A Joint DOD and DOA Estimation Method for Arbitrary Array Bistatic MIMO Radar

Abstract

The present invention provides a method for jointly estimating the DOD and DOA of an arbitrary array bistatic MIMO radar, comprising the following steps: constructing an arbitrary array bistatic MIMO radar system model including a smart reflector; after obtaining a received signal using the radar system in step S1, obtaining a covariance matrix of the received signal after matched filtering by establishing a signal model, defining a direction vector, and a channel matrix; estimating the 2D-DOD angle using a propagation operator algorithm; and obtaining a 2D-DOA angle estimate by combining the 2D-DOD angle obtained by the propagation operator algorithm. The present invention proposes a method for jointly estimating the angle of departure and angle of arrival of an arbitrary array bistatic MIMO radar using a smart reflector. Both the transmitting antenna array and the receiving antenna array are arbitrary array flow types, and the smart reflector can ensure that the signal reaches the receiving array even when the signal is blocked by obstacles.

Description

Technical Field

[0001] The present invention relates to the field of visibility meters, and in particular to a method for jointly estimating DOD and DOA of an arbitrary array bistatic MIMO radar. Background Art

[0002] In recent years, intelligent reflector-assisted radar azimuth estimation has become a hot topic in array signal processing research. Scholars have proposed numerous angle estimation algorithms for intelligent reflector-assisted radars. For example, Z. Chen, J. Tang, and L. Huang ("Robust Target Positioning for Reconfigurable Intelligent Surface Assisted MIMO Radar Systems," in IEEE Transactions on Vehicular Technology, vol. 72, no. 11, pp. 15098-15102, Nov. 2023) discussed the angle estimation problem for IRS-assisted MIMO radars, reformulating it as a high-dimensional sparse inverse problem and solving it via an iterative strategy. C. Huang, A. Zappone, and G. C. Alexandropoulos ("Reconfigurable Intelligent Surfaces for Energy Efficiency in Wireless Communication," in IEEE Transactions on Wireless Communications, vol. 18, no. 8, pp. 4157-4170, Aug. 2019.) explored the use of intelligent reflecting surfaces in multi-user communications in the downlink of multi-antenna base stations and demonstrated that IRS can provide effective assistance in various communication environments. F. Wen, H. Wang, and G. Gui ("Polarized Intelligent Reflecting Surface Aided 2D-DOAEstimation for NLoS Sources," in IEEE Transactions on Wireless Communications.) proposed a method for DOA estimation in NLOS situations with the assistance of intelligent reflecting surfaces, using the normalized vector cross product (NVCP) method to achieve DOA estimation. Z. Yang, P. Chen, and Z. Guo ("Low-Cost Beamforming and DOA Estimation Based on One-Bit Reconfigurable Intelligent Surface," in IEEE Signal Processing Letters, vol. 29, pp. 2397-2401, 2022.) performed a fine estimation of DOA with the assistance of IRS by solving the sparse reconstruction problem based on the atomic norm.P.Chen, Z.Chen, B.Zheng and X.Wang ("Efficient DOA Estimation Method for ReconfigurableIntelligent Surfaces Aided UAV Swarm," in IEEE Transactions on SignalProcessing, vol. 70, pp. 743-755, 2022.) proposed a customized semidefinite programming (SDP) method to achieve excellent DOA estimation performance in a single-receiver channel UAV swarm system assisted by IRS.

[0003] While these cutting-edge research results have greatly advanced the field, they inevitably face some common challenges: first, the enormous computational burden of eigenvalue decomposition of high-dimensional matrices; second, the susceptibility of estimation accuracy to noise interference. Therefore, finding more efficient and robust algorithm designs to overcome these limitations remains an important direction for future research. Summary of the Invention

[0004] The main purpose of the present invention is to provide a method for joint estimation of DOD and DOA of an arbitrary array bistatic MIMO radar, so as to solve the problems of huge computational burden caused by high-dimensional matrix eigenvalue decomposition and susceptibility of estimation accuracy to noise interference in the existing technology of intelligent reflector-assisted radar direction angle estimation.

[0005] To solve the above technical problems, the technical solution adopted by the present invention is: a method for joint estimation of DOD and DOA of an arbitrary array bistatic MIMO radar, comprising the following steps:

[0006] S1. Construct a model of an arbitrary array bistatic MIMO radar system including smart reflective surfaces;

[0007] S2. After obtaining the received signal using the radar system in step S1, a signal model is established, and a direction vector and a channel matrix are defined to obtain a covariance matrix of the received signal after matched filtering.

[0008] S3, using the propagation operator algorithm to estimate the 2D-DOD angle;

[0009] S4, combining the 2D-DOD angle obtained by the propagation operator algorithm to obtain a 2D-DOA angle estimate;

[0010] The above steps complete the joint estimation of DOD and DOA of any array bistatic MIMO radar.

[0011] In the preferred solution, in step S1, a radar system model including an arbitrary transmitting array and a receiving array of a smart reflective surface is constructed, and the specific process includes:

[0012] Assume that the transmitting array has M array elements and the receiving array has N array elements, and the transmitting array and the receiving array are arbitrary arrays, where the position of the mth array element in the transmitting array is: (x tm ,y tm ,z tm ), the position of the nth element in the receiving array is: (x rn ,y rn ,z rn ), the transmitting antenna transmits orthogonal waveforms with the same bandwidth and center frequency;

[0013] An intelligent reflection surface is provided between the transmitting array and the receiving array, and the intelligent reflection surface is composed of Y intelligent reflection units.

[0014] In the preferred solution, in step S2, the covariance matrix of the received signal after matched filtering is obtained, and the specific process includes:

[0015] The 2D-DOD and 2D-DOA of the kth target for the transmitting array and the receiving array are expressed as (θ tk ,φ tk ) and (θ rk ,φ rk ), the output of the receiver can be expressed as:

[0016] X(τ)=[(GVA r )⊙A t ]S(τ)+N(τ) (1) Where ⊙ represents the KhatriRao product, is the channel matrix between the IRS and the receiving array, in, Represents the reflection response of IRS; A t =[a t (θ t1 ,φ t1 ), Among them, θ tk and φ tk represents the elevation and azimuth of the k-th target 2D-DOD, Among them, θ rk ,φ rk represents the elevation and azimuth of the kth target 2D-DOA, A t and A r They are the transmit direction matrix and the receive direction matrix, S(τ)=[s1(τ),s2(τ),...,s K (τ)]T , where f k represents the Doppler frequency, β k represents the amplitude; It represents the array noise at the instant λ, and its covariance matrix is ​​σ 2 I MN , σ 2 represents the noise power; a t (θ tk ,φ tk ) and a r (θ rk ,φ rk ) indicates that the direction vector of the kth reception and transmission is:

[0017] a r (θ rk ,φ rk )=[exp(-j2πp r1 / λ),...,exp(-j2πp rN / λ)] T (2a)

[0018] a t (θ tk ,φ tk )=[exp(-j2πp t1 / λ),...,exp(-j2πp tM / λ)] T (2b)

[0019] Where exp(·) represents the e in the exponential function (·) , p rn =x rn sinθ rk cosφ rk +y rn sinθ rk sinφ rk +z rn cosθ rk ,n×1,2,...,N,p tm =x tm sinθ tk cosφ tk +y tm sinθ tk sinφ tk +z tm cosθ tk , m=1,2,...,M,(·) T represents the transpose of the matrix; λ represents the wavelength;

[0020] The channel matrix G between the IRS and the receiving array is expressed as:

[0021]

[0022] Among them, r 0h represents the distance from the hth element of the IRS to the reference element of the receiving array, r nh is the distance from the hth element of the IRS to the nth element of the receiver array;

[0023] The output X of the receiving end is simply written as:

[0024] X=AS+N (4)

[0025] Where A represents the emission matrix, is the additive Gaussian white noise matrix. For the signal model in the formula, the covariance matrix of L samples is:

[0026]

[0027] in,(·) H Represents the conjugate transpose of a matrix.

[0028] In the preferred solution, in step S3, the 2D-DOD angle is estimated using a propagation operator algorithm, which specifically includes the following sub-steps:

[0029] S31, construct the propagation operator;

[0030] S32. Estimate the emission angle using a propagation operator algorithm.

[0031] In the preferred solution, in step S31, a propagation operator is constructed, and the specific process is as follows:

[0032] The emission matrix A can be divided into two parts, expressed as:

[0033]

[0034] in, is a non-singular matrix, The linear transformation of A0 gives the following expression:

[0035] A s =P s A0(7) Among them, is the propagation operator, P s Estimated to be:

[0036]

[0037] Where Q is The first K columns of H are The last MN-K columns, (·) -1 represents the inverse of the matrix, (·) H Represents the conjugate transpose of a matrix.

[0038] In the preferred solution, in step S32, the transmission angle is estimated using the propagation operator algorithm, and the specific process is as follows:

[0039] Define the matrix P:

[0040]

[0041] Among them I k is a K×K identity matrix, is the propagation operator is a matrix with independent columns.

[0042] Divide the matrix P into:

[0043]

[0044] Among them, P n ∈C M×K , n=1,2,...,N, the relationship between P2 and P1 is:

[0045]

[0046] in, is a non-singular matrix, represented by the first K rows and K columns of the emission matrix A, (·) -1 Represents the inverse of the matrix, for P1 + P2 is decomposed by eigenvalues, and the diagonal matrix formed by eigenvalues ​​is Φ1=diag(exp[j2π(m t1 w 21 +n t1 v 21 +l t1 u 21 ) / λ],...,exp[j2π(m tK w 21 +n tK v 21 +l tK u 21 ) / λ]), m tk = sinθ tk cosφ tk , n tk = sinθ tk sinφ tk , l tk =cosθ tk , w 21 =x t1-x t2 , v 21 =y t1 -y t2 ,u 21 =z t1 -z t2 , Π is a non-singular matrix. Take Construct a 1×K row vector g1 from the diagonal elements of This yields a matrix:

[0047]

[0048] in, Use ρ k Denotes the kth column of B and s = angle (ρ k ), angle represents the calculated phase angle, and s can be expressed as:

[0049]

[0050] in, m tk = sinθ tk cosαφ tk , n t,k = sinθ tk sinφ tk , l tk =cosθ tk ;

[0051] Use the least squares method to solve and

[0052]

[0053] in,(·) + represents the pseudo-inverse of the matrix, and m tk , n tk and l tk estimated value of;

[0054] The azimuth and elevation estimation of 2D-DOD can be expressed as:

[0055]

[0056] in, Denote the estimated azimuth of the kth target in 2D-DOD of the transmitting array, Denotes the estimated elevation angle of the kth target in 2D-DOD with respect to the transmitting array.

[0057] In the preferred solution, in step S4, obtaining a 2D-DOA angle estimate specifically includes the following sub-steps:

[0058] S41, performing spectrum peak search on 2D-DOA to estimate the two-dimensional direction of arrival;

[0059] S42 , estimating a 2D-DOA angle using each set of angles in the 2D-DOD direction matrix.

[0060] In the preferred solution, in step S41, a spectrum peak search is performed on the 2D-DOA to estimate the two-dimensional direction of arrival. The specific process is:

[0061] Decomposing the covariance matrix, we get:

[0062]

[0063] Among them, D s is a K×K diagonal matrix consisting of the largest K eigenvalues, D n is a diagonal matrix consisting of MN-K smaller eigenvalues, E s is the eigenvector corresponding to the largest K eigenvalues, E n are the eigenvectors corresponding to the remaining eigenvalues, (·) H represents the conjugate transpose of a matrix;

[0064] List the spectral function expression of 2D-DOA estimation:

[0065]

[0066] Among them, A=A t ⊙(GVA r ), A is the emission matrix ⊙ is the Khatri-Rao product, is the channel matrix between the IRS and the receiving array, in, represents the reflection response of IRS, A t Estimated value of It has been found in 2D-DOD that θ rk ,φ rk represents the elevation and azimuth angles of the kth target relative to the receiving array 2D-DOA.

[0067] In the preferred solution, in step S42, the 2D-DOA angle is estimated by each group of angles in the 2D-DOD direction matrix. The specific process is:

[0068] By solving the maximum value of the spectrum function expression of the 2D-DOA estimation in step S41, the estimated value of the receiving angle is obtained, which is used when searching for the spectrum peak. t Estimated value of Each angle is brought in separately, and the estimated value is obtained by performing K spectrum peak searches to obtain the estimated elevation angle of the k-th target for the 2D-DOA of the receiving array. and azimuth It is the two-dimensional direction of arrival of the receiving angle.

[0069] This invention provides a joint DOD and DOA estimation method for a bistatic MIMO radar with an arbitrary array. It constructs a bistatic MIMO radar system model that incorporates intelligent reflectors. The model flexibly adapts to arbitrary array layouts, reducing system cost and signal loss. Signal features are effectively extracted through signal processing techniques, matched filtering, and covariance matrix construction. A propagation operator algorithm is introduced to accurately estimate 2D-DOD in two steps, improving the accuracy and stability of angle estimation. Combined with the obtained 2D-DOD information, a spectral peak search technique is used to further estimate 2D-DOA, achieving omnidirectional positioning of targets in four-dimensional space. This invention significantly enhances the real-time response and processing efficiency of radar systems in dynamic environments, making it particularly suitable for tracking fast-moving targets and accurately detecting them in complex environments.

[0070] The beneficial effects of the present invention are

[0071] 1) By jointly estimating the two-dimensional direction of arrival (DOD) and the two-dimensional angle of arrival (DOA), this paper constructs a complete four-dimensional angle estimation framework, providing more accurate target positioning and tracking capabilities in highly dynamic and complex environments, and significantly enhancing the spatial resolution and recognition efficiency of the radar system.

[0072] 2) Suitable for single-snapshot scenarios, it can complete joint DOD and DOA estimation within a single signal acquisition cycle, significantly reducing processing latency and improving the system's real-time performance. This is crucial for applications such as capturing fast-moving targets and monitoring transient events, ensuring the radar system can react quickly and adapt to rapidly changing battlefield or surveillance environments.

[0073] 3) By introducing intelligent reflective surfaces, this invention effectively enhances signal controllability and transmission efficiency without adding additional transmitters, enabling low-cost, low-loss radar system design. The flexibility of intelligent reflective surfaces allows them to be adapted to a variety of deployment scenarios, from concealed installations in urban environments to wide-area coverage in remote areas, enabling high-performance radar operation at a low cost while reducing electromagnetic pollution to the environment.

[0074] 4) This invention's support for arbitrary array structures transcends the traditional radar system's reliance on specific array layouts, enabling more flexible design and customizable configurations based on diverse application scenarios and practical needs, significantly expanding the application scope of radar technology. Whether it's military reconnaissance in complex terrain, traffic management in urban environments, or even rapid deployment in disaster response, the solutions provided by this invention are more closely aligned with practical needs, enhancing the practical value and versatility of radar technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] The present invention will be further described below with reference to the accompanying drawings and examples:

[0076] Figure 1 It is a flow chart of the method for joint estimation of DOD and DOA of arbitrary array bistatic MIMO radar in the present invention;

[0077] Figure 2 It is a simulation diagram of the application scenario of the present invention;

[0078] Figure 3 is a scatter plot of the estimated 2D-DOD of the transmitting array of the present invention;

[0079] Figure 4 It is the estimated spectrum peak diagram of the receiving array 2D-DOA of the present invention;

[0080] Figure 5 Schematic diagram comparing the average RMSE of the algorithm of the present invention and the comparison algorithm with the change of SNR;

[0081] Figure 6 This is a schematic diagram comparing the average RMSE of the algorithm in the present invention and the comparison algorithm as the number of sampling times changes;

[0082] Figure 7 Schematic diagram comparing the running time of the algorithm in the present invention and the comparative algorithm. DETAILED DESCRIPTION

[0083] Example 1

[0084] like Figures 1 to 7 As shown, a joint DOD and DOA estimation method for an arbitrary array bistatic MIMO radar includes the following steps:

[0085] S1. Construct a model of an arbitrary array bistatic MIMO radar system including smart reflective surfaces;

[0086] S2. After obtaining the received signal using the radar system in step S1, a signal model is established, and a direction vector and a channel matrix are defined to obtain a covariance matrix of the received signal after matched filtering.

[0087] S3, using the propagation operator algorithm to estimate the 2D-DOD angle;

[0088] S4, combining the 2D-DOD angle obtained by the propagation operator algorithm to obtain a 2D-DOA angle estimate;

[0089] The above steps complete the joint estimation of DOD and DOA of any array bistatic MIMO radar.

[0090] The present invention proposes a method for jointly estimating 2D-DOD and 2D-DOA of an arbitrary array bistatic MIMO radar, namely, a method for jointly estimating 2D-DOD (Two-Dimensional Direction of Departure) and 2D-DOA (Two-Dimensional Direction of Arrival) of a bistatic MIMO radar assisted by a smart reflector. The bistatic antenna is characterized in that its array flow pattern can be composed of an arbitrary array, such as Figure 2 As shown, the array elements are located in a set two-dimensional space. The two-dimensional space on the left is the transmitting array (Tx), and the two-dimensional space on the right is the receiving array (Rx). In the two-dimensional space, they are all arbitrary array flow types. The signal is transmitted to detect the target, and then the signal is sent to the receiving array. During the signal propagation, there will be obstacles blocking the signal. If the building has an intelligent reflecting surface (IRS) to reflect the signal, so that the signal can reach the receiving array, the signal transmission process with the assistance of the intelligent reflecting surface is completed.

[0091] In the preferred solution, in step S1, a radar system model including an arbitrary transmitting array and a receiving array of a smart reflective surface is constructed, and the specific process includes:

[0092] Assume that the transmitting array has M array elements and the receiving array has N array elements, and the transmitting array and the receiving array are arbitrary arrays, where the position of the mth array element in the transmitting array is: (x tm ,y tm ,z tm ), the position of the nth element in the receiving array is: (x rn ,y rn ,z rn ), the transmitting antennas emit orthogonal waveforms with the same bandwidth and center frequency; without loss of generality, the transmitting array and the receiving array are arbitrary arrays. Furthermore, we assume that direct communication between the transmitting array (Tx) and the receiving array (Rx) is blocked. An intelligent reflecting surface (IRS) can be used as a bridge. The intelligent reflecting surface consists of Y intelligent reflecting units, which can establish a channel between the transmitting array and the receiving array.

[0093] In the preferred solution, in step S2, the covariance matrix of the received signal after matched filtering is obtained, and the specific process includes:

[0094] The 2D-DOD and 2D-DOA of the kth target for the transmitting array and the receiving array are expressed as (θ tk ,φ tk ) and (θ rk ,φ rk ), the output of the receiver can be expressed as:

[0095] X(τ)=[(GVA r )⊙A t ]S(τ)+N(τ) (1)

[0096] Where ⊙ represents the KhatriRao product, is the channel matrix between the IRS and the receiving array, in, Represents the reflection response of IRS; A t =[a t (θ t1 ,φ t1 ), Among them, θ tk and φ tk represents the elevation and azimuth of the k-th target 2D-DOD, Among them, θ rk ,φ rk represents the elevation and azimuth of the kth target 2D-DOA, A t and A r They are the transmit direction matrix and the receive direction matrix, S(τ)=[s1(τ),s2(τ),...,s K (τ)] T , where f k represents the Doppler frequency, β k represents the amplitude; It represents the array noise at the instant λ, and its covariance matrix is ​​σ 2 I MN , σ 2 represents the noise power; a t (θ tk ,φ tk ) and a r (θ rk ,φ rk ) indicates that the direction vector of the kth reception and transmission is:

[0097] a r (θ rk ,φ rk )=[exp(-j2πp r1 / λ),...,exp(-j2πp rN / λ)] T (2a)

[0098] a t (θ tk ,φ tk )=[exp(-j2πp t1 / λ),...,exp(-j2πp tM / λ)] T (2b)

[0099] Where exp(·) represents the e in the exponential function (·) , p rn =x rn sinθ rk cosφ rk +y rn sinθ rk sinφ rk +z rn cosθ rk , n=1,2,...,N,p tm =x tm sinθ tk cosφ tk +y tm sinθ tk sinφ tk +z tm cosθ tk , m=1,2,...,M,(·) T represents the transpose of the matrix; λ represents the wavelength.

[0100] The channel matrix G between the IRS and the receiving array is expressed as:

[0101]

[0102] Among them, r 0h represents the distance from the hth element of the IRS to the reference element of the receiving array, r nh is the distance from the hth element of the IRS to the nth element of the receiver array.

[0103] The covariance matrix of the signal model is obtained as follows:

[0104]

[0105] Among them, D n (·) means taking the nth row of the matrix to construct a diagonal matrix.

[0106] Assume that for L samples, and is a constant, then the received signal of L samples can be expressed as:

[0107] X=[x(τ1),x(τ2),...,x(τ L )] (4b) The output X at the receiving end is abbreviated as:

[0108] X=AS+N(4)where A represents the transmission matrix, is the additive Gaussian white noise matrix. For the signal model in the formula, the covariance matrix of L samples is:

[0109]

[0110] in,(·) H Represents the conjugate transpose of a matrix.

[0111] In the preferred solution, in step S3, the 2D-DOD angle is estimated using a propagation operator algorithm, which specifically includes the following sub-steps:

[0112] S31, construct the propagation operator;

[0113] S32. Estimate the emission angle using a propagation operator algorithm.

[0114] In the preferred solution, in step S31, a propagation operator is constructed, and the specific process is as follows:

[0115] The emission matrix A can be divided into two parts, expressed as:

[0116]

[0117] in, is a non-singular matrix, is the linear transformation of A0, A s Each row vector in can be expressed as a linear combination of the row vectors of A0. Therefore, we can get:

[0118] A s =P s A0(7)

[0119] in, is the propagation operator, P s Estimated to be:

[0120]

[0121] Where Q is The first K columns of H are The last MN-K columns, (·) -1 represents the inverse of the matrix, (·) H Represents the conjugate transpose of a matrix.

[0122] In the preferred solution, in step S32, the transmission angle is estimated using the propagation operator algorithm, and the specific process is as follows:

[0123] Define the matrix P:

[0124]

[0125] Among them, I k is a K×K identity matrix, is the propagation operator, is a matrix with independent columns.

[0126] Combining expressions (8-11), we can get:

[0127]

[0128] Then you can get:

[0129]

[0130] Divide the matrix P into:

[0131]

[0132] Among them, P n ∈C M×K , n=1,2,...,N, according to expressions (9a) and (9b), the relationship between P2 and P1 is:

[0133]

[0134] Where Φ1=diag(exp[j2π(m t1 w 21 +n t1 v 21 +l t1 u 21 ) / λ],...,exp[j2π(m tK w 21 +n tK v 21 +l tK u 21 ) / λ]) and m tk = sinθ tk cosφ tk , n tk = sinθ tk sinφ tk , l tk =cosθ tk , w 21 =x t1 -x t2 , v21 =y t1 -y t2 ,u 21 =z t1 -z t2 , diag means placing the elements on the diagonal of the matrix, is a non-singular matrix, represented by the first K rows and K columns of the emission matrix A, (·) -1 Represents the inverse of the matrix, for P1 + P2 is decomposed by eigenvalues, and the diagonal matrix formed by eigenvalues ​​is The corresponding eigenvector is recorded as Among them, π is a non-singular matrix, take Construct a 1×K row vector g1 from the diagonal elements of , and then define:

[0135]

[0136] We can pass get:

[0137]

[0138] Where Φ2=diag(exp[j2π(m t1 w 32 +n t1 v 32 +l t1 u 32 ) / λ],...,exp[j2π(m tK w 32 +n tK v 32 +l tK u 32 ) / λ]) and w 32 =x t2 -x t3 , v 32 =y t2 -y t3 ,u 32 =z t2 -z t3 By taking Construct a 1×K row vector from the diagonal elements of In this way, we can also calculate This will give you a matrix:

[0139]

[0140] in, Use ρ k Denotes the kth column of B and s = angle (ρ k), angle represents the calculated phase angle. If the spacing between adjacent elements in the receiving matrix does not exceed half a wavelength, then s is within [-π,π], so there is no phase ambiguity:

[0141]

[0142] s can also be expressed as:

[0143]

[0144] in, m tk = sinθ tk cosαφ tk , n t,k = sinθ tk sinφ tk , l tk =cosθ tk ; Use the least squares method to solve and

[0145]

[0146] in,(·) + represents the pseudo-inverse of the matrix, and m tk , n tk and l tk estimated value of;

[0147] The azimuth and elevation estimation of 2D-DOD can be expressed as:

[0148]

[0149] in, Denote the estimated azimuth of the kth target in 2D-DOD of the transmitting array, Denotes the estimated elevation angle of the kth target in 2D-DOD with respect to the transmitting array.

[0150] In the preferred solution, in step S4, obtaining a 2D-DOA angle estimate specifically includes the following sub-steps:

[0151] S41, performing spectrum peak search on 2D-DOA to estimate the two-dimensional direction of arrival;

[0152] S42 , estimating a 2D-DOA angle using each set of angles in the 2D-DOD direction matrix.

[0153] In the preferred solution, in step S41, a spectrum peak search is performed on the 2D-DOA to estimate the two-dimensional direction of arrival. The specific process is as follows:

[0154] Decomposing the covariance matrix, we get:

[0155]

[0156] Among them, D s is a K×K diagonal matrix consisting of the largest K eigenvalues, D n is a diagonal matrix consisting of MN-K smaller eigenvalues, E s is the eigenvector corresponding to the largest K eigenvalues, E n is the eigenvector corresponding to the remaining eigenvalues, E s and E n represent the signal subspace and noise subspace respectively, (·) H represents the conjugate transpose of a matrix;

[0157] Since the signal subspace and the noise subspace are orthogonal, we can get A H E n =0, the spectral function expression of 2D-DOA estimation can be obtained:

[0158]

[0159] Among them, A=A t ⊙(GVA r ), A is the emission matrix ⊙ is the Khatri-Rao product, is the channel matrix between the IRS and the receiving array, in, represents the reflection response of IRS, A t Estimated value of It has been found in 2D-DOD that θ rk ,φ rk represents the elevation and azimuth angles of the kth target relative to the receiving array 2D-DOA.

[0160] In the preferred solution, in step S42, the 2D-DOA angle is estimated by each group of angles in the 2D-DOD direction matrix. The specific process is:

[0161] By solving the maximum value of the spectrum function expression of the 2D-DOA estimation in step S41, the estimated value of the receiving angle is obtained, which is used when searching for the spectrum peak. t Estimated value of Each angle is brought in separately, and the estimated value is obtained by performing K spectrum peak searches to obtain the estimated elevation angle of the k-th target for the 2D-DOA of the receiving array. and azimuth It is the two-dimensional direction of arrival of the receiving angle.

[0162] Example 2

[0163] Further illustrate with reference to Example 1, Figure 1-7 As shown in Figure 1, in order to verify the effectiveness of the framework of the present invention, the Monte Carlo method is used to evaluate the estimation performance. Here, it is assumed that the transmitting array and the receiving array are of arbitrary array flow types, and the array element spacing is less than d = λ / 2, where λ is the wavelength of the electromagnetic wave signal (the inverse of the frequency) and L is the number of sampling times. Assume that K = 3 far-field signals, whose parameters are θ t =[10°,36°,68°],φ t =[15°,50°,-53°],θ r =[25°,45°,55°],φ r = [17°, -10°, 30°]. In addition, assume that L samples have been collected. The results of each figure of the simulation rely on 200 independent trials. In the simulation, the signal-to-noise ratio (SNR) is defined as X and N are both data matrices in expression (1). The performance evaluation is performed using the root mean square error (RMSE).

[0164] First, the scatter plot results of the 2D-DOD estimation obtained by the proposed PM algorithm and the 2D-DOA obtained by the spectrum peak search are shown in Figure 2. Figure 3 and Figure 4 Given, in the figure, M = 6, N = 14, Y = 128, SNR = 10dB, and L = 200. It can be clearly seen that all parameters are correctly estimated and automatically paired. The results show that this framework can provide closed-form solutions for 2D-DOD estimation and 2D-DOA estimation, and can provide good angle estimation in both single-sample and high-noise situations.

[0165] Secondly, Figure 5 The average RMSE performance of 2D-DOD and 2D-DOA estimation at different signal-to-noise ratios (SNRs) is presented in Figure 1, where M = 6, N = 14, Y = 128, and L = 200. To highlight the reliability of the proposed approach, the proposed algorithm is compared with the 2D-MUSIC algorithm. Notably, when the SNR is low (e.g., -10dB ≤ SNR ≤ 20dB), the proposed approach achieves similar RMSE accuracy to the compared algorithms and can achieve accurate direction-finding estimation.

[0166] Figure 6 The average RMSE performance of 2D-DOD estimation and 2D-DOA estimation under different snapshot numbers is given in

[15] , where M=6, N=14, Y=128, and SNR=10dB. Again, the algorithm is compared with the 2D-MUSIC algorithm. It is worth noting that when the number of snapshots is larger (e.g., 50≤L≤1000), the RMSE of the proposed method is close to that of the compared algorithm, and the effect is comparable. Figure 5 similar.

[0167] Figure 7 The comparison of the running time between this algorithm and the comparison algorithm is shown in Figure 5 and Figure 6 The accuracy of the algorithm is close, but the running time is greatly reduced, and it has the characteristics of low complexity.

[0168] In a specific implementation, the present application provides a computer storage medium and a corresponding data processing unit. The computer storage medium is capable of storing a computer program that, when executed by the data processing unit, executes the invention disclosure of a method for joint DOD and DOA estimation for an arbitrary array bistatic MIMO radar, as well as some or all of the steps in various embodiments. The storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

[0169] Those skilled in the art can clearly understand that the technical solutions in the embodiments of the present invention can be implemented by means of computer programs and their corresponding general hardware platforms. Based on this understanding, the technical solutions in the embodiments of the present invention, in essence or in other words, the part that contributes to the prior art, can be embodied in the form of a computer program, i.e., a software product. The computer program software product can be stored in a storage medium and includes a number of instructions for enabling a device including a data processing unit (which can be a personal computer, server, single-chip microcomputer, MUU or network device, etc.) to execute the methods described in various embodiments of the present invention or certain parts of the embodiments.

[0170] The above embodiments are merely preferred technical solutions of the present invention and should not be construed as limiting the present invention. The scope of protection of the present invention shall be the technical solutions set forth in the claims, including equivalent alternatives to the technical features of the technical solutions set forth in the claims. In other words, equivalent alternatives and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A joint DOD and DOA estimation method for an arbitrary array bistatic MIMO radar, characterized in that: The following steps are involved: S1. Construct a model of an arbitrary array bistatic MIMO radar system including smart reflective surfaces; S2. After obtaining the received signal using the radar system in step S1, a signal model is established, and a direction vector and a channel matrix are defined to obtain a covariance matrix of the received signal after matched filtering. S3, using the propagation operator algorithm to estimate the 2D-DOD angle; S4, combining the 2D-DOD angle obtained by the propagation operator algorithm to obtain a 2D-DOA angle estimate; In step S4, a 2D-DOA angle estimate is obtained, which specifically includes the following sub-steps: S41, performing spectrum peak search on 2D-DOA to estimate the two-dimensional direction of arrival; S42, estimating a 2D-DOA angle using each set of angles in the 2D-DOD direction matrix; In step S42, the 2D-DOA angle is estimated by each group of angles in the 2D-DOD direction matrix. The specific process is as follows: By solving the maximum value of the spectrum function expression of the 2D-DOA estimation in step S41, the estimated value of the receiving angle is obtained. When performing the spectrum peak search, A t Estimated value of Each angle is brought in separately, and K spectrum peak searches are performed to obtain the estimated value, and the estimated elevation angle of the k-th target to the 2D-DOA of the receiving array is obtained. and azimuth That is the two-dimensional direction of arrival of the receiving angle; A t is the emission direction matrix; The above steps complete the joint estimation of DOD and DOA of any array bistatic MIMO radar.

2. The method for joint DOD and DOA estimation of an arbitrary array bistatic MIMO radar according to claim 1, characterized in that: In step S1, a radar system model including an arbitrary transmitting array and a receiving array of a smart reflective surface is constructed. The specific process includes: Assume that the transmitting array has M array elements and the receiving array has N array elements, and the transmitting array and the receiving array are arbitrary arrays, where the position of the mth array element in the transmitting array is: (x tm ,y tm ,z tm ), the position of the nth element in the receiving array is: (x rn ,y rn ,z rn ), the transmitting antenna transmits orthogonal waveforms with the same bandwidth and center frequency; An intelligent reflection surface is provided between the transmitting array and the receiving array, and the intelligent reflection surface is composed of Y intelligent reflection units.

3. The method for joint DOD and DOA estimation of an arbitrary array bistatic MIMO radar according to claim 2, characterized in that: In step S2, the covariance matrix of the received signal after matched filtering is obtained. The specific process includes: The 2D-DOD and 2D-DOA of the kth target for the transmitting array and the receiving array are expressed as (θ tk ,φ tk ) and (θ rk ,φ rk ), the output of the receiver can be expressed as: X(τ)=[(GVA r )⊙A t ]S(τ)+N(τ) (1) Where ⊙ represents the KhatriRao product, is the channel matrix between the IRS and the receiving array, in, represents the reflection response of IRS; Among them, θ tk and φ tk represents the elevation and azimuth of the k-th target 2D-DOD, Among them, θ rk ,φ rk represents the elevation and azimuth of the kth target 2D-DOA, A t and A r They are the transmit direction matrix and the receive direction matrix, S(τ)=[s1(τ),s2(τ),...,s K (τ)] T , where f k represents the Doppler frequency, β k represents the amplitude; It represents the array noise at the instant τ, and its covariance matrix is ​​σ 2 I MN ,σ 2 represents the noise power; a t (θ tk ,φ tk ) and a r (θ rk ,φ rk ) indicates that the direction vector of the kth reception and transmission is: a r (i rk ,f rk )=[exp(-j2πp r1 / λ),...,exp(-j2πp rN / l)] T (2a) a t (i tk ,f tk )=[exp(-j2πp t1 / λ),...,exp(-j2πp tM / l)] T (2b) Where exp(·) represents the e in the exponential function (·) , p rn =x rn sinθ rk cosφ rk +y rn sinθ rk sinφ rk +z rn cosθ rk , n=1,2,...,N,p tm =x tm sinθ tk cosφ tk +y tm sinθ tk sinφ tk +z tm cosθ tk , m=1,2,...,M,(·) T represents the transpose of the matrix; λ represents the wavelength; The channel matrix G between the IRS and the receiving array is expressed as: Among them, r 0h represents the distance from the hth element of the IRS to the reference element of the receiving array, r nh is the distance from the hth element of the IRS to the nth element of the receiver array; The output X of the receiving end is simply written as: X=AS+N (4) Where A represents the emission matrix, is the additive Gaussian white noise matrix. For the signal model in the formula, the covariance matrix of L samples is: in,(·) H Represents the conjugate transpose of a matrix.

4. The method for joint DOD and DOA estimation of an arbitrary array bistatic MIMO radar according to claim 3, characterized in that: In step S3, the 2D-DOD angle is estimated using the propagation operator algorithm, which specifically includes the following sub-steps: S31, construct the propagation operator; S32. Estimate the emission angle using a propagation operator algorithm.

5. The method for joint DOD and DOA estimation of an arbitrary array bistatic MIMO radar according to claim 4, characterized in that: In step S31, a propagation operator is constructed. The specific process is as follows: The emission matrix A can be divided into two parts, expressed as: in, is a non-singular matrix, The linear transformation of A0 gives the following expression: TO s =P s A0 (7) in, is the propagation operator, P s Estimated to be: Where Q is The first K columns of H are The last MN-K columns, (·) -1 represents the inverse of the matrix, (·) H Represents the conjugate transpose of a matrix.

6. The method for joint DOD and DOA estimation of an arbitrary array bistatic MIMO radar according to claim 5, characterized in that: In step S32, the transmission angle is estimated using the propagation operator algorithm. The specific process is as follows: Define the matrix P: Among them I K is a K×K identity matrix, is the propagation operator, is a matrix with independent columns; Divide the matrix P into: in, n=1,2,...,N, the relationship between P2 and P1 is: in, is a non-singular matrix, represented by the first K rows and K columns of the emission matrix A, (·) -1 Represents the inverse of the matrix, for P1 + P2 is decomposed by eigenvalues, and the diagonal matrix formed by eigenvalues ​​is Where Φ1=diag(exp[j2π(m t1 w 21 +n t1 v 21 +l t1 u 21 ) / λ],...,exp[j2π(m tK w 21 +n tK v 21 +l tK u 21 ) / λ]), m tk = sinθ tk cosφ tk , n tk = sinθ tk sinφ tk , l tk =cosθ tk , w 21 =x t1 -x t2 , v 21 =y t1 -y t2 ,u 21 =z t1 -z t2 , Π is a non-singular matrix, take Construct a 1×K row vector g1 from the diagonal elements of This yields a matrix: in, Use ρ k Denotes the kth column of B and s = angle (ρ k ), angle represents the calculated phase angle, which can be expressed as: in, Use the least squares method to solve and in,(·) + represents the pseudo-inverse of the matrix, and m tk , n tk and l tk estimated value of; The azimuth and elevation estimation of 2D-DOD can be expressed as: in, Denote the estimated azimuth of the kth target in 2D-DOD of the transmitting array, Denotes the estimated elevation angle of the kth target in 2D-DOD with respect to the transmitting array.

7. The method for joint DOD and DOA estimation of an arbitrary array bistatic MIMO radar according to claim 6, characterized in that: In step S41, a spectrum peak search is performed on the 2D-DOA to estimate the two-dimensional direction of arrival. The specific process is as follows: Decomposing the covariance matrix, we get: Among them, D s is a K×K diagonal matrix consisting of the largest K eigenvalues, D n is a diagonal matrix consisting of MN-K eigenvalues, E s is the eigenvector corresponding to the largest K eigenvalues, E n are the eigenvectors corresponding to the remaining eigenvalues, (·) H represents the conjugate transpose of a matrix; List the spectral function expression of 2D-DOA estimation: Among them, A=A t ⊙(GVA r ), A represents the emission matrix, ⊙ represents the KhatriRao product, is the channel matrix between the IRS and the receiving array, in, represents the reflection response of IRS, A t Estimated value of It has been found in 2D-DOD that θ rk ,φ rk represents the elevation and azimuth angles of the kth target relative to the 2D-DOA of the receiving array.

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