CN113219461A - Millimeter wave radar sparse array design method based on maximized signal-to-noise ratio - Google Patents
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Abstract
The invention discloses a millimeter wave radar sparse array design method based on a maximized signal-to-noise ratio, and relates to the field of target detection of an automatic driving millimeter wave radar; constructing a maximized SINR problem based on an FMCW millimeter wave radar array detection model; under the condition of definite autocorrelation of spatial lag data, designing a sparse array by a successive linear approximation algorithm; under the condition of uncertain autocorrelation of spatial lag data, interpolating autocorrelation values corresponding to missing lag by adopting a low-rank matrix completion method based on semi-definite Toeplitz constraint, and solving the sparse array design problem by a convex optimization method. The method provided by the invention can improve the target detection performance under the resolution constraint and simultaneously meet the requirements of distance and speed resolution, and has good convergence. Furthermore, the beam pattern has lower sidelobes because the proposed method optimizes the reception weights to concentrate the power in the direction of the target while suppressing echoes in other directions.
Description
Technical Field
The invention relates to the field of target detection of an automatic driving millimeter wave radar, in particular to a millimeter wave radar sparse array design method based on a maximized signal-to-noise ratio.
Background
In recent years, with rapid iteration in the automobile industry, millimeter wave radar gradually becomes an indispensable sensor for automatic driving due to its advantages of low cost, high precision, good stability and the like. The millimeter wave radar transmits a designable signal to a free space through a transmitter, receives echoes of a target and other objects through a receiver, and processes the obtained echoes based on a related signal processing method to perceive environment information. Therefore, the system airspace degree of freedom can influence the perception accuracy of the environment information, and the parameter resolution, the measurement accuracy and the clutter suppression performance can be improved by increasing the system airspace degree of freedom, so that the system target detection and estimation capability is improved, and the unmanned environment perception capability is enhanced. However, due to the limited size of the automobile platform, the number of array elements cannot be increased without limit to improve the spatial degree of freedom, and for this problem, researchers select the transceiving array elements to improve the spatial degree of freedom and reduce the system overhead, that is, the design of the sparse array is adopted.
In the case of no interference, Wang et al propose a sparse array design method based on convex relaxation and Iterative Linear Fractional Programming (ILFP), which solves the problem of non-convex antenna selection of a sparse array beamformer. In the case of interference, Hamza et al propose a sparse array design method for receive beamforming with maximum signal-to-interference-and-noise ratios for single-point sources and multi-point sources. Furthermore, Zheng et al propose a sparse array design method for adaptive beamforming that obtains an optimal array configuration based on a maximum signal to interference noise ratio (SINR) criterion, which, however, ignores the angular spreading effect of radio propagation. Aiming at the problem, Hamza et al propose an optimal sparse array design method with local scattering, and solve the influence of angular diffusion effect on detection performance. In order to reduce the influence brought by high side lobe level, Jarske et al propose an array refinement design method with minimized side lobe, i.e. based on completely filling the array, systematically and sequentially removing the sensors. In addition, Leahy et al propose a sparse array design method for optimizing peak sidelobe levels, which relates to the joint design of sensor positions and corresponding beam forming weights thereof. For global optimization tools to solve sparse array beamforming, industries such as Genetic Algorithm (GA) algorithm and convex relaxation method have been widely used for sensor selection problem. The array configuration and weights are adapted to the time-varying perceptual environment, which can be achieved by adjusting the antenna positions and the corresponding weights. In summary, the sparse array design problem can be expressed by maximizing the SINR model, however, maximizing SINR over all possible sparse topologies is a combinatorial optimization problem, which is typically a challenging polynomial solution problem. Furthermore, sparse array optimization design requires estimation of all spatial lag data autocorrelation across the array aperture, whereas existing approaches typically assume that the full correlation matrix is known to design a sparse array.
Disclosure of Invention
Aiming at the problem that the degree of freedom of a millimeter wave radar system is low due to the fact that a limited platform space is automatically driven, and therefore target detection performance is poor, the invention provides a millimeter wave radar sparse array design method based on a maximized signal-to-noise ratio, which comprises the step of constructing a maximized SINR problem based on an FMCW millimeter wave radar array detection model; under the condition that the autocorrelation of the spatial lag data is known, designing a sparse array by a successive linear approximation (SCA) algorithm; under the condition of uncertain autocorrelation of spatial lag data, interpolating autocorrelation values corresponding to missing lag by adopting a low-rank matrix completion method based on semi-definite Toeplitz constraint, and solving the sparse array design problem by a convex optimization method.
Due to the adoption of the technical scheme, the invention can obtain the following technical effects: the method provided by the invention can improve the target detection performance under the resolution constraint and simultaneously meet the requirements of distance and speed resolution, and has good convergence. Furthermore, the beam pattern has lower sidelobes because the proposed method optimizes the reception weights to concentrate the power in the direction of the target while suppressing echoes in other directions. And establishing a transmitting waveform parameter and receiving weight value combined optimization model with distance and speed resolution constraint, thereby realizing improvement of target detection and distance and speed resolution performance of the millimeter wave radar.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a diagram of a sparse array element selection structure under a single interference condition;
FIG. 3 is a graph of average SINR output from various sparse arrays as a function of the angle of incidence of the desired signal under single interference conditions;
FIG. 4 is a diagram of a sparse array element selection structure under a multi-interference condition;
fig. 5 is a graph of average SINR output from various sparse arrays as a function of angle of incidence of a desired signal under multiple interference conditions.
Detailed Description
The implementation steps of the present invention are further described in detail below with reference to fig. 1: the invention provides a method for improving the target detection probability of a millimeter wave radar, namely a millimeter wave radar sparse array design method based on a maximized signal-to-noise ratio, which specifically comprises the following steps:
because the FMCW radar has the characteristics of low cost, high resolution, high integration level and the like, the autopilot millimeter wave radar often transmits FMCW with a constant amplitude characteristic, and the FMCW signal can be expressed as:
s(t)=exp(j2πf0t+jπμt2)
wherein f is0For the initial frequency, μ ═ B/T is the modulation frequency, and B and T are the signal bandwidth and sweep period, respectively.
The millimeter wave radar receiving array is composed of N uniformly spaced and isotropic array elements, and then a signal x (t) received by the millimeter wave radar array element at time t can be represented as:
wherein K is the number of interference sources,is theta0The direction target is directed to the vector of the vector,is thetakAnd d and lambda are the interval between adjacent array elements and the wavelength of a carrier wave respectively, and d is usually less than or equal to lambda/2. v (t) is the receive array noise, which can be modeled as following a Gaussian distribution with a mean of 0 and a covariance of σv 2。siAnd (t) is an interference source signal. At a sampling rate fsThe digital beamforming input signals obtained by sampling are:
after weighting by the beam weighting coefficients, the resulting beam forming output signal is:
y(n)=wHx(n)
where w is a receive weight vector.
Based on the above, the available SINR expression is as follows:
wherein R iss=σ2a(θ0)aH(θ0) Is a target signal covariance matrix, σ2=E{s(n)sH(n) is the target signal power.As a covariance matrix of interference and uncorrelated noise,is the power of the kth interferer. Design weight w to maximize optimization of SINR based on minimum distortion (MVDR) criterionThe problem can be expressed as:
s.t.wHRsw=1
because noise and interference can not be separated from array elements, R is adopted in practical applicationx=Rs+RiIn place of RiThen the above formula can be rewritten as:
s.t.wHRsw=1
solving the above problem requires only receiving the data correlation matrix Rx=E(xxH) And the desired DOA. Based onThe former can be more easily estimated from the received L snapshots x.
wherein, Λmax{. denotes the maximum eigenvalue. The above applies to any array topology.
under the condition that the full correlation matrix is certain, in order to obtain a sparse solution, an additional sparse constraint can be introduced into the maximum SINR problem model, namely:
s.t.wHRsw≥1
||w||0=P
wherein | · | purple sweet0The number of the constraint weight vectors w is represented as the selected sensor number P. The above formula is obviously a non-convex problem and is not easy to solve based on the traditional optimization method. To solve this problem, the objective function in the above equation can be interchanged with a quadratic constraint, i.e.:
s.t.wHRxw≤1
||w||0=P
in general, the receiving weights are complex numbers, and the quadratic function is real number, so the above problem cannot be solved directly. Since the real and imaginary complex terms of the optimal weight vector are usually decoupled, the above problem can be solved by defining the receiving weight real vector and the corresponding correlation matrix, that is:
||w||0=P
To solve the above problem efficiently, the problem can be equivalent to the following successive linear approximation:
||w||0=P
wherein,i denotes the ith iteration. Finally, by minimizing the mixing l1-∞Norm relaxation non-convexoNorm to obtain sparse solution with high efficiency:
s.t.wherein the vectorComprises a real part and an imaginary part of a beam forming weight corresponding to the first sensor, | · caly |, a∞SelectingIs measured. For the initial iteration, the regularization parameter μmay be set to 0 to allow the optimization problem described above to converge quickly. It should be noted that the parameter μ itself does not guarantee that the final solution is sparse. Therefore, to ensure sparsity of the final solution, μ optimal needs to be obtained by binary search within the possible upper and lower limits to ensure that the optimization problem can converge to P sparsity.
And 3, under the condition that the autocorrelation of the spatial lag data is not known, interpolating autocorrelation values corresponding to the missing lags by adopting a low-rank matrix completion method under the semi-positive Toeplitz constraint on the basis of obtaining the autocorrelation of all the spatial lag data of the array aperture, and solving the design problem of the sparse array by adopting a convex optimization method.
The sparse array design based on the SCA algorithm assumes that the full correlation matrix is known, but the full correlation matrix is very difficult to obtain in an actual scene, and a large number of missing correlation lags may occur. Aiming at the problem, the invention provides a semi-positive Toepltiz matrix completion method to effectively utilize an unknown correlation matrix structure so as to improve the detection performance of a designed array. The proposed matrix completion method can be expressed as:
s.t.Toeplitz(l)≥0
wherein Toeplitz (l) returns a symmetric Toeplitz matrix, where l and lHThe first row and the first column of Toeplitz (l) are defined, respectively. Matrix RPFor a received data correlation matrix with a missing correlation lag, the corresponding element of the missing correlation lag is zeroed out. The symbol ≧ represents the Hadamard product, ≧ represents the matrix inequality with the semi-positive definite constraint. The matrix Z is a binary matrix and,the square of the Frobenius norm of the matrix is expressed, where the norm is intended to minimize the sum of the squared errors between the observed correlation values and the corresponding terms of the unknown Toeplitz matrix. The regularization parameter ζ weighs the error term and the tracking heuristic, whose nominal values are typically adjusted based on numerical experience of the problem. The problem is a convex problem, and thus an efficient solution can be obtained based on a multitude of convex optimization toolkits.
Based on the above, the invention provides a millimeter wave radar sparse array design method based on a maximized signal-to-noise ratio, aiming at the problem that the millimeter wave radar has low target detection performance due to the fact that the space freedom of the millimeter wave radar is small due to the limitation of the space of the automatic driving platform. The method comprises the steps of firstly, constructing a problem of maximizing SINR (signal to interference and noise ratio) optimized weight based on an FMCW millimeter wave radar array detection model; secondly, optimizing a weight value based on an SCA algorithm to further realize sparse array design; and finally, in order to obtain the data autocorrelation of all the spatial lags on the array aperture, interpolating autocorrelation values corresponding to the missing lags by adopting a low-rank matrix completion method under the semi-positive Toeplitz constraint. Simulation results show that compared with a sparse array obtained based on an SCA algorithm and an enumeration method, the method can obviously improve the target detection performance of the millimeter wave array radar.
The effects of the present invention can be further illustrated by the following simulations:
the method is compared with the optimal sparse array obtained based on the SCA algorithm and the optimal sparse array obtained by an enumeration method, and the detection performance under the conditions of single interference and multiple interferences is analyzed successively to verify the effectiveness of the algorithm. The simulation environment is as follows: CPU Intel (R) core (TM) i7-7700, RAM 8GB, MATLAB R2016 a. The simulation conditions are as follows: considering that the given receiving sensor number N is 10, the array element spacing d is λ/2, the sensor number P can be selected to be 6, the signal-to-noise ratio SNR is 0dB, the dry-to-noise ratio INR is 20dB, the initialization epsilon is 0.05, and the binary search method range of the sparsity parameter μ is set to be 0.01 to 5.
Assuming that a target signal is in a 10-degree direction and an interference signal is in a-40-degree direction, fig. 2 is a structure diagram for selecting a sparse array element under a single interference condition. Fig. 2(a) shows an initial 6-element sparse array configuration with missing correlation lag and occupying only a small portion of the aperture, with the estimated data correlation matrix randomly selected from 10 array element positions. Fig. 2(b) shows the sparse array configuration designed based on the SCA algorithm, and the resulting optimal sparse array output SINR is 11.23 dB. While fig. 2(c) shows the best SINR array obtained by the enumeration method, the SINR of the array is 11.65dB, it is noted that the possible array configuration is orders of magnitude larger, which may cause the problem to be unable to be solved by enumeration search. And randomly selecting 200 snapshot data, and restoring the whole array Toeplitz estimation through matrix completion of a regularization parameter zeta of 0.5. Fig. 2(d) shows the optimal sparse array configuration achieved by matrix completion, with an SINR of 11.50dB, and better performance is obtained by matrix completion configuration than by SCA algorithm-based optimal configuration.
Assume that the target signal is in the direction of θ [ -30:10:30] ° and that there is a simultaneous disturbance signal position in the direction of-40 °. Solving the SINR obtained by the optimal sparse array in the graph of FIG. 2, and FIG. 3 is a graph of the variation of the average SINR output by various sparse arrays along with the incident angle of the expected signal, as can be seen from FIG. 3, the SINR output by the proposed algorithm is only second to the optimal SINR obtained by the enumeration method, the average error is about 0.2dB, and the maximum error is not more than 0.4dB, compared with the SINR output based on the SCA algorithm, the SINR output by the proposed algorithm is obviously higher than the SINR output based on the SCA algorithm, because the structure of the unknown correlation matrix is effectively utilized by the matrix completion. The detection performance can be obviously improved by the algorithm.
Assume that the target signal is in the 10 ° direction and that there are three interfering signals in the-40 °, -20 °, and 50 ° directions simultaneously. Fig. 4 is a structure diagram of sparse array element selection under the condition of multiple interferences. Fig. 4(a) is an initial 6 array element sparse array configuration in which an estimated data correlation matrix is randomly selected from 10 array element positions, fig. 4(b) is a sparse array configuration designed based on an SCA algorithm, and the SINR of the calculated optimal sparse array output is 10.72 dB. Meanwhile, fig. 4(c) shows the optimal SINR array solved by the enumeration method, and the SINR of the optimal SINR array is 11.35 dB. Randomly selecting 200 snapshot data, recovering full-array Toeplitz estimation through matrix completion with regularization parameter ζ being 0.5, and fig. 4(d) shows that the optimal sparse array configuration is realized through the matrix completion, the SINR is 11.11dB, and the matrix completion configuration has higher output SINR, which indicates that the matrix completion algorithm is still effective for improving the SINR under the multi-interference condition.
Assume that the target signal is in the direction of-30: 10:30, while there are three interfering signals in the-40, -20, and 50 directions. Solving the SINR obtained by the optimal sparse array in fig. 4, fig. 5 is a graph of average SINR performance of various sparse arrays relative to the incident angle of the desired signal, and as can be seen from fig. 5, the SINR can be significantly improved by using the matrix completion method under the condition of multiple interferences, and next to the SINR obtained by the enumeration method, the average SINR of the proposed method is lower than about 0.3dB by using the enumeration method. Therefore, the detection performance of the algorithm can still be improved under the condition of multiple interferences.
The enumeration method has too high computational complexity and is not suitable for practical application. In summary, compared with the sparse array obtained based on the SCA algorithm and the enumeration method, the method can significantly improve the target detection performance of the millimeter wave array radar. Therefore, the algorithm provided by the invention can provide a solid theoretical and engineering realization basis for improving the detection performance of the millimeter wave radar target of the automatic driving platform in practical application.
The embodiments of the present invention are illustrative, but not restrictive, of the invention in any manner. The technical features or combinations of technical features described in the embodiments of the present invention should not be considered as being isolated, and they may be combined with each other to achieve a better technical effect. The scope of the preferred embodiments of the present invention may also include additional implementations, and this should be understood by those skilled in the art to which the embodiments of the present invention pertain.
Claims (6)
1. A millimeter wave radar sparse array design method based on a maximized signal-to-noise ratio is characterized by comprising the following steps:
constructing a maximized SINR problem based on an FMCW millimeter wave radar array detection model;
under the condition of definite autocorrelation of spatial lag data, designing a sparse array by a successive linear approximation algorithm;
under the condition of uncertain autocorrelation of spatial lag data, interpolating autocorrelation values corresponding to missing lag by adopting a low-rank matrix completion method based on semi-definite Toeplitz constraint, and solving the sparse array design problem by a convex optimization method.
2. The millimeter wave radar sparse array design method based on the maximized signal-to-noise ratio as claimed in claim 1, wherein the problem of maximizing SINR is established based on an FMCW millimeter wave radar array detection model, specifically:
the automatic driving millimeter wave radar adopts FMCW with constant amplitude characteristic, and FMCW signals are expressed as:
s(t)=exp(j2πf0t+jπμt2)
wherein f is0Setting mu as initial frequency, setting B/T as modulation frequency, and setting B and T as signal frequency modulation bandwidth and frequency sweep period;
the millimeter wave radar receiving array is composed of N uniformly spaced and isotropic array elements, and then a signal x (t) received by the millimeter wave radar array element at time t is represented as:
wherein K is the number of interference sources,is theta0The direction target is directed to the vector of the vector,is thetakThe direction interference guide vector, d and lambda are the interval between adjacent array elements and the wavelength of the carrier wave respectively, and d is usually less than or equal to lambda/2; v (t) is the receive array noise, modeled as a gaussian distribution with a mean of 0 and a covariance of σv 2;si(t) is the interferer signal; at a sampling rate fsSampling is performed, and the digital beam forming input signal is:
after weighting by the beam weighting coefficients, the beam forming output signal is:
y(n)=wHx(n)
wherein w is a receiving weight vector;
based on the above, the SINR expression is as follows:
3. The millimeter wave radar sparse array design method based on the maximized signal-to-noise ratio as claimed in claim 2, wherein based on the minimum distortion MVDR criterion, the optimization problem of designing the weight w to maximize SINR is represented as:
s.t.wHRsw=1
because noise and interference can not be separated from array elements, R is adopted in practical applicationx=Rs+RiIn place of RiThen the above equation is written as:
s.t.wHRsw=1
solving the above problem requires only receiving the data correlation matrix Rx=E(xxH) And a desired DOA; based onThe received data correlation matrix is estimated from the received L snapshots x;
wherein, Λmax{. denotes the maximum eigenvalue.
4. The millimeter wave radar sparse array design method based on the maximized signal-to-noise ratio as claimed in claim 1, wherein under the condition of the known autocorrelation of the spatial lag data, the sparse array is designed by a successive linear approximation algorithm, specifically:
an additional sparsity constraint is introduced in the maximize SINR problem, namely:
s.t.wHRsw≥1
||w||0=P
wherein | · | purple sweet0Representing the number of the constraint weight vectors w as the number P of the selected sensors; the objective function in the above equation is interchanged with the quadratic constraint, i.e.:
s.t.wHRxw≤1
||w||0=P
the above problem is solved by defining a receiving weight real vector and a corresponding correlation matrix, namely:
||w||0=P
5. The millimeter wave radar sparse array design method based on the maximization of the signal-to-noise ratio as claimed in claim 4, wherein the SINR problem is equivalent to the following successive linear approximation form:
||w||0=P
wherein,i denotes the ith iteration; by minimizing mixing1-∞Norm relaxation non-convexoNorm to obtain sparse solution with high efficiency:
wherein the vectorComprises a real part and an imaginary part of a beam forming weight corresponding to the first sensor, | · caly |, a∞SelectingMaximum value of (d); for the initial iteration, the regularization parameter μ is set to 0, and μ optimal values are obtained by binary search within upper and lower bounds.
6. The millimeter wave radar sparse array design method based on the maximization of the signal-to-noise ratio as claimed in claim 1, wherein the matrix completion method is represented as:
s.t.Toeplitz(l)≥0
wherein Toeplitz (l) returns a symmetric Toeplitz matrix, where l and lHDefining a first row and a first column, respectively, of Toeplitz (l); matrix RPFor a received data correlation matrix with a missing correlation lag, the corresponding element of the missing correlation lag is zeroed out; the symbol ≧ represents the Hadamard product, ≧ represents the matrix inequality with the semi-positive definite constraint; the matrix Z is a binary matrix and,representing the square of the Frobenius norm of a matrix, where the norm is intended to minimize the sum of the squared errors between the observed correlation values and the corresponding terms of the unknown Toeplitz matrix; the regularization parameter ζ weighs error terms and tracking heuristic terms, the nominal value of which is usually adjusted according to numerical experience of the problem; efficient solutions are obtained based on a convex optimization toolkit.
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