CN113219461A - Design method of sparse array of millimeter wave radar based on maximizing signal-to-noise ratio - Google Patents

Abstract

The invention discloses a millimeter-wave radar sparse array design method based on maximizing signal-to-noise ratio, and relates to the field of automatic driving millimeter-wave radar target detection; including the problem of building a maximizing SINR based on an FMCW millimeter-wave radar array detection model; Under the condition that the correlation is known, the sparse array is designed by the successive linear approximation algorithm; under the condition that the autocorrelation of the spatial lag data is not known, the low-rank matrix completion method is used to interpolate the autocorrelation value corresponding to the missing lag based on the semi-positive definite Toeplitz constraint. , and solve the sparse array design problem by convex optimization method. The method proposed in the invention can improve the target detection performance while meeting the requirements of distance and speed resolution under the constraint of resolution, and has good convergence. In addition, the beam pattern has lower side lobes, because the proposed method optimizes the receiving weight to concentrate the power in the direction of the target while suppressing echoes in other directions.

Description

Design method for sparse array of mmWave radar based on maximizing signal-to-noise ratio

technical field

The invention relates to the field of automatic driving millimeter-wave radar target detection, in particular to a sparse array design method of a millimeter-wave radar based on maximizing a signal-to-noise ratio.

Background technique

In recent years, with the rapid iteration of the automotive industry, millimeter-wave radar has gradually become an indispensable sensor for autonomous driving due to its advantages of low cost, high precision, and good stability. Millimeter-wave radar transmits a designable signal to free space through the transmitter, and the receiver receives the echoes of targets and other objects, and then processes the obtained echoes based on relevant signal processing methods to perceive environmental information. It can be seen that the degree of freedom of the system airspace can affect the perception accuracy of environmental information. Increasing the degree of freedom of the system airspace can improve the parameter resolution, measurement accuracy and clutter suppression performance, thereby improving the system target detection and estimation ability and thus enhancing the unmanned environment perception ability. However, due to the limited size of the automotive platform, it is impossible to increase the number of array elements indefinitely to improve the degree of freedom in the airspace. For this problem, researchers choose the transceiver array elements to improve the degree of freedom in the airspace and reduce the system overhead, which is a sparse array design. .

In the absence of interference, Wang et al. proposed a sparse array design method based on convex relaxation and Iterative Linear Fractional Programming (ILFP), which solved the problem of non-convex antenna selection for sparse array beamformers. In the case of interference, Hamza et al. proposed a sparse array design method for receive beamforming with maximum signal-to-interference-noise ratio for single and multi-point sources. In addition, Zheng et al. proposed an adaptive beamforming sparse array design method, which is based on the criterion of maximizing the signal interference noise ratio (SINR) to obtain the optimal array configuration, however, it ignores the angle of radio propagation Diffusion effect. In response to this problem, Hamza et al. proposed an optimal sparse array design method in the presence of local scattering, which solved the influence of angular diffusion on detection performance. In order to reduce the influence of high sidelobe level, Jarske et al. proposed an array refinement design method to minimize sidelobes, that is, based on the fully filled array, the sensors are systematically removed in turn. In addition, Leahy et al. proposed a sparse array design method to optimize peak sidelobe levels, involving the joint design of sensor locations and their corresponding beamforming weights. Global optimization tools for solving sparse array beamforming, such as Genetic Algorithm (GA) algorithm and convex relaxation method, have been widely used in sensor selection problems. The array configuration and weights are adapted to the time-varying sensing environment, which can be achieved by adjusting the antenna positions and corresponding weights. To sum up, the sparse array design problem can be formulated by maximizing the SINR model, however, maximizing the SINR over all possible sparse topologies is a combinatorial optimization problem, which is usually a challenging polynomial solution problem. Furthermore, optimal design of sparse arrays requires estimating the autocorrelation of all spatially lagged data over the array aperture, whereas existing methods typically assume that the full correlation matrix is known to design sparse arrays.

SUMMARY OF THE INVENTION

Aiming at the problem that the limited platform space of autonomous driving leads to the low degree of freedom of the millimeter-wave radar system, which results in poor target detection performance, the present invention proposes a sparse array design method for millimeter-wave radar based on maximizing the signal-to-noise ratio, including FMCW-based millimeter-wave radar. The problem of maximizing SINR in the construction of an array detection model; under the condition that the autocorrelation of the spatial lag data is known, the sparse array is designed by the successive linear approximation (SCA) algorithm; under the condition that the autocorrelation of the spatial lag data is not known, based on the semi-positive definite Toeplitz constraint A low-rank matrix completion method is used to interpolate the autocorrelation values corresponding to the missing lags, and a convex optimization method is used to solve the sparse array design problem.

Due to adopting the above technical solutions, the present invention can achieve the following technical effects: the method proposed in the present invention can improve the target detection performance while meeting the requirements of distance and speed resolution under resolution constraints, and has good convergence. In addition, the beam pattern has lower side lobes, because the proposed method optimizes the receiving weight to concentrate the power in the direction of the target while suppressing echoes in other directions. A joint optimization model of transmitting waveform parameters and receiving weights with range and velocity resolution constraints is established to improve the performance of millimeter-wave radar target detection and range and velocity resolution.

Description of drawings

In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the accompanying drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only These are some embodiments described in this application. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without any creative effort.

Fig. 1 is the flow chart that the present invention realizes;

Fig. 2 is the structure diagram of sparse array element selection under single interference condition;

Figure 3 is a graph showing the variation of the average SINR output of various sparse arrays with the incident angle of the desired signal under a single interference condition;

Fig. 4 is a structure diagram of sparse array element selection under multiple interference conditions;

Figure 5 is a graph showing the variation of the average SINR of various sparse array outputs with the incident angle of the desired signal under multiple interference conditions.

Detailed ways

The implementation steps of the present invention will be described in further detail below in conjunction with accompanying drawing 1: The present invention proposes a method for improving the detection probability of a millimeter-wave radar target, that is, a sparse array design method for a millimeter-wave radar based on maximizing the signal-to-noise ratio, which specifically includes the following step:

Step 1. Construct the problem of maximizing SINR based on the FMCW millimeter-wave radar array detection model;

Because FMCW radar has the characteristics of low cost, high resolution and high integration, autonomous driving millimeter-wave radar often uses FMCW with constant amplitude characteristics. The FMCW signal can be expressed as:

s(t)=exp(j2πf ₀ t+jπμt ² )

Among them, f ₀ is the initial frequency, μ=B/T is the modulation frequency, and B and T are the signal frequency modulation bandwidth and frequency sweep period, respectively.

The millimeter-wave radar receiving array is composed of N uniformly spaced and isotropic array elements, then the signal x(t) received by the millimeter-wave radar array element at time t can be expressed as:

为θ₀方向目标导向矢量，

为θ_k方向干扰导向矢量，d和λ分别为相邻阵元间隔及载波波长，通常d≤λ/2。v(t)为接收阵列噪声，可建模为服从高斯分布，其均值为0，协方差为σ_v ²。s_i(t)为干扰源信号。以采样率f_s进行采样，可得数字波束形成输入信号为：Among them, K is the number of interference sources,

is the target steering vector in the direction of θ ₀ ,

is the interference steering vector in the θ _k direction, d and λ are the adjacent array element spacing and carrier wavelength, respectively, usually d≤λ/2. v(t) is the received array noise, which can be modeled as a Gaussian distribution with a mean of 0 and a covariance of σ _v ² . _si (t) is the interference source signal. Sampling at the sampling rate f _s , the digital beamforming input signal can be obtained as:

After being weighted by the beam weighting coefficient, the beamforming output signal can be obtained as:

y(n)=w ^H x(n)

Among them, w is the receiving weight vector.

Based on the above, the SINR expression can be obtained as follows:

为干扰与不相关噪声的协方差矩阵，

为第k个干扰的功率。基于最小畸变(MVDR)准则，设计权值w以最大化SINR的优化问题可表示为：Wherein, R _s =σ ² a(θ ₀ )a ^H (θ ₀ ) is the target signal covariance matrix, and σ ² =E{s(n)s ^H (n)} is the target signal power.

is the covariance matrix of interference and uncorrelated noise,

is the power of the k-th interference. Based on the minimum distortion (MVDR) criterion, the optimization problem of designing weights w to maximize SINR can be expressed as:

stw ^H R _s w = 1

Since noise and interference cannot be separated from the array elements, in practical applications, R _x =R _s +R _i is used to replace R _i , then the above formula can be rewritten as:

stw ^H R _s w = 1

前者可以较为容易地由所接收L个快照x估计。Solving the above problem only needs to receive the data correlation matrix R _x =E(xx ^H ) and the expected DOA. based on

The former can be estimated relatively easily from the L snapshots x received.

由此，最优输出SINR可表示为：Solving the above formula can get:

Thus, the optimal output SINR can be expressed as:

Among them, Λ _max {·} represents the largest eigenvalue. The above equation applies to any array topology.

Step 2. Design a sparse array by successive linear approximation algorithm under the condition that the spatial lag data autocorrelation is known;

Under the condition that the full correlation matrix is known, in order to obtain a sparse solution, an additional sparse constraint can be introduced into the model of the maximizing SINR problem, namely:

stw ^H R _s w≥1

||w|| ₀ =P

Among them, ||·|| ₀ indicates that the number of constraint weight vectors w is the number P of sensors obtained by selection. The above equation is obviously a non-convex problem, which is not easy to solve based on traditional optimization methods. To solve this problem, the objective function in the above formula can be exchanged with the quadratic constraint, namely:

stw ^H R _x w≤1

||w|| ₀ =P

Usually, the received weight is a complex number, and the quadratic function is a real number, so the above problem still cannot be solved directly. Since the real and imaginary complex terms of the optimal weight vector are usually decoupled, the above problem can be real-valued by defining the receiving weight real vector and the corresponding correlation matrix, namely:

st

||w|| ₀ =P

和

分别为R_s、R_i和w实数化表达。in,

and

R _s , R _i and w are expressed in real numbers, respectively.

In order to solve the above problem efficiently, this problem can be equivalent to the following successive linear approximation form:

st

||w|| ₀ =P

i表示第i次迭代。最后，通过最小化混合l_1-∞范数松弛非凸l_o范数以高效获得稀疏解：in,

i represents the ith iteration. Finally, the non-convex l _o norm is relaxed by minimizing the mixed l _1-∞ norm to efficiently obtain a sparse solution:

其中，向量

包含与第l个传感器对应的波束形成权值实部及虚部，||·||_∞选择

的最大值。对于初始迭代，可将正则参数μ设为0，以使上述优化问题快速收敛。需要注意的是，参数μ本身并不能保证最终解为P稀疏。因此，为保证最终解的稀疏性，需要在可能的上下限范围内通过二进制搜索来获得μ最优值以保证上述优化问题可收敛至P稀疏。st

where the vector

Contains the real part and imaginary part of the beamforming weight corresponding to the lth sensor, || · || _∞ selection

the maximum value of . For the initial iteration, the regularization parameter μ can be set to 0 to make the above optimization problem converge quickly. It should be noted that the parameter μ itself does not guarantee that the final solution is P-sparse. Therefore, in order to ensure the sparsity of the final solution, it is necessary to obtain the optimal value of μ through binary search within the possible upper and lower limits to ensure that the above optimization problem can converge to P-sparse.

Step 3. Under the condition that the autocorrelation of the spatial lag data is not known, the basis is to obtain the autocorrelation of all the spatial lag data of the array aperture, and the low-rank matrix completion method is used to interpolate the autocorrelation values corresponding to the missing lags under the semi-definite Toeplitz constraint. , and solve the sparse array design problem by convex optimization method.

The above sparse array design based on the SCA algorithm assumes that the full correlation matrix is known. However, in actual scenarios, the full correlation matrix is very difficult to obtain, and there may be more missing correlation lags. In view of this problem, the present invention proposes a semi-positive definite Toepltiz matrix completion method to effectively utilize the unknown correlation matrix structure to improve the detection performance of the designed array. The proposed matrix completion method can be expressed as:

stToeplitz(l) ≥ 0

表示矩阵Frobenius范数的平方，式中该范数旨在使观测相关值和未知Toeplitz矩阵相应项之间误差平方总和最小化。正则化参数ζ权衡误差项及追踪启发项，其标称值通常根据问题的数值经验调整。上述问题为凸问题，因此可基于众多凸优化工具包获得高效求解。where Toeplitz(l) returns the symmetric Toeplitz matrix, where l and ^lH define the first row and first column of Toeplitz(l), respectively. The matrix R _P is the received data correlation matrix with the relevant lags missing, and the corresponding elements of the missing relevant lags are set to zero. The symbol ⊙ denotes the Hadamard product and ≥ denotes a matrix inequality with positive semi-definite constraints. The matrix Z is a binary matrix,

represents the square of the Frobenius norm of the matrix, where the norm is designed to minimize the sum of squared errors between the observed correlation values and the corresponding entries of the unknown Toeplitz matrix. The regularization parameter ζ trades off the error term and the tracking heuristic term, and its nominal value is usually adjusted based on the numerical experience of the problem. The above problem is convex and can therefore be solved efficiently based on a number of convex optimization toolkits.

Based on the above, in order to solve the problem that the limited space of the autonomous driving platform makes the millimeter-wave radar less spatial degree of freedom, which leads to the low target detection performance of the millimeter-wave radar, the present invention proposes a sparse millimeter-wave radar based on maximizing the signal-to-noise ratio. Array Design Methods. The proposed method firstly constructs the optimization weight problem of maximizing SINR based on the FMCW millimeter-wave radar array detection model; secondly, it optimizes the weights based on the SCA algorithm to realize the sparse array design; finally, in order to obtain the data autocorrelation of all the spatial lags on the array aperture, a semi-quantitative method is adopted. Low-rank matrix completion method under positive definite Toeplitz constraints to interpolate autocorrelation values corresponding to missing lags. The simulation results show that compared with the sparse array based on the SCA algorithm and the enumeration method, the proposed method can significantly improve the target detection performance of the millimeter-wave array radar.

The effect of the present invention can be further illustrated by the following simulation:

By comparing with the optimal sparse array based on SCA algorithm and the optimal sparse array obtained by enumeration method, and analyzing the detection performance under single interference and multi-interference cases one by one, the effectiveness of the proposed algorithm is verified. The simulation environment is: CPU: Intel(R) Core(TM) i7-7700, RAM: 8GB, MATLAB R2016a. The simulation conditions are: considering the given number of receiving sensors N=10, the array element spacing d=λ/2, the number of sensors P=6 can be selected, the signal-to-noise ratio SNR=0dB, the interference-to-noise ratio INR=20dB, the initialization ε=0.05 , the binary search method for the sparsity parameter μ is set in the range of 0.01 to 5.

Assuming that the target signal is in the 10° direction, and there is an interfering signal in the -40° direction, Figure 2 shows the structure diagram of the sparse array element selection under single interference conditions. Figure 2(a) shows an initial 6-element sparse array configuration with randomly selected 10-element positions to estimate the data correlation matrix. This configuration has missing correlation hysteresis and occupies only a small portion of the aperture. Figure 2(b) shows the sparse array configuration designed based on the SCA algorithm, and the optimal sparse array output SINR is 11.23dB. At the same time, Fig. 2(c) shows the optimal SINR array obtained by the enumeration method, and its SINR is 11.65dB. It is worth noting that the possible array configurations are orders of magnitude larger, which may lead to this problem cannot be solved by enumeration search. L=200 snapshot data is randomly selected, and the full-array Toeplitz estimate is recovered by matrix completion with a regularization parameter ζ=0.5. Figure 2(d) shows the optimal sparse array configuration achieved by matrix completion, and its SINR is 11.50dB, and the matrix completion configuration achieves better performance than the optimized configuration based on the SCA algorithm.

It is assumed that the target signal is in the direction of θ=[-30:10:30]°, and there is an interfering signal in the direction of -40°. Solving the SINR obtained by the optimal sparse array in Fig. 2, Fig. 3 is a graph of the average SINR output of various sparse arrays with the expected signal incident angle. It can be seen from Fig. 3 that the output SINR of the proposed algorithm is second only to that obtained by the enumeration method. Excellent SINR, the average error is about 0.2dB, and the maximum error does not exceed 0.4dB. Compared with the output SINR based on the SCA algorithm, the output SINR of the proposed algorithm is significantly higher than the output SINR based on the SCA algorithm. This is because the matrix completion effectively utilizes the structure of the unknown correlation matrix. It shows that the proposed algorithm can significantly improve the detection performance.

Assuming that the target signal is in the 10° direction, there are three interfering signals in the -40°, -20° and 50° directions at the same time. Figure 4 is a structural diagram of the selection of sparse array elements under multiple interference conditions. Figure 4(a) is the initial sparse array configuration of the estimated data correlation matrix randomly selected from 10 array element positions, and Figure 4(b) is the sparse array configuration designed based on the SCA algorithm, and the obtained optimal sparse array The SINR of the array output is 10.72dB. At the same time, Fig. 4(c) shows the optimal SINR array solved by the enumeration method, and its SINR is 11.35dB. Randomly select L=200 snapshot data, and restore the full-array Toeplitz estimate by matrix completion with regularization parameter ζ=0.5. Figure 4(d) shows the optimal sparse array configuration achieved by matrix completion, and its SINR is 11.11 dB, the matrix completion configuration has a higher output SINR, indicating that the matrix completion algorithm is still effective for improving SINR under multi-interference conditions.

It is assumed that the target signal is in the direction of θ=[-30:10:30]°, and there are three interfering signals in the directions of -40°, -20° and 50° at the same time. Solving the SINR obtained by the optimal sparse array in Figure 4, Figure 5 is the average SINR performance curve of various sparse arrays relative to the expected signal incident angle. It can be seen from Figure 5 that the matrix completion method can be significantly improved under multi-interference conditions. The SINR is second only to the SINR obtained by the enumeration method. The average SINR of the proposed method is about 0.3dB lower than that of the enumeration method. It can be seen that the proposed algorithm can still improve the detection performance under multi-interference conditions.

The computational complexity of the enumeration method is too high and is not suitable for practical applications. To sum up, compared with the sparse array based on the SCA algorithm and the enumeration method, the proposed method can significantly improve the target detection performance of the millimeter-wave array radar. Therefore, the algorithm proposed in the present invention can provide a solid theoretical and engineering realization basis for the improvement of the target detection performance of the millimeter-wave radar of the autonomous driving platform in practical applications.

The embodiments of the present invention have better implementation, and are not intended to limit the present invention in any form. The technical features or combinations of technical features described in the embodiments of the present invention should not be considered isolated, and they can be combined with each other to achieve better technical effects. The scope of the preferred embodiments of the present invention may also include additional implementations, which should be understood by those skilled in the art to which the embodiments of the invention pertain.

Claims (6)

1. a millimeter wave radar sparse array design method based on maximizing signal-to-noise ratio, is characterized in that, comprises: Construct the problem of maximizing SINR based on the FMCW millimeter-wave radar array detection model; Under the condition that the autocorrelation of spatial lag data is known, the sparse array is designed by successive linear approximation algorithm; Under the condition that the autocorrelation of spatial lag data is not known, the low-rank matrix completion method is used to interpolate the autocorrelation values corresponding to the missing lags based on the positive semi-definite Toeplitz constraint, and the sparse array design problem is solved by the convex optimization method. 2. a kind of sparse array design method based on maximizing signal-to-noise ratio millimeter-wave radar according to claim 1, it is characterized in that, based on FMCW millimeter-wave radar array detection model building the problem of maximizing SINR, specifically: The millimeter-wave radar for autonomous driving uses FMCW with constant amplitude characteristics, and the FMCW signal is expressed as: s(t)=exp(j2πf ₀ t+jπμt ² ) Among them, f ₀ is the initial frequency, μ=B/T is the modulation frequency, and B and T are the signal frequency modulation bandwidth and frequency sweep period respectively; The millimeter-wave radar receiving array is composed of N uniformly spaced and isotropic array elements, then the signal x(t) received by the millimeter-wave radar array element at time t is expressed as:

Among them, K is the number of interference sources,

is the target steering vector in the direction of θ ₀ ,

is the interference steering vector in the direction of θ _k , d and λ are the adjacent array element spacing and carrier wavelength, respectively, usually d≤λ/2; v(t) is the receiving array noise, which is modeled as a Gaussian distribution with a mean value of 0, The covariance is σ _v ² ; s _i (t) is the interference source signal; sampling at the sampling rate f _s , the digital beamforming input signal is:

After being weighted by the beam weighting coefficient, the beamforming output signal is: y(n)=w ^H x(n) Among them, w is the receiving weight vector; Based on the above, the SINR expression is as follows:

Wherein, R _s =σ ² a(θ ₀ )a ^H (θ ₀ ) is the target signal covariance matrix, σ ² =E{s(n)s ^H (n)} is the target signal power;

is the covariance matrix of interference and uncorrelated noise,

is the power of the k-th interference. 3. a kind of sparse array design method based on maximizing signal-to-noise ratio millimeter wave radar according to claim 2, it is characterized in that, based on minimum distortion MVDR criterion, design weight w is expressed as the optimization problem of maximizing SINR as:

stw ^H R _s w = 1 Since noise and interference cannot be separated from the array elements, R _x =R _s +R _i is used instead of R _i in practical applications, and the above formula is written as:

stw ^H R _s w = 1 Solving the above problem only needs to receive the data correlation matrix R _x =E(xx ^H ) and the expected DOA; based on

The received data correlation matrix is estimated by the received L snapshots x; Solving the above formula can get:

Thus, the optimal output SINR is expressed as:

Among them, Λ _max {·} represents the largest eigenvalue. 4. A kind of sparse array design method based on maximizing signal-to-noise ratio millimeter wave radar according to claim 1, it is characterized in that, under the condition that the spatial lag data autocorrelation is known, the sparse array is designed by successive linear approximation algorithm, specifically : Introduce additional sparsity constraints in the maximizing SINR problem, namely:

stw ^H R _s w≥1 ||w|| ₀ =P Among them, ||·|| ₀ indicates that the number of constraint weight vectors w is the number of sensors P obtained by selection; the objective function in the above formula is exchanged with the quadratic constraint, that is:

stw ^H R _x w≤1 ||w|| ₀ =P The above problem is real-valued by defining the real vector of receiving weights and the corresponding correlation matrix, namely:

||w|| ₀ =P in,

and

R _s , R _i and w are expressed in real numbers, respectively. 5. a kind of millimeter-wave radar sparse array design method based on maximizing signal-to-noise ratio according to claim 4, is characterized in that, the SINR problem is equivalent to following successive linear approximation form:

||w|| ₀ =P in,

i denotes the ith iteration; relax the non-convex l _o norm by minimizing the mixed l _1-∞ norm to efficiently obtain a sparse solution:

where the vector

Contains the real part and imaginary part of the beamforming weight corresponding to the lth sensor, || · || _∞ selection

The maximum value of ; for the initial iteration, the regular parameter μ is set to 0, and the optimal value of μ is obtained by binary search within the upper and lower limits. 6. a kind of sparse array design method based on maximizing signal-to-noise ratio millimeter wave radar according to claim 1, is characterized in that, the matrix completion method is expressed as:

s.t.Toeplitz(l)≥0 Among them, Toeplitz(l) returns a symmetric Toeplitz matrix, where l and ^lH define the first row and first column of Toeplitz(l), respectively; matrix R _P is the received data correlation matrix with correlation lag missing, missing correlation The corresponding elements of the lags are set to zero; the symbol ⊙ denotes the Hadamard product, ≥ denotes the matrix inequality with positive semi-definite constraints; the matrix Z is a binary matrix,

Represents the square of the Frobenius norm of the matrix, where the norm is designed to minimize the sum of squared errors between the observed correlation values and the corresponding terms of the unknown Toeplitz matrix; the regularization parameter ζ trades off the error term and the tracking heuristic term, and its nominal value is usually Adjusted based on numerical experience of the problem; based on convex optimization toolkit for efficient solutions.

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