Solving Doppler ambiguity in TDM-MIMO radar based on spatial phase change rate

Abstract

Disclosed is a method for resolving Doppler ambiguity in a TDM‑MIMO radar based on a spatial phase change rate. Specifically, disclosed is a TDM MIMO FMCW radar comprising a physical receiver array having a first spacing in a first direction and a plurality of physical transmitters arranged at a second spacing in the first direction. A virtual array signal of a range Doppler bin associated with a scene having a moving object is processed by a phase compensation method, which introduces phase ambiguity between subarrays. A positive or negative spatial phase change rate relative to the first direction is calculated based on an element of the compensated virtual array signal corresponding to one subarray at a time. Thus, based on the spacing, a spatial phase change between pairs of subarrays is predicted. Next, a residual phase shift between the pairs of subarrays is determined by comparing an actual phase shift of the compensated virtual array signal with the predicted spatial phase shift.

Description

Technical Field

[0001] The present disclosure relates to signal processing in time-division multiplexing (TDM) multiple-input multiple-output (MIMO) frequency-modulated continuous-wave (FMCW) radar equipment. In particular, it proposes an improved method for resolving velocity-induced phase ambiguity in virtual radar arrays. Background Art

[0002] A radar array can consist of a single physical transmitter and multiple physical receivers. The effective number of elements in a physical radar array is equal to the number of physical receivers. The number of elements determines the resolution of the radar array. For example, the angular resolution in the angle-of-arrival (AoA) calculation increases as the number of elements in the radar array increases. The AoA of a moving object can be calculated by following these steps:

[0003] 1. Recording of intermediate-frequency (IF) signals for multiple chirps (frequency ramps) and multiple radar array elements.

[0004] 2. Perform two discrete harmonic transforms (eg, Fast Fourier Transform, FFT) for each radar array element to obtain a signal consisting of range-Doppler bins.

[0005] 3. Select a range-Doppler bin corresponding to a moving object in the scene.

[0006] 4. Calculate AoA based on the phase shift between radar array elements, for example, as an angle FFT or AoA FFT.

[0007] In order to increase the effective number of radar array elements, MIMO radars have been proposed. A MIMO radar array has multiple physical receivers and M ≥ 2 physical transmitters, and this produces a r A virtual radar array with M elements, where M r is the number of physical receivers. Figure 1A An example setup with two physical transmitters 10 and four physical receivers 20 is shown. Figure 1BThe generated virtual array is shown, in which two subarrays 40 of eight virtual antenna elements 30 can be identified and traced back to the corresponding physical transmitters that generated them. In addition, within each subarray 40, the spatial configuration (e.g., geometry, orientation) of the virtual antenna elements 30 is the same as the spatial configuration of the physical receiver 20, as emphasized by the consistent use of labels A, B, C, and D.

[0008] The physical transmitters in a MIMO radar can be fed synchronously using a multi-carrier signal (e.g., an orthogonal frequency division multiplexing signal). As an alternative, in order to limit the expenditure on the antenna structure and to be able to feed all physical transmitters from a common signal synthesizer, the concept of a TDM MIMO radar has been proposed, in which the physical transmitters are used in a temporally alternating manner. Figure 5 The operation of a frequency modulated continuous wave (FMCW) type TDM MIMO radar with M=2 physical transmitters is illustrated. Here, frequency is plotted against time, where the solid and dashed lines refer to the chirp signals transmitted from the first and second physical transmitters, respectively. Symbol T c represents the length of the linear frequency modulation signal, T r represents the repetition time of the linear frequency modulation signal, and T f =MT r represents the repetition period of the linear frequency modulation signal for the same transmitting antenna. The frequency axis does not necessarily start at the origin. In a typical millimeter wave radar, each linear frequency modulation signal sweeps from 77 GHz to 81 GHz and lasts for T c =40μs.

[0009] In a TDM MIMO radar, since the observed object has time to move a small radial distance between successive transmissions from different physical transmitters, the subarrays of virtual antenna elements will be separated due to relative velocity induced phase shifts. Knowing the radial velocity of the moving object, the velocity induced phase shift (Doppler correction) can be compensated. Such compensation can make the data from the TDM MIMO radar suitable for AoA calculations as shown below:

[0010] 1. Record IF signals for multiple chirps and multiple radar array elements.

[0011] 2. Perform two discrete harmonic transforms for each radar array element to obtain a signal consisting of range-Doppler bins.

[0012] 3. Select a range-Doppler bin corresponding to a moving object in the scene.

[0013] 4. Compensation for relative velocity induced phase shifts between radar array elements (Doppler correction).

[0014] 5. Calculate AoA based on the compensated phase shift.

[0015] Without step 4 (Doppler correction), the phase offset measured by the virtual receiver will have contributions from both relative velocity and AoA. The present disclosure will mainly be concerned with improvements to step 4. These improvements are useful not only when determining AoA, but in principle in any calculation starting from a phase compensated array signal.

[0016] Many limitations of available Doppler correction techniques are related to frequency folding. Theoretically, it can be shown that the Doppler correction can only be achieved if the radial velocity |v| of the object is less than:

[0017]

[0018] The radar data only enables the radial velocity of a moving object to be determined unambiguously when f D，max represents the maximum Doppler frequency, and f c is a representative carrier frequency, such as the center frequency of a radar chirp. If the moving object has a higher inward or outward radial velocity, then, due to frequency folding (or aliasing), the radar will observe a frequency shifted by an integer multiple of 2f D，max The apparent Doppler frequency of a moving object. This is graphically shown in Figure 6 In the upper part of the figure, the upward arrow indicates the ξ The amplitude peaks in the range Doppler spectra of the four moving objects correspond to four different Doppler frequencies f D，ξ =f D +2ξf D，max , where ξ = -1, 0, 1, 2. Although these velocities are different, the frequency folding in the radar will shift all four Doppler frequency peaks to the fundamental period |f| ≤ f D，max In which they will appear in f D In contrast, any amplitude peaks observed due to the use of the radar will occur when the fundamental period |f|≤f D，max , so the true Doppler frequency is ambiguous from the outset. Resolving this phase ambiguity—conceptually removing frequency folding—is crucial to determining the true Doppler frequency, and therefore the velocity of a moving object.

[0019] Frequency folding also limits the practicality of TDM MIMO radars, i.e., because the relative velocity-induced phase shifts between radar array elements can only be explicitly compensated up to the maximum Doppler frequency f D，max In the case of a linear frequency modulation signal with a repetition time T r In a TDM MIMO radar operating with M physical transmitters, the maximum Doppler frequency is given by:

[0020]

[0021] thus:

[0022]

[0023] Will refer to Figure 6 The second half of this section explains how this affects the max An object moving and imaged by a TDM MIMO radar with M = 4 subarrays. The sequence TX1, TX2, TX3, TX4 refers to the transmit schedule when operating the physical transmitter, and m = 1, 2, 3, 4 are the subarray indices. The quantities plotted are the phases after compensation based on the apparent Doppler frequency has been applied.

[0024] like Figure 6 As shown, in the reference case of ξ=0, the fundamental period |f|≤f D,max The apparent Doppler frequency in is consistent with the true Doppler frequency. When ξ = 0, in fact, no frequency folding occurs and the velocity can be detected unambiguously. Figure 6 As can be seen in the lower part of , the compensated phase of the object grows steadily from one virtual array element to the next, as well as at the three boundaries between subarrays. The compensated phase grows steadily because the AoA is nonzero in the plane of the virtual antenna array, which results in path differences; these AoA-induced phase shifts are independent of the radial velocity of the observed object. For faster moving objects (ξ≠0), the steady phase growth is accompanied by additional phase offsets at each boundary (solid vertical lines) between consecutive subarrays:

[0025]

[0026] Summarizing equation (4), from the 1st to the mth th The phase offset of the subarray is given by:

[0027]

[0028] And the phase offset between subarrays with indices m′ and m is equal to:

[0029]

[0030] The phase offset is what remains after compensating for the relative velocity induced phase shift based on the apparent Doppler frequency. The phase offset can be described in terms of the discrete Fourier transform (DFT) of the virtual array signal for one range Doppler bin, denoted as S(f). More precisely, the phase offset is the value of the mth estimated at the true Doppler frequency.th The phase rotation associated with this DFT of the subarray and the same DFT estimated at the apparent Doppler frequency is:

[0031]

[0032] where |f D |≤f D,max As in step 4 of the second AoA algorithm, compensation for the relative velocity-induced phase shift will effectively subtract the velocity-induced phase shift that separates the different subarrays. After phase compensation, the phase offset between the subarrays still remains in the virtual array signal, which makes it unusable for AoA calculations. Except for the special case where the true Doppler frequency is known, the phase offset cannot be calculated a priori (6). Instead, the phase ambiguity must be resolved by approximate methods or by using supplementary data about the moving object.

[0033] The fact that a phase offset remains in the signal after the relative velocity induced phase shift has been compensated can alternatively be understood as being a result of the velocity uncertainty of the moving object.

[0034] To resolve phase ambiguity, one option is to include spatially overlapping virtual antenna elements in the virtual array. This can be achieved by coordinating the spacing of the physical transmitters with the geometry of the physical receivers. Figure 1A In the example of FIG. 1 , if the separation distance L2 of the physical transmitters 10 ( TX1 ) and 10 ( TX2 ) is reduced to only 3d units, then Figure 1B , the virtual antenna element D in the first subarray 40 (TX1) will coincide with the virtual antenna element A in the second subarray 40 (TX2). By forcing the overlapping virtual antenna elements to have equal phases, the correct phase offset between the two subarrays 40 (TX1), 40 (TX2) can be inferred. However, from a hardware perspective, this approach can be very heavy, because the second virtual antenna element in the overlapping pair will not be supplied with any data other than the first virtual antenna element, and therefore will not contribute to obtaining a better resolution.

[0035] The research paper “Doppler Unambiguity Enhancement for Chirp Sequence Modulated TDM-MIMO Radar” by F. Roos, J. Bechter, N. Appenrodt, J. Dickmann, and C. Waldschmidt (2018 IEEE MTT-S International Conference on Intelligent Mobile Microwaves (ICMIM), 2018, pp. 1-4, doi: 10.1109 / ICMIM.2018.8443352) reports measurements and simulations in which data from a virtual array with M = 2 subarrays were successfully fitted to the phase offset equation (5) for |ξ| = 1. Roos et al. wish to use this direct approach to estimate ξ based on data from a virtual array with more subarrays when reliable phase data are available.

[0036] Patent application US20210293949A1 describes a method in which data from a full virtual array is initially used to estimate multiple tentative AoA values, after different, alternative phase compensations have been applied according to respective speed folding hypotheses. In many automotive applications, such as those considered in US20210293949A1, the total number of speed folding hypotheses (i.e., the values ​​of the ξ parameter to be tried) is manageable because a very large number of hypotheses can be ruled out in advance, taking into account prescribed speed limits, etc. In addition, a reference AoA value is estimated using only data from a single sub-array in the virtual array. Based on a smaller data set, the reference AoA value will be less accurate, but it will certainly not be affected by frequency folding artifacts. From the tentative AoA values, the value that best matches the reference AoA will be selected, and this is the output of the method.

[0037] Patent US10627483B2 is based on the realization that the error introduced in the phase of the virtual array signal after phase compensation produces unique features in the angle FFT spectrum. For example, the angle FFT spectrum may include two peaks caused by an object, which are separated by a characteristic angle (e.g., 3π / 8 radians). These features are detected and used to correct for the case where |v| has exceeded the maximum unambiguously detectable velocity v max Furthermore, US10627483B2 describes a phase compensation method (or Doppler correction method) for removing relative velocity induced phase shifts between radar array elements. Summary of the invention

[0038] It is an object of the present disclosure to provide a computationally efficient method for resolving phase ambiguity between subarrays in a virtual array of a TDM MIMO FMCW radar. Another object is to provide such a method with configurable accuracy so that the implementer can choose to balance accuracy with computational effort as needed. Another object is to provide such a method applicable to radars with two or more physical transmitters. Another object is to provide a method for estimating one-dimensional or two-dimensional angle of arrival based on data from a virtual radar array. Still another object is to provide a signal processing device and a computer program for resolving phase ambiguity.

[0039] At least some of these objects are achieved by the invention as defined by the independent claims. The dependent claims relate to preferred embodiments of the invention.

[0040] In a first aspect, a method for resolving phase ambiguity between subarrays in a virtual array of a TDM MIMO FMCW radar is provided, the TDM MIMO FMCW radar comprising a physical receiver array and a plurality of physical transmitters. The physical receiver array comprises: at least one row of physical receivers having a first spacing L1 in a first direction; and physical transmitters arranged at a second spacing L2 in the same first direction. Each of the subarrays in the virtual array is generated (or synthesized) by a combination of an array of physical receivers and one of the physical transmitters. The method begins by obtaining a virtual array signal of a range Doppler bin associated with a scene having a moving object. The range Doppler bin can be described as an element in the range Doppler spectrum corresponding to a combination of a range interval and a speed interval. The virtual array signal comprises a value of the range Doppler bin for each virtual antenna element of the virtual array. Next, any appropriate phase compensation method is used to compensate for the velocity-induced phase shift of the virtual array signal, and the compensated virtual array signal is obtained as an output. If the speed of the moving object exceeds a threshold, the phase compensation method introduces phase ambiguity between the subarrays. The threshold is a physical constant, not a user-configured value; it can be equal to the maximum unambiguously detectable velocity v estimated for a single subarray. max(see above) or proportional thereto. Next, a spatial phase change rate relative to the first direction (which may be a positive or negative phase growth rate in radians per meter) is calculated based on the elements of the compensated virtual array signal corresponding to one subarray at a time. A spatial phase shift between the subarray pairs is predicted based on the spatial phase change rate relative to the first direction and the second spacing L2. A residual phase shift between the subarray pairs is then determined by comparing the actual phase shift of the compensated virtual array signal with the predicted spatial phase shift. The residual phase shift may include the phase offset between the subarrays discussed above. Finally, the inverse of the residual phase shift is applied to the compensated virtual array signal.

[0041] The proposed method for resolving phase ambiguity between subarrays is effective because the spatial phase change rate can be directly calculated and used to predict the spatial phase shift between subarray pairs. The output data obtained by successfully executing the method is a virtual array signal with no velocity-induced phase shift and no folding-induced residual phase shift. Therefore, the output data is suitable for calculation as if the virtual array signal is collected by a physical array with an equal number of antenna elements.

[0042] In some embodiments, determining the residual phase shift between the pair of subarrays comprises: calculating the difference between the actual phase shift and the spatial phase shift. Optionally, it further comprises: rounding the difference between the actual phase shift and the spatial phase shift to a multiple of 2π / M, where M is the number of physical transmitters having a separation distance in the first direction.

[0043] In some embodiments, determining the residual phase shift between the subarray pairs includes: calculating the actual phase shift as the phase difference between two elements of the compensated virtual array signal corresponding to two homologous virtual antenna elements (e.g., virtual array element A in each subarray in the subarray). In this case, the spatial phase shift corresponds to the phase change between the transmitters, i.e., the distance L2. In other embodiments, determining the residual phase shift between the subarray pairs includes: calculating the actual phase shift as the phase difference between two elements of the compensated virtual array signal corresponding to two non-homologous virtual antenna elements. These two elements do not correspond to virtual antenna elements separated by an integer multiple of the transmitter spacing (distance L2) like homologous virtual antenna elements. In order to make the actual phase difference comparable to the spatial phase shift between the subarray pairs, the actual phase difference is adjusted according to the spatial phase change rate. In this case, the phase difference may need to be increased or decreased by one or more times the receiver spacing (distance L1) multiplied by the spatial phase change rate. An equivalent alternative is to directly compute the spatial phase shift for two non-homologous virtual antenna elements (e.g., by multiplying the spatial phase change rate by the distance of the elements) so that it is directly comparable to the actual phase shift between the non-homologous virtual antenna elements, and use it in the same way as the spatial phase shift between pairs of subarrays.

[0044] In some embodiments, the physical transmitters are used sequentially according to a transmission schedule, and the subarray pairs are consecutive with respect to the transmission schedule (e.g., TX1-TX2 or TX2-TX3). In other embodiments, the subarray pairs are randomly ordered with respect to the transmission schedule (e.g., TX1-TX4).

[0045] In some embodiments, the virtual array has equidistant virtual antenna elements in the first direction. In particular, the ratio of the first spacing L1 to the second spacing L2 may be such that the virtual array has equidistant virtual antenna elements in the first direction. For example, if L2 / L1 is equal to the number of physical receivers M r , then this is the case. Equidistant spacing tends to simplify later computations of the output data where the method is used, especially for AoA estimation.

[0046] In some embodiments, where the array of physical receivers has at least two rows in the first direction, whereby each subarray has at least two rows in the first direction, the residual phase shift is determined as an average of the plurality of rows. This is an example of how an implementer can improve the accuracy of the method by using more input data. Alternatively or additionally, a similar improvement in accuracy may be obtained by calculating the spatial phase change rate as an average of a plurality of subarrays. Still further, alternatively or additionally, the actual phase shift may be compared to the spatial phase shift for at least one additional pair of subarrays (e.g., a pair with equal spatial phase shifts), where the residual phase shift is determined as an average of all of said pairs of subarrays.

[0047] Some embodiments target the following situation, wherein the physical receiver array includes at least one column of physical receivers with a third spacing L3 in the second direction, and wherein the physical transmitters are arranged with a fourth spacing L4 in the second direction. It should be noted that the terms "row" and "column" do not refer to absolute directions, but are purely theoretical naming conventions. Rows and columns do not have to be oriented orthogonally. In these embodiments, the method further includes: calculating a (positive or negative) spatial phase change rate relative to the second direction based on the elements of the compensated virtual array signal corresponding to one subarray at a time; calculating a second spatial phase shift between the second subarray pair based on the spatial phase change rate relative to the second direction and the fourth spacing L4; determining a second residual phase shift between the second subarray pair by comparing the actual phase shift of the compensated virtual array signal with the second spatial phase shift; and applying the inverse of the second residual phase shift to the compensated virtual array signal. In these embodiments, the residual phase shift induced by the Doppler effect relative to the second spatial coordinate is determined and eliminated. The output data of the overall method will be suitable for two-dimensional AoA calculations, for example, the calculations designed to return both the azimuth component and the elevation component of the AoA.

[0048] It is foreseen that in some embodiments, the residual phase shift for all remaining sub-arrays of the virtual array is determined and its inverse is applied. Accordingly, the resulting virtual array signal will not be affected by the velocity-induced phase shift and the folding-induced residual phase shift.

[0049] In another embodiment, a method for calculating the arrival angle of a mobile object based on a virtual array signal of a range Doppler bin captured by a virtual array of a TDM MIMO FMCW radar is provided. The method includes: processing the virtual array signal using the method described above, and calculating the arrival angle based on the processed virtual array signal.

[0050] In a second aspect of the present invention, a signal processing device for a TDM MIMO FMCW radar with a virtual array is provided, wherein the TDM MMIMO FMCW radar comprises a physical receiver array including at least one row of physical receivers with a first spacing in a first direction, and further comprises a plurality of physical transmitters arranged with a second spacing in the first direction, wherein the virtual array comprises subarrays, each subarray being generated by a combination of one of the physical transmitters and the physical receiver array. The signal processing device comprises a processing circuit, the processing circuit being configured to resolve phase ambiguity between subarrays of the virtual array in a virtual array signal including at least one range Doppler bin by executing the above method.

[0051] The signal processing device according to the second aspect generally shares the advantages of the first aspect, and it can be implemented with the same degree of technical variations.

[0052] The invention further relates to a computer program comprising instructions for causing a computer or in particular a signal processing device to perform the above method. The computer program may be stored or distributed on a data carrier. As used herein, a "data carrier" may be a temporary data carrier (e.g., a modulated electromagnetic wave or light wave) or a non-temporary data carrier. Non-temporary data carriers include volatile and non-volatile memories, such as permanent and non-permanent storage media of the magnetic, optical or solid-state type. Still within the scope of a "data carrier", such a memory may be fixedly mounted or portable.

[0053] Generally, all terms used in the claims should be interpreted according to their ordinary meaning in the technical field, unless otherwise explicitly defined herein. Unless otherwise explicitly stated, all references to "an / an / the element, device, component, means, step, etc." should be publicly interpreted as referring to at least one instance of the element, device, component, means, step, etc. Unless explicitly stated otherwise, the steps of any method disclosed herein do not have to be performed in the exact order described. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Various aspects and embodiments will now be described by way of example with reference to the accompanying drawings, in which:

[0055] Figure 1A and Figure 1B A one-dimensional array of physical transmitters and physical receivers and a one-dimensional virtual array generated therefrom are shown;

[0056] Figure 2A and Figure 2B A two-dimensional array of physical transmitters, a one-dimensional array of physical receivers, and a two-dimensional virtual array generated therefrom are shown;

[0057] Figure 3A and Figure 3B A two-dimensional array of physical transmitters, a one-dimensional array of physical receivers, and a two-dimensional virtual array generated therefrom are shown;

[0058] Figure 4A and Figure 4B A two-dimensional array of physical transmitters and physical receivers and a two-dimensional virtual array generated therefrom are shown;

[0059] Figure 5 is a graph of frequency versus time for two physical transmitters in TDM operation;

[0060] Figure 6 illustrates the frequency folding of the Doppler frequency of a moving object (upper half) observed by the radar and how the observed phase of the moving object varies between the virtual array elements of the radar; and

[0061] Figure 7 is a flow chart of a method for resolving phase ambiguity in a TDM MIMO FMCW radar according to embodiments herein. DETAILED DESCRIPTION

[0062] Various aspects of the present disclosure will now be described more fully hereinafter with reference to the accompanying drawings, on which specific embodiments of the present invention are shown. However, these aspects may be embodied in many different forms and should not be construed as limiting; rather, these embodiments are provided by way of example so that the present disclosure will be thorough and complete and fully convey the scope of all aspects of the present invention to those skilled in the art. Throughout the description, the same reference numerals refer to the same elements.

[0063] Figure 1AA one-dimensional array of physical transmitters 10 configured to transmit radio frequency (RF) beams 11 toward a scene and a one-dimensional array of physical receivers 20 configured to receive RF beams 21 reflected by objects (not shown) in the scene are shown. It should be understood that in addition to the physical transmitters 10 and the physical receivers 20, a complete radar equipment may also include, listed from the antenna end onwards: functional level mixing, analog-to-digital conversion, RF front-end processing (based on IF signals), and digital beamforming. The physical transmitters 10 are used according to a configured transmission schedule (here corresponding to a repeating sequence TX1, TX2) (the present disclosure considers a transmission schedule as an arrangement of physical transmitters; this excludes, for example, a transmission schedule TX1, TX1, TX2, TX2).

[0064] Relative to the main direction of transmission and reception (main lobe), corresponding to the vertical direction on the figure, the reflecting object is observed at an angle θ. The angle θ corresponds to the AoA of the object. For the avoidance of doubt, the physical transmitter 10 is typically configured to transmit in all directions within a non-zero angular range, which includes, but is not limited to, the direction at angle θ. Figure 1A As indicated in , further, with respect to a certain constant d, the physical transmitters 10 are spaced apart by L2 = 4d units, and the physical receivers 20 are equidistant by a spacing of L1 = d units.

[0065] With reference to the attached patent claims, it should be noted that Figure 1A The physical transmitter 10 and the physical receiver 20 in the embodiment satisfy the conditions in a common first direction ( Figure 1A There is a requirement for non-zero spacing in the horizontal direction. Figure 1A The rows of physical transmitters 10 and the rows of physical receivers 20 in the embodiment of the present invention may even be arranged to be oriented parallel to each other, but this is not essential for the applicability of the method 700. In fact, this requirement is met as long as the physical transmitters 10 and the physical receivers 20 each have a spacing with a non-zero component in a common first direction, which is for example still the case if the rows of physical receivers 20 are tilted upwards relative to the rows of physical transmitters 10.

[0066] Figure 1B 1 shows a one-dimensional virtual array of virtual array elements 30, which is generated when the array of physical transmitters 10 operates together with the array of physical receivers 20. The virtual array is generated in the sense that, in a linear frequency modulation signal repetition period T fDuring this time, measurement data is read from each physical receiver 20 once for each active physical transmitter 10. (Recall that data from multiple chirp repetition periods is typically required for any velocity calculation, e.g., to provide a Doppler FFT. In other words, data is collected from multiple chirp signals for each virtual array element.) The measurement data thus collected, i.e., the virtual array signals, can be organized into a matrix X having dimensions equal to the dimensions of the virtual array. Figure 1B In the illustrated 1×8 case, the matrix may look like:

[0067] X=[x TX1，A x TXi，B x TX1，C x TX1，D x TX2，A x TX2，B x TX2，C x TX2，D ], (8)

[0068] where x TX1，A represents the measurement data read from the physical receiver 20 labeled A when stimulated by the first physical transmitter 10 (TX1), x TX2，A represents the measurement data read from the same physical receiver 20 when stimulated by the second physical transmitter 10 (TX2), and so on. It can be considered that Figure 1B The virtual array in X is divided into two sub-arrays 40, each of which has a one-to-one relationship with a physical transmitter 10 providing the excitation. Each measurement data entry in X can be, for example, a digital representation of an intermediate frequency (IF) signal obtained by mixing the signal fed to the physical transmitter 10 with the signal received from the physical receiver 20. The digital representation can be, for example, a row matrix of time samples. In addition, each entry in X can be a data structure for collecting measurement data from a plurality of radar chirp signals; for example, the measurement data entry can be represented as a matrix where the chirp signals correspond to rows.

[0069] Except for frequency folding, discussed below, the virtual array signal X is generally indistinguishable from the physical array signal collected by a 1×8 array of physical receivers excited by a single physical transmitter.

[0070] Within each subarray 40, the geometry and orientation of the array of physical receivers 20 are preserved, including their spacing L1. This is visualized by using the same labels A, B, C, D for the physical receivers 20 and virtual antenna elements 30 of each subarray 40. Two virtual antenna elements 30 in different subarrays 40 generated by the same physical receiver 20 will be referred to as homologous in this disclosure. In the figures, two homologous virtual antenna elements 30 share the same label, such as A. The spacing of the subarrays 40 is equal to the spacing of the physical transmitters 10, i.e., L2 units in the first direction.

[0071] Will refer to Figure 2A and Figure 2B , Figure 3A and Figure 3B ,as well as Figure 4A and Figure 4B The effects of using a two-dimensional array of physical transmitters 10 or a two-dimensional array of physical receivers 20, or both, are briefly discussed with reference to the examples in . It is apparent from these examples that the virtual array generated by the array of physical transmitters 10 and the array of physical receivers 20 corresponds to the convolution of these two arrays. For a general introduction to the structure and operation of MIMO radars, please refer to "MIMO Radar" by S. Rao (Application Report SWRA554A, Texas Instruments, Dallas, TX, July 2018).

[0072] exist Figure 2A In FIG. 1 , the array of physical transmitters 10 has two rows and two columns. The column spacing is L2=4d units (first direction, horizontal in the figure), and the row spacing is L4 units (second direction, vertical in the figure). The array of physical receivers 20 has dimensions of 1×4 and has a spacing of L1=d units. Although Figure 2A The physical transmitters 10 in the embodiment are arranged in two orthogonal directions, but such orthogonality is by no means essential for the applicability of the invention. Instead, if applicable, a spacing with a non-zero component in the first or second direction is sufficient.

[0073] exist Figure 2BThe obtained virtual array with four subarrays 40 is shown in , where exemplary inter-element spacing is indicated. The spacing of consecutive virtual antenna elements within a subarray 40 in the first direction is equal to the spacing of the physical receiver 20, i.e., L1 units. The spacing between homologous virtual antenna elements 30 belonging to a subarray pair in the first direction is L2 units (in the TX1-TX2 pair and the TX3-TX4 pair) or zero (in the TX1-TX3 pair and the TX2-TX4 pair). For any pair of homologous virtual antenna elements 30, the spacing relative to the second direction is no greater than L2 units. The spacing between homologous virtual antenna elements 30 belonging to a subarray pair in the second direction is zero (in the TX1-TX2 pair and the TX3-TX4 pair) or L4 units (in the TX1-TX3 pair and the TX2-TX4 pair). The spacing between any pair of non-homologous virtual antenna elements in the first or second direction can be calculated as a linear combination of these basic distances. For example, the distance between the second virtual antenna element B in the third subarray 40 (TX3) and the third virtual antenna element C in the fourth subarray 40 (TX4) is L1+L2 units. Similarly, the distance between the third virtual antenna element C in the third subarray 40 (TX3) and the first virtual antenna element A in the fourth subarray 40 (TX4) is L2-2L1 units.

[0074] use Figure 2B The collected virtual array signals in can be expressed as a matrix with the following overall appearance:

[0075]

[0076] Alternatively, the matrix elements may be arranged in a single row. In this way, data from different chirp signals may correspond to different rows of the matrix.

[0077] exist Figure 3A In the example, the physical transmitter 10 is connected to Figure 2A The physical receivers 20 are arranged with different column spacings, namely 2d units in the first direction, and the rows of the physical receivers 20 are sequentially spaced by d, 3d and d units. Figure 3B As shown in , the obtained virtual array will have Figure 2B The virtual arrays in FIG. 4 have the same 2×8 dimensions, but have different subarray structures. The first subarray 40 (TX1) includes the first, second, fifth and sixth virtual antenna elements 30 on the first row of the virtual array; and the second subarray includes the third, fourth, seventh and eighth virtual antenna elements on the first row. The virtual antenna elements 30 on each row are equidistant, with a spacing d.

[0078] at last, Figure 4AThe case where both the physical transmitter 10 and the physical receiver 20 are arranged in a two-dimensional pattern is shown. More precisely, the physical transmitter 10 and the physical receiver 20 are arranged with non-zero spacing in a first direction (horizontally) and a second direction (vertically). The virtual array obtained is Figure 4B Here, in order to avoid unnecessary repetition, only the virtual array elements 30 in the first subarray 40 (TX1) are labeled with letters A, B, C, ..., H according to the physical receiver 20. It can be understood that this structure and the homology relationship therefrom are also repeated in the other seven subarrays 40 in the same manner. Figure 4A The spacings L1, L2, L3, L4 in the first direction can be any specified value. In order to make the virtual antenna elements 30 equidistant in the first direction, one can set L2 / L1=4. Similarly, if L4 / L3=2, equidistant spacing in the second direction will be obtained.

[0079] Now refer to Figure 7 700 for resolving phase ambiguity between sub-arrays 40 in a virtual array of a TDM MIMO FMCW radar is described by the flowchart in FIG. The method 700 processes the virtual array signal of the range Doppler bin into a compensated virtual array signal, in which the residual phase shift has been reduced or eliminated, while relying on the geometric characteristics of the virtual array, including the corresponding spacings L1, L2 of the physical transmitter 10 and the physical receiver 20 in the first direction. In this way, the method 700 can be executed on a general processor with general data input and data output capabilities.

[0080] Alternatively, a signal processing device having a processing circuit configured to perform method 700 by programming or hard coding may be used. The processing circuit may be, for example, an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), or a system on a chip. Recalling that the radar signal processing chain may include the following series of functional stages, starting from the antenna end: mixing, analog-to-digital conversion, RF front-end processing (based on IF signals), and digital beamforming. Different processing chains may integrate these stages to varying degrees. As such, the signal processing device performing method 700 may be suitable for deployment as a general-purpose radar baseband processor, a combined front-end and beamforming device, or a dedicated digital beamforming device.

[0081] In the first step of method 700 Step 702In, a virtual array signal of a range Doppler bin associated with a scene with a moving object is obtained. For example, the range Doppler bin may be a bin corresponding to a radar reflection of a moving object, i.e., a distance interval containing the distance of the object and a speed interval containing the speed of the object. The virtual array signal of the range Doppler bin may be obtained from a plurality of IF signals corresponding to a plurality of linear frequency modulation signals and corresponding to each virtual array element of the virtual array. In the present disclosure, the term "virtual array signal" is used to refer to a signal having a value for each virtual array element of the virtual array. In Figure 1A In the example of a virtual array depicted in FIG, the IF signal of the leftmost virtual array element (i.e., the data collected by the first physical receiver 20 (labeled A) when excited by the first physical transmitter 10 (TX1)) and the six linear frequency modulation signals c0, c1, ..., c5 may have the following schematic structure:

[0082]

[0083] where t0, t1, ..., t7 are intervals [0, T c ] (in a practical implementation, this discretization can be finer and the calculation can be based on data from a large number of linear frequency-modulated signals). TX1,A Each row of corresponds to one of the linear frequency modulation signals, and each entry can be understood as a time sample of that linear frequency modulation signal. The range information can be obtained by applying a discrete harmonic transform (such as DFT or FFT) to each row in the IF signal. If an FFT is used, the following range spectrum ("range FFT") is generated:

[0084]

[0085] The row dimension of this matrix now corresponds to the range, where r0, r1, …, r7 can be interpreted as range bins, which are intervals in the radial distance of the reflecting object. The column dimension still corresponds to the six chirps, and all the information in the matrix is ​​obtained from Figure 1B The y is derived from the measurement data read from the leftmost virtual array element. TX1,A Applying a further FFT to each column of , we can obtain the range-Doppler spectrum (or "Doppler FFT"):

[0086]

[0087] Matrix z TX1,A Each entry in (usually plural) can be understood as an element in the discrete representation of the range Doppler spectrum. i ,r j The superscript should be understood to refer to the i thVelocity (or Doppler) bin and the jth th The distance bin, or simply the (i,j)th th Range Doppler bin. It is important to note that velocity is a signed quantity in the sense that the range Doppler spectrum allows motion radially toward the radar to be distinguished from motion radially away from the radar.

[0088] The virtual array signal of one range-Doppler bin obtained in step 702 of method 700 can be expressed as the following vector:

[0089]

[0090] where each element is the range Doppler bin for a virtual antenna element 30 of the virtual array, i.e., the matrix entry from equation (12). The phase shift between elements is given as the sum of the velocity induced phase shift, the AoA induced phase shift, and the phase offset at the boundaries between subarrays. As a result of the path difference between the virtual array elements, an AoA induced phase shift can be observed when the AoA is non-zero in the plane of the virtual antenna array. When preparing the AoA estimate, the velocity induced phase shift and the phase offset should be removed first. It is worth noting that once the virtual array signal Z (i,i) If available, step 702 is completed; the above-mentioned signal processing is not an essential part of method 700.

[0091] In the next Step 704 In the embodiment, a phase compensation method is performed on the virtual array signal, thereby obtaining a compensated virtual array signal:

[0092]

[0093] The phase compensation method used in step 704 may be any phase compensation method known per se from the literature. For example, the phase compensation method described in the patent publication US10627483B2 cited above may be applied. The Doppler phase used in this method The representative speed v (eg, center speed) of the speed bin corresponding to the considered moving object, the linear frequency modulation signal repetition time T r and the carrier frequency f. Available phase compensation methods usually require the relative timing of the subarray readouts for further input data, which can be determined according to the transmit schedule. This relative timing usually differs by Figure 5 The repetition time T shown in r The compensated virtual array signal The phase of an element of is given as the sum of the AoA induced phase shift and the phase offset at the subarray boundaries.

[0094] It is known that phase compensation methods, including the phase compensation described in US Pat. No. 10,627,483 B2, suppress or remove the velocity-induced phase shift of the virtual array signal, and if the velocity of the moving object exceeds a threshold value v max , also introducing phase ambiguity. The threshold may correspond to the maximum velocity that can be unambiguously detected using a single subarray; see equation (3), where M=1. For the remainder of the description of method 700, it will be assumed that a moving object has a velocity exceeding the threshold v max The radial velocity causes the phase blur to be offset by the phase at the subarray boundary. The virtual array signal is included in the form of In order to perform the method 700, it is neither necessary to determine the velocity of the moving object nor to compare it with the threshold value v max A comparison is made; whether there is a residual phase shift can be inferred based on the output of step 710.

[0095] In the third step of method 700 Step 706 , the spatial phase rate of change relative to the first direction is calculated. As used in the present disclosure, the spatial phase rate of change R1 (or phase growth rate) refers to a signed quantity in radians per meter or equivalent units. The spatial phase rate of change relative to the first direction can be understood as the (positive or negative) change in phase experienced when moving between two virtual array elements separated by a unit distance in the first direction and belonging to the same subarray, i.e., without any intermediate phase offset due to frequency folding. The spatial phase rate of change can be calculated based on the compensated virtual array signal The calculation is limited to the elements of one subarray at a time. Limiting to one subarray at a time eliminates the unwanted effects of phase offsets.

[0096] The following equation provides a simple estimate of the spatial phase change rate R1 for some subarray m, based on data from two virtual array elements:

[0097]

[0098] Here, e1 is a unit vector in the first direction, and u TXm,A ,u TXm,B is the position vector of the virtual array element, so that the denominator represents the projection of the geometric distance of the virtual array element in the first direction. In this example, the projection is equal to d units. Alternatively, the spatial rate of change R1 can be estimated as:

[0099]

[0100] A more accurate estimate of the rate of change of spatial phase can be obtained by taking an average value over a subarray. Figure 1B In the case of the first subarray 40 (TX1) in , this estimate can be calculated as follows:

[0101] These three denominators are equal to d. It is worth noting that the estimate of the spatial phase change rate does not need to be based on an adjacent pair of virtual antenna elements. It is also not necessary to subtract the phase data and position data from the virtual antenna elements in any particular order; the fact that the numerator and denominator change signs at the same time can solve this problem. In an alternative embodiment, the average value of a subarray is calculated as:

[0102]

[0103] To further improve the accuracy of the spatial phase rate of change estimate, averaging over multiple subarrays may also be applied if this is warranted in an implementation of method 700:

[0104]

[0105] Among them Figure 1B In the example of M=2. Alternatively, in an alternative embodiment, the average value of the plurality of sub-arrays is calculated as:

[0106]

[0107] Another option is to use a software routine from a statistical library to estimate the spatial phase change rate, for example, by feeding the routine input data pairs (x,y) in digital form, e.g.,

[0108]

[0109] And start the regression of y on x.

[0110] In the fourth of method 700 Step 708 In step 706, the spatial phase shift between the subarray pairs is predicted based on the spatial phase change rate estimated in step 706 and the spacing L2 of the subarrays in the first direction. If the subarray pair is adjacent with respect to the first direction, the spatial phase shift can be predicted as the product If there are p intervening subarrays between the subarray pair, the predicted spatial phase shift is

[0111] Next, in step Step 710 By comparing (710.1) the spatial phase shift predicted in step 708 with the compensated virtual array signal The comparison (710.1) is adapted to reveal whether the actual phase shift includes a non-zero phase offset at a boundary (or boundaries) between subarrays.

[0112] Specifically, the residual phase shift between the subarray pairs may be determined (710) by calculating the difference between the actual phase shift and the spatial phase shift. Figure 1B , if the comparison is based on the first and fifth virtual array elements being homologous, then:

[0113] - Actual phase shift:

[0114] -Predicted spatial phase shift: and obtain the residual phase shift as the difference

[0115]

[0116] Expression (16) can be interpreted as the estimate of the phase offset is Where (m′, m=(1, 2) is the index of the subarray pair). Alternatively, if the comparison is based on the non-homologous first and sixth virtual array elements, then:

[0117] - Actual phase shift:

[0118] -Predicted spatial phase shift: As can be seen above, since the first and sixth virtual array elements are separated by L1+L2 units in the first direction, the adjustment term is applied to the predicted spatial phase shift. Equivalently, an equal adjustment term with opposite sign can be applied to the actual phase shift, thus:

[0119] - Actual phase shift:

[0120] -Predicted spatial phase shift: Either way, the adjustment Both provide an adjustment of the phase difference of two elements of the compensated virtual array signal corresponding to two non-cognate virtual antenna elements according to the spatial phase change rate.

[0121] Optionally, to determine (710) the residual phase shift between the pair of subarrays, the difference between the actual phase shift and the spatial phase shift is rounded to a multiple of 2π / M, where M is again the number of physical transmitters 10 having a separation distance in the first direction, according to the theoretical result in equation (4). Alternatively, the more general equation (6) may be used. Preferably, the rounding to a multiple of 2π / M is applied in embodiments where the virtual array has equidistant virtual antenna elements in the first direction. In the above reference Figures 1A to 4B In the example discussed, this value is M = 2. In a 2×3 array of physical transmitters 10, it is possible to have M = 3. Figure 1B In the example of the first and fifth virtual array elements in , after such rounding, the difference is equal to 2π(mm′)ξ * / M, and

[0122]

[0123] Wherein further, M=2 and mm′=1. It is believed that those skilled in the art who have studied the above derivation and annotations will be able to modify the expression (18) in view of equation (6) so that the expression also holds when data from non-homologous virtual array elements are used and / or when the virtual array elements are from non-adjacent subarrays. It is worth noting that the subarray pairs do not need to be contiguous with respect to the transmit schedule for the purposes of these calculations, and if they are non-contiguous, no special modification is required.

[0124] Similar to step 706, the accuracy of the residual phase shift calculated in step 710 may optionally be improved by taking into account additional data. One option is to use data from other sub-array pairs that have equal spatial phase shifts and form an average over all such sub-array pairs. Figure 2B In the example of , for a virtual array element pair having the distance calculated above in the first direction, the comparison may result in the following expression for the residual phase shift:

[0125]

[0126] Again, the difference in parameters, e.g. It can be estimated as an independent variable of the product, for example In theory, the numerator of each term is equal to the phase offset, and averaging over several subarray pairs will tend to cancel random errors, such as measurement noise. Data from other virtual array element pairs, including pairs belonging to the same subarray pair, can be added as needed. In an embodiment where the corresponding pair of virtual array elements is compared for each subarray pair, the residual phase shift can alternatively be calculated according to the following principle:

[0127]

[0128] In this example, the pair of virtual array elements A and D are compared, but it will be appreciated that the principle generalizes to other pairs of virtual array elements (e.g., homologous array elements). In addition, it is optional to round the difference to a multiple of 2π / M, where M=2, because Figure 2A At most two of the physical transmitters 10 in the first direction have a non-zero spacing. Generally, the two physical transmitters are equidistant.

[0129] Another option for improving the accuracy of residual phase shift calculation is possible when the array of physical receivers 20 has two or more rows in the first direction. In the illustrative example, the two or more rows oriented in the first direction are parallel to each other and they have a mutual spacing in the second direction. This condition is Figure 4A The situation shown in is satisfied, where the physical receivers 20 are arranged in a 2×4 configuration. Accordingly, Figure 4B Each of the subarrays 40 in the virtual array in has two rows in the (horizontal) first direction, one row being ABCD and the other row being EFGH. The two rows are separated by L3 units in the (vertical) second direction. According to this optional embodiment of step 710, in one of the various ways discussed above, for row ABCD, a first difference between the actual phase shift and the spatial phase shift, or an average value within the row, is formed. For row EFGH, a second difference between the actual phase shift and the spatial phase shift, or an average value within the row, is formed. To form the second difference, the predicted instances of the spatial phase shift can be reused. The residual phase shift is determined as the average value of the first difference and the second difference. Recall that the independent variable terms in this expression can be collected and estimated along the lines of formula (17).

[0130] After determining the residual phase shift, the next step is to apply its inverse to the compensated virtual array signal Step 712. Figure 1B In the example, this means that the virtual array signal is replaced by

[0131]

[0132] where ψ1 represents the residual phase shift relative to the first direction. is applied to the elements of the virtual array signal corresponding to the second subarray 40 (TX2), i.e. the four elements on the right. Signal (19) is a virtual array signal with no velocity induced phase shift and no folding induced residual phase shift. As such, it is suitable for use in calculations such as AoA estimation as if it were collected by a physical array with an equal number (here eight) of antenna elements.

[0133] In a further development of the method 700, it comprises a step for finding the inverse of the second residual phase shift ψ2 relative to the second direction and applying it. Figure 4A and 4B It is relevant in the case shown in , where the array of physical receivers 20 comprises at least one column of physical receivers. It is assumed that the physical receivers 20 have a third spacing L3 in the second direction and the physical transmitters have a fourth spacing L4 in the second direction.

[0134] In these further developments, the (positive or negative) spatial phase change rate relative to the second direction is estimated (step 714) based on the elements of the compensated virtual array signal corresponding to one subarray at a time. This can be performed along the lines of step 706. More precisely, similar to equation (15), the estimation can be performed as follows:

[0135]

[0136] Where e2 is a unit vector in the second direction. Based on the estimation of the spatial phase change rate relative to the second direction and the fourth spacing L4 Calculate (step 716) the second spatial phase shift between the second sub-array pair, e.g. This can be performed along the lines of step 708. That is, this allows the virtual array signal after compensation to be compared with the The actual phase shift of the second sub-array and the predicted second spatial phase shift are used to determine (step 718) a second residual phase shift ψ2 between the second sub-array pair. This can be performed along the lines of step 710. The inverse of the second residual phase shift can then be applied (step 720) to the compensated virtual array signal. This can be performed along the lines of step 712.

[0137] The application of the inverse of both the first and second residual phase shifts is referenced to the compensated virtual array signal For illustration, the virtual array signal is an 8×8 matrix with a 4×2 block matrix structure, each block having a dimension of 2×4. As in steps 712 and 720, the inverse of the first and second residual phase shifts corresponds to the element-by-element multiplication of the following matrices:

[0138]

[0139] in:

[0140]

[0141] In forming expression (21), the additivity property of the residual phase shift and the equidistance of the physical transmitter 10 with respect to the second direction are used. The equidistance means that the residual phase shift is constant for all consecutive subarrays in the second direction, i.e., equal to ψ2. The additivity property can be realized according to equation (6), where

[0142]

[0143] Accordingly, it is not necessary to determine the residual phase shift for all pairs of subarrays, but rather an additive chain can be formed. For example, between subarrays 40(TX1) and 40(TX6) which are related by two downward shifts and one rightward shift, there will be a total residual phase shift of ψ1+2ψ2.

[0144] Aspects of the present disclosure have been described above mainly with reference to some embodiments. However, as readily understood by a person skilled in the art, other embodiments than the above disclosed embodiments are equally feasible within the scope of the present invention, as defined by the attached patent claims.

Claims

1. A method (700) for resolving phase ambiguity between sub-arrays (40) in a virtual array of a time division multiplexing (TDM) multiple input multiple output (MIMO) frequency modulated continuous wave (FMCW) radar, in, The TDM MIMO FMCW radar comprises an array of physical receivers (20), the array of physical receivers (20) comprising at least one row of physical receivers having a first spacing (L1) in a first direction, and the TDM MIMO FMCW radar further comprises a plurality of physical transmitters (10) arranged at a second spacing (L2) in the first direction, Each of the subarrays in the virtual array is generated by a combination of one of the physical transmitters and the physical receiver array. The method comprises: obtaining (702) a virtual array signal of a range Doppler bin associated with a scene having a moving object, each element of the virtual array signal corresponding to a virtual antenna element of the virtual array; using a phase compensation method to compensate (704) the velocity-induced phase shift of the virtual array signal to obtain a compensated virtual array signal, the phase compensation method introducing a phase ambiguity between the sub-arrays if the velocity of the moving object exceeds a threshold; Calculating (706) a spatial phase change rate relative to the first direction based on elements of the compensated virtual array signal corresponding to one subarray at a time; predicting (708) a spatial phase shift between pairs of subarrays based on the spatial phase change rate relative to the first direction and the second spacing (L2); determining (710) a residual phase shift between the sub-array pairs by comparing (710.1) an actual phase shift of the compensated virtual array signal with the spatial phase shift; and The inverse of the residual phase shift is applied (712) to the compensated virtual array signal.

2. The method according to claim 1, wherein: Determining (710) the residual phase shift between the subarray pairs comprises: A difference between the actual phase shift and the spatial phase shift is calculated.

3. The method according to claim 2, wherein: The virtual array has equidistant virtual antenna elements in the first direction; and Determining (710) the residual phase shift includes rounding the difference between the actual phase shift and the spatial phase shift to a multiple of 2π / M, where M is the number of the physical transmitters.

4. The method according to claim 1, wherein: Determining (710) the residual phase shift includes calculating the actual phase shift as one of: (a) the difference in phase between two elements of the compensated virtual array signal corresponding to two homologous virtual antenna elements, (b) a difference in phase between two elements of the compensated virtual array signal corresponding to two non-cognate virtual antenna elements, the difference being adjusted according to the spatial phase change rate.

5. The method according to claim 1, wherein: The physical transmitters are used sequentially according to a transmission schedule, and the subarray pairs are consecutive with respect to the transmission schedule.

6. The method according to claim 1, wherein: The ratio of the first spacing and the second spacing L1 , L2 is such that the virtual array has equidistant virtual antenna elements in the first direction.

7. The method according to claim 1, wherein: The physical receiver array has at least two rows in the first direction; and The residual phase shift is determined as an average value over a plurality of rows.

8. The method according to claim 1, wherein: The spatial phase change rate is calculated (706) as an average value for the plurality of sub-arrays.

9. The method according to claim 1, further comprising: For at least one other sub-array pair having an equal spatial phase shift, comparing (710.2) the actual phase shift of the compensated virtual array signal with the spatial phase shift, Therein, the residual phase shift is determined (710) as an average value of all the sub-array pairs.

10. The method according to claim 1, wherein: The physical receiver array includes at least one column of physical receivers having a third spacing (L3) in a second direction, and the physical transmitters are arranged at a fourth spacing (L4) in the second direction, The method further comprises: Calculating (714) a spatial phase change rate relative to the second direction based on the elements of the compensated virtual array signal corresponding to one subarray at a time; calculating (716) a second spatial phase shift between a second pair of sub-arrays based on the spatial phase change rate relative to the second direction and the fourth spacing (L4); determining (718) a second residual phase shift between the second sub-array pairs by comparing an actual phase shift of the compensated virtual array signal with the second spatial phase shift; and The inverse of the second residual phase shift is applied (720) to the compensated virtual array signal.

11. The method of claim 1 , further comprising determining residual phase shifts for all remaining sub-arrays of the virtual array and applying their inverses.

12. A method for calculating the arrival angle of a mobile object based on a virtual array signal of a range Doppler bin captured by a virtual array of a TDM MIMO FMCW radar, comprising: processing the virtual array signal using a method according to any one of the preceding claims; as well as The angle of arrival is calculated based on the processed virtual array signal.

13. A signal processing device for a time division multiplexing (TDM) multiple input multiple output (MIMO) frequency modulated continuous wave (FMCW) radar with a virtual array, in, The TDM MIMO FMCW radar comprises an array of physical receivers (20), the array of physical receivers comprising at least one row of physical receivers having a first spacing (L1) in a first direction, and the TDM MIMO FMCW radar further comprises a plurality of physical transmitters (10) arranged at a second spacing (L2) in the first direction, The virtual array includes sub-arrays (40), each sub-array being generated by a combination of one of the physical transmitters and the physical receiver array. The signal processing device comprises processing circuitry configured to resolve phase ambiguities between the sub-arrays of the virtual array in a virtual array signal by the method of any one of the preceding claims.

14. A computer program product comprising instructions which, when the program is executed by a computer, cause the computer to implement the method according to any one of claims 1 to 12.

Images