal; and a processing block arranged for providing a/the correlation signal based on processing the fractional Fourier modulation signal for application in the fractional correlator, more specifically when on the embodiment above and mentioned in claim 2, the fractional Fourier mixer. This embodiment advantageously provides an implementation for generating the correlation signal.

In an embodiment of the frequency modulated continuous wave receiver, the fractional correlator comprises a sidelobe reduction block arranged for reducing at least one sidelobe of the range profile signal, wherein the sidelobe reduction block is applied in the fractional Fourier transform domain. The sidelobe reduction block may be a window function preferably in the fractional Fourier transform domain. The application of the window function may be called weighing the window function. Correlating the digitized mixed received signal and the narrow band modulation signal in the fractional Fourier domain with both signals represented as good as possible provides an optimum or near optimum signal-to-noise ratio. As representation in the fractional Fourier domain is always an approximation, sidelobes are a side effect of the processing, such as transformation from and to the fractional Fourier domain. These sidelobes may cause masking of other signals. In some applications, such as some radar examples, masking of other targets is an issue. The sidelobe reduction block reduces at least one, typically multiple sidelobes, such as the two sidelobes on either side of the signal based on the narrow band modulation signal. The range profile signal with at least one reduced sidelobe provides the advantage of preventing or reducing the change that a sidelobe masks another target.

In a further embodiment of the frequency modulated continuous wave receiver, the sidelobe reduction block provides a sidelobe reduced signal to the fractional Fourier mixer based on the received fractional Fourier signal. The sidelobe reduction block is advantageously arranged between the fraction Fourier receiver transformer and the fractional Fourier mixer.

In a further embodiment of the frequency modulated continuous wave receiver, the sidelobe reduction block provides a sidelobe reduced signal to the inverse Fourier transformer based on the mixed fractional Fourier signal. The sidelobe reduction block is advantageously arranged between the fractional Fourier mixer and the inverse Fourier transformer.

In a further embodiment of the frequency modulated continuous wave receiver, the sidelobe reduction block is integrated in the inverse Fourier transformer such that the inverse Fourier transformation and the sidelobe reduction functionality of the sidelobe reduction block are combined in a single algorithm for advantageously simplifying the algorithm and/or reducing the computational costs.

In a further embodiment of the frequency modulated continuous wave receiver, the sidelobe reduction block provides a sidelobe reduced signal to the processing block based on the fractional Fourier modulation signal. The sidelobe reduction block is advantageously arranged between the fractional Fourier modulation transformer and the processing block for advantageously including this function in the part of the system that is pre-calculated for reducing the -real-time- computational requirements.

In a further embodiment of the frequency modulated continuous wave receiver, the sidelobe reduction block provides a sidelobe reduced signal to the fractional Fourier mixer based on the correlation signal. The sidelobe reduction block is advantageously arranged between the processing block and the fractional Fourier mixer for advantageously including this function in the part of the system that is pre-calculated for reducing the -real-time- computational requirements.

In an embodiment of the frequency modulated continuous wave receiver, the digitizer comprises: a low pass filter arranged for providing a filtered mixed received signal based on low pass filtering the mixed received signal; and an analogue to digital converter arranged for providing the digitized mixed received signal based on the filtered mixed received signal. This embodiment details the digitizer and provides an implementation of the digitizer. In an embodiment of the frequency modulated continuous wave receiver, the wide band continuous wave chirp has a wide bandwidth; the narrow band modulation signal has a narrow bandwidth; and the wide bandwidth relative to the narrow bandwidth is at least 2 times, preferably at least 4 times, more preferably at least 8 times, more preferably at least 16 times, more preferably at least 32 times, most preferably at least 40 times, as wide. This embodiment advantageously provides a reference for narrow and wide band signals relative to each other.

In an embodiment of the frequency modulated continuous wave receiver, the wide band continuous wave chirp has a/the wide bandwidth based on the filters and/or is below 10 GHz, preferably 4 GHz, more preferably 1 GHz; and the narrow band modulation signal has a/the narrow bandwidth below one, preferably a half, more preferably a quarter, of the sampling frequency f_s the digitizer. This embodiment advantageously provides a reference for narrow and wide band signals in absolute terms.

In an embodiment of the frequency modulated continuous wave receiver, the narrow band modulation signal comprises an identification signal. The identification signal advantageously allows to identify the frequency modulated continuous wave from other frequency modulated continuous waves. This identification signal is typically advantageous in a MIMO application of the receiver.

In an embodiment of the frequency modulated continuous wave receiver, the frequency modulated continuous wave receiver is a linear frequency modulation receiver advantageously simplifying the implementation and/or structure of the receiver.

In an embodiment of the frequency modulated continuous wave receiver, the frequency modulated continuous wave receiver is a phase-modulated frequency modulated continuous wave receiver or an OFDM continuous wave receiver or any other information carrying waveform. Both modulations are examples of suitable modulations schemes for this type of receiver. The phase-modulated frequency modulated continuous wave provides the further advantage that the side lobs and/or bandwidth are limited. The phase-modulated frequency modulated continuous wave further provides the advantage of an improved peak-to- average power ratio (PAPR).

In an embodiment of the frequency modulated continuous wave receiver, mixing the narrow band modulation signal and the wide band continuous wave chirp is advantageously based on phase modulating the wide band continuous wave chirp based on the narrow band modulation signal. In an embodiment of the frequency modulated continuous wave receiver, the time delay and the beat frequency advantageously have a linear relation. In an embodiment of the frequency modulated continuous wave receiver, the receiver comprises an receiving antenna arranged for advantageously providing the frequency modulated continuous wave to the antenna input. In an embodiment of the frequency modulated continuous wave receiver, the narrow band modulation signal advantageously encodes an identifier, preferably a unique identifier, for identifying the frequency modulated continuous wave. The unique identifier advantageously allows to identify the frequency modulated continuous wave from other frequency modulated continuous waves. This unique identifier is typically advantageous in a MIMO application of the receiver.

In an embodiment of the frequency modulated continuous wave receiver, the wide band continuous wave chirp has a bandwidth in the range of 1 MHz - 10 GHz, preferably 5 MHz - 5 GHz, more preferably 10 MHz - 1 GHz. In an embodiment of the frequency modulated continuous wave receiver, the wide band continuous wave chirp has a length in the range of 1 ps - 200 ms, preferably 5 ps - 100 ms, more preferably 7 ps - 5 ms, most preferably 10 ps - 1 ms. In an embodiment ofthe frequency modulated continuous wave receiver, the wide band continuous wave chirp has a carrier frequency in the range of 1 - 300 GHz; preferably 2 - 200 GHz, more preferably 3 - 100 GHz, most preferably 3 - 84 GHz. In an embodiment of the frequency modulated continuous wave receiver, the digitizer has a sample frequency in the range of 1 - 400 MHz, preferably 3 - 100 MHz, more preferably 5 - 80 MHz, most preferably 10 - 40 MHz.

In an embodiment ofthe frequency modulated continuous wave transmitter, the signal generator generates the narrow band modulation signal based on encoding an identifier, preferably a unique identifier, for identifying the frequency modulated continuous wave. The unique identifier advantageously allows to identify the frequency modulated continuous wave from other frequency modulated continuous waves. This unique identifier is typically advantageous in a MIMO application of the transmitter. Furthermore, the unique identifier advantageously allows realization of joint communication and/or joint sensing.

In an embodiment ofthe frequency modulated continuous wave transmitter, the transmitter comprises: a fractional Fourier modulation transformer arranged for generating a fractional Fourier modulation signal based on fractional Fourier transforming the narrow band modulation signal; and a processing block arranged for providing a correlation signal based on processing the fractional Fourier modulation signal for application in a frequency modulated continuous wave receiver. This embodiment advantageously provides an implementation for generating the correlation signal. In a further embodiment of the frequency modulated continuous wave transmitter, the transmitter comprises a memory for storing the correlation signal or a constituent part of the correlation signal which is precalculated. The memory advantageously allows to reuse precalculated data, more specifically the memory and the pre-calculating reduce energy usage of the transmitter and/or the accompanying receiver, response time of the accompanying receiver and/or a processor load, if a processor is part of the transmitter and/or the accompanying receiver or at least partly implementing the transmitter and/or the accompanying receiver.

In an embodiment of the frequency modulated continuous wave transmitter, the wide band continuous wave chirp has a bandwidth in the range of 1 MHz - 10 GHz, preferably 5 MHz - 5 GHz, more preferably 10 MHz - 1 GHz. In an embodiment of the frequency modulated continuous wave transmitter, the wide band continuous wave chirp has a length in the range of 1 ps - 200 ms, preferably 5 ps - 100 ms, more preferably 7 ps - 5 ms, most preferably 10 ps - 1 ms. In an embodiment of the frequency modulated continuous wave transmitter, the wide band continuous wave chirp has a carrier frequency in the range of 1 - 300 GHz; preferably 2 - 200 GHz, more preferably 3 - 100 GHz, most preferably 3 - 84 GHz. In an embodiment of the frequency modulated continuous wave transmitter, the digitizer has a sample frequency in the range of 1 - 400 MHz, preferably 3 - 100 MHz, more preferably 5 - 80 MHz, most preferably 10 - 40 MHz.

In an embodiment of the frequency modulated continuous wave transceiver, the one or more frequency modulated continuous wave transmitters is at least two frequency modulated continuous wave transmitters; the at least two frequency modulated continuous wave transmitters depend on any of the mentioned embodiment comprising an identifier; the respective identifiers of the at least two frequency modulated continuous wave transmitters are different; and the one or more frequency modulated continuous wave receivers are arranged for receiving from the at least two frequency modulated continuous wave transmitters. The identifier advantageously allows to identify the frequency modulated continuous wave from other frequency modulated continuous waves. This identifier is typically advantageous in a MIMO application as mentioned in this embodiment.

In an embodiment of the frequency modulated continuous wave transceiver, the one or more frequency modulated continuous wave receivers is at least two frequency modulated continuous wave receivers; and the at least two frequency modulated continuous wave receivers depend on any of the mentioned embodiment comprising an identification signal. The identification signal advantageously allows to identify the frequency modulated continuous wave from other frequency modulated continuous waves. This identification signal is typically advantageous in a MIMO application as mentioned in this embodiment.

In an embodiment of the frequency modulated continuous wave range finder, the range finder is advantageously arranged for use in automotive, surveillance, meteorology, and/or meteorological applications.

In an embodiment of the method, determining comprises: generating a received fractional Fourier signal based on fractional Fourier transforming the digitized mixed received signal; providing a mixed fractional Fourier signal based on mixing the received fractional Fourier signal and a correlation signal based on the narrow band modulation signal; and providing the range profile signal based on inverse Fourier transforming the mixed fractional Fourier signal. This embodiment advantageously provides an implementation of the fractional correlator.

In an embodiment of the method, the fractional Fourier transformer transforms over an angle <p based on one or more predetermined parameters, such as one or more predetermined parameters of the frequency modulated continuous wave and/or the receiver, preferably only one or more predetermined frequency modulated continuous wave and/or receiver parameters, more preferably an oversampling factor y_r, a bandwidth of the frequency modulated continuous wave B, and/or a sample frequency f_s. Differently formulated, in an embodiment, the fractional Fourier transformer transforms over an angle <p, wherein angle <p is independent of the path traversed by the frequency modulated continuous wave. As the angle <p is independent of the path traversed by the frequency modulated continuous wave, the angle <p may advantageously be a design parameter instead of a parameter that needs adjustment during operation or use. The angle <p may advantageously be selected or set in advance such that the method for receiving may be adapted also in advance to the selected or set angle <p. The adaptation may advantageously comprise pre-calculating data or intermediate values used in the method for receiving, such as the correlation signal.

In an embodiment of the method, the method comprises storing the correlation signal or a constituent part of the correlation signal which is precalculated.

The storing advantageously allows to reuse precalculated data, more specifically the storing and the precalculating reduce energy usage of the method for receiving, response time of the method for receiving and/or a processor load, if a processor is part of implementing the method for receiving or at least partly implementing the method for receiving.

In an embodiment of the method, providing a digitized mixed received signal comprises: configuring a filter for providing a filtered mixed received signal based on low pass filtering the mixed received signal; and/or configuring an analogue to digital converter for providing the digitized mixed received signal based on the filtered mixed received signal. This embodiment advantageously provides an implementation for controlling a digitizer and/or hardware or software involved in digitizing the mixed received signal.

In an embodiment of the method, the narrow band modulation signal is an identification signal. The identification signal advantageously allows to identify the frequency modulated continuous wave from other frequency modulated continuous waves. This identification signal is typically advantageous in a MIMO application as mentioned in this embodiment.

In an embodiment of the method, generating a narrow band modulation signal generates the narrow band modulation signal based on encoding an identifier, preferably a unique identifier, for identifying the frequency modulated continuous wave. The unique identifier advantageously allows to identify the frequency modulated continuous wave from other frequency modulated continuous waves. This unique identifier is typically advantageous in a MIMO application of the transmitter.

In an embodiment of the method, the method comprises: generating a fractional Fourier modulation signal based on fractional Fourier transforming the narrow band modulation signal; and providing a correlation signal based on processing the fractional Fourier modulation signal for application in a frequency modulated continuous wave receiver. This embodiment advantageously provides an implementation for generating the correlation signal. In a further embodiment of the method, the method comprises storing the correlation signal or a constituent part of the correlation signal which is precalculated.

In an embodiment of the method, the one or more instances of the transmitting method for transmitting a frequency modulated continuous wave is at least two instances of the transmitting method; the at least two instances of the transmitting method depend on an embodiment of the transmitter comprising an identifier; the respective identifiers of the at least two instances of the transmitting method are different; and the one or more instances of the receiving method are arranged for receiving from the at least two instances of the transmitting methods.

In an embodiment of the method, the one or more instances of receiving method is at least two instances of receiving methods; and the at least two receiving methods depend on an embodiment of the receiver comprising an identifier.

DETAILED DESCRIPTION OF THE FIGURES

Modification of a linearly frequency modulated (LFM) waveform by applying a (multi-carrier) phase modulation to it is an emerging technology for automotive radars. It allows combining the low sampling requirements of LFM signals and waveform diversity of information-carrying waveforms, which is a strongly required element for efficient realization of radar (self)-interference mitigation and joint communication and sensing.

A novel receiver structure, based on Fractional Fourier Transform (FrFT) is proposed, which demonstrates an improved performance over the state-of-the-art solutions for moderate-to-large bandwidth of the information-carrying waveforms with a minor increase in the computational complexity.

SIGNAL MODEL AND MATCHED FILTER RECEIVER

Signal model

Assume the radar transmits a wideband LFM chirp modulated with a narrow-band modulation signal m(t):

where f_c stands for the carrier frequency of the radar, 0 = B/T is the chirp rate, B and T are the bandwidth and the duration of the chirp respectively. Moreover, we assume that the bandwidth of m(t) is much smaller that of the chirp B_m«B.

The signal from (1) impinges on a target at range ro moving with a constant radial velocity vo towards or away from the radar. The reflected signal is received by the radar with the time delay:

attenuated proportionally to the target RCS and two-way propagation of the way by the complex coefficient ao.

Hereinafter, we incorporate all the constant terms of signal processing into aowith no loss of generality. The signal impinging the receiver becomes:

where fo = 2vofc/c and we used (1-2vo)/c = 1 considering that in a typical scenario velocities vo « c. Applying the stretch processing on receive (also called dechirping or deramping), which consists of multiplication of the received signal with the transmitted chirp and filtering out high frequency components, results in:

It comprises of two main components: the delayed modulated signal and the beat frequency. The second item is standard for dechipring of LFM signals. It also comprises Doppler frequency shift due to target motion, which is typically negligible compared to the frequency resolution of the beat signal after applying FFT to it, i.e. fo « fs/N, where f_s is the sampling frequency of the beat signal and N is the number of fast-time samples.

Signal processing - filter bank

The form of (4) can be alternatively interpreted if we denote fvo = 0io as a virtual Doppler frequency shift, which is significantly (about two orders of magnitude) larger than the typical for automotive radar Doppler frequency shift fo in (4). In this formulation it resembles a conventional response of a waveform m(t) with the time delay and Doppler frequency shift fvo. This representation resembles the reception of a general waveform m(t) with a large Doppler shift. In this case, the optimal receiver in white noise may be a matched filter for each range-Doppler hypothesis. It can be realized either via a search over all possible range-Doppler hypothesis or via performing Doppler processing prior to range compression. Due to the explicit relation between the parameters couple fvo = Pio, one-dimensional search over the parameter r is needed. Thus, the receiver calculates for each r:

Modern radars perform baseband signal processing digitally, after the received beat signal is sampled by ADC at the sampling frequency f_s and stored in vector s C C^Nx1:

The reference signal in the integral (5) for the fixed r can be given via a Hadamard product of two vectors a(r) O m(r):

Stacking the steering vectors of beat signal and delayed modulation signal as columns in matrices A = [a(ro), ...., a(TR)] and M = m(ro), ... , m(TR)] respectively, with Nr being the predefined number of range cells, it is possible to write the convolution (5) via a vector product:

This receiver structure may be called compensated stretch processing. The compensation referred in the name of the algorithm realizes the proper shift of the reference modulation signal for each range hypothesis, realized here via matrix M. The filter bank realization of the compensated stretch processing leads to the computational complexity of DFT O(N²).

Waveform analysis and design

The key block of the receiver (5) (or its digital counterpart (8)) correlates the received signal with the time delay and frequency shifted template. That is equivalent to calculating the cross correlation of s(t) and m(t) along the diagonal line in the time delay / Doppler shift domain.

If we further expand (5), considering target Doppler frequency shift as in (4), we get:

TO and X_m(T, fo) defines the ambiguity function of the waveform m(t). It implies that the range response of the proposed processing is determined by the diagonal cut of the ambiguity function X_m(T, fo). This can be alternatively interpreted as a shear of the ambiguity function of the waveform m(t) being modulated by a chirp.

Another consequence of (9) is that the (phase) modulation schemes, optimized for low range sidelobes, e.g Barker, Frank or Zadoff-Chu phase codes, would not preserve this property if they are used to modulate a chirp (1).

FRACTIONAL CORRELATION RECEIVER In a conventional radar signal processing, the time delay (range) and signal frequency shift (Doppler) are typically estimated separately and independent of each other: range via the correlation of the received signal with the replica and Doppler frequency via Fourier transform over slow-time - both with a computational complexity of FFT. The former exploits the fact that correlation in time transforms into a simple multiplication operations in the frequency domain:

where '?> denotes correlation, F ¹¹'²^} is the inverse Fourier transform (the reason for this superscript will be explained shortly); S(f) and M(f) are the Fourier transforms of s(t) and m(t) respectively.

So, the objective is to develop an efficient algorithm to calculate the cross-correlation along the diagonal line in the time delay I Doppler shift domain (5) with the computational complexity of FFT. That can be done using the theory of the fractional Fourier transform (FrFT) and fractional correlation.

With the use of FrFT, the definition (10) can be extended for calculating the cross-correlation along any line in the Doppler-delay plane:

where the operators ■'A>‘^(P and F^*} denotes fractional correlation and the fractional Fourier transform associated with angle <p, measured anti-clockwise from the time axis, such that F^K/2{"} and correspond to the Fourier transform and inverse Fourier transform respectively. Moreover, we denote by S^<p(p)=F^q,{s(t)} and M^<p(p)=F^<,,{m(t)} the <p-th fractional Fourier transform (FrFT) of s(t) and m(t) and p is the argument in this FrFT domain.

The fractional Fourier transform (FrFT) of s(t) is defined for angle <p as:

Time-frequency representation of the modulation signal m(t) and that of the received signal (4) are presented in Fig. 1 . It can be seen that the range information of the target is fully described by the radial displacement p at the angle <p.

The displacement of the signal time-frequency representation by p, <p in polar coordinated corresponds to:

where we used the notation a = _e-j^21T(p°^2/2>^c°^s <r ^sin » _as for the FrFT of s(t) it can be substituted into the constant term of the received signal ao with no loss of generality. Given the property (13) of FrFT and comparing it to (4), the relation of the FrFT parameters to the waveform and radar parameters can be found via:

where y_r is the oversampling factor for range processing. It should be also noted that depending on the sign of the analytical signal in (1) and also on the choice of up/down chirp, the beat frequency can have a negative sign. That should be taken in the account at the output of IQ demodulation. Furthermore, the angle of FrFT is fully determined by the parameters of the radar according to the ratio of scales in relative frequency shift (Pr/f_s) to relative time delay of the signal (r/T) and thus:

The range of the target depends linearly on the parameter po:

and can be directly scaled to the range axis.

The FrFT receiver or transceiver structure or architecture is presented in Fig. 2. An important component of the receiver is the fractional correlation block, which realizes (11).

It is assumed that fractional correlation block operates with the sampled signals. The discrete version of the FrFT (12) can be derived from the discrete Fourier transform by the eigenvalue decomposition of the transformation matrix and maintain most of the properties of the continuous FrFT. It approximates well the continuous fractional Fourier transform for large number of samples.

A faster way to compute an approximation of the continuous fractional Fourier transform exploits the fact that FrFT can be rewritten via a convolution in between two chirp multiplications, which need to be sampled at twice the original sampling rate. The computational complexity of such implementation is O(N log2 <N)), being determined by the realization of the convolution via FFT. This algorithm provides the advantage of low computation load and high accuracy made.

It should be noted that digital calculation of FrFT assumed that the signal is approximately confined to the interval [-T/2, T/2] in time and to the interval [-f_s/2, f_s/2] in frequency. While the former is easy to satisfy be shifting the time axes of Rx signal s(t) and replica m(t) by -T/2, the latter results in folding the signal in FrFT domain for fb > fs/2. To avoid frequency folding, we propose to transmit the modulated signal m(t) with a frequency offset Ar = -f_s/2 + B_m/2, where B_m is the bandwidth of modulation sequence, which insures that the sampled received is time-frequency shifted version of the reference one for ranges:

where AR = c/(2B). The modulation of FMCW therefore leads to the degradation of the maximum detectable range by the factor (f_s - B_m)/fs. Note, that the discussion above assumes the IQ receiver structure; if sampling only I channel, both signals should belong to the interval [0, f_s/2] and thus the frequency offset should be set to Ar = B_m/2.

SIMULATIONS

Consider the waveform with chirp bandwidth B = 200 MHz, chirp duration T = 12.8 ps operating at carrier f_c = 77 GHz and the sampling frequency of the beat signal is f_s = 20 MHz. With thus setup, the maximum range of FMCW is Rmax = 192 m. The signal m(t) is Gaussian minimum shift keying (GMSK) modulated waveform with the time-bandwidth product of GMSK equal to 0.3 and N=64 chips, which corresponds to the modulation signal bandwidth of B_m = fs/4 = 5 MHz. For the range processing, we consider range oversampling y_r = 2, which according to (15) gives <p = arctan(20) = 1 .52. To demonstrate the principle of the FrFT receiver, we assume a noise- free scenario with a single stationary point-like target located at ro =60 m from the radar.

Principles of FRFT receiver/transceiver

The signal representation at all the stages of the fractional correlation (11) is plotted in Fig. 3. Here, we did not apply frequency shift of the modulation signal, described at the end of the previous section, for better visibility (there is no difference in applying this shift or not for a target at ro < Rmax/2). It can be seen that despite the time and frequency shift between the received s(t) and the reference m(t) signals (Fig. 3, a, b), it vanishes in their FrFT representations (Fig. 3,c, d). As a result, their product has a wide and uniform spectrum (Fig. 3,e), which leads to a narrow peak in the reconstructed range profile (Fig. 3,f).

We further compare the performance of the FrFT receiver to that of the filter bank approach or architectureand to that of the group delay receiver (Fig. 4). Simulation results demonstrate that all three receivers have comparable range response for small bandwidth of modulation signal B_m/ fs = 1/64 (Fig. 4, a), but for larger bandwidth of m(t) the performance of group delay receiver or receiver architecture degrades significantly compared to that of filter bank and FrFT approaches or architectures (Fig. 4,b shows the result for B_m / fs = 1/4). The performance of FrFT receiver is similar to that of the filter bank, being different only in the implementation and related to it computational complexity, as we mentioned above.

SNR loss

To better demonstrate the limit of applicability the group delay receiver, we compare Fig. 5 the SNR loss as the function of the code bandwidth B_m / fs normalized by f_s. Similarly to the above, we considered a noise-free scenario with a single target present in the scene at the range ro = 60 + WR m, where WR C [-2.5AR, 2.5AR], models an offset from the defined range grid with a step 0.125AR.

The plots in Fig. 5 show the average (solid line), the best-case and the worst-case (dashed lines) SNR loss for three considered receivers. It can be seen that all three receivers behave similarly for a small code bandwidth, having about 1 dB straddle loss. For large code bandwidth B_m / fs 2 1/8, the matched filter and the FrFT receiver keep having small straddle loss, while the group delay filter leads to a significant (over 10 dB) SNR loss, which is also seen via defocusing of the main lobe of the range response in Fig. 4, b. This performance degradation of the group delay receiver for large bandwidth of the modulation signal m(t) imposes an additional constraint on the choice of the modulation sequence m(t). Finally, it should be noticed that for B_m / fs = 1 all the receivers have degraded performance for observing the target at ro = 60, because a part of the modulated signal spectrum is being rejected by the low pass filter of the receiver.

The bandwidth of the modulation signal has an impact on the maximum detectable target range. We investigate this behaviour via simulations in Fig. 6 for three values of the normalized bandwidth of the modulation signal: B_m / fs = 1/16 (Fig. 6, a), B_m / fs = 1/4 (Fig. 6, b) and B_m / fs = 1/2 (Fig. 6, c). The range axes in Fig. 6 are similar to that in Fig. 4, up to the normalization by a scalar Rmax. It can be seen, that a small bandwidth of the modulation B_m (Fig. 6, a) has almost no impact on the maximum detectable range of the target, while in case of significant modulation bandwidth B_m, SNR loss rapidly increases for r > 0.8Rmax when B_m / fs = 1/4 and for r > 0.6Rmax when Bm I fs = 1/2. These values slightly exceed the criteria defined in (17), while the latter still gives a reasonable estimation of the maximum range for applying dechirping receiver with a modulated LFM waveform.

Computational complexity

Further, we compared the average over 100 trials execution time of each of the three receivers as the function of fast-time samples per chirp (Fig. 7). In this simulation we used two different implementations of FrFT.

The results in Fig. 7 show that the slope of FrFT and group delay receivers follows the trend O(N logz (N)) and the matched filter complexity grows according to O(N²). Two implementations of FrFT have slightly different execution time. For moderate to large number of samples per chirp, the FrFR receiver has over one order of magnitude gain in computational time. The group delay receiver brings the execution time even lower, but its performance for long code sequences is unsatisfactory, as explained above.

CONCLUSION

The new receiver structure for the modulated LFM waveform can be realized in hardware or software. We demonstrated that matched filter processing of this waveform corresponds to calculating the cross-correlation along a diagonal line in the delay-Doppler plane - called Fractional correlation, which can be efficiently implemented via the Fractional Fourier Transform (FrFT). FrFT receiver is introduced and its improved performance over the state-of-the art techniques is demonstrated for moderate-to-large bandwidth of the applied to chirp modulation. It is computationally more efficient and more accurate for target detection than a traditional receiver based on a group delay filter. The larger the receive signal bandwidth is, the higher the performance advantage of the receiver proposed over a traditional receiver is. Figure 1 a schematically shows a time-frequency representation of the received signal and its relation to the FrFT angle <p. On the horizontal axis, time is shown. On the vertical axis, frequency is shown.

Figure 1 b schematically shows a time-frequency representation of the received signal and the correlation signal after transforming them by the FrFT angle <p. Figure 1 b is closely related to figure 1 a. The time-frequency representation of the signals are shown converted and/or rotated to visually show an interpretation of the fractional Fourier transformation over an angle <p. This conversion and/or rotation visually shows the linear relationship for the time delay and the beat frequency and their relation to the argument in Fractional domain p.

Figure 2 schematically shows an FRFT transceiver structure or architecture for modulated FMCW waveforms. The transceiver comprises a transmitter and a receiver. The receiver may be viewed as comprising the blocks in the lower data path. The transmitter and receiver may share the signal generators. Alternatively, one of the transmitter and receiver may comprise one or more of the signal generators providing the generated signal to the other. The signal generators are the chirp generator 210 generating the wide band continuous wave chirp, and the signal generator 220 generating the narrow band modulation signal 137. The transmitter may comprise the antenna output 240, the transmitter mixer 230 and a narrow band modulation signal output 138. The narrow band modulation signal output is arranged for providing the narrow band modulation signal to an frequency modulated continuous wave receiver arranged for receiving the transmitted frequency modulated continuous wave. Figure 9 schematically shows an embodiment of a computer program product 1000, computer readable medium 1010 and/or non-transitory computer readable storage medium comprising computer readable code 1020 according to the invention. The video recording assembly may comprise a part, such as the carrier frame, arranged on a user. The video recording assembly may comprise another part, not arranged on a user. The part not arranged on the user typically may comprise a processing unit for processing the video stream from the video recording assembly. The part not arranged on the user may be typed as an external part, server and/or smartbox. In another embodiments, the video processing unit may be arranged to the carrier frame.

It will also be clear that the above description and drawings are included to illustrate some embodiments of the invention, and not to limit the scope of protection. Starting from this disclosure, many more embodiments will be evident to a skilled person without departing from the scope of the invention as set forth in the appended claims. These embodiments are within the scope of protection and the essence of this invention and are obvious combinations of prior art techniques and the disclosure of this patent. Devices functionally forming separate devices may be integrated in a single physical device.

The term “substantially” herein, such as in “substantially all emission" or in “substantially consists", will be understood by the person skilled in the art. The term “substantially" may also include embodiments with “entirely", “completely", “all", etc. Hence, in embodiments the adjective substantially may also be removed. Where applicable, the term “substantially" may also relate to 90% or higher, such as 95% or higher, especially 99% or higher, even more especially 99.5% or higher, including 100%. The term “comprise" also includes embodiments wherein the term “comprises" means “consists of’.

The term "functionally" will be understood by, and be clear to, a person skilled in the art. The term “substantially" as well as “functionally" may also include embodiments with “entirely", “completely", “all", etc. Hence, in embodiments the adjective functionally may also be removed. When used, for instance in “functionally parallel", a skilled person will understand that the adjective “functionally" includes the term substantially as explained above. Functionally in particular is to be understood to include a configuration of features that allows these features to function as if the adjective “functionally" was not present. The term “functionally" is intended to cover variations in the feature to which it refers, and which variations are such that in the functional use of the feature, possibly in combination with other features it relates to in the invention, that combination of features is able to operate or function. For instance, if an antenna is functionally coupled or functionally connected to a communication device, received electromagnetic signals that are receives by the antenna can be used by the communication device. The word “functionally" as for instance used in “functionally parallel" is used to cover exactly parallel, but also the embodiments that are covered by the word “substantially" explained above. For instance, “functionally parallel" relates to embodiments that in operation function as if the parts are for instance parallel. This covers embodiments for which it is clear to a skilled person that it operates within its intended field of use as if it were parallel.

Furthermore, the terms first, second, third and the like in the description and in the claims, are used for distinguishing between similar elements and not necessarily for describing a sequential or chronological order. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other sequences than described or illustrated herein. Thus, these terms are not necessarily intended to indicate temporal or other prioritization of such elements.

The devices or apparatus herein are amongst others described during operation. As will be clear to the person skilled in the art, the invention is not limited to methods of operation or devices in operation.

It should be noted that the above-mentioned embodiments illustrate rather than limit the invention, and that those skilled in the art will be able to design many alternative embodiments without departing from the scope of the appended claims. In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. Use of the verb "to comprise" and “to include", and its conjugations does not exclude the presence of elements or steps other than those stated in a claim. Also, the use of introductory phrases such as “at least one" and “one or more" in the claims should not be construed to imply that the introduction of another claim element by the indefinite articles "a" or "an" limits any particular claim containing such introduced claim element to inventions containing only one such element, even when the same claim includes the introductory phrases "one or more" or "at least one" and indefinite articles such as "a" or "an." The article "a" or "an" preceding an element does not exclude the presence of a plurality of such elements.

The invention may be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer. In the device or apparatus claims enumerating several means, several of these means may be embodied by one and the same item of hardware. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. The invention further applies to an apparatus or device comprising one or more of the characterising features described in the description and/or shown in the attached drawings. The invention further pertains to a method or process comprising one or more of the characterising features described in the description and/or shown in the attached drawings.

It will be appreciated that the invention also applies to computer programs, particularly computer programs on or in a carrier, adapted to put the invention into practice. The program may be in the form of a source code, a code intermediate source and an object code such as in a partially compiled form, or in any other form suitable for use in the implementation of the method according to the invention. It will also be appreciated that such a program may have many different architectural designs. For example, a program code implementing the functionality of the method or system according to the invention may be sub-divided into one or more sub-routines. Many different ways of distributing the functionality among these sub-routines will be apparent to the skilled person. The sub-routines may be stored together in one executable file to form a self-contained program. Such an executable file may comprise computer-executable instructions, for example, processor instructions and/or interpreter instructions (e g. Java interpreter instructions). Alternatively, one or more or all of the sub-routines may be stored in at least one external library file and linked with a main program either statically or dynamically, e g. at run-time. The main program contains at least one call to at least one of the sub-routines. The sub-routines may also comprise function calls to each other. An embodiment relating to a computer program product comprises computer-executable instructions corresponding to each processing stage of at least one of the methods set forth herein. These instructions may be sub-divided into sub-routines and/or stored in one or more files that may be linked statically or dynamically. Another embodiment relating to a computer program product comprises computerexecutable instructions corresponding to each means of at least one of the systems and/or products set forth herein. These instructions may be sub-divided into sub-routines and/or stored in one or more files that may be linked statically or dynamically.

The carrier of a computer program may be any entity or device capable of carrying the program. For example, the carrier may include a data storage, such as a ROM, for example, a CD ROM or a semiconductor ROM, or a magnetic recording medium, for example, a hard disk. Furthermore, the carrier may be a transmissible carrier such as an electric or optical signal, which may be conveyed via electric or optical cable or by radio or other means. When the program is embodied in such a signal, the carrier may be constituted by such a cable or other device or means. Alternatively, the carrier may be an integrated circuit in which the program is embedded, the integrated circuit being adapted to perform, or used in the performance of, the relevant method.

The various aspects discussed in this patent can be combined in order to provide additional advantages. The mere fact that certain measures are recited in mutually different claims does not indicate that a combination of these measures cannot be used to advantage. Furthermore, some of the features can form the basis for one or more divisional applications. Furthermore, the methods mentioned may be implementable and executable on a computer.

Claims

1. Frequency modulated continuous wave receiver, comprising:

- an antenna input (110) arranged for receiving an antenna signal from a receiving antenna arranged for receiving a frequency modulated continuous wave;

- a receiver mixer (120) arranged for providing a mixed received signal (125) based on mixing the received antenna signal (115) of the antenna and a wide band continuous wave chirp (116);

- a digitizer (130) arranged for providing a digitized mixed received signal (135) based on digitizing the mixed received signal; and

- a fractional correlator (140) arranged for determining a range profile signal (145) indicative of the path length traversed by the frequency modulated continuous wave, wherein the range profile signal is based on correlating in a fractional Fourier transform domain the digitized mixed received signal with a narrow band modulation signal (137); and wherein the frequency modulated continuous wave received at the antenna input and transmitted by a frequency modulated continuous wave transmitter is based on mixing at the frequency modulated continuous wave transmitter of the wide band continuous wave chirp with the narrow band modulation signal.

2. Frequency modulated continuous wave receiver according to the preceding claim, wherein the fractional correlator comprises:

- a fractional Fourier receiver transformer (150) arranged for generating a received fractional Fourier signal (155) based on fractional Fourier transforming the digitized mixed received signal;

- a fractional Fourier mixer (160) arranged for providing a mixed fractional Fourier signal (165) based on mixing the received fractional Fourier signal and a correlation signal (137) based on the narrow band modulation signal; and

- an inverse Fourier transformer (170) arranged for providing the range profile signal based on inverse Fourier transforming the mixed fractional Fourier signal.

3. Frequency modulated continuous wave receiver according to the preceding claim, wherein the fractional Fourier transformer transforms over an angle <p based on one or more predetermined parameters, such as one or more predetermined parameters of the frequency modulated continuous wave and/or the receiver, preferably only one or more predetermined frequency modulated continuous wave and/or receiver parameters, more preferably an oversampling factor y_r, a bandwidth of the frequency modulated continuous wave B, and/or a sample frequency f_s.

4. Frequency modulated continuous wave receiver according to any of the preceding claims 2-3, wherein the correlation signal or a constituent part of the correlation signal is precalculated; and wherein the receiver comprises a memory for storing the precalculated correlation signal or a precalculated constituent part of the correlation signal.

5. Frequency modulated continuous wave receiver according to any of the preceding claims, wherein the fractional correlator comprises:

- a fractional Fourier modulation transformer (180) arranged for generating a fractional Fourier modulation signal (185) based on fractional Fourier transforming the narrow band modulation signal; and

- a processing block (190) arranged for providing a/the correlation signal based on processing the fractional Fourier modulation signal for application in the fractional correlator, more specifically when depending on claim 2, the fractional Fourier mixer.

6. Frequency modulated continuous wave receiver according to any of the preceding claims, wherein the fractional correlator comprises a sidelobe reduction block arranged for reducing at least one sidelobe of the range profile signal, wherein the sidelobe reduction block is applied in the fractional Fourier transform domain.

7. Frequency modulated continuous wave receiver according to the preceding claim, wherein the sidelobe reduction block:

- provides a sidelobe reduced signal, when depending on claim 2, to the fractional Fourier mixer based on the received fractional Fourier signal;

- provides a sidelobe reduced signal, when depending on claim 2, to the inverse Fourier transformer based on the mixed fractional Fourier signal;

- when depending on claim 2, is integrated in the inverse Fourier transformer such that the inverse Fourier transformation and the sidelobe reduction functionality of the sidelobe reduction block are combined in a single algorithm;

- provides a sidelobe reduced signal, when depending on claim 5, to the processing block based on the fractional Fourier modulation signal; and/or

- provides a sidelobe reduced signal, when depending on claims 2 and 5, to the fractional Fourier mixer based on the correlation signal.

8. Frequency modulated continuous wave receiver according to any of the preceding claims, wherein the digitizer comprises:

- a low pass filter arranged for providing a filtered mixed received signal based on low pass filtering the mixed received signal; and

- an analogue to digital converter arranged for providing the digitized mixed received signal based on the filtered mixed received signal.

9. Frequency modulated continuous wave receiver according to any of the preceding claims, wherein the wide band continuous wave chirp has a wide bandwidth; wherein the narrow band modulation signal has a narrow bandwidth; and wherein the wide bandwidth relative to the narrow bandwidth is at least 2 times, preferably at least 4 times, more preferably at least 8 times, more preferably at least 16 times, more preferably at least 32 times, most preferably at least 40 times, as wide.

10. Frequency modulated continuous wave receiver according to any of the preceding claims, wherein the wide band continuous wave chirp has a/the wide bandwidth based on the filters and/or is below 10 GHz, preferably 4 GHz, more preferably 1 GHz; and wherein the narrow band modulation signal has a/the narrow bandwidth below one, preferably a half, more preferably a quarter, of the sampling frequency f_s the digitizer.

11. Frequency modulated continuous wave receiver according to any of the preceding claims, wherein the narrow band modulation signal comprises an identification signal.

12. Frequency modulated continuous wave receiver according to any of the preceding claims, wherein the frequency modulated continuous wave receiver is a linear frequency modulation receiver.

13. Frequency modulated continuous wave receiver according to any of the preceding claims, wherein the frequency modulated continuous wave receiver is a phase-modulated frequency modulated continuous wave receiver or an OFDM continuous wave receiver or any other information carrying waveform.

14. Frequency modulated continuous wave receiver according to any of the preceding claims, wherein mixing the narrow band modulation signal and the wide band continuous wave chirp is based on phase modulating the wide band continuous wave chirp based on the narrow band modulation signal.

15. Frequency modulated continuous wave receiver according to any of the preceding claims, wherein a time delay and a beat frequency have a linear relation.

15. Frequency modulated continuous wave receiver according to any of the preceding claims, comprising an receiving antenna arranged for providing the frequency modulated continuous wave to the antenna input.

16. Frequency modulated continuous wave receiver according to any of the preceding claims, wherein the narrow band modulation signal encodes an identifier, preferably a unique identifier, for identifying the frequency modulated continuous wave.

17. Frequency modulated continuous wave receiver according to any of the preceding claims, wherein the wide band continuous wave chirp has a bandwidth in the range of 1 MHz - 10 GHz, preferably 5 MHz - 5 GHz, more preferably 10 MHz - 1 GHz; wherein the wide band continuous wave chirp has a length in the range of 1 ps - 200 ms, preferably 5 ps - 100 ms, more preferably 7 ps - 5 ms, most preferably 10 ps - 1 ms; wherein the wide band continuous wave chirp has a carrier frequency in the range of 1 - 300 GHz; preferably 2 - 200 GHz, more preferably 3 - 100 GHz, most preferably 3 - 84 GHz; and wherein the digitizer has a sample frequency in the range of 1 - 400 MHz, preferably 3 - 100 MHz, more preferably 5 - 80 MHz, most preferably 10 - 40 MHz.

18. Frequency modulated continuous wave transceiver, comprising:

- one or more frequency modulated continuous wave receivers according to any of the claims 1-16; and

- one or more frequency modulated continuous wave transmitters; wherein a frequency modulated continuous wave transmitter comprises:

- a chirp generator (210) arranged for generating a wide band continuous wave chirp (116);

- a signal generator (220) arranged for generating a narrow band modulation signal (137);

- a transmitter mixer (230) arranged for providing a mixed transmission signal (235) based on mixing the wide band continuous wave chirp and the narrow band modulation signal; and

- an antenna output (240) arranged for providing an antenna signal to a transmitting antenna based on the mixed transmission signal for the transmitting antenna transmitting a frequency modulated continuous wave.

19. Frequency modulated continuous wave transceiver according to the preceding claim, wherein the one or more frequency modulated continuous wave transmitters is at least two frequency modulated continuous wave transmitters; wherein the signal generator of each of the at least two frequency modulated continuous wave transmitters generates the narrow band modulation signal based on encoding an identifier for identifying the frequency modulated continuous wave; wherein the respective identifiers of the at least two frequency modulated continuous wave transmitters are different for identifying the frequency modulated continuous wave; and wherein the one or more frequency modulated continuous wave receivers are arranged for receiving from the at least two frequency modulated continuous wave transmitters.

20. Frequency modulated continuous wave transceiver according to the preceding claim, wherein the one or more frequency modulated continuous wave receivers is at least two frequency modulated continuous wave receivers; and wherein the at least two frequency modulated continuous wave receivers depend on claim 11.

21. Frequency modulated continuous wave transceiver according to any of the preceding claims 18-20, wherein at least one of the one or more frequency modulated continuous wave transmitters comprises an output (138) arranged for providing the narrow band modulation signal to at least one of the one or more frequency modulated continuous wave receivers arranged for receiving the transmitted frequency modulated continuous wave.

22. Range finder comprising a frequency modulated continuous wave transceiver according to any of the claims 18-21 , arranged as radar, preferably MIMO radar, or sonar, preferably MIMO sonar.

23. Range finder according to the preceding claim, wherein the range finder is arranged for use in automotive, surveillance, meteorology, and/or meteorological applications.

24. Method for receiving a frequency modulated continuous wave, comprising:

- providing (910) a digitized mixed received signal based on digitizing a mixed received signal which is based on:

- receiving an antenna signal from a receiving antenna arranged for receiving a frequency modulated continuous wave; and - providing the mixed received signal based on mixing the received antenna signal of the antenna and a wide band continuous wave chirp; and

- determining (920) a range profile signal indicative of the path length traversed by the frequency modulated continuous wave, wherein the range profile signal is based on correlating in a fractional Fourier transform domain the digitized mixed received signal with a narrow band modulation signal; and wherein the frequency modulated continuous wave received at the antenna input and transmitted by a frequency modulated continuous wave transmitter is based on mixing at the frequency modulated continuous wave transmitter of the wide band continuous wave chirp with the narrow band modulation signal.

25. Method according to the preceding claim, wherein determining comprises:

- generating a received fractional Fourier signal based on fractional Fourier transforming the digitized mixed received signal;

- providing a mixed fractional Fourier signal based on mixing the received fractional Fourier signal and a correlation signal based on the narrow band modulation signal; and

- providing the range profile signal based on inverse Fourier transforming the mixed fractional Fourier signal.

26. Method according to the preceding claim, wherein the fractional Fourier transformer transforms over an angle <p based on one or more predetermined parameters, such as one or more predetermined parameters of the frequency modulated continuous wave and/or the receiver, preferably only one or more predetermined frequency modulated continuous wave and/or receiver parameters, more preferably an oversampling factor y_r, a bandwidth of the frequency modulated continuous wave B, and/or a sample frequency f_s.

27. Method according to any of the preceding claims 25-26, comprising storing the correlation signal or a constituent part of the correlation signal which is precalculated.

28. Method according to any of the preceding claims 24-27, wherein providing a digitized mixed received signal comprises:

- configuring a filter for providing a filtered mixed received signal based on low pass filtering the mixed received signal; and/or

- configuring an analogue to digital converter for providing the digitized mixed received signal based on the filtered mixed received signal.

29. Method according to any of the preceding claims 24-28, wherein the narrow band modulation signal is an identification signal.

30. Method for a frequency modulated continuous wave transceiver, comprising:

- one or more instances of the receiving method according to any of the claims 24-29; and

- one or more instances of the transmitting method; wherein the method for transmitting a frequency modulated continuous wave, comprises:

- configuring a chirp generator for generating a wide band continuous wave chirp; and

- configuring a signal generator for generating a narrow band modulation signal; wherein the configuring steps are performed for:

- providing a mixed transmission signal based on mixing the wide band continuous wave chirp and the narrow band modulation signal; and

- providing an antenna signal to a transmitting antenna based on the mixed transmission signal for the transmitting antenna transmitting a frequency modulated continuous wave.

31. Method according to the preceding claim, wherein the one or more instances of the transmitting method for transmitting a frequency modulated continuous wave is at least two instances of the transmitting method; wherein generating of the signal generator of each of the at least two instances of the transmitting method comprises generating the narrow band modulation signal based on encoding an identifier for identifying the frequency modulated continuous wave; wherein the respective identifiers of the at least two instances of the transmitting method are different for identifying the frequency modulated continuous wave; and wherein the one or more instances of the receiving method are arranged for receiving from the at least two instances of the transmitting methods.

32. Method according to the preceding claim, wherein the one or more instances of receiving method is at least two instances of receiving methods; and wherein the at least two receiving methods use the narrow band modulation signal as an identification signal.

33. Computer program product (1000) comprising instructions which, when the program is executed by a processor, cause the processor to carry out any of the methods of claim 23-31.