CN113504522A - Space-time decoupling and super-resolution angle measurement method based on random switching of transmitting antennas - Google Patents

Space-time decoupling and super-resolution angle measurement method based on random switching of transmitting antennas Download PDF

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CN113504522A
CN113504522A CN202110775120.9A CN202110775120A CN113504522A CN 113504522 A CN113504522 A CN 113504522A CN 202110775120 A CN202110775120 A CN 202110775120A CN 113504522 A CN113504522 A CN 113504522A
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CN113504522B (en
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魏少明
洪文衍
王俊
耿雪胤
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Beihang University
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    • G01—MEASURING; TESTING
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Abstract

The invention discloses a space-time decoupling and super-resolution angle measurement method based on random switching of transmitting antennas, which belongs to the field of radar signal processing and specifically comprises the following steps: aiming at a target to be detected, the millimeter wave radar presets a random sequence, switches a single antenna to transmit a single pulse in sequence, and calculates the echo of the single receiving antenna; transmitting K times of pulses by using a single transmitting antenna, and expanding echoes into a three-dimensional matrix by using a receiving antenna and a receiving channel corresponding to the transmitting antenna; performing frequency mixing processing, performing FFT (fast Fourier transform) according to a distance dimension to obtain a one-dimensional range profile corresponding to each target, and distinguishing the targets with different distances; then, carrying out compressed sensing sparse reconstruction and target Doppler spectrum recovery to obtain a distance-Doppler spectrum, and identifying targets with different speeds; detecting spectral peaks, and determining antenna dimensions of each target in the three-dimensional matrix to measure angles by a state space balance method, so that the targets with the same distance and speed are resolved in an angle dimension; the invention improves the angle measurement precision and the super-resolution multiple.

Description

Space-time decoupling and super-resolution angle measurement method based on random switching of transmitting antennas
Technical Field
The invention belongs to the field of radar signal processing, and particularly relates to a space-Time decoupling and super-resolution angle measurement method based on random switching of transmitting antennas, which is used for solving the problems of speed ambiguity, space-Time coupling and low angular resolution under a Time Division Multiplexing-Multiple input Multiple output (TDM-MIMO) system.
Background
The TDM-MIMO technology is widely applied to radar, and a large-scale virtual receiving array can be formed by matching a plurality of transmitting antennas and receiving antennas by using a time division multiplexing principle. Due to the working mode of time division multiplexing, the transmitting antennas are switched in turn in a rotation period, which is the extension of the transmitting period of a single antenna in essence, and the maximum unambiguous speed of a target is reduced. On the other hand, due to the fact that the transmitting antennas are switched sequentially, the receiving array elements have a coupling problem to target space-time sampling, and therefore large errors occur in angle estimation.
The conventional method for improving the non-fuzzy speed is to transmit fast and slow slope frequency modulation signals, and solve the speed fuzzy by using the Chinese remainder theorem, but when the target number is too large, the method has the problem of wrong matching; although the MIMO array radar can obtain a larger aperture by using fewer array elements, the resolution of the traditional angle measurement algorithm is limited by Rayleigh limit, and in order to meet the angle measurement performance requirement of a multi-target scene, a super-resolution angle measurement algorithm based on a state space model is provided.
Due to the sparsity of target Doppler sampling caused by random switching of transmitting antennas, a compressed sensing sparse reconstruction (CS) method can be adopted for processing the target Doppler sampling, so that Doppler sparse recovery is realized, unambiguous velocity estimation is obtained, and the problem of space-time coupling is solved, so that angle super-resolution estimation is carried out on a Doppler unit where a target is located by using a state space algorithm.
Disclosure of Invention
The invention provides a Doppler recovery method based on compressed sensing sparse reconstruction aiming at Doppler non-uniform sparse sampling characteristics during random switching of transmitting antennas, which is combined with state space method angle measurement to realize multi-target speed angle high-resolution estimation, in particular to a space-time decoupling and super-resolution angle measurement method based on random switching of transmitting antennas, and comprises the following steps:
step one, aiming at P targets to be detected, presetting a random sequence by a TDM-MIMO millimeter wave radar, controlling the sequence of each transmitting antenna, and switching each transmitting antenna in sequence;
the MIMO array comprises N transmitting antennas and M receiving antennas; p, N and M are integers.
Each antenna transmits K times of linear frequency modulation continuous wave signals with the switching period, and NK linear frequency modulation continuous wave signals are transmitted together.
Step two, switching the MIMO radar to the nth transmitting antenna to transmit a single pulse, and calculating the superposition echo signal of the P targets received by the mth receiving antenna
Figure BDA0003150643710000011
The superposition echo signal
Figure BDA0003150643710000012
Is NRVector of x 1, NRSampling points for the distance dimension;
superposition of echo signals
Figure BDA0003150643710000021
The calculation formula is as follows:
Figure BDA0003150643710000022
Figure BDA0003150643710000023
in order to be a fast time,
Figure BDA0003150643710000024
t is the total time, τi(t) is echo time delay, τ (t) is 2 (R)i-vit-viknT)/c；RiThe distance of the ith target relative to the radar; v. ofiThe speed of the ith target relative to the radar; c is the speed of light, T is the pulse period; exp (j2 pi f0t) is a carrier frequency signal of a linear frequency modulation signal transmitted by a radar; f. of0Is the signal starting frequency; b is the bandwidth, and B/T is the frequency modulation slope; d is the interval of receiving antenna array elements and has a relation d of lambda/2 with the wavelength lambda; n denotes a transmitting antennaSequence number, m represents the receiving antenna sequence number; thetaiThe angle between the radar and the ith target is taken; k is a radical ofnDenotes a slow time index indicating the order in which the nth transmit antenna transmits the signal K times, KnTo randomly draw K number of sequences from {1, 2., N., NK }.
Step three, the nth transmitting antenna transmits K times of pulses, and the dimension of the composition of all superposed echo signals received by the mth receiving antenna is NRAn echo data matrix S of xK;
the expression is as follows:
Figure BDA0003150643710000025
sKthe superposition echo signal vector received by the mth receiving antenna when the nth transmitting antenna transmits the Kth pulse is shown;
step four, similarly, for the nth transmitting antenna, M receiving antennas form M receiving channels, and N transmitting antennas transmit NM receiving channels, at this time, the dimension of the echo data matrix S is expanded to NR×K×(NM)。
Each channel contains K pulses, and the final dimension is NRX K x (NM) three-dimensional echo data matrix.
Step five, setting a reference signal, and performing frequency mixing processing on each echo signal in the three-dimensional echo data matrix to obtain NRA superimposed baseband signal matrix of xKx (NM) dimensions;
first, a reference signal s is setref(t) is:
Figure BDA0003150643710000026
then, for each echo signal
Figure BDA0003150643710000027
Performing frequency mixing processing to obtain superposed baseband signals which contain target distance, speed and azimuth angle information and correspond to all echo signals; formula for calculation such asThe following:
Figure BDA0003150643710000031
Figure BDA0003150643710000032
r is a distance vector of each target relative to the radar; v is the velocity vector of each target relative to the radar; theta is an angle vector between the radar and each target;
finally, the superposed baseband signals corresponding to the echo signals are combined into NRA superimposed baseband signal matrix of xKx (NM) dimensions;
step six, performing one-dimensional fast Fourier transform on the superposed baseband signal matrix according to the distance dimension to obtain a one-dimensional range profile corresponding to each target, distinguishing targets with different distances, and entering the targets with the same distance into the next step;
superposing peaks formed by echoes of each target in P targets in the baseband signal matrix in a corresponding distance unit to serve as one-dimensional range images of the targets; the coordinate interval of the one-dimensional range profile is a range resolution unit, and the distance between the target located in the same range resolution unit and the radar is the same.
The distance resolution unit is used for calculating the distance resolution according to the effective bandwidth of the radar; the calculation formula is Δ R ═ c/2B.
Seventhly, for the targets with the same distance, performing compressed sensing sparse reconstruction and target Doppler spectrum recovery on each distance resolution unit of each target by using a convex optimization technology to obtain a dimension NRThe distance-Doppler spectrum of the multiplied by NK is used for distinguishing the targets with different speeds, and the targets with the same speed are put into the next step;
the distance-Doppler spectrum is a two-dimensional matrix, x represents a distance coordinate, and y represents a Doppler velocity coordinate; all targets with the same distance and speed correspond to the same spectral peak;
step eight, performing spectral peak search on targets with the same distance-speed, detecting a plurality of spectral peak extreme points, and determining respective corresponding antenna dimensions in a three-dimensional echo data matrix through two-dimensional coordinates of the extreme points to form antenna dimension vectors of the targets;
the method specifically comprises the following steps: each spectrum peak extreme point respectively represents one or more targets with the same distance-speed of the radar; aiming at each spectrum peak extreme point, utilizing the (x, y) coordinates of the extreme point in the range-Doppler spectrum to correspond to a three-dimensional echo data matrix, and acquiring a corresponding z coordinate, namely an antenna dimensional vector of a target;
and ninthly, performing state space balance method angle measurement on the antenna dimensional vectors of the targets with the same distance-speed to obtain three-dimensional parameter estimation results of the targets, so that the targets with the same distance-speed are resolved in an angle dimension.
Firstly, aiming at each target, constructing two Hankel matrixes according to the received data of the antenna dimensional vector of the target;
then, singular value decomposition is carried out on the two Hankel matrixes respectively, and an estimation operator matrix Q of an angle phase is obtained according to the difference of the two Hankel matrixes, wherein the estimation operator matrix Q is diag [ lambda ]1,λ2,…λi,...,λp]，
Figure BDA0003150643710000033
And calculating a target angle;
angle theta of radar to ith targetiThe calculation formula is as follows:
θi＝arcsin(∠(λi)/π)
wherein λiThe phase of the diagonal elements of the operator is estimated for the angle.
And step ten, randomly switching the radar based on the transmitting antenna, and distinguishing targets with different distances, different speeds and different angles.
The invention has the advantages that:
1) compared with the traditional TDM-MIMO system, the invention adopts the random switching of the transmitting antennas, shortens the transmitting period of each transmitting array element, greatly improves the maximum unambiguous speed, destroys the linear coupling of the receiving array elements to the target echo space-time sampling, and eliminates the angle estimation error caused by the speed phase.
2) Compared with the traditional super-resolution method, the time-space decoupling and super-resolution angle measurement method based on the random switching of the transmitting antennas improves the angle measurement precision and the super-resolution multiple on the premise of not needing solution intervention processing.
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FIG. 1 is a schematic diagram of a space-time decoupling and super-resolution angle measurement method based on random switching of transmitting antennas according to the present invention;
FIG. 2 is a flow chart of a space-time decoupling and super-resolution angle measurement method based on random switching of transmitting antennas according to the present invention;
FIG. 3 is a schematic diagram of the coordinates in the range-Doppler spectrum corresponding to a three-dimensional echo data matrix according to the present invention;
FIG. 4 is a graph illustrating the effect of the present invention compared to conventional FFT processing.
Detailed Description
The following detailed and clear description of the embodiments of the present invention is made with reference to the accompanying examples and drawings.
The invention relates to a space-time decoupling and super-resolution angle measurement method based on random switching of transmitting antennas, which comprises the steps of randomly switching the working sequence of the transmitting antennas, disturbing the space of sampling echo signals by receiving array elements and the linear coupling relation of Doppler, recovering Doppler sparse sampling signals under a random switching system through compressed sensing sparse reconstruction processing, improving the maximum unambiguous speed measurement range, and finally performing state space balance angle measurement on a distance-Doppler unit where a target is located to finish the three-dimensional parameter estimation of multiple targets.
As shown in fig. 1, a random sequence is preset in the TDM-MIMO millimeter wave radar, the transmitting antennas transmit signals according to the random sequence, N transmitting antennas are controlled to work in sequence, and each transmitting antenna transmits K chirp continuous wave signals; then, setting a reference signal, performing deskew processing on each target echo to obtain sampling data containing target distance, speed and angle information, obtaining a one-dimensional range profile through range FFT, and distinguishing targets with different relative radar distances; and further introducing Doppler CS reconstruction to a plurality of targets with the same distance to obtain an RD spectrum, performing CFAR detection, and distinguishing the targets with different speeds. Furthermore, the targets with the same speed and distance need to be resolved in the angle dimension, after the spectral peak of the RD spectrum is searched, the corresponding antenna dimension vector of the target with the same distance and speed is determined in the three-dimensional echo data matrix, the vector is subjected to state space balance angle measurement to obtain the three-dimensional parameter estimation result of each target, and finally the targets are distinguished in the angle dimension.
According to the space-time decoupling and super-resolution angle measurement method based on random switching of the transmitting antenna, a radar transmits a linear frequency modulation continuous wave signal with the propagation speed of c to a detection target; the detection target is an object which moves at a high speed and is away from the radar by R; when the transmitted chirp signal reaches a detection target, an echo signal model based on random switching of a transmitting antenna is as follows, wherein s (t) is a transmitting signal, the transmitting signal delay is tau (t) 2(R-vt-vkT)/c, and a reflected signal is as follows:
Figure BDA0003150643710000051
wherein
Figure BDA0003150643710000052
Substituting the time delay tau (t) and performing mixing processing to obtain:
Figure BDA0003150643710000053
as can be seen from the formula (2), when the transmitting antenna is switched randomly, the pulse period of the transmitting antenna is shortened by NtxThe method is equivalent to the sparse sampling of target Doppler, so that a compressed sensing sparse reconstruction method can be utilized to recover the target Doppler spectrum; the space-time sampling coupling term of the array to the target echo is damaged, and the target transmitting antenna steering vector is not mixed with a Doppler phase term, so that the steering vector of the first transmitting antenna can be simultaneously established, and the method is completed by utilizing a state space balance methodAnd performing target angle super-resolution estimation.
As shown in fig. 2, the specific steps are as follows:
the method comprises the steps that firstly, aiming at P targets to be detected, a random sequence is preset in a TDM-MIMO millimeter wave radar, the sequence of each transmitting antenna is controlled, and each transmitting antenna is switched to transmit linear frequency modulation continuous wave signals with K switching cycles in sequence;
the MIMO array comprises N transmitting antennas and M receiving antennas; p, N and M are integers.
Each antenna transmits K times of linear frequency modulation continuous wave signals with the switching period, and NK linear frequency modulation continuous wave signals are transmitted together.
Step two, switching the MIMO radar to the nth transmitting antenna to transmit a single pulse, and calculating the superposition echo signal of the P targets received by the mth receiving antenna
Figure BDA0003150643710000054
Each transmitting antenna transmits a pulse, which is received by a receiving antenna, and the echo signal is NRX 1, is a linear superposition of P targets, NRSampling points for the distance dimension;
for P targets, the formula (1) is rewritten into a superposition echo signal
Figure BDA0003150643710000055
Figure BDA0003150643710000056
Figure BDA0003150643710000057
In order to be a fast time,
Figure BDA0003150643710000058
t is the total time, τi(t) is the echo time delay of the ith target, and τ (t) is 2 (R)i-vit-viknT)/c；RiThe distance of the ith target relative to the radar;vithe speed of the ith target relative to the radar; c is the speed of light, T is the pulse period; exp (j2 pi f0t) is a carrier frequency signal of a linear frequency modulation signal transmitted by a radar; f. of0Is the signal starting frequency; b is the bandwidth, and B/T is the frequency modulation slope; d is the interval of receiving antenna array elements and has a relation d of lambda/2 with the wavelength lambda; n represents the serial number of the transmitting antenna, and m represents the serial number of the receiving antenna; thetaiThe angle between the radar and the ith target is taken; k is a radical ofnDenotes a slow time index indicating the order in which the nth transmit antenna transmits the signal K times, KnTo randomly draw K number of sequences from {1, 2., N., NK }.
Step three, the nth transmitting antenna transmits K times of pulses, and the dimension of the composition of all superposed echo signals received by the mth receiving antenna is NRAn echo data matrix S of xK;
the expression is as follows:
Figure BDA0003150643710000061
sKindicating the vector of the superposition echo signal received by the mth receiving antenna when the nth transmitting antenna transmits the Kth pulse
Figure BDA0003150643710000062
Step four, similarly, for the nth transmitting antenna, M receiving antennas form M receiving channels, and N transmitting antennas transmit NM receiving channels, at this time, the dimension of the echo data matrix S is expanded to NR×K×(NM)。
Each channel contains K pulses, and the final dimension is NRX K x (NM) three-dimensional echo data matrix.
Step five, setting a reference signal, and performing frequency mixing (namely deskew) processing on each echo signal in the three-dimensional echo data matrix to obtain N containing target distance, speed and azimuth informationRA superimposed baseband signal matrix of xKx (NM) dimensions;
since the P targets received by the radar are superposed, they are indistinguishable in the time domain, and therefore, the echo signals are mixed to obtain baseband signals, i.e., each vector s is mixed.
First, a local reference signal s for mixing processing is setref(t) is:
Figure BDA0003150643710000063
then, echo signals for each target
Figure BDA0003150643710000064
Performing mixing processing, wherein the calculation formula is as follows:
Figure BDA0003150643710000071
since in the actual scene the vehicle speed v < c, B τ (t)2The influence of/2T is negligible; equation (5) can be simplified to:
Figure BDA0003150643710000072
for P targets, the above equation is modified:
Figure BDA0003150643710000073
r is a distance vector of each target relative to the radar; v is the velocity vector of each target relative to the radar; theta is an angle vector between the radar and each target;
finally, the superposed baseband signals corresponding to the echo signals are combined into NRA superimposed baseband signal matrix of xKx (NM) dimensions;
step six, performing one-dimensional fast Fourier transformation on the distance dimension of the superposed baseband signal matrix to obtain a one-dimensional distance image corresponding to each target, distinguishing targets with different distances, and entering the targets with the same distance into the next step;
p targets in the superposed baseband signal matrix cannot be distinguished in the time domain, and the signal frequencies after mixing are different, so that FFT can be performed to obtain one-dimensional distance images of the targets, and the targets are separated in the frequency domain.
Forming a peak on the echo of each target with different distances in a corresponding distance unit to be used as a one-dimensional range profile of each target; the coordinate interval of the one-dimensional range profile is a range resolution unit, and the distance between the target located in the same range resolution unit and the radar is the same.
The distance resolution unit is used for calculating the distance resolution according to the effective bandwidth of the radar; the calculation formula is Δ R ═ c/2B.
After the distance dimension processing, considering the existence of multiple targets in one distance resolution unit, it can be expressed as:
Figure BDA0003150643710000081
wherein alpha isp,φpRepresenting the complex amplitude and phase of the objects and P representing the number of objects in the range bin.
Seventhly, for the targets with the same distance, performing compressed sensing sparse reconstruction on the Doppler-antenna dimension (the matrix with the dimensionality of Kx (NM)) corresponding to each distance resolution unit of each target by utilizing an orthogonal matching pursuit algorithm and utilizing a convex optimization technology, and recovering the dimensionality of NRThe distance-Doppler spectrum of the multiplied by NK is used for distinguishing the targets with different speeds, and the targets with the same speed are put into the next step;
the distance-Doppler spectrum is a two-dimensional matrix, x represents a distance coordinate, and y represents a Doppler velocity coordinate; the value of each point represents the intensity of the signal; detecting a plurality of spectral peaks with stronger signals by performing CFAR detection on a target distance-Doppler spectrum; all targets with the same distance and speed correspond to the same spectral peak;
the equation (8) is applied to all range resolution cells, sparse reconstruction is performed for each range cell, if no target exists in the range resolution cell, the amplitude α of the range resolution cell is 0, and if a target exists, the method can recover the target doppler spectrum. And after compressed sensing sparse reconstruction is completed on all the distance resolution units, a target distance-Doppler spectrum is obtained.
Because the radar transmitting antenna is switched randomly, the receiving antenna has random undersampling characteristic to the target Doppler sampling, and the number of targets in the same distance resolution unit meets the sparse characteristic, and the target Doppler spectrum can be recovered by an Orthogonal Matching Pursuit (OMP) algorithm. Considering only the phase term associated with the doppler sample in equation (8), the remaining terms are combined to yield:
Figure BDA0003150643710000082
wherein f isd,p＝2vpT/λ represents the doppler frequency of the pth target within the range resolution cell.
The input of the orthogonal matching pursuit algorithm comprises three parts, namely an original signal y, sparsity K and a sparse transformation matrix D, wherein the result of sparse recovery is a vector x with sparsity K. The sparsity is the number of targets with different doppler in the range resolution unit.
The construction of the sparse transform matrix is divided into two parts, which can be expressed as D ═ phinψ，φnRandom sequence k is assigned to the nth transmitting antennanThe projection matrix of the corresponding row number,/, is a fourier orthogonal basis matrix composed of uniformly quantized doppler steering vectors, and the expression is as follows, where L is the number of doppler resolution cells:
Figure BDA0003150643710000091
the sparse recovery process may be equivalent to solving the following equation:
Figure BDA0003150643710000092
the specific flow of the algorithm is as follows:
1. solving the inner product of the sparse transformation matrix and the residual error, and finding the index eta of the maximum value in the inner product result in the matrix;
2. updating the matrix I, adding the found maximum inner product index eta into the matrix I, finding out corresponding atoms in the sparse transformation matrix according to the eta, and adding the atoms into the reconstructed atom set phi;
3. coefficient vector estimation with sparsity k obtained by using least square method
Figure BDA0003150643710000093
4. And judging whether K is more than K, if so, ending the circulation, otherwise, continuously executing 1.
5. Finally, a restored target Doppler spectrum x is obtainednm＝[α1,α2,...,αL]Wherein
Figure BDA0003150643710000094
And carrying out CFAR detection on the target distance-Doppler spectrum after sparse reconstruction to extract target parameters, and filtering out clutter. A unit average constant false alarm rate detector (CA-CFAR) is selected for detection, the two-dimensional detector is a rectangular window, and in order to prevent target energy from leaking into the reference unit to influence background estimation, the detector comprises an array element to be detected, eight protection units and sixteen reference units. The CFAR detector detects sliding on the target range-Doppler spectrum, and the background power calculation formula is as follows:
Figure BDA0003150643710000095
wherein m isR＝1,2,...,MR，nD＝1,2,...,NDRepresenting the range of the target, the doppler index,
Figure BDA0003150643710000096
indicating the signal power level corresponding to the index. And finally calculating a detector threshold by a normalization factor T and background power:
PCA＝T·Z (14)
and after each distance-Doppler resolution unit is detected, outputting the distance and the Doppler index of the existing target.
Step eight, performing spectral peak search on targets with the same distance-speed, detecting a plurality of spectral peak extreme points, and determining respective corresponding antenna dimensions in a three-dimensional echo data matrix through two-dimensional coordinates of the extreme points to form antenna dimension vectors of the targets;
the method specifically comprises the following steps: each spectrum peak extreme point respectively represents one or more targets with the same distance-speed of the radar; for each spectrum peak extreme point, using the (x, y) coordinate of the extreme point in the range-doppler spectrum to correspond to the three-dimensional echo data matrix, and obtaining the corresponding z coordinate, i.e. the antenna dimension vector of the target, as shown in fig. 3;
and ninthly, performing state space balance method angle measurement on the antenna dimensional vectors of the targets with the same distance-speed to obtain three-dimensional parameter estimation results of the targets, so that the targets with the same distance-speed are resolved in an angle dimension.
Firstly, aiming at each target, constructing two Hankel matrixes according to the received data of the antenna dimensional vector of the target;
a plurality of targets with different angle values exist in the same range-velocity resolution unit, and the corresponding azimuth angles of the different targets are extracted by adopting a state space balance method based on the detected range-Doppler spectrum;
the antenna dimension sampled signal expression of a single range-velocity resolution element is as follows:
Figure BDA0003150643710000101
wherein S is PaThe x 1 dimension includes signal vector of distance and Doppler information, N is noise, A is a guide vector matrix of the receiving and transmitting antenna combination, and the calculation formula is as follows:
Figure BDA0003150643710000102
wherein any element
Figure BDA0003150643710000103
Representing a target angle of
Figure BDA0003150643710000104
Guide vector of, NaAnd NM is the number of MIMO radar virtual receiving array elements. Consider the nthaThe calculation formula of the echo signal model received by each virtual array element is as follows:
Figure BDA0003150643710000105
by rewriting the above formula into a matrix form, a
Figure BDA0003150643710000108
Q is a diagonal matrix, and the expression is as follows:
Figure BDA0003150643710000106
solving for the angle can therefore be converted to solving for the diagonal matrix Q.
Because the array element interval d and the wavelength lambda have a mathematical relationship of d being lambda/2, the formula (18) is replaced by:
Figure BDA0003150643710000107
the diagonal matrix Q of equation (20) is solved by state space balancing.
First N using a virtual receive arraya-1 array element receiving data to construct Hankel matrix
Figure BDA0003150643710000111
The formula is as follows:
Figure BDA0003150643710000112
second using the last N of the virtual receive arraya-1 array element receiving data construction Hankel matrix
Figure BDA0003150643710000113
The formula is as follows:
Figure BDA0003150643710000114
substituting equation (20) into the two Hankel matrices constructed can result in:
Figure BDA0003150643710000115
Figure BDA0003150643710000116
wherein N isj＝NaThe/2 is the matrix beam parameter,
Figure BDA0003150643710000117
the reaction is not allowed to proceed:
Figure BDA0003150643710000118
Figure BDA0003150643710000119
it can be seen that H0And H1The difference of the diagonal matrix Q exists between the two Hankel matrixes, and the diagonal matrix Q can be extracted by utilizing the two Hankel matrixes to extract the target angle.
Then, singular value decomposition is carried out on the two Hankel matrixes respectively, and estimation operator moments of angle phases are obtained according to the difference of the two Hankel matrixesMatrix Q ═ diag [ lambda ]1,λ2,…λi,...,λp]，
Figure BDA00031506437100001110
And calculating a target angle;
angle theta of radar to ith targetiThe calculation formula is as follows:
θi＝arcsin(∠(λi)/π)
wherein λiThe phase of the diagonal elements of the operator is estimated for the angle.
And step ten, randomly switching the radar based on the transmitting antenna, and distinguishing targets with different distances, different speeds and different angles.
The method comprises the steps of firstly utilizing a transmitting antenna to randomly switch and transmit chirp signals to obtain Doppler dimension undersampled echo signals, firstly carrying out Fast Fourier Transform (FFT) on a distance dimension to obtain a one-dimensional distance image of a target, then carrying out compressed sensing sparse reconstruction on each distance resolution unit, recovering an unambiguous Doppler spectrum of the target, and obtaining a distance-Doppler spectrum. And then, performing constant false alarm detection (CFAR) on the range-Doppler spectrum, and performing state space equilibrium method angle measurement on the antenna dimension corresponding to the range-Doppler resolution unit where the target is located to obtain angle estimation of the target, and finally obtaining range-velocity-azimuth parameters of the whole target.
FIG. 4 is a comparison of a simulation diagram of the present invention with conventional FFT processing; wherein the radar parameter settings are shown in table 1:
TABLE 1
Radar parameter Numerical value
Carrier frequency 77GHz
Pulse repetition period 50 microseconds
Number of transmitting antennas 3
Number of receiving antennas 4
Pulse number (each transmitting antenna) 128
The target parameter settings are shown in table 2:
TABLE 2
Target parameter Numerical value
Speed of rotation [12m/s 12m/s]
Angle of rotation [10°15°]
The corresponding real aperture angle resolution is 9.5512 degrees, the maximum unambiguous speed of the sequential switching of the transmitting antennas is 6.4935m/s, and the maximum unambiguous speed of the random switching of the transmitting antennas is 19.4805 m/s. As can be seen from fig. 4(a), the target cannot be distinguished by the conventional FFT method, and the target velocity is blurred; as can be seen from fig. 4(b), the state space method achieves angular super-resolution, distinguishes the targets with angular intervals within the real aperture angular resolution, does not have spatio-temporal coupling for angular estimation, and achieves velocity deblurring.

Claims (7)

1. A space-time decoupling and super-resolution angle measurement method based on random switching of transmitting antennas is characterized by comprising the following specific steps:
firstly, aiming at P targets to be measured, a TDM-MIMO millimeter wave radar presets a random sequence of N transmitting antennas, switches to the nth transmitting antenna in sequence to transmit a single pulse, calculates a single receiving antenna, namely the mth receiving antenna, and receives superposed echo signals of the P targets
Figure FDA0003150643700000011
Then, the nth transmitting antenna transmits K times of pulses in total, and all superposed echo signals received by the single receiving antenna form a dimension NRAn echo data matrix S of xK;
similarly, for the nth transmitting antenna, M receiving antennas form M receiving channels, and N transmitting antennas transmit NM receiving channels, at which time the dimension of the echo data matrix S is expanded to NRxKx (NM), namely forming a three-dimensional echo data matrix;
then, setting a reference signal, and performing frequency mixing processing on each echo signal in the three-dimensional echo data matrix to obtain a three-dimensional superposition baseband signal matrix; performing one-dimensional fast Fourier transform according to the distance dimension to obtain a one-dimensional range profile corresponding to each target, and distinguishing the targets with different distances; meanwhile, each distance resolution unit of each target with the same distance is subjected to compressed sensing sparse reconstruction and target Doppler spectrum recovery by utilizing a convex optimization technology to obtain a dimension NRThe method comprises the steps of multiplying the distance of NK by a distance-Doppler spectrum, identifying targets with different speeds, performing spectral peak search on each target with the same speed, detecting a plurality of spectral peak extreme points, and determining corresponding antenna dimensions in a three-dimensional echo data matrix through two-dimensional coordinates of each extreme point to form antenna dimension vectors of each target; then, for each object with the same distance-velocityThe antenna dimensional vector is used for measuring angles by a state space balance method to obtain three-dimensional parameter estimation results of all targets, so that the targets with the same distance and speed are resolved in an angle dimension;
and finally, the radar is switched randomly based on the transmitting antenna, and the targets with different distances, different speeds and different angles are distinguished.
2. The method of claim 1, wherein the nth transmit antenna transmits a single pulse, and the mth receive antenna receives the echo signals superimposed from the P targets
Figure FDA0003150643700000012
Is NRVector of x 1, NRSampling points for the distance dimension;
the calculation formula is as follows:
Figure FDA0003150643700000013
Figure FDA0003150643700000014
in order to be a fast time,
Figure FDA0003150643700000015
t is the total time, τi(t) is echo time delay, τ (t) is 2 (R)i-vit-viknT)/c；RiThe distance of the ith target relative to the radar; v. ofiThe speed of the ith target relative to the radar; c is the speed of light, T is the pulse period; exp (j2 pi f0t) is a carrier frequency signal of a linear frequency modulation signal transmitted by a radar; f. of0Is the signal starting frequency; b is the bandwidth, and B/T is the frequency modulation slope; d is the interval of receiving antenna array elements and has a relation d of lambda/2 with the wavelength lambda; n represents the serial number of the transmitting antenna, and m represents the serial number of the receiving antenna; thetaiAs the angle of the radar to the ith targetDegree; k is a radical ofnDenotes a slow time index indicating the order in which the nth transmit antenna transmits the signal K times, KnTo randomly draw K number of sequences from {1, 2., N., NK }.
3. The method of claim 1, wherein N is the number of antennas in the space-time decoupling and super-resolution angle measurement method based on random switching of transmitting antennasRThe specific calculation process of the superposed baseband signal matrix with the dimension of xKx (NM) is as follows:
first, a reference signal s is setref(t) is:
Figure FDA0003150643700000021
then, for each echo signal
Figure FDA0003150643700000022
Performing frequency mixing processing to obtain superposed baseband signals which contain target distance, speed and azimuth angle information and correspond to all echo signals; the calculation formula is as follows:
Figure FDA0003150643700000023
Figure FDA0003150643700000024
r is a distance vector of each target relative to the radar; v is the velocity vector of each target relative to the radar; theta is an angle vector between the radar and each target;
finally, the superposed baseband signals corresponding to the echo signals are combined into NRA matrix of superimposed baseband signals of dimension xKx (NM).
4. The method according to claim 1, wherein in the P targets of the superimposed baseband signal matrix, a peak formed by each target echo in a corresponding range unit is used as a one-dimensional range profile of each target; the coordinate interval of the one-dimensional range profile is a range resolution unit, and the distance between a target positioned in the same range resolution unit and the radar is the same;
the distance resolution unit is used for calculating the distance resolution according to the effective bandwidth of the radar; the calculation formula is Δ R ═ c/2B.
5. The method of claim 1, wherein the range-doppler spectrum is a two-dimensional matrix, x represents a range coordinate, and y represents a doppler velocity coordinate; all targets with the same distance and velocity correspond to the same spectral peak.
6. The method for spatio-temporal decoupling and super-resolution goniometry based on transmit antenna stochastic switching of claim 1, wherein each spectral peak extreme point represents one or more targets of the same range-velocity of the radar.
7. The method for spatio-temporal decoupling and super-resolution angle measurement based on random switching of transmitting antennas of claim 1, wherein the process of resolving the targets with the same distance-velocity in the angle dimension is as follows:
firstly, aiming at each target, constructing two Hankel matrixes according to the received data of the antenna dimensional vector of the target;
then, singular value decomposition is carried out on the two Hankel matrixes respectively, and an angle estimation operator matrix Q ═ diag [ lambda ] is obtained according to the difference of the two Hankel matrixes1,λ2,…λi,...,λp]，
Figure FDA0003150643700000025
And calculating a target angle;
angle theta of radar to ith targetiThe calculation formula is as follows:
θi＝arcsin(∠(λi)/π)
wherein λiThe phase of the diagonal elements in the operator matrix is estimated for the angle.
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