Patent Application
20220308160
The present invention is directed to radar systems, and more particularly to radar systems for vehicles and robotics.
The use of radar to determine range, velocity, and angle (elevation or azimuth or both) of objects in an environment is important in a number of applications including automotive radar and gesture detection. Radar systems typically transmit a radio frequency (RF) signal and listen for the reflection of the radio signal from objects in the environment. The FCC and other International Frequency Allocation Organizations have opened up frequency bands in the millimeter wave region for consumer radar-based devices. For example, frequencies in the 70-80 GHz region may be used for medium-range automotive driver-assistance radar and frequencies in the 61-61.5-GHz region may be used for short-range indoor sensors such as motion sensors or people counters and security devices.
A radar system estimates the location of objects, also called targets, in the environment by correlating the transmitted radio signal with delayed echoes of the transmitted signal reflected from said objects and received at the radar receivers. A radar system can also estimate the relative velocity of the target by the Doppler shift of its echoes. A radar system with multiple transmitters and multiple receivers can also determine the angular position of a target. Depending on antenna scanning and/or the number of antenna/receiver channels and their geometry, different angles (e.g., azimuth or elevation) can be determined.
Radars as mentioned above may use any one of a number of transmit waveforms and transmit-receive formats. For example, FMCW chirp radars may be used where the transmitter transmits a swept frequency and the receiver simultaneously receives a frequency different than the momentary transmit frequency according to the echo delay. The beat frequency between the received signal and the transmit signal then yields the delay of the target echo.
Another technique is digital FMCW or PMCW, in which a carrier is frequency- (or phase-)modulated with a digital code using, for example, Gaussian Minimum Shift Keying (GMSK) or Offset Quadrature Phase Shift Keying (OQPSK). The received echoes are correlated with the code to determine the echo amplitudes at different delays. Digital FMCW radar lends itself to be constructed in a MIMO variant in which multiple transmitters transmitting multiple codes are received by multiple receivers that each correlate with all codes. The advantage of the MIMO digital FMCW radar is that the angular resolution is that of a virtual antenna array having an equivalent number of elements equal to the product of the number of transmitters and the number of receivers, termed a virtual antenna array, with associated virtual receivers (VRXs).
Digital FMCW MIMO radar techniques are described in commonly owned U.S. Pat. Nos. 9,989,627; 9,945,935; 9,846,228; and 9,791,551, which are all hereby incorporated by reference herein in their entireties.
In the digital FMCW case, the receiver operates during the transmit time and requires sophisticated means to null-out own transmitter interference. Self-interference or spillover cancellation increases in complexity when the number of MIMO transmitters and receivers increases; therefore, methods are sought to reduce both complexity and power consumption, for which Pulse-Digital MIMO Radar may be used, wherein the transmitter transmits for a short time to fill the go-return pipe for the longest range, followed by a receive period to receive the echoes. The alternating transmit/receive format then repeats.
In both FMCW and Pulse FMCW, the range resolution is related to the instantaneous bandwidth and the angular resolution is related to the size of the antenna array. If the antenna array achieves high angular resolution by means of large aperture using virtual antenna element spacings of more than a quarter wavelength (or half wavelength, depending on the convention), grating lobes appear, which can be mistaken for false targets. There is therefore a need to improve both range and angular resolution over the limits set by prior art technology while avoiding confusion by grating lobes.
There is also a need to consider potential mutual interference between multiple radars operating independently in the same frequency band within range of each other and to devise techniques for mitigation of mutual interference between different, non-collaborating radars.
An exemplary automotive radar comprises an array of transmit antennas and receive antennas connected to a signal processing circuit. In one implementation the antenna arrays may be linear (1-dimensional) arrays to provide radar target resolution only in Azimuth or Elevation while in other implementations the antenna arrays may be two-dimensional and provide target resolution in both Azimuth and Elevation simultaneously.
An exemplary radar device embodiment includes any combination of advanced features including use of sparse arrays with novel, sidelobe-reduction beamforming techniques; dual polarization for interference mitigation; transmit or receiver null-steering, or both, to improve mutual interference and frequency hopping for increasing range resolution and improved mutual interference characteristics by clash detection.
Each transmit array antenna is connected to an associated transmitter and each receive array antenna is connected to an associated receiver, each receiver comprising low-noise amplification, down-conversion to the quadrature (I,Q) baseband using I-Q mixers driven by a common local oscillator, baseband filtering as necessary, programmable gain adjustment as necessary and Digital to Analog (D-to-A) conversion at a sampling rate adequate to capture all spectral components of interest. All of the above signal processing elements are part of the signal processing circuit which may comprise one or more integrated circuit chips.
After D-to-A conversion, each receiver's processing correlates its received signal samples with digital values representing each transmitter's modulation to produce a number of correlations corresponding to different echo delays, there being one such set for each receiver-transmitter combination, in total a number of sets of range correlations equal to the product of the number of transmit antennas with the number of receive antennas and the number of transmitter bursts correlated at successive times. Like correlations obtained at successive times are combined using all postulates of Doppler shift to produce complex values in range-Doppler bins for each VRX. Beamforming over the VRXs then takes place for each range-Doppler bin.
A transmit signal echoed from a reflecting object and received and correlated by a receiver results in a digitized radar echo signal that is the same as would have been produced by a transmit and receive antenna co-located at coordinates which are the mean of the actual transmit and receive antenna coordinates. Such signals, called virtual receiver (VRX) signals, are further combined according to delay and Doppler shift to resolve targets in the four dimensions of azimuth, elevation, range and Doppler.
When the convention for VRX antenna positions is that they are deemed to be located at the mean of the associated physical transmitter and receiver antenna coordinates, a spacing of VRX antennas equal to a quarter wavelength produces a beam pattern which can be scanned over +/−90 degrees, that is, a hemisphere, without grating lobes appearing. An alternative convention is that the VRX antennas are deemed to be located at the sum of the associated TX and RX coordinates, in which case the grating lobe-free spacing is a half wavelength.
When a grating-lobe-free antenna spacing is used, the total antenna aperture is limited by the number of VRXs, that is, by the total acceptable radar complexity. For a given maximum complexity, therefore, the angular resolution can be increased by using wider VRX antenna spacings and tolerating grating lobes. Special techniques are described herein to render grating lobes benign in order to facilitate the use of wider VRX spacings for greater angular resolution.
Range resolution is limited by the bandwidth used. The instantaneous bandwidth is limited by the ability of A-to-D converters to digitize the receiver output. Herein, techniques using burst-to-burst frequency hopping are described to improve the range resolution by combining correlations from a number of instantaneously narrow-band signals that can be digitized by available A-to-D technology, thereby achieving a range resolution commensurate with the whole frequency-hop span.
To improve the angular resolution for a given processing complexity according to one aspect of this invention, the transmit and receive antenna arrays are configured such that the corresponding VRX coordinates are spread in the Azimuthal and Elevation directions in order to mimic a much larger antenna aperture, and the spreading is deliberately irregular in order to minimize sidelobes and grating lobes. Co-filed and commonly owned patent application Ser. No. 17/582,437, entitled “Sparse Antenna Arrays for Automotive Radar,” describes how sparse arrays are constructed to give minimum sidelobe levels, and is hereby incorporated by reference herein in its entirety.
The VRX coordinates may lie on regularly spaced grid points such as a quarter-wave-spaced grid, but not all grid points are necessarily populated with an associated VRX. Such an array is called a “sparse array” and the following steps may be used to reduce and tolerate the array pattern sidelobes that are produced by a sparse array:
(1). Differential beamforming may be used wherein, after resolving VRX signals by range and Doppler shift, products of signals corresponding to the same range and Doppler shift from different VRXs are multiplied (one being complex-conjugated) to form Dyads, also called differential virtual receiver signals (DVRX signals), and the Dyads are weighted and combined using different direction-related phase shifts to produce a set of beam signals. Targets appear as strong beam signals at particular azimuths and elevations when VRX signals resolved into the correct range and Doppler bins for that target are used to form the DVRX signals.
The product of one VRX signal with the conjugate of another gives a Dyad containing a target echo phase related to the difference in the coordinates of the two VRXs. Such a signal can be regarded as having arisen from a differential virtual receiver or DVRX with the difference coordinates. The exemplary antenna array structure used for differential beamforming ensures that DVRX coordinates are as far as possible unique with as few as possible coincidences and well spread to give a desired differential antenna pattern and angular resolution. In differential beamforming, the loss which would normally be expected in multiplying two noisy signals together is compensated by the fact that the number of DVRXs combined is nearly equal to the square of the number of VRXs. In an exemplary system of 16 transmitters and 16 receivers, the number of VRXs is 256 and the number DVRXs may be a little less than 2562 or 65,536.
(2). Differential beamforming as described in (1) is equivalent to and may be performed by N instances of VRX beamforming where N is the number of VRXs and where the VRX signals are weighted by a different weighting function for each of the N VRX beamformings, the moduli-squared of the results of the different VRX beamformings then being further weighted and combined to produce a differentially beamformed result. Note that the magnitude of the further weightings can be absorbed into the different weighting functions, but not their signs, which would be lost in the modulus-squaring operation.
According to an aspect of the exemplary differential beamforming embodiment, the different weighting functions may be Eigenvectors of the N×N matrix which contains the weightings of the Dyads and the further weightings are the associated Eigenvalues. In another aspect of the present embodiment, recognizing that the virtual location of a DVRX corresponding to the product of a VRX signal with itself conjugated is (0,0) and that that location is populated N times, those Dyad weights may be reduced by the factor N in the matrix to give equal weighting to DVRX locations. More generally, if any DVRX location is repeated, the corresponding Dyad weights in the N×N matrix may be reduced by dividing by the number of repeats to produce uniform weighting of each DVRX location. Other than uniform location weighting may also be contrived if beneficial in reducing sidelobes. The net result is that the N×N matrix so contrived will have distinct Eigenvectors and Eigenvalues that can be precomputed and embedded in the design of an exemplary embodiment.
(3). Simplified differential beamforming may be performed, which is a version of (2) above in which fewer than N, for example two, VRX beamformings are performed using different VRX signal weighting functions and the results combined. In the reduced case of only two VRX beamformings using weighting functions denoted herein by Gplus and Gminus, the weighting functions may be scaled so that the moduli-squared or just the moduli of their results can be directly subtracted with no further weighting. Note that according to another aspect of the present embodiment, it was found that subtracting the moduli of the Gplus-weighted VRX beamforming and the moduli of the Gminus-weighted VRX beamforming can produce lower worst-case sidelobes than subtracting the moduli-squared, because the difference in the moduli is converted to decibels by a 20 Log10(x) operation in contrast to the 10 Log10(x) function for the difference in the moduli squared. In another exemplary variant, two or more beamformings are performed using different weighting functions and the minimum of corresponding beams taken. The weighting functions are chosen to give identical main lobe gain but produce different lobes, and the minimum sidelobe level for each direction is thus obtained.
(4). In (3) above, the weighting functions Gplus and Gminus are no longer necessarily constrained to be the Eigenvectors of any matrix, but may be optimized by any suitable optimization technique such as Monte Carlo, or the method of steepest descent using gradients, to produce the most desirable antenna pattern, typically that with the lowest worst case sidelobes.
The resolution of VRX signals into different range and Doppler bins is carried out before beamforming, and then any of the above beamforming methods may be applied to any or all range-Doppler bins to resolve targets in each range-Doppler bin by boresight.
Resolution by range is performed by correlating a segment of received VRX signal samples with the corresponding segment of transmitted signal samples to obtain a complex number for each delay between the transmit samples and the received samples. The transmitted signal is modulated with binary bits using a form of OQPSK, preferably raised cosine binary FM as described in commonly owned U.S. Pat. No. 10,191,142 and entitled “Digital frequency modulated continuous wave radar using handcrafted constant envelope modulation,” which is hereby incorporated by reference herein in its entirety.
Complex correlation results are then obtained for different numbers of bits delay between the transmitted signal samples and the received VRX signal samples, and possibly for fractional bit delays by correlating with several sample-shifts per bit.
The Doppler frequency resolution is of the order of the reciprocal of the total time over which such segments are collected, called the scan time. Doppler analysis may comprise performing a Fourier transform, such as an FFT, across a set of like-range correlation results calculated from bursts transmitted at successive times.
Doppler shift is caused by target velocity (×2) which equals rate of change of go-and-return range. When the Doppler frequency is high due to a high target velocity relative to the radar, a target echo may not be in the same range bin over the entire time period over which burst segments are collected for Doppler analysis, a phenomenon called “range walking” which blurs both Doppler and range resolution. A special Doppler analysis is described in which the range-walking is predicted based on each Doppler shift being analyzed, so that Doppler analysis takes place over a sliding set of range bins to compensate for range walking for each Doppler shift independently. The sliding between range bins is preferably done by interpolating between adjacent range bins to obtain smooth sliding, or alternatively by jumping to an adjacent bin when it is predicted to have become the principal one that would contain the target echo. The need for compensation for range-walking during Doppler analysis may be reduced by systematically phase-retarding the frequency reference used for transmit signal generation (for a forward looking radar with positive forward velocity) and phase-advancing the frequency reference used for receive local oscillator generation and sampling. This is termed “removing eigenvelocity” such that the Doppler shift depends only on the target velocity and not the target-to-radar relative velocity. Thus, a speedometer signal may be input to the radar to facilitate such eigenvelocity compensation.
Because range resolution is related to bandwidth, the resolution may be improved by causing the signal to probe a wide range of frequencies during each scan time. This may be done by frequency hopping between different transmit/receive periods. Frequency hopping is carried out either by digitally applying phase ramps to the transmit signal, or by taking a time-out to change the synthesizer frequency and then resuming the alternating transmit/receive format, or a combination of both. When frequency shifts are performed by digital phase ramping, the transmit and receive sample rates are high enough to represent both the bit modulation and the frequency shift, so there are many samples per bit. Range correlations are performed for each transmit/receive period in sample shifts of this elevated sample rate, thus obtaining range correlations in finer delay steps than one bit and combined from one Tx/Rx period to another so as to obtain a range resolution inversely proportional to the total bandwidth over which hopping occurs. Moreover, a Doppler resolution is obtained in frequency steps that are the reciprocal of the total time spanned by the frequency hop pattern, called the scan time.
Transmit bursts are filled by modulating the RF carrier with a digital code. The code should be such as to minimize cross-correlation between different range correlations and between different transmitter codes. It is described how this achieved by selecting bits from an M-sequence to fill the bursts with code modulation. The bits may be selected from time-offset parts of the M-sequence according to the frequency hop deviation from a mean frequency, irrespective of the order in which the hops are transmitted. Different transmitters use the same M-sequence with greater time offsets so that no two range correlations for any transmitter are performed with the same shift of the M-sequence. Such linking of code-offset to frequency offset is found to reduce unwanted range-to-range or Doppler-to-Doppler cross correlations.
When hopping is carried out by a combination of digital phase ramping for smaller frequency offsets combined with synthesizer side-stepping for larger offsets, the sample rate increase is only commensurate with the instantaneous transmitted bandwidth, that is with the digital ramping part of the frequency hopping. However, to get the advantage of the full hop-bandwidth, samples are required at a rate commensurate with the full bandwidth. In this case, the receive sample stream may be upsampled using FFT interpolation as part of the range correlation operation, which uses cyclic convolution. Finally, having obtained a set of range correlations and carried out a range-walking-compensated Doppler analysis to obtain a set of VRX signals per range and per Doppler, beamforming is carried out over the set of VRX signals obtained for each range-Doppler combination to determine the strongest signal azimuth and elevation using coarse beamforming, and further refines the angular position of the strongest signal so-determined by examining a region around the coarse position using fine-resolution beamforming.
Using the refined angular position and the determined signal complex amplitude, the illumination of the VRXs that gave rise to that target signal is determined and subtracted, where prestored calibration values for the phase and amplitude mismatch of the VRXs in different directions may be employed, as well as potential modeling of the effects of null-steering. The calibration-corrected VRX values for the strongest target are subtracted from the actual VRX values and thus remove both the strongest signal and any sidelobes thereof. Beamforming is then repeated on the residual VRX signals to determine the second strongest signal, and so forth to discover all targets of interest for the given range/Doppler bin. The processing of a given range-Doppler bin is terminated by a STOP criterion which determines when residuals of subtraction no longer reliably indicate the presence of even weaker targets than those already found. The processing is repeated in principle for all range/Doppler combinations, but processing may be curtailed by sparsification, which can use the history of previous scans to indicate where targets of interest lie and do not lie. Successive subtraction is also curtailed as mentioned above by implementing a stop test to determine if residual signals are real, noise, or artefacts.
All of the above processing may be carried out using dual-polarization receive antennas and duplicated processing chains up to a point in the chain where interference can be discriminated from wanted signals by polarization and partly or completely eliminated thereby. The wanted signal polarization is assumed to be the same as that transmitted (or opposite hand, if circular). Typically, 45-degree linear polarization has the advantage that an oncoming interfering radar of the same type will be cross-polarized. Circular polarization has the advantage that an oncoming radar of the same type will have the same polarization as that transmitted while wanted target echoes have the opposite polarization to that transmitted. Since polarization is not accurately maintained when reflected from an irregular object, there is still a gain to be had in adaptive polarization processing.
A dual-polarization receive antenna can comprise co-located crossed dipoles. Alternatively, the crossed dipoles can be in offset locations, thus giving rise to different VRX arrays for the two polarizations. The advantage of that is that the polarization of grating lobes is different than the polarization of the main lobe, thus providing extra grating lobe suppression.
To improve the mutual interference characteristics between different radars in different vehicles beyond that achievable by different codes, polarizations and frequency hop patterns, the radar transmit antennas may be driven in such a way as to produce zero illumination (nulls) in specified directions. Since the transmitters do not transmit the same code, a novel method to achieve such nulls is described whereby the signal that would be received at a specified position is calculated and then the negative of it is transmitted in a narrow beam focused on that position using the same transmitters and antennas. The receive antennas can also be phased so as to produce nulls in specified directions. The effect of transmit or receiver nulling or both is modelled in the signal processing when a detected target signal is subtracted from the receive signals to reveal a weaker target. The position distortion of a target lying near a null may also be modelled and corrected.
Embodiments of the present invention thus provide for a radar system that provides for greater immunity to interference from other radar systems, particularly from chirp radars. Exemplary embodiments also provide “good citizen” measures that help to reduce interference that might be caused to other radar systems.
An exemplary radar system providing the benefits of the preceding paragraph includes dual polarization receive channels in the expectation that interference will be a different polarization than the desired radio signals transmitted by own transmitters and reflected from targets in the environment. The polarization of interference can, in one implementation, be determined in a quiet period of own radar and thereafter used to adapt the receive antenna polarization to minimize the ratio of unwanted to wanted signals. The radar system also provides improved signal handling dynamic range to avoid receive channels saturating at the A-to-D converter stage before the radio signal has reached the digital signal processing domain. Signals that are digitized and recorded in memory can be processed “offline,” that is retrospectively, in different ways or even in time-reversed sample order to best detect wanted targets amid interference.
In an aspect of the present invention, an exemplary radar system embodiment includes a transmit pipeline that includes a plurality of transmitters. The radar system also includes a receive pipeline that includes a plurality of receivers. The transmitters are configured to transmit radio signals. The receivers are configured to receive radio signals that include the transmitted radio signals transmitted by the transmitters and reflected from objects in the environment. The receive pipeline is configured to provide interference immunity from interfering radio signals transmitted by other radar systems.
In an aspect of the present invention, the interfering radar systems may be chirp radars.
In another aspect of the present invention, the transmit pipeline and/or the receive pipeline is configured to avoid transmitting radio signals that interfere with the other radar systems.
In a further aspect of the present invention, the receive pipeline comprises exemplary dual polarization receive channels. The interfering radio signals are a different polarization than the radio signals transmitted by the transmitters and reflected from targets in the environment.
In yet another aspect of the present invention, the receive pipeline is configured to provide improved signal handling dynamic range to avoid receive channels saturating at the A-to-D converter stage before the radio signal has reached the digital signal processing domain.
In another aspect of the invention, Doppler analysis is performed by a method that compensates for range-walking.
In yet another aspect of the invention, fine range resolution is achieved by using a total bandwidth during a radar scan time comprising many alternating transmit-receive burst periods by changing the frequency used for a burst period either by digital phase-ramping or by side-stepping a frequency synthesizer that generates the transmit/receive center frequencies.
In another aspect of the invention, eigenvelocity may be removed by reducing the transmit frequency reference and increasing the receive frequency reference according to the radar's own forward speed, or vice versa for a rear-looking radar.
All information determined by the radar regarding range, azimuth, elevation and Doppler of target objects is output to a higher level of processing which may track targets from scan to scan and provide collision avoidance warnings or actions.
These and other objects, advantages, purposes and features of the present invention will become apparent upon review of the following specification in conjunction with the drawings.
The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.
Referring to the drawings and the illustrative embodiments depicted herein, wherein numbered elements in the following written description correspond to like-numbered elements in the figures, a radar system provides for greater immunity to interference from other radar systems, particularly chirp radars. The exemplary radar system also provides “good citizen” measures that help to reduce interference that might be caused to other radar systems. The radar system will include exemplary dual polarization receive channels in the expectation that interference will be a different polarization than the desired radio signals transmitted by own transmitters and reflected from targets in the environment. The radar system also provides improved signal handling dynamic range to avoid receive channels saturating at the A-to-D converter stage before the radio signal has reached the digital signal processing domain.
As illustrated in
An exemplary radar system operates by transmitting one or more signals from one or more transmitters and then listening for reflections of those signals from objects in the environment by one or more receivers. By comparing the transmitted signals and the received signals, estimates of the range, velocity, and angle (azimuth and/or elevation) of the objects can be estimated.
There are several ways to implement a radar system. One way, illustrated in
A radar system with multiple antennas, multiple transmitters, and multiple receivers is shown in
The radar system 300 may be connected to a network via an Ethernet connection or other types of network connections 314, such as, for example, CAN-FD and FlexRay. The radar system 300 may also have memory (310, 312) to store software used for processing the signals in order to determine range, velocity, and location of objects. Memory 310, 312 may also be used to store information about targets in the environment. There may also be processing capability contained in the ASIC 316 apart from the transmitters 203 and receivers 204.
The description herein includes an exemplary radar system in which there are NT transmitters and NR receivers. Each transmitter transmits a different code and each receiver correlates with each transmitter code to produce NT×NR virtual radar signals, one for each transmitter-receiver pair. For example, a radar system with eight transmitters and eight receivers will have 64 pairs or 64 virtual radars (with 64 virtual receivers). When three transmitters (Tx1, Tx2, Tx3) generate signals that are being received by three receivers (Rx1, Rx2, Rx3), each of the receivers is receiving the transmission from each of the transmitters reflected by objects in the environment. Each receiver can attempt to determine the range and Doppler of objects by correlating with delayed replicas of the signal from each of the transmitters. The physical receivers may then be “divided” into three separate virtual receivers, each virtual receiver correlating with delay replicas of one of the transmitted signals.
There are several different types of signals that transmitters in radar systems employ. A radar system may transmit a pulsed signal or a continuous signal. In a pulsed radar system, the signal is transmitted for a short time and then no signal is transmitted. This is repeated over and over for a length of time termed the scan time. The processor collects and processes everything received over the scan time which is chosen to be long enough to receive enough target energy to detect reliably and to be able to resolve Doppler with fine precision. A typical scan time range is between 10 ms and 30 ms. A typical transmit burst length is 2 μs and is followed by a 2 μs receive period. There are thus an exemplary 4,095 transmit/receive periods in a typical 16 ms scan time. Shifts of a 4,095-bit M sequence may thus be used to fill the 4,095 transmit bursts with digital code modulation.
When the signal is not being transmitted, the receiver listens for echoes or reflections from objects in the environment. In some radars a single antenna is used for both the transmitter and receiver and the radar transmits on the antenna and then listens to the received signal on the same antenna. This process is then repeated.
In a continuous wave radar system, the signal is continuously transmitted. There may be an antenna for transmitting and a separate antenna for receiving.
Another classification of radar systems is in the modulation of the signal being transmitted. A first type of continuous wave radar signal is known as a frequency modulated continuous wave (FMCW) radar signal. In an FMCW radar system, the transmitted signal is a continuous sinusoidal signal with a varying frequency. By measuring a time difference between when a certain frequency was transmitted and when the received signal contained that frequency, the range to an object can be determined. By measuring several different time differences between a transmitted signal and a received signal, velocity information can be obtained. If the frequency changes smoothly in a ramp fashion, the radar may be known as a chirp radar.
A second type of continuous wave signal used in radar systems is known as a phase modulated continuous wave (PMCW) radar signal. In a PMCW radar system, the transmitted signal from a single transmitter is a continuous sinusoidal signal in which the phase of the sinusoidal signal varies. Typically, the phase during a given time period (called a chip period or chip duration) is one of a finite number of possible phases. The spreading code could be a binary code (e.g., +1 or −1). A spreading code consisting of a sequence of chips, (e.g., +1, +1, −1, +1, −1 . . . ) is mapped (e.g., +1−>0, −1—>1) into a sequence of phases (e.g., 0, 0, 90, 0, 270 . . . ) that is used to modulate a carrier signal to generate the radio frequency (RF) signal. The spreading code could be a periodic sequence or could be a pseudo-random sequence with a very large period, so it appears to be a nearly random sequence. Herein, a particular choice of spreading code is shown to provide advantages, namely, successive bits of an M-sequence equal in length to the number of transmit bursts in the scan period are placed as the first bit of each successive burst and then a shift of them M-sequence is placed as the second bit of each burst and so on until the burst if filled with a desired number of bits. The resulting signal has a bandwidth that is proportional to the rate at which the phases change, called the chip rate, which is the inverse of the chip duration=1/T. By comparing the return signal to the transmitted signal, the receiver can determine the range and the velocity of reflected objects.
In one implementation, a burst of transmit signal (e.g., a PMCW signal) is transmitted over a short time period (e.g., 1 microsecond) and then turned off for a similar time period. The receiver is only turned on during the time period where the transmitter is turned off. In this approach, reflections of the transmitted signal from very close targets will only comprise the last few bits transmitted because the receiver is not active during a large fraction of the time when the reflected signals are being received. However, since nearby objects produce strong reflected signals, enough energy is received in those few bits per burst to detect them. Thus, it is desirable that the first received bit, and being the last bit transmitted and reflected from the nearest object, collected one from each burst in the scan, should as far as possible be orthogonal to the set of second receive bits collected over the scan and representing the second nearest reflecting object. The latter is the purpose of using M-sequences spread over the scan, which will be described in greater detail in the following paragraphs.
The radar sensing system of the present invention may utilize aspects of the radar systems described in U.S. Pat. Nos. 10,261,179; 9,971,020; 9,954,955; 9,945,935; 9,869,762; 9,846,228; 9,806,914; 9,791,564; 9,791,551; 9,772,397; 9,753,121; 9,599,702; 9,575,160, and/or 9,689,967, and/or U.S. Publication Nos. 2018/0231656, 2018/0231652, 2018/0231636, and 2017/0309997, and/or U.S. provisional applications, Ser. No. 62/486,732, filed Apr. 18, 2017, Ser. No. 62/528,789, filed Jul. 5, 2017, Ser. No. 62/573,880, filed Oct. 18, 2017, Ser. No. 62/598,563, filed Dec. 14, 2017, Ser. No. 62/623,092, filed Jan. 29, 2018, and/or Ser. No. 62/659,204, filed Apr. 18, 2018, which are all hereby incorporated by reference herein in their entireties.
Digital frequency modulated continuous wave (FMCW) and phase modulated continuous wave (PMCW) are techniques in which a carrier signal is frequency or phase modulated, respectively, with digital codes using, for example, GMSK. Digital FMCW radar lends itself to be constructed in a MIMO variant in which multiple transmitters transmitting multiple codes are received by multiple receivers that decode all codes, as mentioned above. The advantage of the MIMO digital FMCW radar is that the angular resolution is that of a virtual antenna array having an equivalent number of elements equal to the product of the number of transmitters and the number of receivers. Digital FMCW MIMO radar techniques are described in U.S. Pat. Nos. 9,989,627; 9,945,935; 9,846,228; and 9,791,551, which are all hereby incorporated by reference herein in their entireties.
As illustrated in
In order to achieve the accuracy of, for example, a 10-bit conversion, the amount of interference subtracted in the analog domain has to be added back in in interference re-adder 480 with high accuracy. The method envisaged to do this is that each level (perhaps 16 to 64 levels) of each of the coarse D-to-A converters 460 will have an auto-learned digital word to describe it which will be adaptively learned to a high accuracy so that when that level is subtracted in the analog domain in unit 450 an accurate digital value will be added back in the digital interference re-addition unit 480.
After the A-to-D converters 470 of limited word length, the digital signal processing thereafter can have whatever word length is needed to avoid digital saturation. The analog interference subtraction should occur as early as possible in the analog path. In one exemplary embodiment, the analog interference subtraction is performed after down-conversion to the (1,0) baseband, as subtraction is more complex and more power consuming if the predictions are mixed up to 80 GHz for subtraction in the RF domain; and moreover, that has been found to a give a significant noise factor degradation.
For dual-polarization receivers, the balanced dual-polarization antenna (V,H) connection can comprise four ball-bonds in a square. When arranged in the above way, the signals are nominally spatially orthogonal and any residual coupling between them is unimportant given that the dual polarization antenna may be crossed-dipoles for example.
With the availability of the dual-polarization signals from NR receivers and both polarizations, the digital radar signal analysis can comprise, as described in the incorporated patents, of an FFT-based scheme for burst-by-burst correlation of the received signal in each channel with the known transmitter codes. If this is done, note that transmitting GMSK (or UMSK as defined in the incorporated patents) using the GSM-type 90-degree per bit pre-rotation coding reduces the correlation to correlating a complex received signal with a real template, rather than a full complex correlation. There might however be even faster and less power consuming correlation methods that need no multiplies, which can be used when the same received signal is to be correlated with many binary codes (many shifts of many different codes is a large number of binary correlations). These are based on the fact that the number of possible bit patterns of finite length, such as 8, is 256 times however many codes are correlated with, and since the same 256-bit patterns will reoccur many times in many codes, 8 signal samples need be combined only once in all 256 ways, and by doing it in Gray code order, only one new addition is required for each combination. The latter alone is an 8:1 speed up and is disclosed in expired U.S. Pat. No. 5,931,893 entitled “Efficient Correlation over a Sliding Window.” Other correlation methods are described herein when the correlation is performed using multiple samples per bit in frequency hopping systems to obtain finer ranger resolution.
There is an advantage in the per-pulse FFT correlation method. That is, when the signal is temporarily available in the frequency domain, narrow-band interference stands out and can be clipped, nulled or otherwise mitigated.
An advance on interference nulling in the spectral domain only is to perform a rough beamforming over all antenna channels for each FFT component. A rough beamforming over, for example, 16 receive channels can be a 16-point FFT. Whatever is used, it should be an easily invertible, information lossless transform, but not necessarily an orthogonal transform like the FFT. The combination of a 256-pt FFT for correlation with a 16-pt FFT over corresponding spectral components of the 256-pt FFT is in fact a 256×16 2-D FFT, which is a 2,048 pt Walsh-Fourier transform. The difference between a 2,048 pt Fourier transform and a Walsh-Fourier transform is that the former has twiddles at each stage while the latter omits twiddles between certain stages corresponding to the “Walsh” part. So, there are no twiddles between the 256 pt correlation FFT and the 16 pt beamforming FFT.
After a rough beamforming of each FFT component, the signal is in the 3D domain of spectrum and space. Nulling out big components at particular frequencies and particular spatial directions removes less of the wanted signal energy, thus causing less loss of wanted target detection sensitivity and producing fewer artefacts. Moreover, the directions from which other-radar interference is received are likely to be long-term and thus carry over from one burst to another. Likewise, in a dual-polarized radar, the principal interference polarization can be determined per frequency and coarse direction and is likely to be stable for at a least a few 1 μs bursts. Therefore, the directions and polarizations to de-weight can be determined per spectral component, resulting in substantial interference mitigation with little loss of wanted signal. This technique of nulling components of a 2,3 or even 4-dimensional transform) over different domains (e.g. frequency, azimuth, elevation and polarization) can be considered to be a further generalization of the technique described in expired U.S. Pat. No. 5,831,977, entitled “Subtractive CDMA system with simultaneous subtraction in code space and direction-of-arrival space.” The advantage of nulling in a multiple domain transform space is that a smaller fraction of the total transform components is deleted to reduce interference and thus there is less wanted signal distortion upon returning to the original domains with an inverse transform.
Thus, the addition of polarization as an additional domain (even though the order of its transform is only 2) provides another dimension in which to segregate interference. Since the polarization of other radar interference is also likely to be long-term stable, it can be determined solidly and then the following algorithm can be used to annul it to great advantage even though the polarization domain has only two points:
For each spatio-spectral component to be cleaned up, form αV+βH where V and H are the horizontal and vertical components (or other cross-polarized components such as +/−45), such that the resulting polarization, which is determined by the ratio of α to β, is orthogonal to the interferer's polarization, but the scaling of α and β is chosen to leave the signal component unattenuated; at least within reason—if the polarizations of the signal and interferer were close, α and β would become large, magnifying noise, so there is in that case a compromise between noise magnification and signal loss that is known from many other similar problems.
So, using all 4 domains—spectral, 2 spatial and polarization, substantial reduction of interference from other radars can already be obtained at the per-burst stage. Note that it is also known to divide a burst into a smaller number of periods corresponding to, for example, 256 samples, a convenient FFT size, which is then called a “pulse,” a burst comprising several such pulses. Interference excision in the 4 domains can occur on a per-pulse basis, and then, while still in the transform domain, the results are combined and subjected to a single inverse transform. It is possible that only a single polarization, the above weighted combination of V and H, need be passed on to be accumulated over all pulses and processed further in Doppler analysis and eventual beamforming, thus restricting the extra complexity of dual polarization to the early stages of processing. Inverting the rough beamforming needs to be done only once on the accumulated pulse transforms and likewise the inverse 256-point FFT, the outputs of which are signals segregated by range.
The additional complexity introduced for spatio-spectral-polarization interference nulling is thus a doubling of the number of correlation FFTs to be performed, as there is one for each polarization. This is needed on the assumption that different interferers in different parts of the spectrum or lying in different directions might have different polarizations, so even though their polarizations may be known in advance, if they are not the same, polarization combination cannot be done ahead of the FFT and rough beamforming FFT; rather, the interferers have to be separated by spectrum and direction in order to apply a polarization nulling adapted to each one.
In the exemplary embodiment illustrated in
Thus, one exemplary embodiment disclosed herein includes an exemplary radar system that provides for greater immunity to interference from other radar systems, particularly from chirp radars. The exemplary radar system also provides “good citizen” measures that help to reduce interference that might be caused to other radar systems. A first technique disclosed to achieve the latter is the use of transmit nulling to place nulls in the direction of other oncoming radars such that they are not illuminated by our radar's transmissions.
Since the MIMO radar transmits different uncorrelated codes from each transmitter, there is no way that they alone form a beam or a null. However, given the direction of an oncoming radar, the composite signal that an object in that direction would receive from our own transmitters can be calculated by applying the conjugate of the phase factors that are used to form receive beams in that direction, and which are likely already available for the latter requirement and possibly already stored in a look-up table for many thousands of different directions to avoid real-time sine/cosine calculations. Moreover, the phases received from the interfering radar can be determined by correlating the received interference as between the receive antennas and, using transmit and receive antenna calibration information, the transmit phases necessary to place nulling beam on the same location can be determined. Having determined the composite signal that would be received at the oncoming radar, a novel transmit nulling technique comprises adding the negative of it, properly phased, to all transmitters so as to form a beam pointed only at the oncoming radar and which will thus null out all of our radar's transmissions only at that point, leaving wanted targets in different locations more or less still illuminated. Since each transmitter is now transmitting the sum of two signals, its normal code plus the nulling signal, it has to be a linear transmitter even if the code modulation alone is constant-envelope. However, the linearity requirement is not excessive if seeking only of the order of 15-20 dB of interference mitigation. Typically, the transmitter would be backed off 5 dB from saturation and the resulting efficiency loss is tolerated while interference mitigation operation is active.
Assuming for now that “beam domain” comprises a number of different narrow beam directions, to prevent illumination of targets in that direction that beam signal is set to null before using IFFT 1302 to transform back from beam domain to antenna signal domain. The signal outputs of IFFT 1302 are then D-to-A converted and up-converted to the transmit frequency and amplified to a transmit power level in modulators and PAs 1301, and then transmitted from respective antennas 1300.
As pointed out above, this method must be modified if the transmit antenna spacings are not regular, as an FFT/IFFT does not then provide good beamforming. For clarity, the matrix formulation of a more general method is illustrated as
If UL×N is the collection of L steering vectors from the N transmit antennas to the L desired null directions and CN×1 is a vector of code bits, then what would be received at the L null locations is given by UL×N CN×1, which is an L×1.column vector.
Now multiply that by VN×L and subtract from the code vector to obtain [IN×N−VN×L UL×N]]CN×1.
Now when that is transmitted, what is received in the null directions is UL×N[IN×N−VN×L UL×N]]CN×1=[UL×N−UL×N VN×L UL×N]]CN×1.
Now letting VN×L=U*N×L [U*N×L UL×N]−1, the above becomes [UL×N−UL×N U*N×L [U*N×L UL×N]−1 UL×N]]CN×1≡0 as the inverse matrix cancels with UL×N U*N×L leaving[UL×N−UL×N]] which is zero.
However, what is received in any collection of directions U′ that are not the null directions is [U′L×N−U′L×N U*N×L [U*N×L UL×N]−1 UL×N]]CN×1.
Now U′L×N U*N×L [U*N×L UL×N]−1 does not cancel to unity.
It may be noted that, for orthogonal null directions, the inverse matrix [U*N×L UL×N]−1 is a diagonal matrix of values 1/N, ( 1/16 here), which provides the necessary scaling for the nulling beam to be of unity gain. In general this matrix provides the correct scaling to generate deep nulls where desired.
The oncoming radars receive phased combinations of our transmitted codes given by VC. The result is a new column vector that depends on the code bits and the null directions.
Since the code bits are only +1 or −1, this suggests a way of precomputing the signals to be transmitted and storing them in a look up table for use as long as the null directions are constant, maybe for hundreds of transmit bursts i.e. 100's of microseconds during which time an oncoming radar will hardly have changed bearing. Note that, given linear transmitters, there is no reason not to use a linear modulation such as OQPSK. For OQPSK, only the output of
Referring to
The receive antennas may also be combined in null processing to reduce received interference from oncoming radars of the same or different type. Since interference does not separate by range or Doppler, receive nulling is performed before range or Doppler computations. In one implementation, the receiver A-to-D outputs are captured during a period that own transmitters are silent. Such periods may occur for other reasons such as synthesizer sidestepping in frequency hopping modes. The D-to-A outputs are then processed to determine the principal directions (and polarizations, if dual polarization receivers are used) from which interference is being received. If receiver channel amplitude differences have been calibrated out, this analysis yields an interference phase for each channel. This is used to construct U,V vectors in the same way as for transmit nulling, that is, a narrow beam is formed focused on the interference by multiplying the receiver signals with vectors that are the conjugate of the received phases (receive steering vectors) and then an appropriate amount ( 1/16 here) is subtracted from each of the receive antenna signals before performing range correlation and Doppler processing.
Bit 2001-1 is the second to last bit transmitted in the first burst and is received overlapping bit 2000-1 from a target 1-bit time of go-return delay further away. Likewise bit 2001-2 is received from that second nearest target as an echo of the second last transmitted bit of the burst. It is desirable that, when the receiver correlates received samples 2000-1 . . . 2000-n over the whole scan that the correlation with bits 2001-1 . . . 2001-n over the whole scan should as far possible be zero. This is achieved by choosing bits 2000-1 to 2000-n to be a first shift of an M-sequence and bits 2001-1 . . . 2001-n to be a second shift of the same M-sequence, as it is known that maximum correlation between different shifts of an M sequence is −1/M. Therefore, the number of bursts n over which correlation is performed, also called the scan period, is chosen to be the length of an M-sequence, for example 4,095. For 2 μs Tx and 2 μs Rx, the TX/RX period is 4 us and the scan period is 4,095×4 us or approximately 16 ms.
Doppler shift due to a moving target causes the phase of like bits in successive received bursts such as 2000-1, 2001-1 . . . 200n−1 to rotate systematically. Thus, the samples are derotated by amounts corresponding to hypothesized Doppler shifts before accumulating across the scan, thereby obtaining range correlations for a complete set of Doppler hypotheses. The results form a 2D data set called the range-Doppler bins. For later echoes that provide two or more receivable bits during the receive period, the correlation of those bits can be accumulated over a burst without relative Doppler phase untwisting as the Doppler phase rotation during a 2 μs burst can be neglected. Thus, partial correlations are first obtained over one burst at a time, corresponding to the first received bit (2000-1) for the earliest echo, the sum of the first and second received bits (2000-1 plus 2001-1) for the second earliest echo, and so forth, where “correlation” implies that the known bit polarities of the M-sequence are removed before accumulation to ensure that all contributions for a valid target echo are additive. Then the partial correlations from different bursts are combined with all possible Doppler phase untwistings to fill the range-Doppler bins. The operation as just described can be performed by subjecting the partial correlations to a DFT or a FFT, which can employ a weighting function to reduce sidelobes. However, for high Dopplers, the signal echo does not appear in the same range bin across the whole scan, a phenomenon called “range-walking” for which compensation techniques will be disclosed.
The second to last bits transmitted shall be chosen to be a different shift of the same code, for example, the (cyclically) adjacent shift bn−1 . . . b2 b1 bn and so forth. It may seem that the burst contents then just shift through the code from burst to burst. It will be shown later that choosing adjacent bits in the burst to be non-adjacent shifts of the code can reduce residual range-to-range correlations when using frequency hopping. Without frequency hopping however, the range-to-range unwanted cross correlation properties of the M-sequence placed as in
Since it is also necessary to keep the 16 transmitter signals as far as possible orthogonal, this can be done either by reducing the number of bits per burst to say 256, which only uses 1/16th of the available code shifts, leaving the rest for the other transmitters, or else by differentiating the different transmitters by inverting their burst signals using an assigned Walsh code per transmitter. Inverting a burst transmission does not change the correlation of a transmitter signal with an echo of itself, and therefore, does not destroy the good autocorrelation properties of the M-sequence, but renders different transmitters orthogonal or near-orthogonal to each other. Instead of different Walsh codes, different shifts of a different M=4,095 sequence, of which there are several, could be used to impose an overall burst sign change.
In an initial simulation it was noticed that transmitter to transmitter correlations were higher than expected, this was found to be because the last bit transmitted, due to filter tails, has a waveform that merges into a bit beyond the last bit which was always the same polarity. The phase at the end of the last bit was therefore always the same. Since this is the first sample received, the first samples received were the same for all transmitters and this correlation dies out only slowly when using a low bitrate and many samples per bit, such as, 16 bits sampled at 256 samples per bit.
Partial range correlations may be computed per bit or per sample. Thus, a burst may contain 256 bits represented by 16 samples per bit and correlation may be performed for each of the 4,096 samples received over the 2 μs receive period. The partial correlations are computed for each burst as follows:
For the earliest sample received after the end of the transmit burst, the partial correlation is that sample times the conjugate of the last transmitter sample.
The next partial correlation is the product of the first sample received with the conjugate of the second last transmitted sample plus the second sample received times the conjugate of the last transmitted sample, and so forth as shown in
In
S1.T*n
S1.T*n−1+S2.T*n
S1.T.*n−2++S3.T*n and so forth, which are the desired burst-wise partial correlations.
It is well known that cyclic convolution of two sequences can be efficiently performed by multiplying the FFT of one sequence by the conjugate of the FFT of the other and then inverse Fast-Fourier Transforming the result.
In the case of
The 4,096 samples could represent 256 bits at 16 samples per bit, 128 bits at 32 samples per bit, all the way down to, for example, 16 bits at 256 samples per bit or even one bit at 4,096 samples. The number of samples and bits is merely exemplary and is related to the desired granularity of range. For example, correlating with 4,096 samples that span a 2 μs period gives a range granularity of:
0.5*3e8×2e−6/4,096 meters=7.3 centimeters or 3″ approximately.
The range resolution however is not the same as the granularity of calculation but depends on the sharpness of the autocorrelation function of the transmitted signal, which is the Fourier Transform of its power spectrum. When the number of bits per burst is small, the bandwidth is narrow, and the range resolution is much coarser than the granularity of calculation by a factor of approximately the number of samples per bit. Such oversampling of the range however may be useful if an algorithm is used to search for the correlation peak, which would occur after beamforming to raise the signal to noise ratio.
Frequency hopping from burst to burst is a way for spanning more bandwidth over the scan than the bandwidth used by one burst. It is also a way of dodging interference from other, non-collaborating radars. For example, if the burst format is 16 bits sampled at 256 samples per bit, giving 4,096 I,Q values modulated on to the 80 GHz carrier per burst, the I,Q values can be digitally phase-rotated in a phase ramp to digitally create a frequency offset. The phase ramp considered is an integral number m of 2π rotations over the burst. The phase rotation per sample is thus 2 mπ/4,096. Rotations of more than 180 degrees per sample would alias to rotations of less than 180 degrees in the opposite direction and moreover rotations of that magnitude would cause diametric signal transitions in the I/O plane, which are problematic in systems endeavoring to use nearly constant-envelope transmissions. Therefore, to stay well away from that region, the maximum rotation per sample allowed is 90 degrees per sample, so the value of m ranges from −512 to +512 maximum.
With digital phase rotation as a way of frequency hopping, the receiver might need to A-to-D convert the received signal at 4,096 complex samples per burst despite the fundamental bandwidth of the signal being much lower, were it not for the frequency offset. In one implementation, a similar phase ramp can be applied to the receive local oscillator to remove the phase ramp and center the received signal in a narrower bandwidth, allowing some analog narrowband filtering and thus a lower A-to-D conversion rate. Note that the response time of any narrowband analog filtering may result in a delay after the transmitter stops before received signals can be discerned. This ring-down time limitation on minimum range can be alleviated by blanking the filter's poles until after transmission stops e.g., by turning on a shorting MOSFET across capacitors. It can also be alleviated by at least partially restricting the signal bandwidth with digital filters that process the signal in time-reversed sample order. Nevertheless, the impulse of the analog filter must be allowed to build up before any signal is available at full amplitude, limiting the observation of very small delays.
If the A-to-D conversion rate is less than the 4,096 samples per burst proposed for convolution, the collected samples must be upsampled to that number. For example, if there are 32 bits per burst and the receiver samples the signal at 8 samples per bit to obtain 256 samples, then the 256 samples must be upsampled 16:1 to obtain 4,096 samples and the samples of each burst so upsampled shall correctly represent their frequency offsets from the mean.
The ideal interpolator for frequency limited signal samples is to perform a Fourier Transform on the samples and to then perform an inverse transform using a higher order Transform, with the higher order input frequency amplitudes set to zero, to obtain a greater number of output samples than input samples that are still spectrally contained to the spectrum of the original input. Thus, performing a 256-point FFT on 256 samples and plugging the 256-point spectrum into an 8,192 point transform along with 7,936 zeros and inverse Fourier transforming the 8,192-point array, will perfectly upsample the 256 samples to 8,192 samples. Moreover, by plugging the 256 frequency samples into the 8,192-point transform off-center, the desired frequency offset of the burst from the mean frequency of the scan is correctly modelled. It was explained above that the highest offset frequency considered is a phase ramp slope of +/−512 times 211 per 2 μs period. The frequency step size is 211 per 2 μs period, which is 500 KHz. The frequency step size of an 8,192-point transform having a time span of 2 μs is also 500 KHz. If frequency index 4,097 corresponds to zero frequency (DC) in the 8,192 point transform and frequency point 129 of the 256 point transform likewise corresponds to zero frequency, then inserting frequency point 129 from the 256 point transform into point 4,097 of the 8,192 point transform corresponds to zero frequency offset of the burst. If however, the burst phase ramp is m times 211 over the 2 μs period, corresponding to m×500 KHz offset, the frequency index 129 of the 256 point transform shall be inserted into frequency point 4,097+m of the 8,192 point transform, with other points likewise shifted, and zeros inserted elsewhere.
Since an 8,192-point transform is required for cyclic convolution, there is no need to perform an inverse transform at this stage; rather, the 8,192 point transform is multiplied by the conjugate of the Fourier transform of the 4,096 transmitted IQ samples padded with 4,096 zeros, and then the inverse transform is performed to obtain the desired set of partial correlations. If the transmitted waveform was generated with fewer than 4,096 IQ points, then it too may be upsampled using the same technique. If the transmit waveform was generated without digital ramping but frequency offset by modulating the local oscillator phase, then it too may have its frequency offset represented by plugging its smaller transform with the correct offset into the larger 8,292-point transform. In such cases it may be noted that effort can be saved by avoiding multiplies or adds with zero in any of the transform operations.
The above method is illustrated in the block diagram of
Referring to
The I-sample stream enters I D-to-A converter 3000-A and the Q-samples enter Q D-to-A convertor 3000-B. The analog output signals from the D-to-A convertors are low-pass filtered in filters 3001-A and 3001-B. It is common for the digital samples to have been generated in a way that already controls the main part of the spectrum of the modulation so that low-pass filters 3001-A and B can be relatively wide, just to remove sampling frequency components and beyond. These filters are often known as “roofing filters”.
The now smooth analog IQ signals are applied to balanced modulators 3002-A and 3002-B along with Cosine and Sine carrier signals at the final radar frequency in the 80 GHz region. The balanced modulators can be Gilbert cells using MOSFETs fabricated in a 28 nM silicon process, or smaller.
Summing junction 3003 sums the balanced mixer outputs and feeds them to power amplifier 3004 and hence to antenna 3005.
The frequency of the cosine and sine carriers is a center frequency f plus an offset mdf in this method of frequency hopping. In this method, the transmit sample rate, D-to-A convertors and low-pass filters need only have a bandwidth commensurate with the modulation bitrate, and not commensurate with the wider bandwidth of the modulation plus frequency offset mdf. However, note the caution expressed above with regard to the minimum range of targets that can be detected due to longer filter impulse response times in either the transmitter, the receiver or both.
After the transmitted signal is reflected from target 3011 and received at receive antenna 3006, it is amplified in low noise amplifier 3007 and down-converted in balanced mixers 3008-A, 3008-B against 80 GHz cosine and sine carriers to obtain analog (baseband) I,Q signals. It is assumed that the cosine and sine carriers are at the exact same frequency f+mdf as in the case of the transmitter, so that the receiver is centered on the transmit frequency; but this is not imperative. If there is a difference in the transmit and receive local oscillators such that the receiver is not centered on the transmit frequency, it would be necessary to increase the bandwidth of low pass filters 3009-A and B and to increase the sample rate of A-to-D converters 3010-A and B to accommodate the modulation bandwidth plus the transmit-receive frequency offset. bin the case of a forward-looking radar, the transmit frequency may be slightly lowered by the one-way Doppler and the receive center frequency slightly raised by the one-way Doppler due to the radar's own speed, such that reflections from static objects are received with no Doppler shift. Small offsets, such as might be used as mentioned above to remove eigenvelocity, can be ignored.
The transmit and receive frequency offsets can be produced by digitally phase rotating the local oscillators, using balanced mixers in a single-sideband upconvertor configuration, or alternatively can be produced by synthesizer sidestepping. For the latter, a time-out of perhaps 4 to 8 μs must be taken to give the synthesizer time to settle after a frequency change, so this would not be the preferred method to change frequency between every burst, but rather would be used a few times per scan, that is once every 100 or so bursts.
After low pass filtering the received analog I,Q signals in filters 3009-A,B, they are A-to-D converted in 3010-A and B and the results collected in receive buffer memory 3100. Again, note that, if filters 3009-A and B and the sample rate of converters 3010A and B are too restrictive, the attendant long impulse response means that the receiver signal will not be fully developed in time to respond to very short delay echoes from very nearby targets. Methods to minimize this effect by receiver blanking during the transmit period and time-reverse processing were mentioned above.
Because narrowband filters are desirable to suppress other-radar interference, it is conceivable to have a dual-bandwidth receiver whereby the analog IQ signals are sampled in a wide bandwidth using a high A-to-D rate for an initial part of the receive period where early target echoes would be found and simultaneously low pass filtered by narrower band filters 3009A,B and A-to-D converted at a slower rate for sampling later echoes. Since both early and late processing would simply be different instances of the processing described herein, they will not be described separately.
Assuming that the receiver is centered on the transmitter frequency, and that the number of receive samples N1/2 collected over a burst in receive buffer memory 3100 is the same as the number of transmit IQ samples N1/2 collected in transmit buffer memory 3000, then it is desired to perform the zero-padded cyclic convolution of one with the other. Thus, the N1/2 samples of each are zero-padded to N1 samples and subjected to N1-point FFTs 3101 and 3102. The conjugate of the transmit sample FFT values are then multiplied point-by-point with corresponding values of the receive FFT in multiplier 3103. The result is N1 values, which if inverse transformed, would represent partial range correlations without regard to frequency offset. These cannot be accumulated with partial correlations from other bursts using different frequency offsets because frequency change completely alters the phase of an echo due to there being thousands of wavelengths distance to the target and back. To accumulate partial correlations from different bursts therefore, the FFT of their correlations from multiplier 3103 must be frequency shifted according to the frequency offset used and inserted into 8192-point IFFT buffer 3104 with the correct offset m from center. The spectral center or “DC” has been defined above as frequency index 4097 in the 8,192-point buffer and the corresponding DC term of the N1 transform is therefore placed into 8,192-point buffer position 4097+m. As explained above, m ranges from −512 to +512 as an exemplary number. Therefore, the N1 frequency points from multiplier 3103 are inserted into N1 positions of the 8192 point buffer centered on position 4097+m which can range between a center of 4097−512 to 4097+512.
In principle, it is possible to accumulate sets of N1 values additively from different bursts in an 8,192-point buffer before performing an inverse 8,192-point FFT. However, this would only yield range correlations for zero-Doppler targets.
To accumulate range correlations across different bursts taking account of the phase rotations due to different Dopplers, the range correlations have to be accumulated in many different ways corresponding to all Dopplers of interest. The number of Doppler frequencies that can be resolved is equal to the number of bursts in the scan, for example 4,095. Therefore, ultimately the number of range-doppler bins that will be populated is (4,095)2 or over 16 million. It is likely that previous scans would be used to indicate a much-reduced subset of interest in order to save memory and processing, a process known as “sparsification.”
An alternative method of frequency hopping does not necessarily involve changing the local oscillator frequencies by applying a phase ramp thereto, but rather by applying a phase ramp digitally to the transmit IQ samples, which implies that the sample rate is large enough to represent both modulation and the largest frequency offset. In this case the receiver can be of either type but may also not choose to change its local oscillator frequency but simply use a bandwidth and A-to-D convertor rate that is large enough to represent both modulation and the largest frequency offset. It is clear that hybrids of both methods could also be used, where smaller frequency offsets are applied by digital phase ramping and larger offsets are applied by local oscillator frequency changes by either phase ramping or synthesizer side-stepping.
Due to the need to accumulate range correlations over many bursts taking account of different Dopplers, the contents of 8,192-point buffer 3104 are IFFTed for every burst to obtain partial range correlations rather than the Fourier transform thereof. These are held in a 2D memory with dimensions (range,time) where time refers to the time of the burst in which the range correlations were collected. This memory is in principle of size (rounded up) 4096×4096 or 16 megawords complex per VRX. This memory can be an external cache, as specific memory technologies are more cost efficient than combining bulk memory with custom processing. Alternatively, a smaller memory of sparsified range-time bins can be used. In this case the record in the memory comprises the range index, the burst number or time index and a complex correlation value.
The data from cache may be read back for Doppler analysis where an analysis for each range point is performed along the time axis with phase twists corresponding to different Dopplers.
The issue of range-walking has already been mentioned above, whereby a high-speed and thus high-Doppler target may not lie in the same range bin across the whole scan. If no attempt is made to deal with that, a blurring of both range and Doppler resolution results. However, because Doppler shift is rate of change of range, when an analysis is being performed to compute the correlation for a specific Doppler assumption, it can be exactly predicted how the target will move from one range to another, and thus the track through the range-time bins along which values are accumulated can shift range at the predicted times to follow the signal as it “walks” through successive range bins over the scan.
A medium speed Doppler correlation starts at a given point on the left, but knowing that, for the hypothesized speed/Doppler the target will get systematically nearer over the scan, the track moves up to a one-bin shorter range periodically at predicted times, as illustrated by the BLUE track. There is one such BLUE track starting at every possible range on the left. Alternatively, the range walking correlation can be usefully performed backwards. Starting at a given point on the right, accumulation of complex values occurs from right to left with the range increasing as the target gets further way at older times, (if it is oncoming, or the range reduces for older times if it is a receding target), the complex values being phase-un-twisted before accumulation based on the hypothesized Doppler shift. There is one such track for every terminal range on the right, and the advantage is target parameters related to the last range rather than an out-of-date range are successively obtained.
A high-speed, high-Doppler target has its Doppler accumulation track changing likewise through the grid, but shifting range more often, as illustrated by the PURPLE track.
A computer simulation can be performed in the absence of noise to observe the range-walking effect. In practice, a real radar may not have a sufficient signal-to-noise ratio before beamforming over all VRXs to display the effect satisfactorily. In the absence of noise, a simulation can produce a heat map corresponding to the grid of
The axes of
The target amplitude is unity, which is color white. It may be seen that the white stripe migrates to one range bin shorter from the beginning of the scan at the bottom to the end of the scan at the top. The range bin sizes in this simulation were 0.5 ns delay apart, corresponding to one of the 4,086 burst samples and corresponding to about 6″ in go-return-distance or 3″ in range. That this is indeed commensurate with the speed may be seen as follows:
10 MPH=10×63360 inches/hour=10×63360/3600=176 inches per second. The scan period is 4095×4 μs=0.01638 seconds.
Change in range over the scan is 176×0.01638=2.88 inches which is approximately one range bin.
Thus, with range resolution as fine as 3″, since range-walking starts to be significant already at only 10 MPH, range-walking compensation is highly desirable.
After Doppler analysis, the cache memory holds range-Doppler bin values which replace the range-time bin values. Simulation in the absence of noise can also produce 2D heat maps with range-Doppler axes instead of the range-time axes of FIGS. 19,20 and 21. The most dramatic illustration of the benefits of range-walking compensated Doppler analysis is obtained by comparing range-Doppler heat maps for a 250 MPH relative target speed computed with and without range-walking compensation.
In
The preferred method of compensation is to interpolate smoothly between range bins rather than the abrupt switching illustrated in
It was mentioned above that an extra (N+1)th M-sequence bit is needed to fill bursts with N bits and keep different ones of the radar's transmitter signals orthogonal over the scan. This is true even if there are zero bits per scan, that is, the burst is filled with CW. The extra bit is used to determine whether the CW signal is one way up or the other way up as between different transmitters. The extra bit can form an M-sequence over the scan and a different shift of the M-sequence used for different transmitters, thereby ensuring near-orthogonality. Thus, a pure frequency hopping system with no burst code modulation can be envisaged. Each burst generates a phase ramping of the carrier signal corresponding to a chosen frequency offset. The ramping is preferably a phase change of an integral number of 2π radians over the burst, but not more than +90 degrees per sample. Each transmitter preferably uses the same frequency at the same time when the objective is to keep the momentary frequency occupancy over the burst low so as not to interfere with other radars except in the case of a random frequency clash. Thus, each transmitter uses the same phase-ramped signal but inverted or not inverted according to its assigned M-sequence bit for that burst. The correlation of a received echo signal with a transmit signal yields a VRX signal phase that depends on the frequency used for the burst. When the phase ramp changes the transmitter phase by 2 mπ over a 2 μs burst the frequency offset produced is m×500 KHz. Thus, the hop-set comprises frequencies spaced by 500 KHz. If the frequencies are used in order, increasing by 500 KHz each burst, the VRX phase produced will increase by an increment each time also. This systematic phase increase is removed when burst-wise correlations are accumulated according to the block diagram of
If however, the hop-frequencies are not used in order lowest to highest, the resulting phase twist of the VRX signal form an order-scrambled Fourier sequence. The correlation of the scrambled Fourier sequence with the M-sequence is the same as a Fourier component of a scrambled M sequence which could be higher than 1/M. Therefore, in order to preserve the −36 dB cross-correlation between different transmitters, the order of use of M-sequence bits to differentiate them is tied to the order of use of frequencies in the hop set.
The main lobe of the autocorrelation function of pure frequency-hopped CW as described above is shown in
The sidebands of a sine(x)/x) function do not fall off very quickly, as can be seen in
In calculating
When a function shown on for example a ‘scope or spectrum analyzer has wild ripples or noise, sometimes called “grass” because of the traditional green ‘scope trace, a video filter is sometimes used on the ‘scope signal to smooth out the ripples. It would indeed be possible to run a short FIR filter across the range correlations and it was determined that an appropriate filter would be: 0.5Z+1+0.5Z−1.
The effect of this “video filtering” is shown in
Another way to reduce the skirts without broadening the main lobe is to add code bits within the bursts, that is to use an “N” greater than 0 and in the region 16 to 256, always with the (N=1)th bit for reasons previously described. The effect of placing code bits in the burst would be expected to produce an autocorrelation function which was the product of the pure FHCW autocorrelation function and the code autocorrelation function, which is much wider. The width of the FHCW main lobe is approximately one sample while the width of the code autocorrelation is roughly one bit, so its autocorrelation function is wider by a factor equal to the number of samples per bit.
Yet another way to lower the autocorrelation skirts is to employ a weighting function across the different frequency points correlated. Rather than deweight different bursts, which weakens their contribution to defeating noise, certain frequencies can be emphasized more than others by including them twice or more in the total number of hop frequencies.
Frequency hopping worsens the code autocorrelation function for range-to-range cross-correlations from sidelobes of magnitude 1/M (−72 dB) to 1/√M as previously explained. The resulting range-range cross-correlation function is shown in
There was a hint that the phenomenon seen in
Much experimentation with different shift spacings and M-sequences remains, to determine if further improvements are possible, which can be performed by a person skilled in the art based on the teachings above.
It has thus been described how range correlations can be performed with arbitrary IQ sample content in bursts, ranging from pure FHCW ramps to mixed FH and code modulation and eventually to pure code with no FH. It has been described also how the partial correlations are combined by FFT or preferably range-walking compensated analysis to separate targets by Doppler shift. It is appropriate to mention at this point that, to avoid confusion between the phase changes of burst correlations caused by hopping to systematic phase changes caused by Doppler, the phase changes due to the hopping frequency pattern should be as unlike the systematic phase ramps of a Fourier sequence as possible. One type of frequency hopping would be adaptive avoidance of interfering radars. In that case, a running metric can be kept of the resemblance to a Fourier sequence and priority given dynamically to frequency choices for subsequent bursts that decreased the resemblance.
Frequency hopping has the desirable characteristic that, unlike CDMA, the interference to or from other devices is related to the probability of a clash and not very dependent on the strength of the interference. The latter is called the “near-far” tolerance, which is much better for FH than CDMA. Moreover, damaging clashes can be detected by a sudden increase in signal level, and excised from subsequent processing.
Once a set of complex numbers is achieved for all VRXs for the same range and Doppler, beamforming over the VRXs can be carried out to separate targets also by Azimuth and elevation. The beamforming algorithms to be described are independent and agnostic of which of the above methods is used to produce a set of range-Doppler bins per VRX.
Beamforming will be described in terms of:
Letting θ be the Azimuth angle of a target at distance R.
Letting φ be the Elevation angle of the target.
Then the target's coordinates are X=R cos(φ)sin(θ); Y=R sin(φ); Z=R cos(φ)cos(θ).
The plane of the array is the X,Y plane with Z=o. Consider an antenna in the plane of the array located at (x,y,0). The distance from the antenna to the target is: d=√(R cos(φ)sin(θ)−x)2+(R sin(φ)−y)2+(R cos(φ)cos(θ))2.
d=√R
2−2R(x cos(φ)sin(θ)+y sin(φ))+x2+y2
d=R√1−2(x cos(φ)sin(θ)+y sin(φ))/R+(x2+y2)/R2
which for large R compared to (x,y) is
R(1−(x cos(φ)sin(θ)+y sin(φ))/R)=R−x cos(φ)sin(θ)−y sin(φ).
The amount R is common all antennas so does not affect relative path distance and so can be dropped.
The path phase shift factor between target and the antenna at (x,y,0) is therefore:
Exp[−jK(x cos(φ)sin(θ)+y sin(φ)
where K is the “wave number”=2Ø/λ.
Phase factor=Exp[−jK·x cos(φ)sin(θ)]·Exp[−jK·y sin(φ)].
Thus, the phase factor is the product of two-phase factors, one depending only on the antenna's x-coordinate in the array and the other depending only on the antenna's y coordinate in the array. The first is the same for all antennas with the same x coordinate and the second factor is the same for all antennas with the same y coordinate.
In a MIMO radar, Nrx receivers have coordinates {xrx(i),yrx(i)}, i=1:Nrx and Ntx transmitters have coordinates {xtx(j),ytx(j)}, j=1:Ntx. The total phase factor for sum of the go and return distances is the product of the phase factors for each of the go and return distances, that is:
e
−jK·xrx(i)cos(φ)sin(θ)
e
−jK·yrx(i)sin(φ)
e
−jK·xtx(j)cos(φ)sin(θ)
e
−jK·ytx(j)sin(φ);
which can also be written as:
e
−jK[xrx(i)+xtx(j)] cos(φ)sin(θ)
e
−jK[yrx(i)+ytx(j)]sin(φ).
Using the convention that the virtual radar location is the sum of the Tx and Rx coordinates therefore, the location
[(xrx (i)+xtx (j)), (yrx (i)+ytx(j))] is the virtual radar location which can be renamed [Xvrx(1),Yvrx(1)].
Therefore, given the virtual radar antenna locations and the target azimuth θ and elevation φ the received signal phases at the virtual antennas can be calculated.
Unshaped beamforming comprises multiplying each signal that is received by receiver(i) from transmitter(j) by the conjugate of the above factor (just dropping the minus sign) and summing over i and j so as to phase them all together, producing a beam that is probing for a target in the direction (θ, φ).
Traditional radar rotated the antenna mechanically to produce beams in different directions at successive times. When an antenna array is used and the signals are captured digitally, they can be processed in different ways to form beams in all directions simultaneously.
It is advantageous to compute beams in equal increments of variables u=cos(φ)sin(θ) and v=sin(φ) rather than in equal increments of θ and φ.
The above phase factor can then be written:
e
−jK[Xvrx·u+Yvrx·v].
Xvrx·u+Yvrx·v is the dot product of the antenna location coordinates with the sightline direction cosines (u,v) and represents the antenna vector offset from array center resolved in the sightline direction, which is the relevant distance that causes relative phase shifts between antennas.
The maximum possible value of u=cos(φ)sin(θ) is ±1 and likewise the maximum possible value of v=sin(φ) is ±1. Therefore, the range ±1 may be divided into 2Naz equal steps of 1/Naz and u is allowed to range from an integral number of steps Iaz=−Naz steps to Iaz=+Naz steps to cover −90 to +90 degrees of azimuth. The same steps could be used for Elevation, but typically only a smaller range of elevation is of interest in automotive radar, so v only ranges from an integral number of steps Iel=−Nel steps to Iel=+Nel steps where Nel<<Naz.
Beamforming is also simplified if the VRX locations are all on a regular grid, even when the grid points are sparsely populated, and if the grid spacing is a multiple of some integral fraction of a wavelength. For example, if the grid spacing is λ/16, then the VRX locations can be expressed as (Ix,Iy) λ/16.
The phase-retarding distance then becomes:
Xvrx·u+Yvrx·v=λ(Ix·Iaz+Iy·Iel)/(16Naz).
Then multiplying by the wavenumber K=2π/λ, obtain the phase retard:
2π(Ix·Iaz+Iy·Iel)/(16Naz).
Letting ω=−2π/(16Naz), the phase factor then becomes:
ω|Ix·Iaz+Iy·Iel|16Naz.
The integer Ix·Iaz+Iy·Iel may be reduced modulo 16Naz as additional factors of 2π do not change the complex exponential value. Thus, only 16Naz values arise which could be stored in a lookup table addressed by |Ix·Iaz+Iy·Iel|16Naz.
Beamforming comprises calculating the 2D array of complex numbers B(Iaz, Iel) for all Iaz and Iel of interest as shown by the following pseudocode:
FOR Iaz=−Naz to +Naz
FOR Iel=−Nel to +Nel
B(Iaz,Iel)=0
FOR Ivrx=1 TO Nvrx
k=|Ix(Ivrx)·Iaz+Iy(Ivrx)·Iel|16Naz
BEAM((Iaz,Iel)=B(Iaz,Iel)+VRX(Ivrx)ωk
Next Ivrx
Next Iel
Next Iaz
The above pseudocode accumulates, for each beam azimuth and elevation direction, all Nvrx VRX signal values numbered VRX(1) VRX(Nvrx), phase-twisted by a power k of w that is proportional to the quantized antenna location vector (Ix(Ivrx), Iy(Ivrx) in the plane of the array resolved in the direction given by the azimuth and elevation variables u and v quantized to Iaz,Iel steps of 1/Naz.
The above is an efficient method for computer simulations, but a much more efficient hardware implementation has been devised for chip implementation.
The variable u=cos(φ)sin(θ) is allowed to range from −1 to +1 to cover the azimuth range −90<θ<+90, but u can only have a magnitude of 1 at θ=+90 when elevation φ=0.
In
When the antenna array to be subjected to beamforming is a linear array of regularly spaced antennas with no gaps, beamforming can be efficiently performed with a 1-dimensional FFT. The beams span exactly ±90 degrees when the antenna spacing is λ/2. If the antenna spacing less than λ/2, some of the beams so computed will represent non-physical locations; when the antenna spacing is greater than λ/2, the beams will span less than ±90 degrees, but objects beyond that span and up to 90 degrees away will exhibit a phase change between antenna elements greater than 180 degrees which cannot be distinguished from a phase change of between 0 and −180 degrees. The object will thus be aliased to a “grating lobe” on the other side of the scan.
Regularly spaced arrays on a rectangular grid with every grid point occupied can also be efficiently beamformed with a 2D FFT. If the number of rows is N1 and the number columns is N2, then beamforming comprises performing N2-point FFTs along rows followed by N1-point FFTs along columns of the first FFT output values. The behavior with different antenna spacings is the same as for the 1D case but in each dimension separately.
If antenna spacings are not regular, but irrational values, then beamforming is performed by multiplying the antennas signals with a matrix of steering vectors, the elements of which are ExpjKX(vrx·u+Yvrx·v) as shown above, which phases however are not now integer multiples of a basic phase shift unit, and so the beamforming cannot done fast with an FFT.
If the antenna spacings lie on a regular rectangular grid, but not every grid point is populated, the array is termed a “sparse array.” Beamforming can be carried out using a 2D FFT, but the sizes of the FFTs have to equal the total number of grid points spanned by the array in each dimension, which can be much greater than the number of antennas elements of the sparse array. The use of FFTs in that case could involve more computation than treating the array as an irrationally-spaced array. In either case, when a sparse array is beamformed, sidelobes/grating lobes arise due to the missing grid points cause different beams to no longer be orthogonal.
In a MIMO radar, the VRX array to be beamformed arises from a conjunction of the transmit and receive antenna arrays. Each pair comprising a transmitter and a receiver gives rise to a VRX at coordinates which are the sum of the transmitter and receiver coordinates.
Placing a unit amplitude target signal at 0 degrees elevation and azimuth, the resultant beamforming of the array of
An interesting feature of computing beams in u,v space is that the image is doubly periodic. That is, if the wanted signal is shifted to the left, the entire image of
Sidelobes are proportional in amplitude to the target signal from which they derive; therefore, a method of preventing sidelobes from being mistaken for false targets was developed, based on identifying through beamforming the strongest echo, and then subtracting it, which also removes its sidelobes, revealing weaker targets beneath. The second strongest target is then identified and subtracted, and so forth. Before describing successive subtraction in signal strength order in more detail however, steps taken to reduce sidelobes of a sparse array will be described.
Co-filed and commonly owned patent application Ser. No. 17/582,437, entitled “Sparse Antenna arrays for Automotive Radar,” described a systematic way to arrive at Tx and Rx arrays that will produce a VRX array having the lowest possible sidelobes. This application was incorporated by reference above in its entirety. The inventive sparse arrays are based on the realization that every pair of antennas produces a main lobe, which when the antennas are all properly phased is in the same place for all pairs but produces sidelobes in different angular positions depending on the vector joining the two antenna locations. Thus, if different pairs of antennas have vectors joining them that are all different, in both length and direction, they will not produce sidelobes in the same place that are additive, but rather the sidelobe energy will be more evenly spread over the F.OV. The optimum design of sparse arrays to achieve the above has a strong synergy with the theory of differential arrays.
Beamforming of an array can be expressed in matrix/vector form as follows:
Using the definition of variables as in the mathematics above, to form a beam in direction (Iaz, Iel) with VRX antennas having locations in the plane of the array given by Ix(Ivrx), Iy(Ivrx) where Ivrx is the index of the VRX, each VRX signal is phase-untwisted by multiplying it by ωk
where k=|Ix(Ivrx)·Iaz+Iy(Ivrx)·Iel|16Naz.
Placing the 256 values of ωk, one for each VRX, in a row vector V, and placing the 256 VRX signal values in a column vector S, the complex value B of a beam in the direction with indices Iaz, Iel is B=V·S.
If row vectors for each beam direction are arranged under each other to form a matrix [V] of size (2Naz+1)(2Nel+1)×256, then the beam values are given by the (2Naz+1)(2Nel+1)-element column vector B=[V]S.
It would be normal to enquire which of the computed beams was the strongest, in other words, the magnitude of the beams is of primary interest and not their phase, which depends on the arbitrary reflection coefficient of the target object. Whether the beams are compared in magnitude |B|, magnitude squared |B|2 or in dBs as 20 Log10|B| or 10 Log10(|B|2) is immaterial.
The magnitude squared of a single beam B=V·S is given by:
B*B=S#[V#V]S, where # means conjugate transpose. This is the sum of each VRX signal value times the conjugate of another weighted by a phase factor V that is a complex exponential of the difference in phases between them due to the conjugation of one of the V's; namely elements of [V#V] are of the form ω|Ix(Ivrx1)·Iaz+Iy(Ivrx1)·Iel−Ix(Ivrx2)·Iaz−Iy(Ivrx2)·Iel|16Naz or
ω|{Ix(Ivrx1)−Ix(Ivrx2)}·Iaz+{Iy(Ivrx1)−Iy(Ivrx2}·Ie1)·Iel|16Naz.
That is, it looks like beamforming with antennas, the coordinates of which are the difference {Ix(Ivrx1)−Ix(Ivrx2)}, {Iy(Ivrx1)−Iy(Ivrx2} between pairs of antenna coordinates for Ivrx1 and Ivrx2. These are called “differential VRXs” or DVRXs. If there are 256 VRXs, then there are 2562 DVRXs, but they are not necessarily all in distinct virtual locations. Obviously, there are 256 DVRXs at location (0,0), corresponding to the 256 times Ivrx1 and Ivrx2.are the same VRX, and there may be others that accidently have the same location.
Due to the periodicity of the beamformed pattern in (u,v) coordinates, it is only necessary to consider the sidelobe pattern for a target located at (0,0). The pattern for any other target position is the same, merely shifted cyclically in (u,v) space, while maintaining the same separations and amplitudes of sidelobes relative to the main beam. Thus to form any beam, the phase factors are first applied to each VRX (i.e., form R=S·V element by element without implied summation, R now being a column vector of the same size as S and V as indicated by the overlining, and then these may be summed with weights equal to 1 to give the magnitude square of the beam, that is:
|B|2=R# [1] R, where [1] is a matrix with unity in every position. Calculating the above for every beam produces a set of differentially-beamformed beams which, however, is exactly the same as normal beamforming followed by taking the modulus squared of the beams.
Because there are repeated locations among the DVRXs, flat weighting of the DVRXs all with 1 is not flat location weighting. Because all DVRXs corresponding to the diagonal of the matrix [1] have the same location, that location is 256:1 overpopulated. Therefore, the diagonal of the matrix can be reduced by a factor 256, and any other elements in the matrix corresponding to duplicated VRX positions can be divided by the number of times the position is duplicated in order to produce flat location weighting.
The DVRX array formed by the VRX array of
The expression B=R# [1] R above can be factorized by noting that any matrix [G] can be expressed as [E][Λ][E] T where [E] is the matrix of Eigenvectors of [G] and [Λ] is a diagonal matrix of its eigenvalues. Since:
Therefore, B=R#[1] R=R#[E][Λ][E]T R=B#[Λ]B where the vector B is obtained by beamforming R with the Eigenvector matrix [E] of the matrix of all 1's, [1].
The magnitude squared of each of the beamformings with different eigenvectors are then weighted with the corresponding diagonal elements of [Λ] and added. However, a matrix of 1's having all the rows the same has rank of only 1 and therefore only one non-zero eigenvalue exists equal to 1/256, the corresponding eigenvector of which is all 1's. Therefore, only one beamforming is necessary, the magnitude of which will be the desired answer.
However, after position weight-flattening, the matrix [1] is no longer all 1's and has different eigenvalues, half of which are positive and the other half negative. Differential beamforming then amounts to performing 256 beamforming, each with different eigenvector, and adding or subtracting the results according to the sign and weight of the corresponding diagonal element of [Λ].
Unfortunately, full differential beamforming done any way is 256 times more onerous than regular beamforming, which is prohibitive. After experimenting by using only the largest positive eigenvalue and the largest negative eigenvalue, it was realized that the two beamforming weights were no longer constrained to be Eigenvectors of anything, and the corresponding eigenvalues could be premultiplied into the weight vectors. Therefore, two length 256 weight vectors, called Gplus and Gminus were defined, and their values sought that would give the most desirable beam patterns, defined as unity gain to the wanted target and minimum worst case sidelobe level. In one implementation, a first beamforming would form for every direction, Bplus=Gplus·R and a second beamforming would form Bplus=Gminus·R and then the magnitude squared of the beam would be given by |Bplus|2−|Bminus|2. Moreover, the sum of the Gplus values is constrained to be unity so as to give unity gain to the wanted signal when all VRXs add in phase, and for the same reason the sum of the Gminus is constrained to be zero, so that it is does detract from the wanted signal amplitude. The above expression would be converted to an amplitude in dBs by:
10 Log10(∥Bplus|2−|Bminus|2|) The additional modulus brackets ∥ ensures that |Bplus|2−|Bminus|2. is always rendered positive within the log function. The expectation is that an optimum choice of Gplus and Gminus will result in the sidelobes of Bplus and Bminus canceling without affecting the wanted signal amplitude.
If indeed the sidelobes of Bplus and Bminus could be similar in amplitude after squaring, a further thought was that they might also be similar in amplitude before squaring, so that the expression ∥Bplus|−|Bminus∥ could be equally valid, but with the advantage that it converts to dBs by
20 Log 10∥Bplus|−|Bminus∥.
Addings or subtracting the results of two or more beamformings is not the only conceivable way of combining different beamformings to reduce sidelobe levels from a sparse antenna array. Another conceivable method is to perform several beamformings using different weighting functions, each constrained to give unity gain in the wanted direction, and then to determine the minimum response in each direction. Since the different have unity gain to the wanted target, all of the beams will have equal response to the target but will exhibit sidelobes of different amplitude and/or in different places. Therefore, taking the minimum across all does not reduce the wanted signal response but retains the lowest sidelobe of all in each direction.
The general principle of combining multiple beamformings is shown in
While some analytic methods were found for minimizing the sum of sidelobe levels, minimizing the worst sidelobe level (a MINIMAX problem) is too non-linear for analytic solution. Therefore, a Monte Carlo search was used for optimum weighting functions Gplus and Gminus, for which several significant program acceleration algorithms were found.
The Monte Carlo search for best for a best length 256 Gplus and best length 256 Gminus is a 512-variable optimizing problem. The figure of demerit to be minimized is the sidelobe of greatest amplitude anywhere in the F.OV. excluding a keep-out area around the main lobe. As there are (2Naz+1)(2Nel)+1) beams to consider, where Naz=256 and Nel=32, this amounts to 33,345 beams to consider at each iteration, less the keep-out area. The keep-out area was tailored to mask the main lone and consisted of an ellipse of principal radii 15 steps in the u direction and 6 steps in the v direction. Within this ellipse, values are set to zero after beamforming as indicated by the black hole in
The first acceleration algorithm noted that, if a new modified Gplus,Gminus pair does not reduce the beam that was previously the largest, then the solution can be rejected based on recalculating only that beam. Thus a new beamforming is only carried out after finding a new Gplus,Gminus that reduces the previous worst case beam, as shown in the flow chart of
Referring to the flow chart of
At step 5214, Gplus and Gminus are randomly perturbed, keeping the sum of the Gplus equal to 1 and the sum of Gminus equal to zero. This can be done by forming the sum of Gminus values after perturbation and subtracting 1/256th of the sum from each. In the Gplus case, form the sum and subtract 1/256th of the difference between the sum and unity from all; alternatively, divide by the sum.
At step 5216, only the beam that was previously the worst case, the indices of which were saved in step 5212, is recomputed with the new Gplus, Gminus values, and the amplitude compared with the previous worst case at step 5218. If it is worst, the new Gplus, Gminus are rejected and a return to step 5210 takes place, otherwise proceed to step 5220. Steps 5220, 5222, 5224, 5226, and 5228 comprise a loop to recalculate all beam values, monitoring at step the loop 5224 whether any beam is worse than the previous worst sidelobe. If any beam is worse, then a return is made to step 5210, otherwise if all beams are recalculated without a return to step 5210, a new better solution has been found and a return is made to step 5212 to save it as the current best.
The purpose of the sort is the expectation that testing beams with a new Gplus, Gminus value is likely to reject a worse solution more rapidly if the previously strongest beams are tested first. Thus, steps 5312 to 5320 are analogous to the loop of steps 5220 to 5228 in
The algorithm of
The improved VRX array produced by the incorporated and co-filed Sparse MIMO arrays application is shown in
The sidelobe pattern of the array of
“Contrast” in a radar refers to the ability to detect weak targets in the presence of strong targets. The method developed to improve contract here comprises detecting the strongest target by beamforming a given set of VRX signals for a given range-Doppler bin, subtracting its contribution to the VRX signals, and then beamforming again with the strongest target signal gone to detect the second strongest target, and forth. The basic method of subtracting a target signal from the VRX signals is to weight the steering vector for the index of the strongest beam with the determined complex amplitude of the strongest beam and subtract it. Subtraction of the target signal in principle eliminates all sidelobes that it produces also. The ultimately achievable contract depends on how accurate the subtraction of the strongest signal can be. Limiting factors to accuracy are:
(i) Quantization of the target position in (u,v) space.
(ii) Position and amplitude corruption due to another strong nearby overlapping target.
(iii) VRX antenna and processing channel mismatches that are not modeled in the subtracted steering vector; particularly mismatches that depend on the antenna look-angle, i.e. on (u,v).
(iv) Position distortion caused by the use of transmit or receive nulling.
Noise is not so much of an issue in causing subtraction errors, because the error is only of the order of the noise level. Only weak signals will have significant noise-induced subtraction errors, but their importance is diminished in proportion to the signal strength.
The above limitations will be addressed one by one with explanation of the steps that can be taken to minimize the errors.
Quantization of the target position estimate arises due to computing beams only at a limited number of equal steps of (u,v). If steps of u,v are such that several beams are computed within the −3 dB beamwidth of the array, the beams are said to be spatially oversampling. With a modest amount of oversampling, such as between 2:1 and 3:1 the target position may be determined more accurately by interpolation between adjacent beam values. However, given the extremely large number of beamformings that have to be done, the consequent short time available for each, and consideration of how to design chip hardware for parallel processing, a different method called “zoom beamforming” has been developed which seems more practical in the circumstances. Zoom beamforming comprises utilizing the cyclic shift properties of (U,V) space to shift the radar image such that the strongest identified target appears at (u,v)=(0,0), and then to perform a zoomed-in beamforming around a small area centered on (0,0) with much finer steps. The target is centered on (0,0) by multiplying the VRX values by the steering vector used for its beam, thus removing the VRX phases such that a new beamforming on the shifted VRX values will find the target with a zero-phase steering vector, which corresponds to (u,v)=(0,0). The new beamforming is performed with steering vectors computed in very much finer steps of (U,V) for example, 256 steps of u and 32 steps of v but with the step size reduced by a factor 8.
To prepare for zoom beamforming, the value of w defined above by:
4ω=−271(16Naz) is precomputed and stored in even finer steps such as given by ω=−2π(128Naz), where only every 8th value is used in normal beamforming, but every value is used in fine beamforming. Thus, if NAZ=256, a table of 32,768 values of ω is precomputed and stored, at least for a software implementation such as would be used for simulation.
Commonly owned U.S. patent application Ser. No. 17/582,359, entitled “N-point Complex Fourier Transform Structure having only 2N Real Multiplies, and other Matrix Multiply Operations,” describes a fully parallel engine that can be constructed on a silicon chip to perform all operations in parallel related to multiplication of a complex vector by a complex matrix, the elements which are complex exponentials. In the beamforming application, the matrix is indeed a matrix of steering vectors which are complex exponentials of antenna phases needed to create beams in each desired direction in (u,v) space. This application is hereby incorporated by reference herein in its entirety. In the Application, it is described how in parallel to compute the product of an 8,192×256 complex matrix with a 256-element complex vector to obtain an 8192 complex result in as little as 2 ns. In this application, the 256-element vector is the set of 256 VRX signal values corresponding to one range-Doppler bin. The complex matrix is a set of 8129, 256-element steering vectors, each element which is the complex exponential of a phase. The beamforming engine starts by using serial arithmetic to stream the 256 VRX values through a serial adder tree that computes all 256 possible combinations of 8 VRX signals at a time, where a combination comprises either adding a VRX signal to the combination or not, a binary choice. It is shown in the incorporated application how this may be done with one serial adder per desired combination by computing them in Grey-Code order whereby only one of said binary choices is changed from one combination to another. There are 32 such adder trees to deal with all 256 VRX signals, each producing a digital result serially on 256 serial lines, a total of 8192 serial lines.
The 8129×256 complex matrix comprises cosines and sines which range from −1 to +1. To eliminate minuses, 1 is added to all cosine or sine components and then the result divided by two so that every real and imaginary part lies between 0 and 1. This is equivalent to adding a matrix of all 1's to the real parts and likewise to the imaginary parts, and to compensate for that in the final product, the sum of all real parts of the VRX vector must be subtracted from the real part of every result and the sum of the imaginary parts of the VRX vector must be subtracted from the imaginary part of the result, which is done on-the-fly in parallel using single-bit serial adders.
The binary bit pattern of each now always positive matrix value is now examined and a row of bits of like significance through the matrix shall multiply the VRX vector. Taking 8 bits a time, the result of multiply that with 8 VRX values is already available on one of the 8,192 serial lines formed with binary choices corresponding to whether a VRX value is added or not that matched the 8-bit pattern. Thus, a serial adder is placed on the crossover of the appropriate serial line to pick up that partial product and connect it to the partial products selected by the other 31 groups of 8 matrix row bits.
After performing the above for each row of matrix bits of different significance the results must be added with a shift corresponding to the matrix bit place significance. Where this scheme achieves it efficiency over conventional matrix-vector multiplication is by delaying combining the partial products from each multiplication, combining partial products of the same significance form each multiplication, and delaying combining partial products of different significance until the end. The latter step, equivalent to a shift and add multiplication, means that in effect the matrix-vector multiplication is performed using only one multiplication per output value.
Having obtained 8,182 output values, that with the largest magnitude must be identified, which requires forming the sum of the squares of the real and imaginary parts of each value. To do this, a serial squaring circuit may be used as shown in
Suppose we have the square of an X received bit serially up to bit i so far, in other words
S
i
=X
2
i=(ai,ai−1 . . . a2,a1)2.
To account for place significance, the convention for where the binary points are is:
Xi is less than 1, i.e. it is 0. aiai−1 . . . a2,a1.
Since the square of something less than 1 is less than 1 too, and has twice as many bits,
Si=0. s2i s2i−1 . . . s2 s1
Now we receive bit ai+1 and we want to update to Si+1
The update is:
X
i+1=½Xi+1/2ai+1.
e.g. if ai+1=1, Xi+1=0. 1 aiai−1 . . . a2a1
or if ai+1=0, Xi+1=0. 0 aiai−1 . . . a2a1
S
i+1=1/4Si+¼ai+1+½ai+1Xi,
which means:
The above is performed by the register structure of
There is at the top a 16-bit register (4000) to receive X serially, LSB first. Below that is the same register, just showing the contents after the new bit ai+1 is shifted in. At the bottom there a 32-bit register (4001) to receive S, the square of X. The register above that is the same register just showing the new bit ai+1 shifted in. Between the two is a 16-bit adder (4002) that adds the old X to the shifted S. There may be a carry, which goes into the MSB of the square register (4001). The result is shifted back into the square register to be the updated square. Although this could all be done in one clock cycle per bit in principle, because the S-register is updated twice per new bit input, it may have to run at half speed. However, of the 32 clock cycles needed to square a 16 bit value, there is a 16-clock overlap with the beamformer so the squarer adds only 16 more clock cycles.
Suppose we have received 111 so far so Xi=0.111 “7”
and Si will be 0.110001 “49”
Now we receive another “1”: Shift it into both:
The procedure works for 1's complement negative numbers with a small error: We get the square of X+1 instead e.g. the square of −1
1111111111111111 is 0000000000000000 (zero instead of 1).
This error is likely tolerable given that we only want to identify the strongest target, and even the second strongest will suffices if it is as close as 1 LSB.
The method can be extended to the sum of squares as follows:
Let X be received bit serially LSB first as a1,a2,a3, etc., and suppose bit as has already been processed. Likewise, Y is received bit serially as b1, b2, b3, etc., and bi has already been processed.
Let Si be X2+Y2 up to the ith bits ai and bi Then:
This translates to the following sequence: Since the sum of two squares, each being less than 1, can be greater than 1, Si now has one bit extra (carry bit) to the left of the binary point.
Clock1: Load ai+1 into the carry bit of the Xi register;
Load bi+1 into the carry bit of the Yi register;
Apply ai+1 .AND. Xi to a first input of a 3-way adder;
Apply bi+1 .AND. Yi to a second input of the 3-way adder
with Si being the 3rd input, the adder having 2 carries
Shift right Xi,Yi and Si, clocking the adder output,
including both carries into Si plus its extra carry bit.
Let the adder ripple through again, now adding Xi and Yi
to the Si register and generating up to 2 carries.
Clock 2: Shift the adder output right into Si plus its carry bit to
get the answer s.ssssss . . . s which will be 33 bits long if
X and Y were each 16 bits long. Suppose we have received 3 bits so far, with
Suppose now the next bits a4 and b4 of X and Y are both 1
Doing the sum of squares simultaneously thus only needs a single output register and effectively both squares are computed and added in parallel.
Having obtained the squared magnitudes of each beam, it is desired to know which is the largest. For this purpose, the square registers are read out MSB first into a magnitude comparator. A magnitude comparator determines which value presented serially MSB first is the first to be binary 1 while the other is binary 0. This is described in expired patent U.S. Pat. No. 5,187,675, and entitled “Maximum Search Circuit,” which is hereby incorporated by reference herein. The circuit also includes traceback to yield the index of the value, which was the largest, as required for the current application. This circuit may also be adapted to output the complex value of largest magnitude, by propagating the complex values that were deemed to give the largest sum of squares at each comparison through the tree to the comparator tree output. According to the index, the un-weighted VRX signals are then multiplied by an associated steering vector to shift the radar image to centralize the largest target on (u,v)=(0,0). The centralized VRX values are then applied to the fine beamformer which is constructed similarly to the coarse beamformer but using steering vectors that are in much finer angular steps, and there are not so many of them. The fine beamformer therefore occupies only a fraction of the chip area taken by the coarse beamformer and operates in parallel to fine beamform the previously found target in a range-Doppler bin while the coarse beamformer is working on a different set of VRX values corresponding to a different range-Doppler bin. The fine-beamformer operates on VRX values that are not weighted by Gplus or Gminus, but rather shifted by the centralization operation.
The centralization operation requires multiplication of the 256 complex element VRX signal set with a 256-element complex steering vector. For this purpose, a fully parallel set of 256 complex multipliers is made available and used for various purposes, including multiplying the VRX signals with the 256-element (real) vectors Gplus and Gminus prior to application serially to the beamforming.
The beamformer shall actually beamform the VRX signals using Gplus weights and again using Gminus weights in separate operations and subtract the magnitude of one from the other. This requires a square root operation to be performed after the sum of squares operation. It is well known how to perform a square root operation on a binary value to yield a binary word of half the length in bits. Therefore, although the sum of squares operations doubles the word length, the square root operation halves it again. The square root circuit operates on serial data most significant bit first, as does the magnitude comparator, therefore registers are needed to store sum-of-square values in order to reverse the direction from LSB first to MSB first.
The square root operation is needed only every two coarse beamformings. The various operations of weighting with Gplus or Gminus, coarse beamforming, squaring, square-rooting, centralization and fine beamforming may be overlapped as between different VRX sets and pipelined so as maximize throughput.
The output for fine beamforming is a refined position index of the strongest target and its complex echo value made with unweighted data. The fine steering vector for the refined position is obtained for example from a look up table. The fine steering vector is modified by combining it with any amount of nulling signal that was added to each transmitter to model the transmit codes combined with nulling signals that were transmitted, if nulling is in use, and then the phase and amplitude of each VRX component is adjusted by calibration factors that were predetermined during radar calibration to model uncorrected VRX phase and amplitude mismatches. The calibration of a radar determines calibration factors for each Tx and Tx averaged over all (U,V) and are combined to produce an average VRX calibration factor. These calibration factors are removed early in the processing chain, at least before coarse beamforming.
Now that the position of a target is known, the residual calibration factors for VRXs for the particular (u,v) sector in which the target lies can be applied to the steering vector to obtain the most accurate representation of what was transmitted. Then the steering vector, so modified by nulling signals and sector-wise VRX calibration is multiplied by the determined complex echo amplitude and subtracted from the VRX signals applied to the fine beamformer to subtract the just-found target's contribution as accurate as possible, and with it, all sidelobes and grating lobes of sparse beamforming.
An alternative is to apply the residual VRX calibration factors, that depend of the (u,v) of the target found from coarse beamforming, to the unweighted VRX values prior to fine beamforming; however, they must still be applied also to the steering vector for the fine position found from fine beamforming in determining the subtraction signal.
As a result of pipelining, it is possible that a first stage of subtraction is done for all range-Doppler bins of interest leaving in them modified sets of VRX signals with the strongest signal now gone. The set, or a further sparsification thereof, is then passed through the entire chain again to determine and subtract second-strongest targets, and so forth until all targets of significance have been located in the four dimensions of range, Doppler, azimuth and elevation.
The importance of obtaining fine positions for accurate subtraction is illustrated with the aid of
Although it was mentioned that, if transmit nulling is used, the actual subtracted signal should include the nulling signal combined with the transmitter signals, there is still a potential position error caused when a wanted target is close to a null. A simulation has determined the position error versus proximity of the target to a null and true and apparent position are compared in
Another mechanism for target position error is when two targets are so close that their beams partially overlap. At some point it would be expected that a radar might interpret two very close targets of equal amplitude as a single target midway between the two.
Because subtraction residuals may be larger than a weak target, they can be detected as false targets and subtracted before the weak target's turn to be the strongest beam. As it can be difficult to discriminate between such a false target and a weak target close to a strong target, it is desirable to reduce these residuals.
A method of reducing residuals caused by two or more nearby signals causing amplitude, phase and position estimation error is multipass subtraction, after subtracting a second strong target, the amount subtracted for a first strong target is added back and its position and complex amplitude estimated again, now with the second target gone. After subtracting the new estimate, the amount of second target subtracted can be added back and it re-estimated again. Such backtracking can be done to any depth for which computational resources suffice. Ultimately “joint detection” of multiple targets comprises finding the smallest number of target positions and amplitudes that jointly explain the received VRX signals to an accuracy approaching the noise level. Joint detection is computationally burdensome and can be done in increasing stages, where the strongest first detected, subtracted and second strongest signal identified. Then, using those clues as an initial starting point, a joint detection iteration optimizes their two amplitudes and positions to minimize the residual energy when they are subtracted. Then a third signal is identified, and so forth. By simulation it was verified that iterative multipass subtraction converged to the joint-detection result. Joint detection may be simplified by noting that, given a hypothesis of target positions, their amplitudes that minimize the residual can be analytically determined and substituted to obtain the lowest possible residual for those target amplitudes. The positions are then searched by any means, such as Monte-Carlo or steepest descent method using gradients, to obtain the optimum positions.
Accordingly, an exemplary radar system includes any combination of advanced features including use of sparse arrays with sidelobe-reduction beamforming techniques; dual polarization for interference mitigation; transmit or receiver null-steering, or both, to improve mutual interference and frequency hopping for increasing range resolution, and improved mutual interference characteristics by clash detection.
Changes and modifications in the specifically-described embodiments may be carried out without departing from the principles of the present invention, which is intended to be limited only by the scope of the appended claims as interpreted according to the principles of patent law including the doctrine of equivalents.
The present application claims the filing benefits of U.S. provisional application, Ser. No. 63/140,567, filed Jan. 22, 2021, which is hereby incorporated by reference herein in its entirety.
| Number | Date | Country | |
|---|---|---|---|
| 63140567 | Jan 2021 | US |
