CN114325626A - Bistatic MIMO target positioning method based on one-bit sampling - Google Patents

Abstract

The invention relates to the technical field of array signal processing, in particular to a bistatic MIMO target positioning method based on one-bit sampling, which comprises the steps of firstly arranging bistatic MIMO radar arrays, constructing constraint of an optimization problem according to the structure of multi-bit received data, simultaneously obtaining a multi-bit atomic norm minimization problem through convex relaxation of a target function, constructing constraint between theoretical data and one-bit observation data according to the characteristic that one-bit quantization does not change the positive and negative values, introducing a sparse disturbance vector to solve the optimization problem, then respectively searching two noiseless covariance matrixes obtained by solving the optimization problem by using MUSIC spectral peaks to obtain estimated values of targets DOA and DOD, and finally pairing two groups of angle estimated values by applying the proposed angle pairing algorithm, wherein one-bit data is used for reducing the system cost and the power consumption, and the angle estimation can be realized only by echo data of a single pulse, and thus also for fast moving objects.

Description

A bistatic MIMO target localization method based on one-bit sampling

technical field

The invention relates to the technical field of array signal processing, in particular to a bistatic MIMO target positioning method based on one-bit sampling.

Background technique

MIMO (Multiple-Input Multiple-Output) refers to the technology of using multiple antennas to send and receive signals in the field of wireless communication. MIMO radar uses multiple antennas to transmit mutually orthogonal waveforms at the same time, and uses multiple antennas to receive reflected echoes from the target. , MIMO radar target positioning refers to the estimation of DOD and DOA by using array signal processing technology according to the received reflected echo data. In the past decade, MIMO radar has attracted extensive attention due to its advantages in object detection and localization.

In order to solve the problem of MIMO radar target positioning parameter estimation, many algorithms have been used, such as the subspace algorithm based on eigenvalue decomposition and the compressed sensing algorithm based on signal sparsity. The above two types of algorithms both use multi-bit quantized data, but There are problems of high hardware cost and high data storage requirements of the system, so one-bit quantization is introduced into the research of MIMO radar target positioning. However, the existing methods are only for monostatic MIMO radar and require multiple pulse data, while for It is impractical to acquire multiple pulse echo data from a fast moving target.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a bistatic MIMO target locating method based on one-bit sampling, which aims to overcome the problem that it is difficult to collect multiple pulse echo data for fast moving targets in the prior art, and only needs the echo data of a single pulse. wave data, and use a one-bit ADC to quantify the received data, reducing system cost and power consumption.

To achieve the above object, the present invention provides a bistatic MIMO target positioning method based on one-bit sampling, comprising the following steps:

Arrange bistatic MIMO radar arrays;

Use the structure of multi-bit received data to construct constraints to obtain a multi-bit atomic norm minimization problem;

A one-bit atomic norm minimization optimization problem is proposed;

Use MUSIC technology to solve the DOA and DOD of the signal respectively;

Angle pairing for DOA and DOD.

Wherein, the bistatic MIMO radar array is two uniform linear arrays arranged on a plane, and for each receiving array element, a one-bit ADC is used to quantize the received data.

Among them, using the structure of multi-bit received data to construct constraints, the process of obtaining the multi-bit atomic norm minimization problem includes the following steps:

Define a noise-free covariance matrix according to the representation of the received data;

Build atomic sets based on the structure of noise-free covariance matrices;

According to the properties of atomic norm, the corresponding rank minimization problem is proposed;

The convex relaxation of the rank minimization problem is the minimization of the trace, and the objective function is modified;

The multi-bit observation data is introduced to constrain the optimization problem, and the final multi-bit atomic norm minimization problem is obtained.

Among them, in the process of proposing the optimization problem of one-bit atomic norm minimization, new constraints are constructed according to the characteristics that one-bit sampling does not change the original data symbol, and then the objective function is modified according to the sparsity of the disturbance vector.

Among them, the process of using the MUSIC technology to solve the DOA and DOD of the signal respectively is the process of using the MUSIC spectral peak search to obtain the estimated values of the target DOA and DOD.

Among them, in the process of performing angle pairing for DOA and DOD, first construct corresponding array flow patterns according to DOA and DOD respectively, and then use sorting matrix to assist in pairing operation.

The present invention provides a bistatic MIMO target positioning method based on one-bit sampling. First, the bistatic MIMO radar array is arranged, and then the constraints of the optimization problem are constructed according to the structure of the multi-bit received data, and the objective function is convexly relaxed to obtain The multi-bit atomic norm minimization problem, and then construct the constraints between the theoretical data and the one-bit observation data according to the characteristic that one-bit quantization does not change the positive and negative values, and introduce sparse perturbation vectors to solve the optimization problem. The two noise-free covariance matrices use the MUSIC spectral peak search to obtain the estimated values of the target DOA and DOD. Finally, the proposed angle pairing algorithm is used to pair the two sets of angle estimates. The invention only needs the echo data of a single pulse. Angle estimation can be achieved, so it is also suitable for fast moving targets, while using one bit of data, reducing system cost and power consumption.

Description of drawings

In order to illustrate the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that are used in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only These are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained from these drawings without creative efforts.

FIG. 1 is a schematic flowchart of a bistatic MIMO target positioning method based on one-bit sampling according to the present invention.

FIG. 2 is a schematic diagram of the arrangement of the bistatic MIMO radar array of the present invention.

FIG. 3 is a schematic diagram of the variation relationship between the root mean square error of DOA and DOD in a simulation experiment with SNR according to a specific embodiment of the present invention.

FIG. 4 is a schematic diagram showing the variation relationship between the root mean square error of DOA and DOD in a simulation experiment according to a specific embodiment of the present invention and the number of samples.

FIG. 5 is a schematic diagram of distribution of estimated angles in a simulation experiment according to a specific embodiment of the present invention.

Detailed ways

The following describes in detail the embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary, and are intended to explain the present invention and should not be construed as limiting the present invention.

The relevant English terms involved in the present invention are as follows, and follow-up only uses English to describe:

Analog-to-digital converter (analog-to-digital convert, ADC);

Departure angle (direction-of-departure, DOD);

Arrival angle (direction-of-arrival, DOA).

Referring to FIG. 1, the present invention proposes a bistatic MIMO target positioning method based on one-bit sampling, including the following steps:

S1: Arrange bistatic MIMO radar array;

S2: Use the structure of multi-bit received data to construct constraints to obtain the multi-bit atomic norm minimization problem;

S3: Propose a one-bit atomic norm minimization optimization problem;

S4: Use MUSIC technology to solve the DOA and DOD of the signal respectively;

S5: Angle pairing for DOA and DOD.

The bistatic MIMO radar array is two uniform linear arrays arranged on a plane. For each receiving array element, a one-bit ADC is used to quantize the received data.

The process of obtaining a multi-bit atomic norm minimization problem using the structure construction constraints of the multi-bit received data includes the following steps:

Define a noise-free covariance matrix according to the representation of the received data;

Build atomic sets based on the structure of noise-free covariance matrices;

According to the properties of atomic norm, the corresponding rank minimization problem is proposed;

The convex relaxation of the rank minimization problem is the minimization of the trace, and the objective function is modified;

The multi-bit observation data is introduced to constrain the optimization problem, and the final multi-bit atomic norm minimization problem is obtained.

In the process of proposing the one-bit atomic norm minimization optimization problem, new constraints are constructed and the objective function is modified according to the characteristic that one-bit sampling does not change the original data symbol.

The process of using MUSIC technology to solve the DOA and DOD of the signal respectively, specifically the process of using the MUSIC spectral peak search to obtain the estimated values of the target DOA and DOD.

In the process of angle pairing for DOA and DOD, the corresponding array flow pattern is first constructed according to DOA and DOD respectively, and then the pairing operation is performed with the assistance of sorting matrix.

Specifically, below in conjunction with embodiment and accompanying drawing, the algorithm of the present invention is described in further detail:

Step 1: Set up the antenna array:

A bistatic MIMO radar system as shown in Figure 1 is set up, and each receiving array element uses a one-bit ADC to quantize the received data. The number of elements of the transmitting array is M, and the array spacing is d. The number of elements of the receiving array is N, and the array spacing is also d. λ is the signal wavelength. This embodiment has K targets and the signal is modeled as a narrowband uncorrelated quadrature coded signal. The noise on the receiving array elements is zero-mean additive white Gaussian noise, and the noise is independent of the signal.

Therefore, before the one-bit quantization operation, the data received by the receiving array at time t can be expressed as:

Among them, Q is the total number of pulses, β _k is the reflection coefficient of the k-th target, ω _k =(2πv _k T _p )/λ is the corresponding Doppler frequency, v _k is the moving speed of the target, and T _p is the Pulse duration, s(t)=[s ₁ (t),...,s _M (t)] ^T represents the transmitted waveform vector, ( ) ^T represents the transpose, z _q (t)∈C ^N represents the addition The Gaussian noise vector, a(φ) and b(θ) represent the transmit and receive array flow patterns, and have the following forms:

a(φ)=[1,e ^{j(2πdsinφλ)} ,...,e ^{j(2π(M-1)dsinφ/λ)} ] ^T

b(θ)=[1,e ^{j(2πdsinθλ)} ,...,e ^{j(2π(N-1)dsinθ/λ)} ] ^T

where θ and φ are the DOA and DOD parameters of the signal.

The array observation data before one-bit quantization is expressed in matrix form as:

X _q =BΣΔ _q A ^T S+Z _q

Among them, S=[s(0),s(T _s ),...,s((L-1)T _s )]∈C ^M×L is the transmit data matrix, T _s represents the sampling interval, and L represents a The number of samples within a pulse, Z _q ∈ C ^N×L represents the complex matrix containing noise and quantization error, A=[a(φ ₁ ),...,a(φ _K )]∈C ^M×K and B= [b(θ ₁ ),...,b(θ _K )]∈C ^N×K represent the transmit and receive array flow pattern matrices, respectively, Σ and Δ _q are two diagonal matrices with the following structure:

Σ=diag([β ₁ ,...,β _K ])

When considering one-bit quantization, the observed data matrix is:

Y _q =Q ₁ (X _q -H _q )

表示复值量化函数，sign(·)表示符号函数，

和

分别表示复矩阵的实部和虚部。Among them, H _q is the known quantization threshold,

represents a complex-valued quantization function, sign( ) represents a sign function,

and

represent the real and imaginary parts of a complex matrix, respectively.

Step 2: Formulate the multi-bit atomic norm minimization optimization problem:

The invention adopts the atomic norm minimization technology, and needs to determine an atomic set according to the observation data. To do this, first look at the noise-free part of the observed data and define the noise-free covariance matrix:

At this point, the multi-bit observation matrix can be written as:

X _q =R _q S+Z _q

The corresponding set of atoms can be defined as:

The atomic l ₀ norm of R _q refers to the minimum number of atoms in G that can represent R _q , namely

According to the properties of the atomic norm, the above formula can be calculated by a positive semi-definite optimization problem as follows:

Among them, Tu ₁ and Tu ₂ are Hermitian Toeplitz matrices constructed with u ₁ and u ₂ as the first column, respectively.

Convex relaxation of the rank minimization problem of the NP-hard matrix H of the above formula to minimize the trace, that is to say, change the objective function to tr(Tu ₁ )+tr(Tu ₂ ), and introduce noisy multi-bit The observation data constrains R _q to obtain the final multi-bit atomic norm minimization problem:

||X _q -R _q S|| _F ≤ε

where ε is a custom parameter affected by noise and quantization error, and ||·|| _F is the Frobenius norm.

Step 3: Propose a one-bit atomic norm minimization optimization problem:

First, Y _q =Q ₁ (X _q -H _q )=Q ₁ (R _q S+Z _q -H _q ), after column vectorization, vec(Y _q )=vec(Q ₁ (R _q S+Z _q -H _q )).

Based on the multi-bit atomic norm minimization problem, a new constraint is constructed according to the characteristic that one-bit sampling does not change the original data symbol

A sparse perturbation vector p _q is then introduced to remove the effects of unknown random noise and quantization errors in z _q , and then the one-bit constraint can be updated as:

Here, p _q is a sparse vector parameter with the same dimension as z _q . In order to enhance the sparsity of the perturbation vector p _q , the objective function needs to be modified. Finally, the following one-bit atomic norm minimization problem is obtained, and u ₁ is solved, u ₂ and R _q

Among them, ||·|| ₁ represents the vector one norm.

Step 4: Use the MUSIC technique to solve the DOA and DOD of the signal separately:

Decomposing T(u ₁ ) and T(u ₂ ) features, we have

Among them, (·) ^H represents the conjugate transpose, and U _sr is the N×K-dimensional received signal subspace, which is stretched by the eigenvectors corresponding to the K largest eigenvalues of Tu ₁ . Σ _sr is a K × K dimensional diagonal matrix that contains the K largest eigenvalues of Tu ₁ . _Unr is an N×(NK) dimensional received noise subspace, which is stretched by the eigenvectors corresponding to the (NK) smallest eigenvalues of Tu ₁ . Σ _nr is a (NK)×(NK) dimensional diagonal matrix that contains the (NK) smallest eigenvalues of Tu ₁ . U _st is an M×K dimensional transmitted signal subspace, stretched by the eigenvectors corresponding to the K largest eigenvalues of Tu ₂ . Σ _st is a K × K dimensional diagonal matrix that contains the K largest eigenvalues of Tu ₂ . U _nt is an M×(MK) dimensional emission noise subspace, stretched by the eigenvectors corresponding to the (MK) smallest eigenvalues of Tu ₂ . Σ _nt is a (MK) × (MK) dimensional diagonal matrix containing the (MK) smallest eigenvalues of Tu ₂ .

Then, DOA and DOD estimates can be obtained, respectively, using MUSIC peak search:

where (·) ^* represents conjugation.

Step 5: Angle Pairing:

Because the noise-free covariance matrix estimated in steps 2 and 3 can be approximated as:

That is, when the two sets of angles are paired successfully, the sorting matrix Λ is a diagonal matrix. And according to the above formula, the approximate estimated value of the sorting matrix can be obtained

表示伪逆。Angle pairing can be performed based on this, where

represents the pseudo-inverse.

以任意的角度顺序构造接收阵列流型

然后用估计出的DOD角度

以全部的排列组合形式构造所有可能的阵列流型

(共K！种结果，其中(·)！表示阶乘)。再将通过求解步骤2或步骤3的优化问题估计出的无噪声协方差矩阵

构造出的

和全部的K！个

代入上面Λ的估计式中，求出K！个排序矩阵Λ的估计值，找到其中K个最大的元素位于对角线上的Λ。求出这个Λ的

和

为配对好的发射和接收阵列流型，这两个阵列流型相同列序号包含的角度就对应于同一目标。分别找到这K组列向量对应的K对角度，即完成配对操作。The specific method is to accept the array flow pattern B as the benchmark, and use the estimated DOA angle

Construct receive array manifolds in arbitrary angular order

Then use the estimated DOD angle

Construct all possible array manifolds in all permutations and combinations

(A total of K! kinds of results, where (·)! represents factorial). Then the noise-free covariance matrix estimated by solving the optimization problem of step 2 or step 3

constructed

and all K! indivual

Substitute into the estimation formula of Λ above to find K! An estimate of the sorting matrix Λ, find the Λ where the K largest elements are located on the diagonal. Find this Λ

and

For paired transmit and receive array patterns, the angles contained in the same column number of the two array patterns correspond to the same target. Find the K pairs of angles corresponding to the K groups of column vectors respectively, that is, to complete the pairing operation.

Further, three groups of simulation experiments are also designed in the present invention. Please refer to FIG. 3 , FIG. 4 and FIG. 5 for the experimental results. The first set of experiments are the proposed one-bit atomic norm minimization algorithm (referred to as 1b-ANM algorithm in the experiment), the proposed multi-bit atomic norm minimization algorithm (abbreviated as mb-ANM algorithm in the experiment), effective Array aperture expansion technology (referred to as EAET algorithm in the experiment) [8] shows the relationship between the root mean square error of DOA and DOD estimation with the signal-to-noise ratio when the number of samples in a single pulse is 128. The second set of experiments is that the number of samples in a single pulse of the mb-ANM algorithm and the EAET algorithm is fixed to 32 under the condition of a signal-to-noise ratio of 10dB, while the number of samples of the 1b-ANM algorithm gradually increases. At this time, the DOA and DOD estimates Root mean square error as a function of the number of samples. The third group of experiments gives the distribution of the angle estimates of the 1b-ANM algorithm when the signal-to-noise ratio is 10dB, which is used to verify the effectiveness of the proposed angle pairing step.

The number of random experiments in the three groups of experiments are all 100, the arrays used are the same, the number of receiving and transmitting array elements is 18, the array spacing is d=λ/2, and the real and imaginary parts of H _q obey the same uniform distribution. The number of incident targets in the first two groups of experiments is K=2, and the target angles are (0°, 30°) and (20°, 40°) respectively. The number of incident targets in the third group of experiments is K=8, and the target angles are (-60°, -20°), (-40°, 50°), (-30°, -50°), (-10 °, 0°), (10°, -10°), (20°, 40°), (40°, -40°) and (50°, 20°). The Doppler frequency of the k-th target is set to ω _k =0.1k, the magnitude of the reflection coefficient β _k is set to 1, and the phase is uniformly distributed in [0, 2π].

The above disclosure is only a preferred embodiment of the present invention, and of course, it cannot limit the scope of rights of the present invention. Those of ordinary skill in the art can understand that all or part of the process of implementing the above embodiment can be realized according to the rights of the present invention. The equivalent changes required by the invention still belong to the scope covered by the invention.

Claims (6)

1. a bistatic MIMO target positioning method based on one-bit sampling, is characterized in that, comprises the following steps: Arrange bistatic MIMO radar arrays; Use the structure of multi-bit received data to construct constraints to obtain a multi-bit atomic norm minimization problem; A one-bit atomic norm minimization optimization problem is proposed; Use MUSIC technology to solve the DOA and DOD of the signal respectively; Angle pairing for DOA and DOD. 2. the bistatic MIMO target positioning method based on one-bit sampling as claimed in claim 1, is characterized in that, The bistatic MIMO radar array is two uniform linear arrays arranged on a plane. For each receiving array element, a one-bit ADC is used to quantize the received data. 3. the bistatic MIMO target positioning method based on one-bit sampling as claimed in claim 1, is characterized in that, The process of obtaining a multi-bit atomic norm minimization problem using the structure construction constraints of the multi-bit received data includes the following steps: Define a noise-free covariance matrix according to the representation of the received data; Build atomic sets based on the structure of noise-free covariance matrices; According to the properties of atomic norm, the corresponding rank minimization problem is proposed; The convex relaxation of the rank minimization problem is the minimization of the trace, and the objective function is modified; The multi-bit observation data is introduced to constrain the optimization problem, and the final multi-bit atomic norm minimization problem is obtained. 4. the bistatic MIMO target positioning method based on one-bit sampling as claimed in claim 1, is characterized in that, In the process of proposing one-bit atomic norm minimization optimization problem, according to the characteristic that one-bit sampling does not change the original data symbol, new constraints are constructed, and then the objective function is modified according to the sparsity of the disturbance vector. 5. the bistatic MIMO target positioning method based on one-bit sampling as claimed in claim 1, is characterized in that, The process of using MUSIC technology to solve the DOA and DOD of the signal respectively, specifically the process of using the MUSIC spectral peak search to obtain the estimated values of the target DOA and DOD. 6. The bistatic MIMO target positioning method based on one-bit sampling as claimed in claim 1, is characterized in that, In the process of angle pairing for DOA and DOD, the corresponding array flow pattern is first constructed according to DOA and DOD respectively, and then the pairing operation is performed with the assistance of sorting matrix.

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