CN110632558B - Method for jointly calculating MIMO radar sparse array and pulse train - Google Patents

Abstract

The invention discloses a method for jointly calculating a sparse array and a pulse train of an MIMO radar, belongs to the field of signal processing, particularly relates to the joint design problem of sparse array, sparse pulse train and space-time adaptive processing under the conditions of limited radar system complexity and clutter existence, and is suitable for the joint processing of the sparse array, the sparse pulse train and clutter suppression of the MIMO radar. By optimizing the joint design of the receiving and transmitting antenna array and the transmitting pulse train, the number of the receiving and transmitting antennas and the number of the transmitting pulses are reduced, and the complexity of the system is reduced. Meanwhile, the weight vectors are split and replaced, so that an optimization problem which can ensure the detection performance of the system and is easy to solve is obtained, and the calculation complexity is further reduced through a greedy algorithm.

Description

Method for jointly calculating MIMO radar sparse array and pulse train

Technical Field

The invention belongs to the field of signal processing, particularly relates to a combined design problem of sparse array, sparse pulse train and space-time adaptive processing under the conditions of limited complexity of a radar system and clutter existence, and is suitable for combined processing of the sparse array, the sparse pulse train and clutter suppression of an MIMO radar.

Background

In modern society, radar systems are increasingly used in commercial areas, such as smart cars, drones, and the like. Applications in the commercial field not only demand radar performance, but also limit the complexity of the radar system.

MIMO (Multiple Input Multiple Output) radar can be used to improve system performance, which has many advantages over conventional radar by using Multiple antennas and pulses. (see J.Li and P.Stoica, "MIMO radar with coordinated antenna," IEEE Signal Processing Magazine, vol.24, no.5, pp.106-114, sep.2007.) however, the use of a large number of antennas and pulses would result in a radar system that is too complex. Considering that the complexity of the system is related to the number of antennas and pulses used, the MIMO radar is sparsely processed in a space domain and a slow time domain so as to reduce the complexity of the system.

In the spatial domain, a sparse array can be used to reduce the number of antennas, and the sparse array is designed so that only little performance is lost while reducing the complexity of the system. The same idea can also be applied to the slow time domain, reducing the number of transmit pulses by designing a sparse burst. In the invention, the sparse array and the sparse pulse train are jointly designed, and the performance is optimized under the condition of limited complexity.

In practical situations, clutter often exists in an observation area, the echo of the clutter is often stronger than that of a target, and therefore, the clutter suppression is an inevitable process. The space-time adaptive processing technology is an effective method for suppressing clutter. (J.Ward, "Space-time adaptive Processing for air front," in Proc.IEEE International Conference on Acoustics, speech, signal Processing, may.1995, pp.2809-2812.) the complexity of Space-time adaptive Processing techniques often increases with increasing data dimensions. For high-dimensional data, methods such as compressed sensing and sparse array are adopted to reduce the computational complexity of space-time adaptive processing.

At present, many considerations are given to design sparse arrays, and optimization is usually performed by using a certain performance as an index to obtain an optimal sparse array, which also includes clutter suppression by using a space-time adaptive processing technology. Some people also consider sparse pulses and combined sparse arrays and sparse pulses, but most of them use sparse arrays and sparse pulses as the background of problem research, and in such background, detecting or estimating parameters, how to design an optimal sparse structure is not the focus of consideration. Of course, the optimal sparse array and sparse pulse are considered in the joint design, but in the design process, the existence of the clutter is not considered, and in the practical problem, the clutter is inevitable, and the clutter suppression is also a very important research content.

Disclosure of Invention

The invention provides a scheme of MIMO radar low-complexity array and pulse series combined design by taking the signal-to-noise-ratio output after the maximization of space-time adaptive processing weighting as a criterion. By the scheme, a sparse array and sparse pulse train design scheme which enables the output signal-to-noise ratio to be maximum when clutter exists can be obtained under the allowable number of the antennas and the pulses, and therefore the complexity of the system is reduced while the performance of the system is kept.

The technical scheme of the invention is as follows: a method for jointly calculating a sparse array and a pulse train of an MIMO radar is characterized by comprising the following steps:

step 1: the range that will allow the transmit antenna to be placed 0,Z _T ]And range of the receiving antenna 0,Z _R ]Respectively dispersed into M and N uniform lattice points with the spacing of d _T And d _R (ii) a The allowed total emission pulse number is L, and the pulse interval is T; due to limited complexity, only M _S Less than or equal to M transmitting antennas and N _S N receiving antennas can be placed, each transmitting antenna has L _S Less than or equal to L pulses can be transmitted;

and 2, step: the signals received by the N possible receiving antennas are written in vector form y by matched filtering, i.e.

Wherein, y _t Representing the echo signal of the target, provided that there are a total of Q targets, p _q And s _t，q Respectively representing the reflection coefficient and the guide vector of the qth target; y is _c Representing clutter echo signals, assuming clutter comprising a total of P scattering points, η _q And s _c，p Respectively representing the reflection coefficient and the guiding vector of the p clutter scattering point; y is _n Representing noise, assuming zero mean and variance σ ² The white gaussian process of (a);

and step 3: adding a weight vector w to the matched and filtered signals, and calculating the optimal weight vector w to enable the output signal-to-noise ratio to be maximum; defining the output signal-to-noise ratio as the ratio of the output target signal power and the output clutter-to-noise power, i.e.

Wherein R is _u ＝R _c +R _n ，R _c As a clutter covariance matrix, R _n In the form of a noise covariance matrix,

and R _n ＝σ ² I, E represents expectation, and I represents an identity matrix;

and 4, step 4: the weight vector w is subjected to a split rewrite,

w＝w _V ⊙w _S

wherein, the two vectors indicate corresponding multiplication between elements of the two vectors; w is a _S Is a selection vector with elements other than 0, namely 1, which indicates which grid points are not selected or are selected; for selected antenna or pulse position, w _V Contains the same weight as w;

and 5: the vector w will be selected according to the placement of the antennas and the transmission of the pulses _S The separation into three different parts is carried out,

wherein, w _R ＝[w _R，1 ...，w _R，N ] ^T Represents a receive antenna selection vector in which each element corresponds to a receive antenna with sparsity | | w _R || ₀ ＝N _S ；w _T ＝[w _T，1 ，...，w _T，M ] ^T Representing a transmit antenna selection vector in which each element corresponds to a transmit antenna with a sparsity of w _T || ₀ ＝M _S ；w _P ＝[w _P，1，L ，...，w _P，M，L ] ^T Representing a pulse selection vector in which each element corresponds to a successive pulse, w _P，m，L ＝[w _P，m，1 ，...，w _P，m，L ] ^T Has a sparsity of w _P，m，L || ₀ ＝L _S，m ，L _S，m Represents the number of pulses that the mth transmit antenna can transmit;

step 6: building a joint optimization problem

Wherein the content of the first and second substances,

diag(w _S ) Representing diagonal elements with w _S A diagonal matrix of equal elements;

and 7: using w _S Substitution of w _V The optimization problem is simplified as follows:

wherein the content of the first and second substances,

for removing corresponding w in matrix or vector _S The operator of the row or column of item 0;

is that

The inverse operator of (2) indicates that the corresponding 0 row or 0 column is added back to the original matrix and vector;

and step 8: solving the optimization problem in step 7 by a greedy algorithm to obtain the optimal w _S Inverting the optimal weight vector w to further invert the optimal weight vector w

And finally determining the positions and pulse trains of the transmitting antenna and the receiving antenna.

The invention reduces the number of the receiving and transmitting antenna and the transmitting pulse and reduces the complexity of the system by optimizing the combined design of the receiving and transmitting antenna array and the transmitting pulse train. Meanwhile, the weight vectors are split and replaced, so that an optimization problem which can ensure the detection performance of the system and is easy to solve is obtained, and the calculation complexity is further reduced through a greedy algorithm.

Drawings

FIG. 1 shows the variation of the output SNR of different sparse structures with the input SNR, including the sparse structure obtained by the joint design of the present invention, and other two sparse uniform structures (US-FS and US-FA);

FIG. 2 is a beam diagram of a sparse structure for joint calculation according to the present invention with a fixed input signal-to-noise-and-noise ratio of-15.54 dB;

FIG. 3 is a beam diagram of a US-FA sparse uniform structure (US-FA) at a fixed input signal-to-noise-and-noise ratio of-15.54 dB.

Detailed Description

For convenience of description, the following definitions are first made:

bold capital letters represent matrices, bold lowercase letters represent vectors, (·) ^* Denotes conjugation, (. Cndot.) ^T Showing transposition, (.) ^H Representing conjugate transpose, diag (-) representing block diagonal matrix, the values on the diagonal being the values of the corresponding vector, E [ ·]Expressing expectation, | | O | | calving ₀ Is represented by ₀ The norm, i.e., the number of non-zero elements,

indicates that the kronecker product, indicates that the elements of the two vectors are multiplied correspondingly,

to remove matrix or vector correspondences w _S The operator of the row or column of the 0 term,

is that

The inverse of (3) indicates that 0 entries are added back to the original matrix and vector.

Consider a co-located antenna MIMO radar system. The range allowing the placement of the transmit and receive antennas is [0,Z, respectively _T ]And [0,Z _R ]. To simplify the analysis, [0,Z _T ]And [0,Z _R ]Respectively dispersed into M and N uniform lattice points with the spacing of d _T And d _R . Due to limited complexity, only M _S Less than or equal to M transmitting antennas and N _S N receiving antennas can be placed. If a transmitting antenna is placed at the M-th lattice point, M =1, …, M, its transmitted signal can be written as

Wherein h is _m (T), T is a narrow-band pulse signal with 0. Ltoreq. T.ltoreq.T, and satisfies the following orthogonality property

T denotes a Pulse Repetition Interval (PRI). (1) Wherein L represents s _m Total number of pulses in (t). To reduce complexity, a sparse vector is introduced later to select the pulses of the transmit part.

Suppose there are Q moving targets. If a receiving antenna is placed at the nth lattice point, N =1, …, N, then the low-pass equivalent signal of the target echo it receives can be expressed as

Therein, ζ _q Q =1, …, Q, representing the reflection coefficient of an object, assuming that the reflection coefficients of different objects are independent of each other. Tau. _q ， f _D，q ，θ _R，q And theta _T，q Respectively representing the time delay, doppler frequency, arrival of the q-th targetAngle (DOA) and departure angle (DOD). λ is the carrier wavelength. Separating signals originating from different transmitting antennas and from different pulses by a set of matched filters, i.e.

Stacking these signals can result in an NML-dimensional target vector,

wherein the content of the first and second substances,

is the steering vector for the qth target. In the formula (5), the compound represented by the formula (I),

and

respectively, the receive and transmit steering vectors, and the time steering vector, for the qth target.

It is assumed that the clutter consists of P scattering points. Similar to the previous analysis, the clutter echo can be modeled as

Wherein, mu _p P =1, …, P, denotes the reflection coefficients of the clutter, assuming they are independent identically distributed gaussian random variables. Tau. _c，p ， f _c，D，p ，φ _R，p And phi _T，p Respectively representing the time delay, the Doppler frequency, the arrival angle and the departure angle of the p < th > clutter scattering point. Through matched filtering, the NML dimension clutter vector can be written as

Wherein the content of the first and second substances,

and is

Thus, the observation signal after matched filtering can be expressed as

For clutter suppression, the observed signal is weighted by a space-time adaptive processing technique, y, i.e. w ^H y；

Wherein

Is a NML x 1 dimensional weight vector.

The goal is to find the optimal weight vector w to maximize the output signal-to-noise ratio SCNR _out 。

Rewriting the weight vector w into the form

w＝w _V ⊙w _S (10)

Wherein w _S Is a selection vector with elements other than 0, i.e. 1, indicating which grid pointsEither unselected or selected. For selected antenna or pulse position, w _V Containing the same weight as w.

The vector w will be selected according to the placement of the antennas and the transmission of the pulses _S Is divided into three different parts

Wherein, w _R ＝[w _R，1 ，...，w _R，N ] ^T Represents a receiving antenna selection vector with sparsity of w _R || ₀ ＝N _S ；

w _T ＝[w _T，1 ，...，w _T，M ] ^T Represents a transmit antenna selection vector with sparsity of w _T || ₀ ＝M _S ；

w _P ＝[w _P，1，L ，...，w _P，M，L ] ^T A vector of pulse selections is represented, and,

wherein w _P，m，L ＝[w _P，m，l ，...，w _P，m，L ] ^T Has a sparsity of w _P，m，L || ₀ ＝L _S，m ，L _S，m Indicating the number of pulses that the mth transmit antenna can transmit. Note that w is defined according to the formula (10) _S ，w _R 、w _T And w _P Are all non-0 or 1.

Bringing formula (10) into SCNR _out In the expression and in consideration of the restriction of the formula (11) on the number of pulses and antennas, the following optimization problem is established

Wherein the content of the first and second substances,

diag(w _S ) Represents the diagonal element and w _S A diagonal matrix of equal elements.

(12) The problem in the formula is an NP-hard problem, and it is difficult to directly obtain the result. Thus, introducing a w _S Substitution of w _V The method of (1). For any given w _S The formula (12) can be rewritten as

To simplify the analysis, the target echo signal is passed through a filter for space-time adaptive processing without distortion by applying a constraint to equation (13), i.e.

The optimization problem then becomes

It can be seen that the optimization problem in equation (14) is the classical least-square distortion-free response (MVDR) problem, the result of which can be expressed as

Where α is a scalar that satisfies the constraints of an equation, it has no effect on the signal to noise ratio function and can therefore be ignored.

Bringing equation (15) back into equation (12), the optimization problem can be simplified to

From this, the optimization problem becomes only with the selection vector w _S In this regard, it can be solved by a greedy algorithm with a low computational complexity. Is represented by the formula (16)To obtain w _S Then, w can be obtained from the formula (15) _V And finally obtaining w from the formula (10). In the optimization problem described above, the clutter plus noise covariance matrix R _u Can be estimated by many effective methods and this problem is not considered in the present invention.

Working principle of the invention

At the receiving end, after each receiving antenna receives the echo signal, the received signal is matched and filtered, and signals from different transmitting antennas and different pulses can be separated. The obtained signal samples are piled up to obtain an NML-dimensional observation signal vector

The NML signal samples correspond exactly to the positions of all possible M transmit antennas, L transmit pulses and N receive antennas. But due to the limitation of the complexity of the system, the number of the antenna and the pulse is less than NML, and the number of the non-0 elements in the signal sample y is reduced correspondingly. Therefore, the NML samples can be manipulated to design sparse arrays and pulse trains.

Since clutter exists in an observation region and an echo of the clutter is generally stronger than a signal echo, the clutter needs to be suppressed in order to improve system performance, and space-time adaptive processing is an effective clutter suppression technology. The weight is added to the observation signal y by utilizing the space-time self-adaptive processing technology to enable the output signal noise-to-noise ratio to reach the maximum, namely w ^H y，

Wherein

Is a nmlx 1 dimensional weight vector.

In the weight vector w, there are a total of NML elements corresponding to all possible positions of the pulse, transmit and receive antennas, but only a portion of them are valid due to system complexity constraints. A limited number of pulses and antennas may be placed at each corresponding feasible point.For a lattice point of an unassigned pulse or antenna, its corresponding element in w is set to 0; for a lattice point assigned to a pulse or antenna, its corresponding element in w will be optimized to maximize the output signal-to-noise ratio. When the limited number of transmitting antennas M _S Number of receiving antennas N _S And the number of pulses L _S Far less than the total number of lattices, i.e. N _S M _S L _S NML ≦ weight vector w is obviously a sparse vector with sparsity N _S M _S L _S . The sparsity of the weight vector just reflects the sparsity of the array and the pulse train and the limited positions of the antennas and the pulse at the lattice points. Therefore, the optimal sparse array and the optimal pulse train can be obtained by optimizing the weight vector w, and the clutter can be suppressed to maximize the output signal-to-noise ratio. Therefore, the joint design of sparse arrays, sparse pulses and space-time adaptive processing can be realized.

Each element in the weight vector w has two meanings, one represents the position of the antenna and the pulse in the sparse array and the sparse pulse train, and the other represents the weight for suppressing clutter. Thus, the weight vector w can be divided into two parts

w＝w _V ⊙w _S (18)

w _S Is a selection vector with elements other than 0, i.e., 1, a 1 indicates that the grid point is selected, i.e., the location where the antenna is placed or the pulse is transmitted, and a 0 indicates no. For selected antenna or pulse position, w _V Containing the same weight as w.

For the selection vector w _S Since there are three parts of the transmit array, transmit pulse and receive array, the three parts need to be sparsely designed. The selection vector w may be selected according to the placement of the respective antennas and the transmission of the pulses _S Is divided into three different parts

w _T 、w _P And w _R Is also non-0 or 1,is the selection vector for each of the three parts, showing the selection of each of the three parts.

For the optimization problem to be built, because the weight vector w is divided into w _S And w _V Two parts, then w is the optimization problem _S And w _V Two variables need to be optimized. Wherein, because w _S Is not 0, i.e. 1, so it is better optimized, and w _V Because of the optimization involved in the values of the elements, it is relatively difficult. So if a relationship between these two variables can be found, w will be _V By w _S To show that the difficulty of solving the optimization problem is greatly reduced. Thus, by adding a limiting condition, the target echo signal is passed through a filter for space-time adaptive processing without distortion, i.e. the filter

Convert the problem into a classical least square error undistorted response problem, w _v By w _S To indicate that is

To this end, the optimization problem is only related to w _S In this regard, it may be solved by a greedy algorithm. At the time of obtaining the optimum w _S After, by w derived before _S And w _V W, an optimum w can be obtained _V And w.

Two examples are given to illustrate the advantages of the design result with respect to the joint design of sparse arrays, sparse pulses, and space-time adaptive processing. In both examples, it is assumed that each of the possible fields contains M =3, n =12 and L =15 uniform grid points, which are each spaced apart by d _T ＝6λ，d _R = λ/2 and T =0.002s, where the carrier wavelength λ = c/f _c Carrier frequency f _c ＝10 ⁹ Hz, c represents the speed of light. For convenience, only sparse receive arrays and transmit bursts are jointly designed in the example, which means that there is a total of M _S = M =3 transmitting antennas, N _S =6 receiving antennas and L _S，m ＝L _S =10 pulses available for placement and transmissionAnd (4) shooting. Assuming 2 targets, their reflection coefficients are assumed to be equal, with angles and Doppler frequencies of 0 DEG, 50Hz, respectively]And [56 °,30Hz]. Suppose that the clutter contains 3 scattering points with angles and Doppler frequencies of 40 DEG, -30Hz][-60°，110Hz]And [ -10 °, -125Hz]. In example 1, an input signal to noise ratio SCNR is defined _in ＝|y _t | ² /E[|(y _c +y _n )| ² ]. Two sparse uniform structures are considered. The first sparse uniform structure has the same grid spacing (US-FS), i.e., the receive array grid spacing d _R = λ/2, pulse lattice spacing T =0.002s; the second sparse uniform structure (US-FA) keeps the aperture of the array and pulse constant, and its receiving array lattice spacing d _R ＝d _R，US-FA ＝(N-1)d _R /N _S =11 λ/12, pulse lattice spacing T = T _US-FA ＝(L-1)T/L _S =0.0028s. In example 2, let SCNR _in = 15.54dB, and the other parameter settings are the same as in example 1.

For example 1, it can be seen from fig. 1 that the output snr increases with increasing input snr, and the output snr obtained from the structure of the joint design is always higher than that obtained from the two sparse uniform structures, which means that the proposed joint design has better performance than the two sparse uniform structures under the same complexity constraint. For example 2, the beam pattern obtained from the sparse structure of the joint design in fig. 2 has two distinct peaks, while the beam pattern obtained from the US-FA structure in fig. 3 has several peaks in the area without the target due to clutter contamination, and the comparison result between fig. 2 and fig. 3 means that the sparse structure of the joint design has a higher output signal-to-noise ratio than the US-FA structure, which further corroborates the result obtained in example 1.

Claims (1)

1. A method for jointly calculating a sparse array and a pulse train of an MIMO radar is characterized by comprising the following steps:

step 1: the range that will allow the transmit antenna to be placed 0,Z _T ]And range of the receiving antenna 0,Z _R ]Respectively dispersed into M and N uniform lattice points with the spacing of d _T And d _R (ii) a The allowed total emission pulse number is L, and the pulse interval is T; due to limited complexity, only M _S Less than or equal to M transmitting antennas and N _S N receiving antennas can be placed, each transmitting antenna has L _S Less than or equal to L pulses can be transmitted;

and 2, step: the signals received by the N possible receiving antennas are written in vector form y by matched filtering, i.e.

Wherein, y _t Representing the echo signal of the target, provided that there are a total of Q targets, p _q And s _t,q Respectively representing the reflection coefficient and the guide vector of the qth target; y is _c Representing clutter echo signals assuming clutter containing a total of P scattering points, η _p And s _c,p Respectively representing the reflection coefficient and the guide vector of the p-th clutter scattering point; y is _n Representing noise, assuming zero mean and variance σ ² The white gaussian process of (a);

and step 3: adding a weight vector w to the matched and filtered signal, and calculating the optimal weight vector w to enable the output signal-to-noise ratio to be maximum; defining the output signal-to-noise ratio as the ratio of the output target signal power and the output clutter-to-noise power, i.e.

Wherein R is _u ＝R _c +R _n ，R _c As a clutter covariance matrix, R _n In the form of a noise covariance matrix,

and R _n ＝σ ² I, E represents expectation, and I represents an identity matrix;

and 4, step 4: the weight vector w is subjected to a split rewrite,

w＝w _V ⊙w _S

wherein, the two vectors indicate corresponding multiplication between elements of the two vectors; w is a _S Is a selection vector with elements other than 0, namely 1, which indicates which grid points are not selected or are selected; for selected antenna or pulse position, w _V Contains the same weight as w;

and 5: the vector w will be selected according to the placement of the antenna and the transmission of the pulse _S The separation into three different parts is carried out,

wherein w _R ＝[w _R,1 ,...,w _R,N ] ^T Representing a receive antenna selection vector, where each element corresponds to a receive antenna with sparsity | | w _R || ₀ ＝N _S ；w _T ＝[w _T,1 ,...,w _T,M ] ^T Representing a transmit antenna selection vector in which each element corresponds to a transmit antenna with a sparsity of w _T || ₀ ＝M _S ；w _P ＝[w _P,1,L ,...,w _P,M,L ] ^T Representing a pulse selection vector in which each element corresponds to a successive pulse, w _P,m,L ＝[w _P,m,1 ,...,w _P,m,L ] ^T Has a sparsity of w _P,m,L || ₀ ＝L _S,m ，L _S,m Represents the number of pulses that the mth transmit antenna can transmit;

step 6: building a joint optimization problem

||w _T || ₀ ＝M _S ,||w _P,m,L || ₀ ＝L _S,m ,

||w _R || ₀ ＝N _S ,w _S ∈{0,1} ^NML×1 ,

w _P ＝[w _P,1,L ,...,w _P,M,L ] ^T .

Wherein the content of the first and second substances,

diag(w _S ) Represents a diagonal element with w _S A diagonal matrix of equal elements;

and 7: using w _S Substitution of w _V The optimization problem is simplified as follows:

||w _R || ₀ ＝N _S ,w _S ∈{0,1} ^NML×1 ,

w _P ＝[w _P,1,L ,...,w _P,M,L ] ^T .

wherein, the first and the second end of the pipe are connected with each other,

for removing corresponding w in matrix or vector _S The operator of the row or column of item 0;

is that

The inverse operator of (2) indicates that the corresponding 0 row or 0 column is added back to the original matrix and vector;

and step 8: solving the optimization problem in step 7 by a greedy algorithm to obtain the optimal w _S Inverting the optimal weight vector w to further invert the optimal weight vector w

And finally determining the positions and pulse trains of the transmitting antenna and the receiving antenna.

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