Methods and Apparatus for Velocity Detection in MIMO Radar Including Velocity Ambiguity Resolution

Abstract

In accordance with described examples, a method determines if a velocity of an object detected by a radar is greater than a maximum velocity by receiving on a plurality of receivers at least one frame of chirps transmitted by at least two transmitters and reflected off of the object. A velocity induced phase shift (φ.sub.d) in a virtual array vector S of signals received by each receiver corresponding to a sequence of chirps (frame) transmitted by each transmitter is estimated. Phases of each element of virtual array vector S are corrected using φ.sub.d to generate a corrected virtual array vector S.sub.c. A first Fourier transform is performed on the corrected virtual array vector S.sub.c to generate a corrected virtual array spectrum to detect a signature that indicates that the object has an absolute velocity greater than a maximum velocity.

Claims

1. An integrated circuit comprising: at least two ports coupled to receive a plurality of chirps transmitted by at least two transmitters and reflected off of an object; a processor configured to: estimate a velocity induced phase shift (φ.sub.d) in a virtual array vector S of signals based on signals received by each receiver corresponding to a sequence of chirps (frame) transmitted by the at least two transmitters; correct the phases of each element of virtual array vector S using φ.sub.d to generate a corrected virtual array vector S.sub.c; perform a first Fourier transform on the corrected virtual array vector S.sub.c to generate a corrected virtual array spectrum; and analyze the corrected virtual array spectrum to detect a signature that indicates that the object has an absolute velocity greater than a maximum velocity.

2. The integrated circuit of claim 1 in which the processor is further configured to correct the corrected virtual array vector S.sub.c using a phase error vector corresponding the signature and perform a second Fourier transform on a resulting matrix to determine if the signature is removed from the resulting matrix.

3. The integrated circuit of claim 1 in which the processor further determines a correct velocity of the object.

4. The integrated circuit of claim 3 in which the correct velocity is determined using formulas $v_{\mathrm{est}}=\frac{{\varphi }_d.Math.\lambda }{4.Math.\pi .Math..Math.T_c},$ where T.sub.c is a chirp period and λ is a wavelength of the chirps and v.sub.true=v.sub.est+2v.sub.max (if v.sub.est<0) or v.sub.true=V.sub.est2v.sub.max (if v.sub.est>0), where v.sub.true is the correct velocity and v.sub.max is determined by the formula $v_{\max }=\frac{\lambda }{4.Math.T_c}.$

5. The integrated circuit of claim 1 in which the at least two ports is four ports.

6. The integrated circuit of claim 1 further including circuitry for driving at least one of the at least two transmitters.

7. The integrated circuit of claim 1 in which the processor further determines if the signature is caused by multiple objects by analyzing S.sub.c.

8. A method for determining if a velocity of an object detected by a radar is greater than a maximum velocity, comprising: receiving on a plurality of receivers at least one frame of chirps transmitted by at least two transmitters and reflected off of the object; estimating a velocity induced phase shift (φ.sub.d) in a virtual array vector S of signals received by each receiver corresponding to a sequence of chirps (frame) transmitted by each transmitter; correcting phases of each element of virtual array vector S using φ.sub.d to generate a corrected virtual array vector S.sub.c; performing a first Fourier transform on the corrected virtual array vector S.sub.c to generate a corrected virtual array spectrum; and analyzing the corrected virtual array spectrum to detect a signature that indicates that the object has an absolute velocity greater than a maximum velocity.

9. The method of claim 8 further comprising correcting the corrected virtual array vector S.sub.c using a phase error vector corresponding the signature and performing a second Fourier transform on a resulting matrix to determine if the signature is removed from the resulting matrix.

10. The method of claim 8 further comprising determining a correct velocity of the object.

11. The method of claim 10 in which the correct velocity is determined using formulas $v_{\mathrm{est}}=\frac{{\varphi }_d.Math.\lambda }{4.Math.\pi .Math..Math.T_c},$ where T.sub.c is a chirp period and λ is a wavelength of the chirps and v.sub.true=v.sub.est+2v.sub.max (if v.sub.est<0) or v.sub.true=v.sub.est−2v.sub.max (if v.sub.est>0), where v.sub.true is the correct velocity and v.sub.max is determined by the formula $v_{\max }=\frac{\lambda }{4.Math.T_c}.$

12. The method of claim 8 in which the plurality of receivers is four receivers.

13. The method of claim 8 further comprising determining if the signature is caused by multiple objects by analyzing S.sub.c.

14. A radar system comprising: at least two transmitters configured to transmit a plurality of chirps; at least two receivers receiving the chirps reflected off of an object; a processor configured to: estimate a velocity induced phase shift (φ.sub.d) in a virtual array vector S of signals received by each receiver corresponding to a sequence of chirps (frame) transmitted by each transmitter; correct the phases of each element of virtual array vector S using φ.sub.d to generate a corrected virtual array vector S.sub.c; perform a first Fourier transform on the corrected virtual array vector S.sub.c to generate a corrected virtual array spectrum; and analyze the corrected virtual array spectrum to detect a signature that indicates that the object has an absolute velocity greater than a maximum velocity.

15. The radar system of claim 14 in which the processor is further configured to correct the corrected virtual array vector S.sub.c using a phase error vector corresponding the signature and perform a second Fourier transform on a resulting matrix to determine if the signature is removed from the resulting matrix.

16. The radar system of claim 14 in which the processor further determines a correct velocity of the object.

17. The radar system of claim 16 in which the correct velocity is determined using formulas $v_{\mathrm{est}}=\frac{{\varphi }_d.Math.\lambda }{4.Math.\pi .Math..Math.T_c},$ where T.sub.c is a chirp period and λ is a wavelength of the chirps and v.sub.true=v.sub.est+2v.sub.max (if v.sub.est<0) or v.sub.true=v.sub.est−2v.sub.max (if v.sub.est>0), where v.sub.true is the correct velocity and v.sub.max is determined by the formula $v_{\max }=\frac{\lambda }{4.Math.T_c}.$

18. The radar system of claim 14 in which the at least two receivers is four receivers.

19. The radar system of claim 14 in which the at least two transmitters is four transmitters.

20. The radar system of claim 14 in which the processor is further configured to determine if the signature is caused by multiple objects by analyzing S.sub.c.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0008] FIG. 1 is a schematic diagram of an FMCW radar.

[0009] FIG. 2 is a graph of a chirp signal.

[0010] FIG. 3 is a graph of an interleaved chirp signal.

[0011] FIG. 4 is a schematic diagram of another radar.

[0012] FIG. 5 is a schematic diagram of a radar system having two transmitters.

[0013] FIG. 6 is a graph showing the combined impact of velocity and angle of arrival.

[0014] FIG. 7 is a graph showing Fourier transforms of an ideal and an erroneous corrected matrix.

[0015] FIG. 8 is a flow diagram of a method aspect of the present application.

[0016] FIG. 9 is a flow diagram of another method aspect of the present application.

[0017] FIG. 10 shows a TDM-MIMO radar system having another architecture.

[0018] FIG. 11 is a graph showing Fourier transforms of an ideal and an erroneous corrected matrix for the architecture of FIG. 10.

[0019] FIG. 12 is a graph showing Fourier transforms of an ideal and of erroneous corrected matrixes for two objects in a range-Doppler bin.

DETAILED DESCRIPTION

[0020] Corresponding numerals and symbols in the different figures generally refer to corresponding parts unless otherwise indicated. The figures are not necessarily drawn to scale.

[0021] The term “coupled” may include connections made with intervening elements, and additional elements and various connections may exist between any elements that are “coupled.”

[0022] FIG. 1 is a schematic diagram of an FMCW radar 100. In FIG. 1, the radar 100 is arranged with a single transmitter 102 transmitting a frame 108 as described below regarding FIG. 2. The frame 108 reflects off object 106 with the reflected signals 110-1-110-4 received by 4 receivers 104-1-104-4, respectively. With a single TX antenna transmitting a frame of chirps to a single RX antenna, the relative motion of an object with respect to the radar induces a phase change (φ.sub.d) in the received signal across subsequent chirps. Each antenna is driven by circuitry that may be partially or wholly incorporated into an integrated circuit. For example, an integrated circuit may generate the signals and apply the signals to the antenna using one or more power transistors or power modules. The driving circuitry may be discrete components or several components incorporated into a module. In some configurations, one integrated circuit may drive multiple antennas. In other configurations, a separate circuit drives each antenna and a common processor to analyze the signals.

[0023] FIG. 2 is a graph 200 of the chirp signal received on an RX antenna. Received chirp 212-0 is the reference chirp and the first chirp in frame 208. Received chirp 212-1 is shifted φ.sub.d by the Doppler effect from its timing as transmitted. Received chirp 212-2 is shifted 2φ.sub.d from its timing as transmitted. Thus, there is a linear progression ([0, φ.sub.d, 2φ.sub.d . . . (N−1) φ.sub.d]) of the phase of the received signal across chirps. This phase progression will be seen in the corresponding peaks of a range-FFT (further explained hereinbelow) across chirps, when the range-FFT is performed on digitized samples corresponding to the received IF signal for each chirp. This sequence is depicted in FIG. 2 (For simplicity, here and elsewhere in this document, the initial phase value is referred to as zero). The linear progression in the phase of the received signal allows for estimation of φ.sub.d using a Fourier transform across subsequent chirps. The estimation can be accomplished using fast Fourier transform (FFT) devices and techniques on the received signal across subsequent chirps. The phase change φ.sub.d is directly proportional to the velocity of the object, which is given by Equation 1:

[00001]$\begin{array}{cc}{\varphi }_d=\frac{4.Math.\pi .Math..Math.T_c.Math.v}{\lambda }& \left[1\right]\end{array}$

[0024] where T.sub.c is the chirp periodicity (i.e. time from start of one chirp to the next) and λ is the wavelength corresponding to the start frequency of the chirp.

[0025] Thus, after φ.sub.d has been estimated (for example, by using an FFT), the velocity of the object can be estimated as ν.sub.est using Equation 2:

[00002]$\begin{array}{cc}{v}_{\mathrm{est}}=\frac{{\varphi }_d.Math.\lambda }{4.Math.\pi .Math..Math.T_c}& \left[2\right]\end{array}$

[0026] The parameter φ.sub.d is a phase quantity that can only be unambiguously estimated if it lies between −π and π radians. The limit on φ.sub.d directly imposes a limit on the value of the maximum velocity (v.sub.max) that can be unambiguously estimated. Substituting φ.sub.d=π in equation [2] gives Equation 3, which yields the following value of v.sub.max.

[00003]$\begin{array}{cc}{v}_{\max }=\frac{\lambda }{4.Math.T_c}& \left[3\right]\end{array}$

[0027] Thus, the maximum unambiguous velocity (±v.sub.max) that can be measured by the radar directly depends on the chirp period T.sub.c. A smaller T.sub.c yields a higher v.sub.max. The periodicity T.sub.c refers to the time between the start (or any corresponding point) of consecutive chirps from the same TX antenna. So, all other aspects being equal, the v.sub.max for a TDM-MIMO radar configuration with two TX antennas would be half that of the single TX radar configuration. FIG. 3 illustrates this point in frame 308. Graph 300 includes chirps 312-0-312-(N−1) that are transmitted by one transmitter (TX) and are interleaved in time with chirps 314-0-314-(N−1) from a second transmitter. T.sub.c is the period of chirps from one transmitter. FIG. 3 illustrates the period, where T.sub.c is measured from the end of chirp 312-0 to the end of chirp 312-1. In contrast with a single transmitter TDM-MIMO as illustrated in FIG. 2 where T.sub.c runs from the end of chirp 212-0 to the end of chirp 212-1, the period T.sub.c in FIG. 3 is twice as long. In general, a TDM-MIMO system with M transmitters has a period M times the period of a single transmitter system. However, as noted above in equation [3], v.sub.max is inversely proportional T.sub.c. Thus, the greater the number of transmit antennas that are used, the lower the maximum velocity v.sub.max.

[0028] In FIG. 1, the object 106 is directly in front of transmitter 102 and receivers 104-1-104-4. This example is a special case where, because the object is at a position perpendicular to the TDM-MIMO array, the received chirps will arrive at all the receivers essentially at the same time. Most objects being detected are at an angle relative to the TDM-MIMO system.

[0029] FIG. 4 is a schematic diagram of another radar 400. Elements in FIG. 4 that are numbered in a similar manner to elements in FIG. 1 perform similar functions. For example, elements 402, 404-1-404-4 and 406 perform similar functions to elements 102, 104-1-104-4 and 106 in FIG. 1. In FIG. 4, object 406 is at an angle θ relative to transmitter (TX) 402 and receivers (RX) 404-1-404-4. A signal transmitted from transmitter 402 reflects off an object 406 and receivers 404-1-404-4 receive the signal. Receivers 404-1-404-4 have uniformly spaced antennas having a spacing d.sub.ant. The signal arriving at each successive RX antenna is delayed with respect to the previous antenna due to the additional distance d that the signal must traverse; this situation is illustrated by the right triangle between receivers 404-3 and 404-4 in FIG. 4. This additional delay translates to a phase difference φ.sub.a between the signal arriving at adjacent RX antennas. There is thus a linear progression in the phase of the signal arriving at successive RX antennas [0, φ.sub.a, 2φ.sub.a, 3φ.sub.a]. This linear progression allows for estimation of φ.sub.a using, for example, an FFT. The phase difference across antennas φ.sub.a relates to the angle of arrival (θ) of the object. Having estimated φ.sub.a, the angle of arrival θ can be estimated using Equation 4:

[00004]$\begin{array}{cc}\theta ={\sin }^{-1}.Math.\frac{{\varphi }_a.Math.\lambda }{2.Math.\pi .Math..Math.d_{\mathrm{ant}}}& \left[4\right]\end{array}$

[0030] Where d.sub.ant is the distance between adjacent RX antennas.

[0031] FIG. 5 is a schematic diagram of a TDM-MIMO system 500 having two transmitters 502-1 and 502-2. Elements in FIG. 5 numbered in a similar manner to elements in FIG. 4 perform similar functions. For example, elements 502, 504-1-504-4 and 506 perform similar functions to elements 402, 404-1-404-4 and 406 in FIG. 4. Controller and processor 508 controls transmitters 502-1 and 502-1 and receivers 504-1-504-4 and processes signals received on receivers 504-1-504-4. Controller and processor 508 may partially or wholly incorporated into an integrated circuit or integrated circuits. For example, an integrated circuit may generate the signals and apply the signals to the antenna using one or more power transistors or power modules. The driving circuitry may be discrete components or several components incorporated into a module. In some configurations, one integrated circuit may drive multiple antennas. In other configurations, a separate circuit drives each antenna and a common processor to analyze the signals. In some configurations, the controller portion and the processor portion are formed in the same integrated circuit or may be separate integrated circuits. The processor portion of the integrated circuit may include a CPU, a digital signal processor (DSP), a mixed signal processor (MSP), a reduced instructions set computer (RISC) core such as an ARM core, a microcontroller, or another suitable processor.

[0032] A TDM-MIMO system like system 500 uses multiple transmitters to increase the effective length of the linear phase progression of φ.sub.a and thus improve the quality of angle estimation. FIG. 5 illustrates the use of multiple transmitters and the effect of the angle estimation. Note that the signal from transmitter 502-2 must travel an additional distance D with regard to transmitter 502-1. This additional distance that chirps transmitted from transmitter 502-2 must travel relative to chirps transmitted from transmitter 502-1 contributes an additional phase difference to the signal at each of the receiver antennas. In FIG. 5, the spacing between transmitters 502-1 and 502-2 is chosen to be four times the spacing between adjacent receiver antennas. However, the principles described herein apply to any spacing between the transmitters. Proportionally, this additional phase difference works out to be 4φ.sub.a. Thus, for each receiver antenna, the signal seen by the receiver from transmitter 502-1 and transmitter 502-2 has a phase difference of 4φ.sub.a. With this configuration, system 500 operates as follows: [0033] a. First, transmitter 502-1 transmits and the phase seen at receivers 504-1-504-4 is [0 φ.sub.a 2φ.sub.a 3φ.sub.a], respectively. [0034] b. Subsequently, transmitter 502-2 transmits and the phase seen at receivers 504-1-504-4 is [4φ.sub.a 5φ.sub.a 6φ.sub.a 7φ.sub.a].

[0035] The received signal obtained from consecutive transmission from transmitter 502-1 and transmitter 502-2 can be concatenated together to create a longer signal sequence whose phase has the following linear progression: P=[0 φa 2φa 3φa 4φa 5φa 6φa 7φa], which provides a better estimation of φ.sub.a. Thus, in TDM-MIMO, signals received at the RX antenna array due to time division multiplexed transmissions across multiple TX antennas can be suitably sequenced to create a signal sequence whose length is equal to: the Number_of_transmit_antennas X Number_of receive_antennas. This signal sequence is referred to herein as the “virtual array signal.” Herein, the virtual array signal itself is denoted S, and the phase corresponding to this sequence is denoted by P.

[0036] One process for generating the virtual array signal first involves two dimensional FFT (2D-FFT) processing for each transmit/receiver pair as explained below. An Intermediate Frequency (IF)-signal is obtained by mixing the transmitted chirp with the corresponding received chirp. A range-FFT is performed on the digitized samples corresponding to the IF signal. The range-FFT resolves objects in range and produces a series of bins each bin corresponding to a range value. A signal at a bin indicates an object at that range. This processing is done for each chirp on each transmitter/receiver pair for an entire frame. For each transmitter/receiver pair, a Doppler-FFT is then performed for each range-bin across chirps. This 2D-FFT (i.e., range-FFT followed by a Doppler-FFT) processing generates a two dimensional FFT grid and one such 2D-FFT grid is generated for each transmitter/receiver pair. The virtual array signal S is then generated by picking a signal sample corresponding to a specific range-Doppler bin across all the generated 2D-FFT grids for every receiver transmitter pair (see, e.g., Song, et al., “Enhancing Doppler estimation via newton interpolation for automotive FMCW radars”, International Conference on Information and Communication Technology Convergence (ICTC) 2014, pp. 615-616 (2014), which is incorporated by reference in its entirety herein).

[0037] FIG. 6 is a graph 600 showing the combined impact of velocity and angle of arrival. Elements in FIG. 6 numbered in a similar manner to elements in FIG. 5 perform similar functions. For example, chirps 612-0-612-(N−1) and chirps 614-0-614-(N−1) perform similar functions to chirps 312-0-312-(N−1) and chirps 314-0-314-(N−1) in FIG. 3. The discussion hereinabove with respect to FIG. 5 implicitly assumes a stationary object. For an object with relative motion with respect to the radar, the phase offset seen at the receivers will have a contribution due to both the relative velocity and angle of arrival. Regarding FIG. 6, T.sub.c′ refers to the time between the start of successive chirps from the same transmit antenna. Also, φ.sub.d refers to the velocity induced phase difference at the receiver between consecutive chirps emanating from the same transmit antenna. Thus, the corresponding velocity induced phase difference between adjacent transmissions from transmitters 602-1 and 602-2 (FIG. 5) is 0.5φ.sub.d. When transmitter 602-1 transmits, the phase of the received signal at the four receivers 604-1-604-4 is [0 φ.sub.a 2φ.sub.a 3φ.sub.a], respectively, as shown in set 620-1. For a signal emanating from transmitter 602-2, the signal at the four receivers 604-1-604-4 has an angle of arrival induced phase-offset of [4φ.sub.a 5φ.sub.a 6φ.sub.a 7φ.sub.a]. Because transmissions from transmitter 602-2 are delayed from transmitter 602-1 by 0.5T.sub.c, this induces an additional phase of 0.5φ.sub.d as shown in set 620-2. Thus, the phase P of the virtual array signal S that incorporates the effect of both the angle of arrival and the relative velocity is given by Equation 5:

P=[0 φ.sub.a 2φ.sub.a 3φ.sub.a 0.5φ.sub.d+4φ.sub.a 0.5φ.sub.d+5φ.sub.a 0.5φ.sub.d+6φ.sub.a 0.5φ.sub.d+7φ.sub.a]  [5]

[0038] As seen in equation [5], the phase P of the virtual array signal S depends on both the angle of arrival (via φ.sub.a) and the relative velocity (via φ.sub.d). Estimation of velocity and angle of arrival are thus coupled. Determining velocity and angle of arrival can be determined using the following technique:

[0039] a. Step 1 [0040] Estimate the Relative Velocity Induced Phase (φ.sub.d) [0041] Determine the phase differences (φ.sub.d) at each RX antenna due to successive chirps transmitted by a specific TX antenna. This processing is sometimes called “Doppler FFT processing”. This is done by FFT processing the signal received at an RX antenna due to chirps transmitted from a specific TX antenna. Note that, typically, a range-FFT is first done on the ADC samples corresponding to each chirp, prior to performing the “Doppler-FFT across chirps in a frame. The estimate of φ.sub.d is used to estimate the velocity v of the object using equation [2]. In practice, similar processing is repeated across all TX-RX antenna pairs and the results averaged to yield a better estimate of φ.sub.d (e.g., the Doppler FFTs across multiple TX-RX antenna pairs may be non-coherently averaged and this non-coherently averaged FFT is then used to estimate φ.sub.d.)

[0042] b. Step 2 [0043] Doppler Correction [0044] The estimate of φ.sub.d in Step 1 is used to remove the dependence of the virtual array signal S on φ.sub.d by multiplying the last four elements of S by

[00005]$e^{-j\left(\frac{{\varphi }_d}{2}\right)}.$

This operation creates a corrected virtual array signal S.sub.c, whose phase P.sub.c) is given by Equation 6:

P.sub.c=[0 φ.sub.a 2φ.sub.a 3φ.sub.a 4φ.sub.a 5φ.sub.a 6φ.sub.a 7φ.sub.a]  [6]

[0045] c. Step 3 [0046] Angle Estimation [0047] From equation [6], the phase P.sub.c of the corrected virtual array signal S.sub.c has a linear progression in φ.sub.a. An FFT on P.sub.c will thus yield an estimate of φ.sub.a. This estimate of φ.sub.a is used in equation [4] to determine the angle of arrival θ.

[0048] The technique above assumes that the relative velocity of the object (v) was within v.sub.max (i.e. |v|<v.sub.max). Any violation of this constraint would result in an erroneous estimate of φ.sub.d and consequently errors in the estimated velocity (v) and in S.sub.c (and its phase P.sub.c). Also, as noted hereinabove, the achievable v.sub.max is inversely proportional to the number of transmitters (e.g., by a factor of 2 for two transmitters) because T.sub.c increases proportionally to the number of transmitters.

[0049] In an aspect, the limitation of v.sub.max as stated above is ameliorated in TDM-MIMO radar. The following process is used. If |v| exceeds v.sub.max, then errors in the estimate of φ.sub.d also effect the Doppler correction (Step 2 hereinabove) that was done prior to angle estimation (Step 3 hereinabove). The errors thus introduced in the phase P.sub.c of the corrected virtual array signal S.sub.c result in unique signatures in its angle-FFT spectrum. These signatures are detected and used to correct for a condition where |v| has exceeded v.sub.max as further explained hereinbelow.

[0050] If |v|>v.sub.max, then |φ.sub.d| will exceed π resulting in an erroneous estimate of φ.sub.d in Step 2 of the method described above. For example, if φ.sub.d exceeds π (i.e., φ.sub.d=π+Δ), the value of φ.sub.d estimated in Step 1 (φ.sub.d.sub._.sub.est) will be −π+Δ. Likewise; if the value of φ.sub.d is less than −π (i.e., φ.sub.d=−π−Δ), then φ.sub.d.sub._.sub.est=π−Δ. Thus, the estimation error φ.sub.d−φ.sub.d.sub._.sub.est=±2π. This estimation error results in an error in the phase of P.sub.c, the erroneous phase is given by Equation 7:

P.sub.c=[0, φ.sub.a 2φ.sub.a 3φ.sub.a π+4φ.sub.a π+5φ.sub.a π+6φ.sub.a π+7φ.sub.a]  [7]

[0051] In Equation 7, the error terms are n added to each of the last four entries. Thus, a vector of the error (“phase error vector”) for this radar architecture is φ.sub.error=[0 0 0 0 ππππ].

[0052] FIG. 7 is a graph 700 showing the FFT of an ideal S.sub.c (i.e. where v is less than v.sub.max) and of an S.sub.c having the phase error shown above in equation [7]. The ideal corrected virtual array signal S.sub.c (i.e. with its phase P.sub.c denoted by equation [6]), results in curve 702 with a single peak in the angle-FFT (corresponding to the estimate of φ.sub.a and thus θ). An erroneous S.sub.c (i.e. with the phase P.sub.c denoted by equation [7]) instead results in curve 704 that has two peaks in its angle-FFT. Further the two peaks in the FFT spectrum are separated by 3π/8 radians and have equal power. Thus, any angle-FFT that displays the properties of 1) two peaks and 2) the peaks are separated by 3π/8 has a high likelihood of being indicative of a situation where |v| has exceeded v.sub.max. Therefore, an over v.sub.max condition can be determined using the following checks: [0053] 1) Check 1: Does the FFT of S.sub.c have two peaks of equal power that are separated by 3π/8 radians from each other? [0054] 2) Check 2: If check one is positive, negate the last 4 samples of S.sub.c and re-compute the angle-FFT. Since negating a sample is equivalent subtracting π from its phase, this restores the erroneous phase (equation [7]) to the ideal phase (equation [6]). [0055] 3) Check 3: Confirm that the FFT resulting from Check 2 has a single peak that is located midway and equidistant from the two peaks of the erroneous angle-FFT. [0056] 4) Check 4: If checks 1-3 are passed, then perform an additional check to ensure that the two peaks are not due to the presence of two objects in the same range-Doppler bin (in the 2D-FFT grid). A procedure for this is described hereinbelow. [0057] 5) Check 5: If checks 1-4 are passed, then a velocity excursion beyond v.sub.max is flagged. True velocity is computed using Equation 8:

v.sub.true=v.sub.est+2v.sub.max (if v.sub.est<0) or v.sub.true=v.sub.est−2v.sub.max (if v.sub.est>0)   [8]

[0058] FIG. 8 is a flow diagram of an aspect method 800. Method 800 starts with step 802. In step 804, an estimate of the Doppler phase shift φ.sub.d is determined using Doppler FFT processing as described hereinabove. Step 805 removes the dependence of the virtual array signal S by, for example, multiplying the last four elements of S by

[00006]$e^{-j\left(\frac{{\varphi }_d}{2}\right)}.$

. Step 806 determines φ.sub.a using the angle FFT processing as described hereinabove. Step 808 determines if the FFT of S.sub.c has two peaks that are separated by 3π/8 radians. (In practice the separation between the two FFT peaks may be subtracted from 3π/8 and the absolute value of this difference is compared against an SNR based threshold.) If not, determine the velocity directly from φ.sub.d and no v.sub.est adjustment is necessary. If the FFT of S.sub.c has two peaks that are separated by 3π/8 radians, step 810 negates the samples of S.sub.c affected by φ.sub.error and the angle FFT is recomputed. Step 812 confirms that the recomputed angle FFT has a single peak midway between the peaks of the erroneous angle FFT. For other architectures (i.e. not two transmitters and four receivers) |v|>v.sub.max causes other error signatures. Thus, for these other architectures, other error signatures characteristic of the other architecture are detected in step 808 and 812. If the error appropriate signature is not found, an accurate velocity cannot be determined from this data and the process ends with step 818. If the appropriate signature is found, a determination must be made in step 814 if the two peaks were caused by one object using the method described hereinbelow regarding FIG. 9. If only one object is present in the bin, then the formulae shown in step 816 (equations [8]) determines the true velocity v.sub.true. The method ends with step 818. If more than one object is detected, the process ends without result with step 818.

[0059] Check 4 (step 814) hereinabove uses a single object confirmation method that can be used to confirm that the dual-peaks (curve 704) correspond to single object (with an erroneous phase) and is not due to the presence of two objects in the same range-Doppler bin. This can be determined using an eigenvalue based method and relying on the following fact: for a single object, the eigenvalues of the 2×2 correlation matrix corresponding to the corrected virtual array signal S.sub.c, will have a single dominant eigenvalue. The corrected virtual array signal S.sub.c is an 8 element vector, with the elements 1-4 corresponding to the received signal at the four antennas from TX1 and the elements 5-8 corresponding to the received signals from TX2 as shown in Equation 9:

[00007]$\begin{array}{cc}{S}_c=\begin{array}{cc}[\underset{\underset{\mathrm{TX}.Math..Math.1}{}}{\begin{array}{cccc}{s}_1& s_2& s_3& s_4\end{array}}& \underset{\underset{\mathrm{TX}.Math..Math.2}{}}{\begin{array}{cccc}{s}_5& s_6& s_7& s_8\end{array}}]\end{array}& \left[9\right]\end{array}$

[0060] The following method determines if one or two objects is present in the same range-Doppler bin: [0061] 1. Determine a set Q of 2×1 vectors r.sub.k=[s.sub.k, s.sub.k+1] consisting of adjacent elements from S.sub.c and that correspond to the same TX antenna. Thus, r.sub.1=[s.sub.1 s.sub.2] is part of set Q, while r.sub.4=[s.sub.4 s.sub.5] is not included in Q because s.sub.4 is a signal received from TX1 and s.sub.5 is a signal that is received from TX2. [0062] 2. Compute the 2×2 correlation matrix R=Σ.sub.Q r.sub.k r.sub.k.sup.T where r.sup.T is the transpose of r. [0063] 3. Compute the two eigenvalues of R. Computation of the two eigenvalues is a known mathematical process that only requires solving a quadratic equation, for which a computationally simple closed form solution exists. [0064] 4. Compute the ratio of the two eigenvalues (ratio of the smaller eigenvalue to the larger eigenvalue). Compare this ratio to a signal-to-noise ratio (SNR) threshold. The signal contains “one object” if ratio is less than the threshold or “more than 1 object” if ratio is more than threshold. The SNR threshold is determined experimentally or can be mathematically derived from the characteristics of the radar system.

[0065] FIG. 9 is a flow diagram of an aspect method 900. Method 900 determines if more than one object is in a range-Doppler bin. Step 902 determines a set of 2×1 vectors that do not span transmitters as discussed hereinabove. A 2×2 correlation matrix is then determined from the set of vectors in step 904. Step 906 computes the eigenvalues of the correlation matrix and step 908 computes the ratio of these eigenvalues. Step 910 determines, based on a comparison of a ratio of the eigenvalues to a noise threshold, if there is more than one object (912) or one object (914).

[0066] The example techniques described hereinabove are directed to the two transmitter (2TX) by four receiver (4RX) architecture of FIG. 5. However, the aspects of this application have wider applicability. In the aspects of the present application, exploiting the phase errors in the corrected virtual array signal may be used in many architectures. In the 2TX×4 RX case the error (φ.sub.error in the phase P.sub.c of the corrected virtual array signal S.sub.c includes an additional phase of π in its last 4 elements. FIG. 7 illustrates the corresponding error signatures in the FFT spectrum. Other architectures can have different errors φ.sub.error error in the phase P.sub.c of the corrected virtual array signal S.sub.c and correspondingly different signatures in the FFT spectrum.

[0067] For example, FIG. 10 shows a TDM-MIMO system 1000 having another architecture including 4 TX antennas (1002-1-1002-4) and 8 RX antennas (1004-1-1004-8). System 1000 is detecting, among other data, the angle and velocity of object 1006. In practice, such an architecture is usually realized by cascading multiple radar chips to increase the availability of TX/RX antennas.

[0068] With 4 TX and 8 RX antennas the corrected virtual array signal would consist of 8×4=32 samples. The ideal phase of corrected virtual array signal for the architecture of FIG. 10 is a linear phase progression of length 32 as shown in Equation 9:

P.sub.c=[0 φ.sub.a 2φ.sub.a 3φ.sub.a . . . 32φ.sub.a]  [9]

[0069] An excursion in the positive direction (i.e., v>v.sub.max) results in the following erroneous P.sub.c given by Equation 10:

P.sub.c32 [0 φ.sub.a 2φ.sub.a 3φ.sub.a 4φ.sub.a 5φ.sub.a 6φ.sub.a 7φ.sub.a (π/2)+8φ.sub.a (π/2)+9φ.sub.a (π/2)+10φ.sub.a (π/2)+11φ.sub.a (π/2)+12φ.sub.a (π/2)+13φ.sub.a (π/2)+14φ.sub.a (π/2)+15φ.sub.a π+16φ.sub.a π+17φ.sub.a π+18φ.sub.a π+19φ.sub.a π20φ.sub.a π+21φ.sub.a π+22φ.sub.a π+23φ.sub.a (−π/2)+24φ.sub.a (−π/2)+25φ.sub.a (−π/2)+26φ.sub.a (−π/2)+27φ.sub.a (−π/2)+28φ.sub.a (−π/2)+29φ.sub.a (−π/2)+30φ.sub.a (−π/2)+31φ.sub.a].   [10]

[0070] Similarly, an excursion in the negative direction (i.e., v<−v.sub.max) results in the following erroneous P.sub.c given by Equation 11:

P.sub.c=[0 φ.sub.a 2φ.sub.a 3φ.sub.a 4φ.sub.a 5φ.sub.a 6φ.sub.a 7φ.sub.a (−π/2)+8φ.sub.a (−π/2)+9φ.sub.a (−π/2)+10φ.sub.a (−π/2)+11φ.sub.a (−π/2)+12φ.sub.a (−π/2)+13φ.sub.a (−π/2)+14φ.sub.a (−π/2)+15φ.sub.a π+16φ.sub.a π+17φ.sub.a π+18φ.sub.a π+19φ.sub.a π+20φ.sub.a π+21φ.sub.a π+22φ.sub.a π+23φ.sub.a (π/2)+24φ.sub.a (π/2)+25φ.sub.a (π/2)+26φ.sub.a (π/2)+27φ.sub.a (π/2)+28φ.sub.a (π/2)+29φ.sub.a (π/2)+30φ.sub.a (π/2)+31φ.sub.a].   [11]

[0071] The corresponding signatures in the FFT spectrum of S.sub.c are shown in graph 1100 of FIG. 11. Curve 1102 is an ideal (no excursion) spectrum. Curve 1104 is a spectrum where v>v.sub.max. Curve 1106 is a spectrum where v<−v.sub.max.

[0072] Thus, an aspect method is more generally described as follows: [0073] 1. Estimate the relative velocity induced phase across chirps (φ.sub.d). [0074] 2. Correct the phases of the virtual array signal S using φ.sub.d to generate a corrected virtual array signal S.sub.c. [0075] 3. If |v|>|v.sub.max| then the phase P.sub.c of S.sub.c will have an error (φ.sub.error) that induces specific signatures in the spectrum of S.sub.c [0076] 4. Perform an FFT on S.sub.c and analyze the spectrum to detect the signatures that indicate that |v|>|v.sub.max|. [0077] a. Additional checks may involve: multiplying S.sub.c element by element with e.sup.−jφerror and performing an FFT on the resulting signal to determine a corrected φ.sub.a. [0078] b. Perform additional computations on S.sub.c to determine if multiple objects may be causing the signature.

[0079] The techniques discussed hereinabove are computationally simple. However, these techniques can only detect and correct for velocity aliasing if there is only one dominant object in a range-Doppler bin. In an additional aspect of the present application, an alternate solution, which is computationally more involved, alleviates some of this restriction. With a scenario where there are N objects in the same range-Doppler bin, then the corrected virtual array signal S.sub.c would ideally consist of N complex tones and a frequency spectrum of S.sub.c will ideally reveal N peaks. However, the presence of objects with a relative velocity that exceeds v.sub.max will result in erroneous estimation of φ.sub.d and a consequent error (φ.sub.error) in the phase P.sub.c of S.sub.c. This generally manifests itself in additional peaks in the frequency spectrum of S.sub.c. For example, for the radar architecture of FIG. 5, φ.sub.error=[0 0 0 0 ππππ] which corresponds to a phase discontinuity of π in the phase of S.sub.c. Graph 1200 of FIG. 12 illustrates this for the case of N=2. The ideal spectrum consists of two peaks as shown in curve 1202. The erroneous spectrum caused by |v|>v.sub.max includes additional peaks. This is shown for N=2 in curve 1204, which includes a total of 3 peaks. In an aspect, an error condition when N=2 is determined by: [0080] 1. Performing a spectral analysis on the corrected virtual array signal (S.sub.c). [0081] 2. Constructing a second corrected virtual array signal (S.sub.c′) by multiplying S.sub.c with e.sup.−jφerror where φ.sub.error refers to the phase error vector. In addition, a spectral analysis on S.sub.c40 is performed. [0082] 3. Comparing the results of the two spectral analyses in steps 1 and 2. Two approaches for this spectral analysis and comparison are possible

[0083] Method 1 (FFT based spectral analysis): Perform an FFT on S.sub.c and S.sub.c′ and estimate the number of peaks (for example, k and k′) in each of the spectra. If k>k′ it indicates an error condition (i.e. the presence of one or more objects with |v|>v.sub.max). In practice, such a technique might be problematic because of the limited length of the FFT, SNR considerations etc. A more robust technique is Method 2 described below.

[0084] Method 2 (eigenvalue based analysis): Using eigenvalue based techniques estimate the number of objects (for example, m and m′) corresponding to S.sub.c and S.sub.c′. If m>m′ it indicates an error condition (i.e. the presence of one or more objects with |v|>v.sub.max). In many cases, the comparison of the number of estimated objects (m and m′), can be replaced by an appropriate comparison of the eigenvalues of the correlation matrix computed using S.sub.c and S.sub.c′ as illustrated herein below.

[0085] The following is an example method based on Method 2: [0086] Step 1: Ascertain the number of objects present in the range-Doppler bin by (a) computing the 3×3 correlation matrix R using all consecutive triads of S.sub.c that correspond to the same TX antenna and (b) estimating the eigenvalues of R and then estimating the number of objects using the relative values of these eigenvalues. If the number of objects is determined to be 1, then use the method described hereinabove regarding FIGS. 1-7. If the number of objects is determined to be 2, then follow the steps hereinbelow. If the number of objects is determined to be greater than 2 then the method terminates without a result. [0087] Step 2: Let r.sub.k=[s.sub.k s.sub.k+1 s.sub.k+2]. Compute the 3×3 correlation matrix of S.sub.c denoted by R=Σ.sub.k=1:6 r.sub.kr.sub.k.sup.T and compute the eigenvalues of R. λ is equal to the smallest of these eigenvalues. Smoothing techniques such as the “forward-backward” smoothing technique that are known in literature can be used while computing S.sub.c. [0088] Step 3: Determine the correlation matrix R′ of S.sub.c′ using the process of Step 2 above. λ′ is equal to the smallest of the eigenvalues of R′. [0089] Step 4: Compute the ratio λ′/λ and compare this with two thresholds T1 and T2 that are determined experimentally or mathematically for a particular radar architecture. [0090] If λ′/λ>T1, then there are no error conditions (i.e. both the objects have a velocity<v.sub.max). [0091] If T1>λ′/λ>T2, then one of the objects has a velocity>v.sub.max. [0092] If λ′/λ<T1, then both objects have a velocity>v.sub.max.

[0093] In an example aspect, an integrated circuit includes at least two ports coupled to receive a plurality of chirps transmitted by at least two transmitters and reflected off an object and a processor. The processor is configured to estimate a velocity induced phase shift (φ.sub.d) across chirps transmitted from one of the transmitters to one of the ports; select a virtual array vector S of signals received by each port corresponding to a sequence of chirps (frame) transmitted by each transmitter; correct the phases of each element of virtual array vector S using φ.sub.d to generate a corrected virtual array vector S.sub.c; perform a first Fourier transform on the corrected virtual array vector S.sub.c to generate a corrected virtual array spectrum; and analyze the corrected virtual array spectrum to detect a signature that indicates that the object has an absolute velocity greater than a maximum velocity.

[0094] In another example aspect, the processor is further configured to correct the corrected virtual array vector S.sub.c using a phase error vector corresponding to the signature and perform a second Fourier transform on a resulting matrix to determine if the signature is removed from the resulting matrix.

[0095] In another example aspect, the processor further determines a correct velocity of the object.

[0096] In yet another example aspect, the correct velocity is determined using formulas:

[00008]$v_{\mathrm{est}}=\frac{{\varphi }_d.Math.\lambda }{4.Math.\pi .Math..Math.T_c},$

where T.sub.c is a chirp period and λ is a wavelength of the chirps; and v.sub.true=v.sub.est+2v.sub.max (if v.sub.est<0) or v.sub.true=v.sub.est−2v.sub.max (if v.sub.est>0), where v.sub.true is the correct velocity and v.sub.max is determined by the formula

[00009]$v_{\max }=\frac{\lambda }{4.Math.T_c}.$

[0097] In another example aspect, integrated circuit includes four ports.

[0098] In another example aspect, the integrated circuit further includes circuitry for driving at least one of the at least two transmitters.

[0099] In another example, the processor further determines if the signature is caused by multiple objects by analyzing S.sub.c.

[0100] In yet another example aspect, a method determines if a velocity of an object detected by a radar is greater than a maximum velocity by receiving on a plurality of receivers at least one frame of chirps transmitted by at least two transmitters and reflected off the object. A velocity induced phase shift (φ.sub.d) across chirps transmitted from one of the transmitters to one of the receivers is estimated. A virtual array vector S of signals received by each receiver corresponding to one chirp transmitted by each transmitter is selected. Phases of each element of virtual array vector S are corrected using φ.sub.d to generate a corrected virtual array vector S.sub.c. A first Fourier transform is performed on the corrected virtual array vector S.sub.c to generate a corrected virtual array spectrum and the corrected virtual array spectrum is analyzed to detect a signature that indicates that the object has an absolute velocity greater than a maximum velocity.

[0101] In yet another aspect, the corrected virtual array vector S.sub.c is corrected using a phase error vector corresponding the signature and a second Fourier transform on a resulting matrix is performed to determine if the signature is removed from the resulting matrix.

[0102] In another aspect, a correct velocity of the object is determined.

[0103] In another aspect, the correct velocity is determined using formulas

[00010]$v_{\mathrm{est}}=\frac{{\varphi }_d.Math.\lambda }{4.Math.\pi .Math..Math.T_c},$

where T.sub.c is a chirp period and λ is a wavelength of the chirps and v.sub.true=v.sub.est+2v.sub.max (if v.sub.est<0) or v.sub.true=v.sub.est−2v.sub.max (if v.sub.est>0), where v.sub.true is the correct velocity and v.sub.max is determined by the formula

[00011]$v_{\max }=\frac{\lambda }{4.Math.T_c}.$

[0104] In yet another aspect, there are four receivers.

[0105] In another aspect, it is determined if the signature is caused by multiple objects by analyzing S.sub.c.

[0106] In another aspect, a radar system includes at least two transmitters configured to transmit a plurality of chirps. The system also includes at least two receivers receiving the chirps reflected off of an object and a processor. The processor is configured to: estimate a velocity induced phase shift (φ.sub.d) across chirps transmitted from one of the transmitters to one of the receivers; select a virtual array vector S of signals received by each receiver corresponding to a sequence of chirps (frame) transmitted by each transmitter; correct the phases of each element of virtual array vector S using φ.sub.d to generate a corrected virtual array vector S.sub.c; perform a first Fourier transform on the corrected virtual array vector S.sub.c to generate a corrected virtual array spectrum; and analyze the corrected virtual array spectrum to detect a signature that indicates that the object has an absolute velocity greater than a maximum velocity.

[0107] In yet another aspect, the processor is further configured to correct the corrected virtual array vector S.sub.c using a phase error vector corresponding to the signature and perform a second Fourier transform on a resulting matrix to determine if the signature is removed from the resulting matrix.

[0108] In yet another aspect, the processor further determines a correct velocity of the object.

[0109] In a further aspect, the correct velocity is determined using formulas

[00012]$v_{\mathrm{est}}=\frac{{\varphi }_d.Math.\lambda }{4.Math.\pi .Math..Math.T_c},$

where T.sub.c is a chirp period and λ is a wavelength of the chirps and v.sub.true=v.sub.est+2v.sub.max (if v.sub.est<0) or v.sub.true=v.sub.est−2v.sub.max (if v.sub.est>0), where v.sub.true is the correct velocity and v.sub.max is determined by the formula

[00013]$v_{\max }=\frac{\lambda }{4.Math.T_c}.$

[0110] In another aspect, the radar system includes four receivers.

[0111] In another aspect, the radar system includes four transmitters.

[0112] In yet another aspect, the processor is further configured to determine if the signature is caused by multiple objects by analyzing S.sub.c.

[0113] Modifications are possible in the described example aspects, and other alternative arrangements are possible that are within the scope of the claims.