CN112698289B

CN112698289B - MIMO radar target information recovery method based on compressed sensing

Info

Publication number: CN112698289B
Application number: CN202011423746.5A
Authority: CN
Inventors: 席峰; 梁诗儿; 李�杰
Original assignee: Nanjing University of Science and Technology
Current assignee: Nanjing University of Science and Technology
Priority date: 2020-12-08
Filing date: 2020-12-08
Publication date: 2024-05-17
Anticipated expiration: 2040-12-08
Also published as: CN112698289A

Abstract

The invention discloses a MIMO radar target information recovery method based on compressed sensing, which expands a traditional one-dimensional atomic norm algorithm into two-dimensional application to sparse target information recovery of an MIMO radar based on undersampling, then simulates the sparse target information recovery, and observes the influence of parameter recovery conditions under single target and multi-target conditions and different SNR on target parameter recovery errors under the algorithm. The invention not only maintains the resolution and the performance, but also reduces the number of antennas and the cost.

Description

MIMO radar target information recovery method based on compressed sensing

Technical Field

The invention belongs to the field of radar signal processing, and particularly relates to a MIMO radar target information recovery method based on compressed sensing.

Background

MIMO radar (multiple input multiple output radar) exhibits great potential in terms of flexibility and performance to develop advanced modern radars, bringing new theories and challenges. MIMO radars are classified into juxtaposed MIMO radars and distributed MIMO radars. Here we use a collocated MIMO radar system that exploits waveform diversity based on the mutual orthogonality of the transmitted signals. This creates a virtual array caused by the phase difference between the transmit and receive antennas. Such a system has a higher resolution than a phased array system with the same number of elements and transmissions, which contributes to the popularity of MIMO. This increased performance comes at the cost of greater complexity in the transmitter and receiver design. The research of the target tracking technology of the statistical MIMO radar describes that the target parameter recovery method of the traditional MIMO radar is to perform oversampling on a received signal, then match a filter, then perform wave beam forming and detect a peak value. Although the method can accurately recover the parameter information of the target, the method has very high requirements on the complexity and equipment of the system, and the cost is greatly increased.

We then propose to apply compressed sensing to MIMO radars to reduce the number of antennas or the number of samples per receiver, while recovering the target parameter information well without reducing resolution. Since CS-based MIMO radar requires fewer measurements for reliable target detection than conventional MIMO radar, power can be saved during data transmission to the fusion center, thereby extending the lifetime of the wireless network. And the MIMO radar system is arranged in a fusion center, all received data are processed in a combined mode, and information of potential targets is extracted through a CS method. Compared with the traditional method, the CS method greatly reduces the measurement quantity required by the fusion center to reliably detect the target. The transmission power savings obtained will significantly extend the lifetime of the wireless network. The advantages of MIMO radar are maintained while the measurements required for each receive antenna are significantly reduced.

Disclosure of Invention

The invention aims to provide a MIMO radar target information recovery method based on compressed sensing, which is based on undersampling, so that the resolution and the performance are maintained, the number of antennas is reduced, and the cost is reduced.

The technical solution for realizing the purpose of the invention is as follows: a MIMO radar target information recovery method based on compressed sensing expands a traditional one-dimensional atomic norm algorithm into two-dimensional application to sparse target information recovery of the MIMO radar based on undersampling, and comprises the following specific steps:

step 1, under the architecture of a classical MIMO radar, generating a transmitting signal and a receiving signal;

step 2, under the condition of considering single pulse, sampling the space and time of the received signal:

Firstly, carrying out fast Fourier transform on a received signal in a time domain, randomly taking k signal samples out of the obtained Fourier coefficients, and carrying out a matched filter; selecting a certain number of antennas from the total transmitting antennas and the receiving antennas as transmitters and receivers according to the sampling rate in a space domain;

step 3, generating a k-dimensional vector from the received signals of the k sampling points, and representing the k-dimensional vector by using a Van der Waals determinant;

step 4, defining a low-rank matrix X, and recovering the structured low-rank matrix X to obtain a distance sequence D and an azimuth sequence C of the target parameters;

step 5, pairing the distance sequence D and the azimuth sequence C of the target parameters so that the distance and the azimuth correspond to the targets of the distance sequence D and the azimuth sequence C and are arranged in the sequence;

And 6, performing simulation, and observing the influence of parameter recovery conditions under single-target and multi-target conditions and different SNR on target parameter recovery errors under the algorithm.

Compared with the prior art, the invention has the remarkable advantages that:

(1) On the basis of keeping the space and time resolution unchanged, the cost and the complexity of the device are greatly reduced. The number of antennas and the number of receivers are reduced.

(2) Meanwhile, the distance and the azimuth of the target are restored, the one-dimensional atomic norm algorithm is expanded to two dimensions, and the performance of the method is higher than that of the traditional sparse perception restoration algorithm in terms of restoration conditions and errors.

Drawings

Fig. 1 shows a MIMO radar array according to the present invention, wherein fig. (a) is a standard array, and fig. (b) is a sparse array.

Fig. 2 is a graph of the result of recovering target parameters by the atomic norm algorithm of a single target.

Fig. 3 is a graph of the result of recovering target parameters by the atomic norm algorithm of l=7 targets.

Fig. 4 is an error plot for target recovery for different SNRs.

Fig. 5 is a flowchart of a MIMO radar target information recovery method based on compressed sensing according to the present invention.

Detailed Description

The invention is described in further detail below with reference to the accompanying drawings.

The MIMO radar target information recovery method based on compressed sensing utilizes the concept of compressed sensing based on undersampling. The method breaks the connection between the sampling rate and the time resolution and the number of antennas and the spatial resolution. The method adopts low sampling rate, so that a low-speed ADC can be used, the cost, the power consumption and the complexity can be reduced greatly, and the performance can be similar to that of the prior art. The time resolution, the sampling rate and the number of antennas are broken through, the spatial undersampling is realized by a sparse antenna transmitting array and a sparse antenna receiving array, and the time domain undersampling is realized by a xampling system. Thus, it can be explicitly expressed as an estimate of the distance and orientation of the object. The method is characterized in that compression is realized in space and time, and the number of antennas and the number of samples acquired by each receiver are reduced while the distance and azimuth resolution are maintained.

Considering spatial compression, a collocated MIMO radar with M < T transmit antennas and Q < R receive antennas whose positions are randomly and uniformly selected within the aperture of a virtual array, i.eAnd/>Z is the normalized aperture, parameters ζ _m and ζ _q are the array parameters determined by the transmit and receive arrays. A random sparse antenna array is generated as in fig. 1.

Considering time compression again, we first derive the fourier coefficients of the received signal. In order to obtain fourier coefficients from low-rate samples of the received signal, we use the undersampling scheme as follows: for each received transmission, an arbitrary k value is obtained at a time, and frequency components are extracted from k sampling points of the received signal after appropriate simulation and processing. After obtaining the corresponding fourier coefficients, we apply matched filters to different transmitter channels using their non-overlapping nature in frequency.

The adopted target recovery algorithm is a two-dimensional atomic norm algorithm, and is improved and expanded on the basis of a general one-dimensional atomic norm algorithm. First we need to convert the range-azimuth joint estimation problem to that of low rank matrix recovery, and then apply atomic norm minimization to recover the low rank matrix.

Firstly, we need to convert the matrix into vandermonde matrix form, define the matrices D and C, and the information in the matrices D and C is the parameter time delay and azimuth angle of the target to be recovered. Our problem is to recover the target parameter distance and azimuth from the received signal y to recover the structured low rank matrix X from the received signal vector y. This is a non-convex problem, so we need to turn the rank minimization, which relaxes the non-convex problem, into trace minimization, converting this into a convex optimization problem, which is finally solved with the CVX convex optimization toolbox in Matlab.

After recovering the low rank matrix, the distance sequence and the azimuth sequence are obtained to be arranged randomly, so that the distance and azimuth parameter information is needed to be paired, so that the distance and the azimuth are arranged in the sequence corresponding to the targets of the distance and the azimuth.

Referring to fig. 5, the method for recovering MIMO radar target information based on compressed sensing according to the present invention comprises the following steps:

Step 1, the collocated MIMO radar generally adopts a virtual ULA structure, wherein the structure comprises R receivers and by/>, spaced apartThe T transmitters that are spaced apart (and vice versa) form two ULA. Here, λ is the signal wavelength. Coherent processing of the resulting TR channel generates a virtual array equivalent to/>Spacing receivers and normalizing aperture/>Is provided). Each transmit antenna transmits P pulses such that the mth transmit signal s _m (t) is:

Where P denotes the number of pulses, f _c denotes the carrier frequency, h _m (t) denotes that FDMA is to follow a generic model, Each pulse is broken down into N _c slots and has a duration of delta _t. t is time, τ is pulse repetition interval, p is pulse sequence, we use FDMA method to take advantage of the narrow nature of the transmitted waveform. In FDMA, the number of slots N _C =1, the characteristic parameter w _mu =1, the duration δ _t =0, and the center frequency f _m is selected from [ -TB _h/2,TB_h/2 ]. /(I)Can be regarded as a frequency-shifted version of the low-pass pulse v (t) =h ₀ (t), whose fourier transform H ₀ (ω) has a bandwidth of B _h, so that it is possible to obtain:

H_m(ω)＝H₀(ω-2πf_m).

ω is phase.

The transmitted pulses are reflected by the target and collected at the receiving antenna. Simplifying assumptions are made about the structure of the array and the position and motion of the target, thereby simplifying the representation of the received signal. Because the invention adopts single pulse, the received signal x _q (t) at the q-th antenna after demodulation to the baseband is:

Wherein the intermediate parameter η _mq＝(ξ_m+ζ_q) λ/c is determined by the positions of the transmitter and the receiver. The location of the antennas may be randomly chosen uniformly over the aperture range of the virtual array. I.e. by And/>The decision, where M represents the number of transmitters and Q represents the number of receivers, the parameters ζ _m and ζ _q are the array parameters determined by the transmit array and the receive array.

And 2, breaking the relation between the time resolution and the sampling rate and the number of antennas, wherein the spatial undersampling is realized by using a sparse antenna transmitting array and a sparse antenna receiving array, and the time domain undersampling is realized by using a xampling system. Thus, it can be explicitly expressed as an estimate of the distance and orientation of the object. After undersampling in the space-time domain, compression is realized in space and time, and the number of antennas and the number of samples acquired by each receiver are reduced while the distance and azimuth resolution are maintained. Considering that the space and time are sampled at this time, first, the fourier expression is derived from the received signal:

Where the fourier coefficients c _q k are obtained from the low-rate samples of the received signal, τ is the pulse repetition interval and k is the number of samples. We use subNyquist sampling schemes (for each received transmission to allow a set of arbitrary kappa to be obtained, the signal samples are received after appropriate analog preprocessing from K point to point by the k= |kappa|frequency component-hence MK fourier coefficients are obtained at the receiver of each MK sample, with K coefficients per band or transmission), after obtaining fourier coefficients we split them into channels for each transmitter, taking advantage of the fact that they do not overlap in frequency. Applying a matched filter, the normalized and aligned fourier coefficients of the channel between the mth transmitter and the qth receiver can be finally obtained:

Wherein the array parameters L represents the target number to be recovered, there are a total of L targets to be recovered, q represents the receiver number, m represents the transmitter number, R represents the number of transmit antennas, and our goal is to recover τ _l,θ_l from this.

Step 3, firstly, we consider the case of a single target. K points are sampled at the q-th receiver of the m-th transmit antenna. The above equation becomes:

wherein the cross-sectional parameters Representing radar cross section, in order to make the result more obvious and popular, the most suitable low-pass filter is directly considered as ideal selection, and the interference of external factors is removed. Because of f _m＝mB_h, while array parameters/>There are a total of M transmit antennas so the received signal can also be expressed as:

before using the atomic norm algorithm we need to define the following vandermonde determinant:

three intermediate variables are defined:

The known antenna array randomly selects M antennas from the T antennas as transmitting antennas, and the receiving antennas need to sum pulse signals transmitted by signals of the M transmitting antennas. Thus, a matrix G is introduced, which is an mxt-dimensional matrix containing only 0,1, the dimensions of each row corresponding to T antennas, and each row of the matrix G having a position of 1, which is the randomly selected transmit antenna coordinate. Examples: g is A total of m=3 antennas were chosen as transmit antennas. The m=1 antenna is the fifth antenna of the five antennas, the m=2 antenna is the second antenna of the five antennas, and the m=3 antenna is the third antenna of the five antennas. The location of 1 in G is random.

Then the above equation may yield the received signal as:

Last define intermediate variables Then the echo signals received by the Q receivers are combined so the received signal is expressed as:

Introducing a K-dimensional vector I _K＝[1,1,...,1]^T of all 1, the above formula can be:

Then, the KQ dimension vector I _KQ which is 1 and the Q dimension vector I _Q which is 1 are introduced, and the same kind of items are combined and simplified, so that the method can be obtained:

step4, performing joint estimation of the target parameter distance-azimuth angle through atomic norm minimization:

We turn the problem of joint estimation of range-azimuth into the problem of recovery of low rank matrices with atomic norm minimization. What we want to estimate is the parameter information of L targets, their azimuth angles are { θ ₁,θ₂,...,θ_l }, and the distance is { τ ₁,τ₂,...,τ_l }. Our problem translates into estimating the required range and azimuth parameters of the target from our measurements y.

Set sequence vector for storing target azimuthSequence vector/>, storing target time delay

Then there are:

defining a matrix k×q matrix X: first order

Wherein due toAnd/>The received signal for a single target is as follows: next we consider all targets:

next, let the Then/>

Next, an azimuth matrix and a delay matrix are defined:

D＝[d(τ₁),d(τ₂),...,d(τ_l)]^T；

C＝[c(θ₁),c(θ₂),...,c(θ_l)]^T。

defining a diagonal matrix: Λ=diag [ α ₁,...,α_l ]

Obtaining

X＝D·Λ·C^T

The information in matrices D and C is the parametric delay and azimuth of the target we want to recover. It can be seen that the low order matrix X determines the target information we need to know, and from the above equation it can be seen that matrix X has a certain inherent structure, D and C are two vandermonde matrices. Our problem is converted to recovering the structured low rank matrix X from vector y. In order that the structuring of matrix X is not lost at all times we define the following set of atoms:

wherein/> Is an MK vector,/>Is an MQ dimension vector, parameter/>Phi is three unknowns in the atomic set and is set forth herein only for the purpose of introducing the atomic set concept. Then a definition is made in matrix X as the/>, of the above formulaThe minimum atomic number of matrix X, that is, the minimum atomic l ₀ norm of the target matrix, is the minimum number of atoms that can be represented, so:

Meanwhile, the rank minimization problem of the conversion rank of the I X I _A,0 can be solved:

Wherein tope (u ₁) and tope (u ₂) are the topril expansion matrices of unknown vectors u ₁ and u ₂, and matrix H is our defined matrix of rank L. Next, because the non-convex problem is not well solved, we turn the rank minimization of the relaxed non-convex problem into trace minimization, and the original problem of recovering the structured low rank matrix X becomes a convex optimization problem:

Where R (-) represents a matrix, the missing position is 0 and the missing position is 0.σ ² refers to the power spectral density given a constraint in noisy environments, typically noise.

The CVX convex optimization tool box in Matlab can solve the convex problem, so the problem is solved. Therefore, the atomic norm algorithm can be known to recover signal information like a sparse reconstruction algorithm, and can recover originally lost information in a received signal and still perform parameter estimation of the signal under the condition that a data part is lost. The atomic norm algorithm selects the appropriate atomic composition received signals from which the complete signal can be recovered. After solving the low rank matrix H and vectors tope (u ₁) and tope (u ₂) with the CVX toolbox, vandermonde decomposition of tope (u ₁) and tope (u ₂) according to the known target number can yield two vectors { phi ₁,φ₂,...,φ_l },This is the distance and azimuth of the parameter information corresponding to each target that we need to obtain.

Step 5, after obtaining two sequences of the distance and the azimuth by solving the low-rank matrix, because the distance and the azimuth in the sequence are arranged randomly and are not arranged according to the targets, we need to pair the parameter information of the distance and the azimuth so that the distance and the azimuth correspond to the targets in the sequence. This allows the final result to be presented more intuitively to our eye. We first decompose the matrix H of rank L mentioned above to obtain:

Matrix U ₁ is an MK by L matrix, and matrix U ₂ is an MQ by L matrix. The next work we want to do is to decompose eigenvalues of the above Toeplitz matrices tope (u ₁) and tope (u ₂):

tope(u₁)＝W₁∑₁W₁ ^H (2)

Defining vector W ₁ and vector V ₂ are two intermediate vectors of length L ₁ and L ₂ respectively,

W₁＝[w(φ₁),w(φ₂),...,w(φ_L1)]

Since it can be obtained from the formula (1)And/>From this, in conjunction with equation (2), we know that there is an L ₁ XL matrix O ₁ to make the matrix/>And the presence of a L ₂ ×L matrix O ₂ makes the matrixThe matrix X above can become:

In (3) Is a matrix of L ₁×L₂, thus establishing a relationship between the two parameter distance sequences and the azimuth sequence. Thus, the matrix capable of effectively pairing the distance and the azimuth angle to be estimated becomes:

Here the symbol Meaning the Moore-Penrose pseudo-inverse (Moore-Penrose), we can choose the range azimuth position corresponding to the position of the largest L values in the matrix O to be the desired parameter position of the L targets in practical application.

Step 6, we next used 9 transmit antennas and 6 receive antennas in the simulation, with a bandwidth B _h of 2x 10 ⁶ HZ, a Pulse Repetition Interval (PRI) τ of 3.5 x 10 ^-6 s, a carrier frequency f _c = 10GHz, and a signal to noise ratio SNR = 30dB. Next, we estimate the parameter distance and azimuth of the target with atomic norm algorithm under single target and multi-target conditions, respectively, to get the result. The error of the algorithm in recovering the target information for different signal-to-noise ratios is calculated by the following formula:

Distance error

Azimuth error

The simulation results are shown in fig. 2-4, and we can see that under the condition of undersampling, the improved atomic norm algorithm can recover the target parameter information under the conditions of single target and multiple targets more perfectly. Figure 4 we can see that the range error and azimuth error recovered by the algorithm tend to settle and settle to a small value at signal to noise ratios greater than 30 dB.

Claims

1. A MIMO radar target information recovery method based on compressed sensing is characterized in that: based on undersampling, a traditional one-dimensional atomic norm algorithm is expanded into two-dimensional application to sparse target information recovery of the MIMO radar, and the method comprises the following specific steps:

Step 4, defining a low-rank matrix X, and recovering the structured low-rank matrix X to obtain a distance sequence D and an azimuth sequence C of the target parameters; the method comprises the following steps:

Defining a KXQ matrix X, letting Defining a distance sequence D= [ D (τ ₁),d(τ₂),...,d(τ_l)]^T, a sequence vector C= [ C (θ ₁),c(θ₂),...,c(θ_l)]^T; wherein θ _l and τ _l are target azimuth and distance to be recovered), defining a diagonal matrix Λ=diag [ α ₁,...,α_l ]; obtaining X=D·Λ·C ^T; L represents the target number, α _l represents the cross-sectional parameter,/>Representing a conjugate matrix of X;

2. The method for recovering target information of MIMO radar based on compressed sensing as claimed in claim 1, wherein step 3, generating a k-dimensional vector from the received signals of the k sampling points, and using a vandermonde determinant to represent the k-dimensional vector is as follows:

Receiving a signal Expressed as:

wherein the cross-sectional parameters Representing radar cross section, f _c being carrier frequency, B _h representing bandwidth, θ _l representing target azimuth to be recovered, τ _l representing target distance to be recovered; m represents the number of transmitters, R represents the number of transmitting antennas, q represents the number of receivers, K represents the total number of samples, and M represents the number of transmitters;

The vandermonde determinant form is:

Defining four intermediate vectors as a _K(τ_l)、a_T(θ_l)、a_T(τ_l)a_q(θ_l respectively), wherein

T represents the number of receiving antennas, Q represents the number of receivers, and τ represents time delay; thus, a matrix G is introduced, wherein the matrix G is an M multiplied by T dimensional matrix only comprising 0 and 1, the dimension of each row corresponds to T antennas, and each row of the matrix G has a position of1, and the position is the coordinates of the transmitting antenna selected randomly; i _KQ is a KQ-dimensional vector of all 1, I _Q is a Q-dimensional vector of all 1, I _K is a K-dimensional vector of all 1,For receiving a signal vector.

3. The method for recovering target information of MIMO radar based on compressed sensing according to claim 1, wherein in step 5, the distance sequence D and the azimuth sequence C of the target parameters are paired so that the distance and the azimuth correspond to their targets arranged in the sequence, specifically as follows:

Defining a matrix H with a rank of L, decomposing the matrix H to obtain a Toeplitz matrix, decomposing eigenvalues of the Toeplitz matrix, and simplifying the matrix H to obtain a matching matrix of L ₁×L₂ The distance azimuth position corresponding to the position of the largest L values in the matrix O is selected to be the required parameter position of the L targets, wherein the intermediate vector W ₁ and the vector V ₂ are two Toeplitz matrices with the lengths of L ₁ and L ₂ respectively, and the characteristic values are decomposed to obtain two vectors, and the symbol/>Meaning a moore-penrose pseudo-inverse.