Omnidirectional reconfigurable metasurface auxiliary array radar transmitted beam forming method for non-line-of-sight target perception

Abstract

The invention discloses an omni-directional reconfigurable metasurface-assisted array radar transmitted beam forming method for non-line-of-sight target perception, and aims at an omni-directional reconfigurable metasurface-assisted array radar to maximize the main lobe gain of a transmission region and a reflection region as a target function. Constructing an optimization model by taking the array emission energy and the transmission coefficient and the reflection coefficient of the omnidirectional reconfigurable metasurface as constraints, and performing equivalent transformation on the optimization model; constructing a scaling form augmented Lagrange function of the optimization model after the equivalent transformation, decomposing the optimization model after the equivalent transformation into a plurality of sub-problems based on an ADMM criterion, and solving each sub-problem by adopting non-convex quadratic constraint quadratic programming and positive semidefinite relaxation technologies, and obtaining an optimized emission weight and a transmission coefficient and a reflection coefficient of the omni-directional reconfigurable metasurface through iteration. The STARS-assisted array radar provided by the invention realizes full space coverage, and has better performance in the aspect of main lobe gain compared with a standard RIS-assisted array radar.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing and array signal processing, and specifically relates to an omnidirectional reconfigurable metasurface-assisted array radar transmission beamforming method for non-line-of-sight target perception. Background Art

[0002] In complex urban environments, the line-of-sight path between the radar transmitter and the target is blocked, which poses a severe challenge to target perception. Reconfigurable intelligent surfaces (RIS) are used to create non-line-of-sight paths to expand the detectable area because they can intelligently adjust the incident signal. However, RIS requires that the radar transmitter and the target are located on the same side, which limits the detectable area to a hemispherical range. In order to achieve full spatial coverage, multiple RIS need to be deployed, but this will increase the hardware cost. The omnidirectional reconfigurable metasurface (STARS) is the key to solving this problem. Unlike traditional RIS, STARS divides the entire area into a transmission area and a reflection area, and can transmit or reflect the incident signal in the two areas respectively, thereby obtaining 360° full coverage.

[0003] STARS was originally used in wireless communications to expand coverage, improve spectrum efficiency, and achieve secure communications. Due to its significant advantages, STARS is also used in Integrated sensing and Communication (ISAC) systems to simultaneously improve the perception and communication performance of non-line-of-sight paths. For example, Wang et al. used STARS to improve parameter estimation performance by reducing the Cramer-Rao bound of radar target parameters. For details, see the document "Z. Wang, X. Mu, and Y. Liu, "STARS enabled integrated sensing and communications," IEEE Transactions on Wireless Communications, vol. 22, no. 10, pp. 6750-6765, 2023.". Wang et al. maximized the average irradiation power of multiple radar targets under the constraints of communication user quality of service (QoS) and eavesdropping user confidentiality rate. For details, see the document "C. Wang, C.-C. Wang, Z. Li, DW Kwan Ng, K.-K. Wong, N. Al-Dhahir, and D. Niyato, "STAR-RIS-enabled secure dual-functional radar-communications: Joint waveform and reflective beamforming optimization," IEEE Transactions on Information Forensics and Security, vol. 18, pp. 4577-4592, 2023.". Zhang et al. achieved multi-target detection by maximizing the minimum SINR of all radar targets, see the literature "Z. Zhang, W. Chen, Q. Wu, Z. Li, X. Zhu, and J. Yuan, "Intelligent omnisurfaces assisted integrated multi-target sensing and multi-user MIMO communications," IEEE Transactions on Communications, vol. 13, pp. 4591-4606, 2024". However, all these studies detect non-line-of-sight targets in a hemispherical space and need to know the direction of the target. Summary of the invention

[0004] The invention discloses an omnidirectional reconfigurable supersurface-assisted array radar transmission beamforming method for non-line-of-sight target perception.

[0005] The technical solution adopted by the present invention is: an omnidirectional reconfigurable metasurface-assisted array radar transmit beamforming method for non-line-of-sight target perception, comprising:

[0006] For the array radar assisted by omnidirectional reconfigurable metasurface, the optimization model is constructed with the objective function of maximizing the main lobe gain of the transmission area and the reflection area, and the array transmission energy and the transmission coefficient and reflection coefficient of the omnidirectional reconfigurable metasurface are used as constraints, and the optimization model is equivalently transformed.

[0007] The scaled augmented Lagrangian function of the optimization model after equivalent transformation is constructed. Based on the ADMM criterion, the optimization model after equivalent transformation is decomposed into several sub-problems. Each sub-problem is solved by non-convex quadratic constrained quadratic programming and semi-positive definite relaxation technology, and the optimized emission weights and the transmission coefficient and reflection coefficient of the omnidirectional reconfigurable metasurface are obtained through iteration.

[0008] Preferably, the optimization model constructed by maximizing the main lobe gain of the transmission area and the reflection area is as the objective function, and the array emission energy and the transmission coefficient and reflection coefficient of the omnidirectional reconfigurable metasurface are as constraints:

[0009]

[0010] Where w is the transmit weight vector of the array radar, V t and V r are the transmission coefficient matrix and reflection coefficient matrix of the omnidirectional reconfigurable metasurface STARS, θ s and are the wave departure angles of STARS in the transmission and reflection regions, respectively. STARS has a total of N units, v t,n and v r,n are the transmission coefficient and reflection coefficient of the nth unit of the omnidirectional reconfigurable metasurface STARS, and P is the maximum available transmission power.

[0011] Preferably, the specific method for performing equivalent transformation on the optimization model is:

[0012] definition Defining auxiliary variables and Convert the optimization model to:

[0013]

[0014] In the formula, a H (θ s )and are the steering vectors of STARS in the transmission and reflection regions, respectively, and G is the channel matrix between the transmitting array and STARS.

[0015] Preferably, the scaled augmented Lagrangian function of the optimization model after equivalent transformation is constructed as follows:

[0016]

[0017] Among them, ρ>0 is the penalty factor, and are dual variables, S and Q are the numbers of discrete main lobe grid points in the transmission and reflection regions, respectively.

[0018] Preferably, based on the ADMM criterion, the optimization model after equivalent transformation is decomposed into several sub-problems, namely:

[0019] Sub-question 1:

[0020]

[0021] Sub-question 2:

[0022]

[0023] Sub-question 3:

[0024]

[0025]

[0026] In the formula, the superscript k is used to represent the number of iterations.

[0027] Preferably, the specific method for solving sub-problem 1 is:

[0028] Define z 1,s =h s +δ s , z 2,q =y q +λ q , z=[z 1,1 ,...,z 1,S ,z 2,1 ,...,z 2,Q ] T , a 1,s =a H (θ s )V t G, A=[a 1,1 ,...,a 1,S ,a 2,1 ,...,a 2,Q ]H , ignoring irrelevant items, subproblem 1 is transformed into

[0029]

[0030] The Lagrange multiplier method is used to solve Specifically:

[0031] The Lagrangian function is defined as:

[0032]

[0033] Among them, λ>0 is the Lagrange multiplier, and the first-order optimal condition of the Lagrange function is:

[0034] z H A(A H A+λI L ) -2 A H z=P

[0035] definition and The eigenvalue decomposition of where D = diag([r1,...,r L ]) is the eigenvalue matrix with the eigenvalues ​​arranged in descending order, and V is the corresponding eigenvector matrix;

[0036] definition The first-order optimal condition is equivalently expressed as:

[0037]

[0038] Use the linear search method to obtain the optimal λ ＊ , the optimal solution to sub-problem 1 is:

[0039] w ＊ =(A H A+λ ＊ I L ) -1 A H z.

[0040] Preferably, the specific method for solving sub-problem 2 is:

[0041] According to the properties of diagonal matrices, V i q=diag(q)v i , i∈{t,r},v i Yes V i The corresponding column vector v i =diag(V i ), where q = Gw; define z t =[z 1,1,…,z 1,S ] T , z r =[z 2,1 ,…,z 2,Q ] T , ignoring irrelevant items, transform subproblem 2 into:

[0042]

[0043] Among them, B t =A t diag(q), B r =A r diag(q), and A t =[a H (θ1),...,a H (θ S )],

[0044] The above formula is a non-convex and non-homogeneous QCQP problem, which can be equivalently expressed as the following homogeneous QCQP form:

[0045]

[0046] in,

[0047] Use SDR to solve subproblem 2 of the homogeneous QCQP form, and define Meet Y i ≥0 and rank(Y i )=1, then the SDR form of sub-problem 2 in QCQP form is:

[0048]

[0049] Subproblem 2 in SDR form is a convex problem, which is solved using a standard convex optimization solver. is an approximate rank-one solution, then the corresponding suboptimal solution is:

[0050]

[0051] Preferably, the specific method for solving sub-problem 3 is:

[0052] Definition s =a H (θ s )V t Gw-δ s , Ignoring the constant term, subproblem 3 can be simplified to:

[0053]

[0054] In the simplified subproblem 3, h s ,y q There is a coupling between and ε. When ε is fixed, the optimal h s and q It is expressed as:

[0055]

[0056] The optimal h s and q Substitute this into the simplified subproblem 3, and we get an optimization problem that only concerns the variable ε:

[0057]

[0058] Among them, when |g s When |>ε, otherwise When |g q When |>ε, otherwise

[0059] Define [σ1,…,σ P ] and [η1,...,η I ]for and After removing duplicates and arranging in descending order, [σ1,...,σ P ,η1,…,η I ] After removing duplicates and sorting in descending order, we get [u1,...,u K ];

[0060] Let u0 = 0 and u K+1 =∞,[u1,…,u K ] becomes a piecewise function N(ε)

[0061] N(ε)={N k (ε)|u k-1 ≤ε≤u k ,k=1,...,K},

[0062] in, Here P' and I' satisfy and is the kth subfunction, which transforms N(ε) into a quadratic function form N k (ε) = a k ε 2 +b k ε+c k ,in:

[0063]

[0064] Due to a k >0, The minimum value of Decide;

[0065] By selecting the minimum value in the K+1 segment function, the optimal ε is:

[0066]

[0067] According to the optimal h s and q The calculation formula calculates the optimal and

[0068] Preferably, the specific process of obtaining the optimized emission weights and the transmission coefficient and reflection coefficient of the omnidirectional reconfigurable metasurface through iteration is:

[0069] S1: Through w ＊ =(A H A+λ ＊ I L ) -1 A H z, obtain the emission weight of the k+1th iteration;

[0070] S2: Pass Obtain the transmission coefficient and reflection coefficient of the omnidirectional reconfigurable metasurface of the k+1th iteration;

[0071] S3: According to the formula and

[0072]

[0073] Get the ε of the k+1th iteration k+1 ,

[0074] S4: According to the formula:

[0075]

[0076] Get the k+1th iteration

[0077] S5: Determine whether the iteration stop condition is met: and If satisfied, the emission weights, transmission coefficients and reflection coefficients of STARS obtained in the current iteration are taken as the final results; otherwise, return to step S1.

[0078] Compared with the prior art, the present invention has the following significant advantages: compared with the traditional RIS-assisted array radar, which covers only one hemisphere, the STARS-assisted array radar can achieve 360° full-space detection. In addition, experimental results show that the STARS-assisted array radar can have significant performance improvements in both main lobe gain and side lobe level. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] In order to more clearly illustrate the present technical solution, the following drawings required for use in the prior art description are briefly introduced.

[0080] Figure 1 This is a model diagram of the STARS auxiliary array radar.

[0081] Figure 2 is the convergence curve of the objective function and the dual variable, Figure 2 (a) in is the convergence curve of the objective function. Figure 2 (b) in the figure is the dual variable convergence curve.

[0082] Figure 3 Comparison of the transmission beam performance in the transmission area.

[0083] Figure 4 Comparison of transmit beam performance in the reflection area. DETAILED DESCRIPTION

[0084] The present invention, namely, an omnidirectional reconfigurable metasurface-assisted array radar transmit beamforming method for non-line-of-sight target perception, is further explained below with reference to the accompanying drawings and examples.

[0085] An omnidirectional reconfigurable metasurface-assisted array radar transmit beamforming method for non-line-of-sight target perception uses STARS to assist traditional array radar and achieves 360° all-round detection of non-line-of-sight targets.

[0086] Using the omnidirectional reconfigurable metasurface (STARS) to assist the digital transmitting array, 360° all-round detection of non-line-of-sight targets is achieved. Under the constraints of array transmission energy and STARS transmission / reflection coefficients, a transmit beamforming method based on alternating direction methods of multipliers (ADMM) is proposed. Under the constraints of array transmission energy and STARS transmission / reflection coefficients, the algorithm aims to maximize the main lobe gain of the transmission / reflection area at the same time. The final problem is defined as a maximum minimization problem under non-convex constraints. Based on the ADMM framework, the original problem is decomposed into several easy-to-solve sub-problems, and then the non-convex quadratically constrained quadratic program (QCQP) and semi-definite relaxation (SDR) techniques are used to solve it. The specific implementation steps are as follows:

[0087] Step 1: For the array radar assisted by the omnidirectional reconfigurable metasurface STARS, the beam emitted by the array radar first hits the omnidirectional reconfigurable metasurface, and then is reflected or projected onto the object by the omnidirectional reconfigurable metasurface. The illumination range of the non-line-of-sight signal is divided into two areas: transmission and reflection. The STARS in the present invention adopts an energy splitting model to synchronize transmission and reflection signals, and has N units.

[0088] Define V t and V r are the transmission and reflection coefficient matrices of STARS, respectively, which are expressed as where β i,n ∈[0,1], is the amplitude and phase shift of the nth unit. Since each unit of STARS must obey the law of energy conservation, its transmission coefficient and reflection coefficient satisfy |v t,n | 2 +|v r,n | 2 =1. Define the transmit weight vector of the array radar as w=[w1,w2,…,w L ] T ,satisfy Where P is the maximum available transmit power.

[0089] The main lobe direction in the transmission and reflection areas of the array radar is discretized, that is, and where S and Q are the numbers of discrete main lobe grid points in the transmission and reflection regions, respectively.

[0090] Define f(θ s ,w,V t )=a H (θ s )V t Gw and are the radiation beam patterns of the transmission and reflection regions, respectively, where is the STARS guidance vector, θ s and are the wave separation angles of STARS in the transmission and reflection regions, k is the wave number, d is the array element spacing of STARS, and G is the channel matrix between the transmitting array and STARS.

[0091] In order to maximize the main lobe gain in both the transmission and reflection regions, the optimization problem is modeled as follows:

[0092]

[0093] Step 2: By definition And define auxiliary variables and Problem (1) is equivalently transformed into

[0094]

[0095] Step 3: Define the scaled augmented Lagrangian function of problem (26) as

[0096]

[0097] Among them, ρ>0 is the penalty factor, and is the dual variable.

[0098] Based on the ADMM criterion, solving problem (2) can be reduced to the following sub-problems:

[0099]

[0100]

[0101] Step 4: Define z 1,s =h s +δ s , z 2,q =y q +λ q , z=[z 1,1 ,...,z 1,S ,z 2,1 ,...,z 2,Q ] T , a 1,s =aH (θ s )V t G, A=[a 1,1 ,...,a 1,S ,a 2,1 ,...,a 2,Q ] H , ignoring irrelevant terms, transforming problem (4) into

[0102]

[0103] The Lagrange multiplier method is used to solve problem (9). The Lagrange function is defined as

[0104]

[0105] Where λ>0 is the Lagrange multiplier. The first-order optimal condition of formula (10) is

[0106] z H A(A H A+λI L ) -2 A H z=P. (11)

[0107] definition and The eigenvalue decomposition of where D = diag([r1,...,r L ]) is the eigenvalue matrix with eigenvalues ​​in descending order, and V is the corresponding eigenvector matrix. Definition Formula (11) can be equivalently expressed as

[0108]

[0109] Use the typical linear search method to obtain the optimal λ ＊ , thus the optimal solution to problem (9) is

[0110] w ＊ =(A H A+λ ＊ I L ) -1 A H z. (13)

[0111] Step 5: According to the properties of diagonal matrices, V i q=diag(q)v i , i∈{t,r}, where q=Gw. Define z t =[z 1,1 ,…,z 1,S ] T , zr =[z 2,1 ,…,z 2,Q ] T , ignoring irrelevant terms, transforming problem (5) into

[0112]

[0113] Among them, B t =A t diag(q), B r =A r diag(q), and A t =[a H (θ1),...,a H (θ S )],

[0114] Problem (14) is a non-convex and non-homogeneous QCQP problem, which can be equivalently expressed as the following homogeneous QCQP form:

[0115]

[0116] in,

[0117] Use SDR to solve problem (15), define It satisfies Y i ≥0 and rank(Y i )=1, then the SDR form of problem (15) is

[0118]

[0119] Problem (16) is a convex problem and can be solved using a standard convex optimization solver. is the approximate rank-one solution of problem (14), then the suboptimal solution of problem (14) is

[0120]

[0121] Step 6: Define g s =a H (θ s )V t Gw-δ s , Ignoring the constant term, problem (6) is simplified to:

[0122]

[0123] In problem (18), h s ,y qThere is coupling between and ε. However, when ε is fixed, the optimal h s and q It can be displayed as:

[0124]

[0125] Substituting equation (19) into problem (18), we can obtain an optimization problem only about the variable ε

[0126]

[0127] Among them, when |g s |ε>, otherwise Same when |g q When |>ε, otherwise

[0128] Define [σ1,…,σ P ] and [η1,…,η I ]for and After removing duplicates and arranging in descending order, [σ1,...,σ P ,η1,...,η I ] After removing duplicates and sorting in descending order, we get [u1,…,u K ]. Let u0 = 0 and u K+1 =∞, turning it into a piecewise function N(ε)

[0129] N(ε)={N k (ε)|u k-1 ≤ε≤u k ,k=1,...,K}, (21)

[0130] in, is the kth subfunction. Convert N(ε) into a quadratic function N k (ε) = a k ε 2 +b k ε+c k ,in

[0131]

[0132] Due to a k >0, The minimum value of Decide.

[0133] By selecting the minimum value in the K+1 segment function, the optimal ε can be obtained. ＊ for

[0134]

[0135] Once ε ＊ is determined, the optimal and

[0136] In summary, the algorithm flow of this optimization problem is as follows:

[0137] 1) Input parameters: Ω t ,Ω r ,ρ,K max ,τ

[0138] 2) Initialization settings:

[0139] 3) Start iteration:

[0140] i. Obtained by formula (13): w k+1 ;

[0141] ii. Through formula (17), we can obtain:

[0142] iii. Using equations (22) and (19), we can obtain: ε k+1 ,

[0143] iv. Determine by equations (7) and (8) and

[0144] vk=k+1

[0145] 4) If and The loop stops.

[0146] 5) Output: emission weight w, transmission and reflection coefficients V of STARS t and V r .

[0147] The present invention studies the omnidirectional transmission beamforming problem of STARS-assisted array radar under the constraints of radar transmission power and STARS transmission / reflection coefficient.

[0148] Example

[0149] Through MATLAB simulation, the omnidirectional reconfigurable metasurface-assisted array radar transmit beamforming method for non-line-of-sight target perception of the present invention is further illustrated.

[0150] 1) Simulation system parameter settings

[0151] In the experiment, the distance between STARS and the transmitting array is 15m, and the channel G follows the Rice distribution. Each simulation is a uniform linear array with L = 16, the array element spacing is d = λ / 2, the maximum transmit power P = 16W, and the maximum number of iterations K max = 2000 and ADMM tolerance is τ = 10 -5 The scaled dual and auxiliary variables are initialized randomly.

[0152] 2) Beam diagram drawing

[0153] In order to intuitively show the effect of the transmit beamforming method, the obtained weight vector w and the transmission and reflection coefficients V of STARS are used. t 、V r After weighted combination, the transmit beam diagram of the STARS-assisted array radar is finally drawn and compared with the transmit beam diagram of the RIS-assisted array radar. The horizontal coordinates of the beam diagram are the transmission area of ​​[-180°, 0°] and the reflection area of ​​[0°, 180°], and the vertical coordinate is the result of the minimum value of the main lobe gain in the two areas normalized to the path loss and converted into dB.

[0154] 3) Metrics

[0155] In the present invention, it is necessary to measure the effect of the final beamforming. In addition to drawing the beam diagram, it is also necessary to use the minimum main lobe gain as an indicator.

[0156]

[0157] Where: f(θ s ,w,V t )and They are the radiation patterns in the transmission / reflection areas respectively. Under the same initial conditions, the larger the minimum main lobe gain, the better the beamforming effect.

[0158] 4) Result analysis

[0159] The present invention has carried out three example simulations in total.

[0160] Figure 1 This is a model diagram of the STARS auxiliary array radar; Figure 2 is the convergence curve of the objective function and dual variable of the proposed algorithm; Figure 3 and Figure 4 The performance of the STARS-assisted transmitting array and the standard RIS-assisted transmitting array is compared in the two cases of N=64 and N=128.

[0161] exist Figure 1In , a STARS-assisted radar transmitter is considered, whose transmitting array is a uniform linear array of L units, and STARS is composed of N transmissive-reflective metasurfaces. Assuming that the line-of-sight path between the transmitting array and the target is blocked, the target can only be detected through the non-line-of-sight path generated by STARS.

[0162] exist Figure 2 In (a) and (b), it can be observed that: as the number of iterations increases, the objective function gradually converges to a stable value, while the dual variable gradually decreases and tends to zero. These phenomena prove the convergence of the algorithm proposed in the present invention.

[0163] exist Figure 3 and Figure 4 In the above figure, the transmission / reflection regions are set to [-120°, -100°] and [100°, 120°], and two standard RIS are used to independently form transmission and reflection beams as comparison objects, and the number of their metasurface units is N. RIS =N / 2. This is equivalent to STARS in a mode switching state, where half of the units work in the transmission mode and the other half work in the reflection mode. Figure 3 In the figure, it can be observed that in the transmission region, the mainlobe gain of the STARS-assisted array is 1.85dB and 1.19dB higher than that of the standard RIS-assisted array when N=64 and N=128. In addition, STARS significantly reduces the sidelobe level compared to the standard RIS. Specifically, the integrated sidelobe level is 10.47dB and 13.63dB lower than that of the standard RIS. Similarly, by Figure 4 It can be observed that in the reflection region, the main lobe gain of the STARS-assisted array is 1.85 dB and 1.19 dB higher than that of the standard RIS-assisted array when N=64 and N=128, and the integrated sidelobe level is 10.35 dB and 13.29 dB lower than that of the standard RIS.

[0164] In summary, the STARS-assisted array radar transmit beamforming method of the present invention has good comprehensive performance. Compared with the beamforming method of the standard RIS-assisted array, the proposed method has higher mainlobe gain and lower sidelobe level. This shows that STARS is an effective method for achieving full-space non-line-of-sight target perception.

Claims

1. A transmit beamforming method for an omnidirectional reconfigurable metasurface-assisted array radar for non-line-of-sight target perception, characterized in that: include: For the array radar assisted by omnidirectional reconfigurable metasurface, the optimization model is constructed with the objective function of maximizing the main lobe gain of the transmission area and the reflection area, and the array transmission energy and the transmission coefficient and reflection coefficient of the omnidirectional reconfigurable metasurface are used as constraints, and the optimization model is equivalently transformed. The scaled augmented Lagrangian function of the optimization model after equivalent transformation is constructed. Based on the ADMM criterion, the optimization model after equivalent transformation is decomposed into several sub-problems. Each sub-problem is solved by non-convex quadratic constrained quadratic programming and semi-positive definite relaxation technology, and the optimized emission weights and the transmission coefficient and reflection coefficient of the omnidirectional reconfigurable metasurface are obtained through iteration.

2. The omnidirectional reconfigurable metasurface-assisted array radar transmit beamforming method for non-line-of-sight target perception according to claim 1 is characterized in that: Taking maximizing the main lobe gain of the transmission area and the reflection area as the objective function, and taking the array emission energy and the transmission coefficient and reflection coefficient of the omnidirectional reconfigurable metasurface as constraints, the optimization model is constructed as follows: Where w is the transmit weight vector of the array radar, V t and V r are the transmission coefficient matrix and reflection coefficient matrix of the omnidirectional reconfigurable metasurface STARS, θ s and are the wave departure angles of STARS in the transmission and reflection regions, respectively. STARS has a total of N units, v t,n and v r,n are the transmission coefficient and reflection coefficient of the nth unit of the omnidirectional reconfigurable metasurface STARS, and P is the maximum available transmission power.

3. The omnidirectional reconfigurable metasurface-assisted array radar transmit beamforming method for non-line-of-sight target perception according to claim 2 is characterized in that: The specific method for equivalent transformation of the optimization model is: definition Defining auxiliary variables and Convert the optimization model to: In the formula, a H (θ s )and are the steering vectors of STARS in the transmission and reflection regions, respectively, and G is the channel matrix between the transmitting array and STARS.

4. The omnidirectional reconfigurable metasurface-assisted array radar transmit beamforming method for non-line-of-sight target perception according to claim 3 is characterized in that: The scaled augmented Lagrangian function of the optimization model after the equivalent transformation is constructed as follows: Among them, ρ>0 is the penalty factor, and are dual variables, S and Q are the numbers of discrete main lobe grid points in the transmission and reflection regions, respectively.

5. The omnidirectional reconfigurable metasurface-assisted array radar transmit beamforming method for non-line-of-sight target perception according to claim 4 is characterized in that: Based on the ADMM criterion, the optimization model after equivalent transformation is decomposed into several sub-problems, namely: Sub-question 1: Sub-question 2: Sub-question 3: In the formula, the superscript k is used to represent the number of iterations.

6. The omnidirectional reconfigurable metasurface-assisted array radar transmit beamforming method for non-line-of-sight target perception according to claim 5 is characterized in that: The specific method to solve sub-problem 1 is: Define z 1,s =h s +δ s , z 2,q =y q +λ q , z=[z 1,1 ,...,z 1,S ,z 2,1 ,...,z 2,Q ] T , a 1,s =a H (θ s )V t G, A=[a 1,1 ,...,a 1,S ,a 2,1 ,...,a 2,Q ] H , ignoring irrelevant items, subproblem 1 is transformed into The Lagrange multiplier method is used to solve Specifically: The Lagrangian function is defined as: Among them, λ>0 is the Lagrange multiplier, and the first-order optimal condition of the Lagrange function is: z H A(A H A+λI L ) -2 A H z=P definition and The eigenvalue decomposition of where D = diag([r1,...,r L ]) is the eigenvalue matrix with the eigenvalues ​​arranged in descending order, and V is the corresponding eigenvector matrix; definition The first-order optimal condition is equivalent to: Use the linear search method to obtain the optimal λ ＊ , the optimal solution to sub-problem 1 is: w ＊ =(A H A+λ ＊ I L ) -1 A H z。 7. The omnidirectional reconfigurable metasurface-assisted array radar transmit beamforming method for non-line-of-sight target perception according to claim 6 is characterized in that: The specific method to solve sub-problem 2 is: According to the properties of diagonal matrices, V i q=diag(q)v i , i∈{t,r},v i Yes V i The corresponding column vector v i =diag(V i ), where q = Gw; define z t =[z 1,1 ,…,z 1,S ] T , z r =[z 2,1 ,…,z 2,Q ] T , ignoring irrelevant items, transform subproblem 2 into: where B t = A t diag(q), B r = A r diag(q), and A t = [a H (θ1),..., a H (θ S )], The above formula is a non-convex and non-homogeneous QCQP problem, which can be equivalently expressed as the following homogeneous QCQP form: in, Use SDR to solve subproblem 2 of the homogeneous QCQP form, and define satisfy and rank(Y i )=1, then the SDR form of sub-problem 2 in QCQP form is: Y t (n+1,n+1)=1,Y r (n+1,n+1)=1, Subproblem 2 in SDR form is a convex problem, which is solved using a standard convex optimization solver. is an approximate rank-one solution, then the corresponding suboptimal solution is:

8. The omnidirectional reconfigurable metasurface-assisted array radar transmit beamforming method for non-line-of-sight target perception according to claim 7, characterized in that: The specific method to solve sub-problem 3 is: Definition s =a H (θ s )V t Gw-δ s , Ignoring the constant term, subproblem 3 can be simplified to: In the simplified subproblem 3, h s ,y q There is a coupling between and ε. When ε is fixed, the optimal h s and q It is expressed as: The optimal h s and q Substitute this into the simplified subproblem 3, and we get an optimization problem that only concerns the variable ε: Among them, when |g s When |>ε, otherwise When |g q When |>ε, otherwise Define [σ1,…,σ P ] and [η1,…,η I ]for and After removing duplicates and arranging in descending order, [σ1,…,σ P ,η1,...,η I ] After removing duplicates and sorting in descending order, we get [u1,...,u K ]; Let u0 = 0 and u K+1 =∞, and [u1,...,u K ] becomes a piecewise function N(ε) N(e)={N k (e)|u k-1 ≤ε≤u k ,k=1,...,K}, in, Here P' and I' satisfy and is the kth subfunction, which transforms N(ε) into a quadratic function form N k (ε) = a k ε 2 +b k ε+c k ,in: Due to a k >0, The minimum value of Decide; By selecting the minimum value in the K+1 segment function, the optimal ε is: According to the optimal h s and q The calculation formula calculates the optimal and 9. The omnidirectional reconfigurable metasurface-assisted array radar transmit beamforming method for non-line-of-sight target perception according to claim 8, characterized in that: The specific process of obtaining the optimized emission weights and the transmission coefficient and reflection coefficient of the omnidirectional reconfigurable metasurface through iteration is as follows: S1: Through w ＊ =(A H A+λ ＊ I L ) -1 A H z, obtain the emission weight of the k+1th iteration; S2: Pass Obtain the transmission coefficient and reflection coefficient of the omnidirectional reconfigurable metasurface of the k+1th iteration; S3: According to the formula and Get the ε of the k+1th iteration k+1 , S4: According to the formula: Get the k+1th iteration S5: Determine whether the iteration stop condition is met: and If satisfied, the emission weights, transmission coefficients and reflection coefficients of STARS obtained in the current iteration are taken as the final results; otherwise, return to step S1.

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