Intelligent metasurface-assisted low-bit quantization array non-line-of-sight signal source DOA (direction of arrival) estimation method

Abstract

The invention discloses an intelligent metasurface-assisted low-bit quantization array non-line-of-sight signal source DOA estimation method, and the method comprises the steps: processing a received signal through employing a low-precision ADC after a receiving array antenna receives an echo signal scattered by a target and reflected by an RIS, constructing an RIS equivalent channel, employing an RIS equivalent channel matrix as an auxiliary variable, and carrying out the estimation of the DOA of a low-bit quantization array non-line-of-sight signal source. The method comprises the following steps: quantizing a signal, estimating the quantized signal, converting an angle estimation problem into a convex optimization problem, solving the convex optimization problem by utilizing a CVX toolbox in Matlab software, constructing two one-dimensional Toeplitz matrixes respectively containing target DOA and DOD information, solving a signal angle by utilizing one-dimensional Vandermonde decomposition, and performing angle matching, and the DOA and DOD joint estimation of the non-line-of-sight signal source is realized. According to the method, the active regulation and control capability of the RIS, the low-bit quantization technology and the atom norm minimization algorithm are creatively fused, high-precision and real-time DOA and DOD estimation can be achieved in the non-line-of-sight environment while low-bit quantization is achieved, and the method has higher engineering practical value.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing technology, and in particular relates to a method for estimating the DOA of a low-bit quantized array non-line-of-sight signal source with intelligent metasurface assistance. Background Technology

[0002] Direction of Arrival (DOA) estimation is a core research area in array signal processing, aiming to determine the azimuth of a signal source by processing the signals received by the array antenna. For DOA estimation of non-line-of-sight signal sources, traditional methods such as multipath radar technology and methods based on Received Signal Strength (RSS) and Time Difference of Arrival (TDOA) have limitations: multipath radar technology faces difficulties in acquiring effective information, while methods based on RSS and TDOA are limited by hardware conditions, resulting in lower estimation accuracy and resolution.

[0003] The development of reconfigurable intelligent surfaces (RIS) offers a new approach to solving non-line-of-sight propagation problems. A RIS is an artificial electromagnetic surface composed of a large number of programmable electromagnetic units. By dynamically controlling the electromagnetic properties (such as amplitude and phase) of the control unit, it achieves intelligent control of spatial electromagnetic waves. It has advantages such as low cost and real-time programmability, and can act as a relay in non-line-of-sight signal reception, improving signal transmission quality through directional reflection.

[0004] Atomic Norm Minimization (ANM) is a sparse signal processing method based on the compressed sensing framework. This method transforms the DOA estimation problem into a sparse optimization problem by constructing a set of atoms in the signal space, and then solves it using semidefinite programming (SDP). ANM does not require discretization, avoiding off-grid errors, and can achieve super-resolution DOA estimation under conditions of limited snapshot numbers or low signal-to-noise ratio.

[0005] Low-bit quantization (LBS) refers to the use of a low-resolution analog-to-digital converter (ADC) to digitize the received signal, typically employing 1-bit to 4-bit LBS to reduce hardware cost, power consumption, and data processing complexity. In the field of DOA estimation, LBS is applied in large-scale MIMO systems or IoT scenarios to address high data rates and energy efficiency requirements. However, LBS introduces significant quantization noise and nonlinear distortion, leading to signal information loss and affecting angle estimation accuracy.

[0006] In the study "Application of Low-Bit Quantization in Direction-of-Arrival (DOA) Estimation in MIMO-OFDM Systems," existing technologies have proposed a 1-bit quantization-based DOA estimation method. This method reduces quantization errors through compressed sensing theory, but its performance is limited in non-line-of-sight (NLS) environments, and it does not consider RIS-assisted path enhancement. While the low-bit quantization DOA estimation method described in this proposal reduces hardware costs, it suffers from the following drawbacks: Quantization error amplification: In NLS propagation environments, signal attenuation is severe, and low-bit quantization further introduces nonlinear distortion, leading to a decrease in signal-to-noise ratio (SNR) and a significant increase in the root mean square error (RMSE) of angle estimation. Especially under low SNR conditions (e.g., SNR < -10dB), the estimation performance deteriorates drastically. Insufficient adaptability: This method does not consider RIS-assisted path reconstruction and cannot utilize controllable reflections to optimize signal quality, thus limiting estimation accuracy in complex NLS scenarios.

[0007] In "Low-Precision DOA Estimation via Atomic Norm Minimization," existing techniques explored the adaptability of atomic norm minimization in low-bit reception by handling quantization noise through regularization. However, this approach suffers from high computational complexity and lacks optimization for non-line-of-sight scenarios. Furthermore, our proposed solution also exhibits high computational complexity: to compensate for quantization noise, an additional regularization term is introduced, increasing the burden of solving the semidefinite programming problem and extending the average runtime, which is detrimental to real-time applications. It also suffers from poor robustness: in cases with a small number of snapshots (e.g., L < 20), the quantization error and noise combine, leading to the failure of Toplitz matrix decomposition and an increased angle matching error rate.

[0008] These shortcomings collectively highlight the challenges of non-line-of-sight (DOA) estimation under low-bit reception: the interaction between quantization noise and propagation loss makes it difficult for traditional methods to balance accuracy and efficiency. Summary of the Invention

[0009] The purpose of this invention is to overcome the inherent defects of existing low-bit DOA estimation techniques and propose a smart metasurface-assisted low-bit quantization array non-line-of-sight signal source DOA estimation method. Under non-line-of-sight propagation conditions, the electromagnetic control capability of the RIS (Radio Resonance Array) is used as a signal relay to construct an effective propagation path from the target through the RIS to the receiver, fundamentally solving the signal acquisition problem for non-line-of-sight target DOA estimation. At the receiver, a low-precision ADC is used to sample and quantize the received signal, significantly reducing hardware costs and power consumption. With the increasing number of radar array antennas, this method can solve the problem at a lower cost. In the atomic norm minimization method, the angle estimation problem is transformed into a convex optimization problem, and the CVX tool is introduced for optimization. By constructing and decomposing a one-dimensional Topletz matrix to obtain DOA and DOD respectively, the method has high resolution and does not require mesh partitioning, greatly reducing the complexity of angle estimation. Even with the signal enhancement of the RIS and the super-resolution characteristics of the atomic norm minimization algorithm, high angle estimation accuracy can still be maintained under low-bit quantization conditions.

[0010] To achieve the objective of this invention, a method for estimating the DOA of a low-bit quantized array non-line-of-sight signal source with intelligent metasurface assistance is disclosed, comprising the following steps:

[0011] Step 1: Transmitting signals from the transmitting array antenna: The M-element transmitting antenna array transmits M mutually orthogonal unit power waveforms to initialize the azimuth of arrival (DOA) and azimuth of departure (DOD) information of K incoherent targets within the observable area;

[0012] Step 2: RIS reflects the target echo signal: RIS consists of Q reflection units. The reflection coefficient of each unit is adjusted in real time by the phase control matrix v to reflect the echo signal scattered by the target in a directional manner, thus constructing a complete "transmitter-target-RIS-receiver" non-line-of-sight signal transmission link.

[0013] Step 3: Receive signal from the receiving array antenna: The N-element receiving antenna array receives the RIS reflected signal, and accumulates L snapshots to construct the received signal matrix Y;

[0014] Step 4: Construct the equivalent channel matrix: Based on the known RIS phase control matrix v and the RIS-to-receiver channel matrix G, construct the equivalent channel matrix S;

[0015] Step 5: Perform low-bit quantization on the received signal: Use a low-precision analog-to-digital converter to perform low-bit quantization on the received signal matrix Y to obtain the quantized signal matrix Z;

[0016] Step 6: Estimate angle parameters based on LQANM algorithm: Use the atomic norm minimization algorithm under low bit quantization to transform the angle estimation problem into a semi-positive definite programming problem for the quantization matrix Z, and solve it to obtain the Topletz matrix and the optimization variable X;

[0017] Step 7: Obtain DOA and DOD estimation results: Perform Vandermonde decomposition on the estimated Toplez matrix to obtain the estimated angles, use the optimization variable X to perform angle matching, and finally obtain the DOA and DOD estimation results for K targets.

[0018] Furthermore, in step 1, the system employs a MIMO array. The transmitting end is a uniform linear array with M antennas, the RIS is a uniform linear array with Q elements, and the receiving end is a uniform linear array with N antennas. The spacing between the transmitting antenna arrays and the spacing between the RIS elements are equal to the base spacing, i.e., d. T =d Q =d; Let be the signal wavelength; assume there are K incoherent targets within the same range gate of the radar system, and the transmission steering vector is... This represents the direction vector between the transmitter and the k-th target; The transpose of the matrix is ​​represented; for the k-th target, its emission angle DOD is denoted as... The receiving angle DOA is denoted as .

[0019] Furthermore, in step 2, the RIS, as a reconfigurable smart metasurface that can be adjusted in real time, directs the echo signal scattered by the target to the receiving antenna after reflection by the RIS; the channel matrix from the RIS to the receiving end is... This represents the channel phase correspondence between the receiving array antenna and the RIS array elements; the phase control signal of the RIS is... There are L configurations, representing the active control of the RIS array elements by each snapshot; the target radar cross section (RCS) coefficient remains unchanged between snapshots. Remain unchanged; among which Represents the RCS amplitude. Represents RCS phase; receive direction vector .

[0020] Furthermore, in step 3, the RIS-reflected signal is transmitted to the receiving antenna array to construct a complete signal link of "transmitter—target—RIS—receiver"; the signal received by the receiving array antenna is:

[0021]

[0022] in The noise level is the channel noise within the l-th snapshot.

[0023] Further, in step 4, the RIS channel relationship matrix is ​​constructed using the known channel matrix G of the RIS and the receiving antenna, and the phase control signal v; in the absence of noise, the channel correlation part is first defined:

[0024] Utilizing the Kronecker product's associativity: ;

[0025] The receive vector is transformed into: ;

[0026] Extract the channel matrix portion outside the accumulation terms and rename it to a new matrix vector:

[0027]

[0028] Collect L snapshots to obtain the complete received signal:

[0029]

[0030] To extract the channel component from the received signal vector, the received signal vector needs to be vectorized:

[0031]

[0032] Define the channel matrix

[0033] The vectorized signal model is then:

[0034]

[0035] Finally, the complete channel matrix vector is constructed using G and v:

[0036]

[0037]

[0038] .

[0039] Furthermore, in step 5, each RF link at the receiving end uses a pair of real-value quantizers to quantize the real and imaginary parts of the received signal:

[0040]

[0041]

[0042] in For quantization function, ;

[0043] For quantization interval, Take the minimum value. Round up;

[0044]

[0045] b is the number of quantization bits. When b = 1 to 4, it is low-bit quantization; Z is the received signal after low-bit quantization.

[0046] Furthermore, in step 6, the signal model analysis yields...

[0047]

[0048]

[0049] By constructing an equivalent channel matrix S as an auxiliary, the angle estimation problem is transformed into a convex optimization problem; and optimization variables are set. Construct the matching matrix U.

[0050] ;

[0051] Make the matching matrix U approximate the quantized received signal Z, and satisfy the quantization constraints during the iteration process:

[0052]

[0053] The objective optimization function is:

[0054]

[0055] The constraints are:

[0056]

[0057] In the formula Given two one-dimensional Toeplitz matrices, Indicates that it is from its first line A defined Toeplitz matrix. Similarly, the specific representation is as follows:

[0058]

[0059]

[0060] In the formula The incoherence coefficient;

[0061] The optimization variable X is:

[0062]

[0063] The convex optimization problem was solved using the CVX toolbox in Matlab, and the results were obtained. .

[0064] Furthermore, utilizing the special structure of the Topletz matrix, a one-dimensional Vandermonde decomposition is performed on the Topletz matrix; thus obtaining the angle. and However, the angle order does not match the true order value. Therefore, we use the X estimated by the algorithm to perform angle matching. The steps are as follows:

[0065] First, construct the direction vector using the estimated angle results. and We use exhaustive enumeration to list all possible permutations and combinations.

[0066] Then, using the Kronecker product property: Construct the estimation result matrix

[0067]

[0068] Calculate the residual with X, and take the result corresponding to the smallest residual value as the matching result.

[0069] Furthermore, in step 7, the LQANM algorithm is used to process the angle estimation results, that is, the DOD and DOA estimation results of the target are obtained.

[0070] Compared with existing technologies, the significant advancement of this invention lies in the significant advantages of the atomic norm minimization DOA estimation method based on reconfigurable intelligent metasurfaces (hereinafter referred to as the LQANM method) proposed in this invention under low bit quantization conditions. This method innovatively integrates the active control capability of RIS, low bit quantization technology, and the atomic norm minimization algorithm. Under low bit quantization conditions, this invention effectively improves non-line-of-sight channel conditions and optimizes system estimation accuracy by leveraging the active control capability of RIS, while reducing hardware costs and power consumption. Simultaneously, the atomic norm minimization algorithm avoids discrete grid errors, resulting in higher-precision estimation results. In summary, this system can achieve high-precision, real-time DOA and DOD estimation in non-line-of-sight environments while using low bit quantization, demonstrating greater engineering practical value.

[0071] To more clearly illustrate the functional characteristics and structural parameters of the present invention, further explanation is provided below in conjunction with the accompanying drawings and specific embodiments. Attached Figure Description

[0072] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0073] Figure 1 This is a schematic diagram of the system flow of the present invention;

[0074] Figure 2 This is a schematic diagram of the angle estimation results using the atomic norm method;

[0075] Figure 3 This is a schematic diagram of the noise-free (bit=2) algorithm estimation result;

[0076] Figure 4 This is a schematic diagram of the noise-free (bit=20) algorithm estimation results;

[0077] Figure 5 This is a diagram illustrating the impact of snapshot count on DOD estimation;

[0078] Figure 6 This is a diagram illustrating the impact of snapshot count on DOA estimation;

[0079] Figure 7 This is a diagram illustrating the impact of the number of snapshots on computation time;

[0080] Figure 8 This is a schematic diagram illustrating the impact of signal-to-noise ratio on DOD estimation;

[0081] Figure 9 This is a schematic diagram illustrating the impact of signal-to-noise ratio on DOA estimation;

[0082] Figure 10 This is a schematic diagram illustrating the impact of the number of RIS array elements on DOD estimation;

[0083] Figure 11 This is a schematic diagram illustrating the impact of the number of RIS array elements on DOA estimation;

[0084] Figure 12 This is a schematic diagram illustrating the impact of the number of RIS array elements on computation time. Detailed Implementation

[0085] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0086] This invention proposes a method for estimating the Direct Occurrence (DOA) of a non-line-of-sight (NAS) signal source using atomic norm minimization with the aid of a smart metasurface under low-bit quantization conditions. This method introduces a smart metasurface as a signal relay to solve the NAS propagation problem between the target and the receiver. After the receiving array antenna receives the echo signal reflected from the RIS (Reflection Signal Reflection), a low-precision ADC is used to process the received signal. Simultaneously, an equivalent RIS channel matrix is ​​constructed, and the RIS channel vector is used as an auxiliary variable to estimate the quantized signal. The angle estimation problem is transformed into a convex optimization problem, which is solved using the CVX toolbox in Matlab. Two one-dimensional Toeplitz matrices containing the target's DOA and DOD information are constructed. Then, one-dimensional Vandermonde decomposition is used to obtain the signal angle, and angle matching is performed to achieve joint estimation of the DOA and DOD of the NAS signal source. The system flowchart is shown below. Figure 1 This includes the following steps:

[0087] Step 1: Transmitting signals from the transmitting array antenna: The M-element transmitting antenna array transmits M mutually orthogonal unit power waveforms to initialize the azimuth of arrival (DOA) and azimuth of departure (DOD) information of K incoherent targets within the observable area;

[0088] Step 2: RIS reflects the target echo signal: RIS consists of Q reflection units. The reflection coefficient of each unit is adjusted in real time by the phase control matrix v to reflect the echo signal scattered by the target in a directional manner, thus constructing a complete "transmitter-target-RIS-receiver" non-line-of-sight signal transmission link.

[0089] Step 3: Receive signal from the receiving array antenna: The N-element receiving antenna array receives the RIS reflected signal, and accumulates L snapshots to construct the received signal matrix Y;

[0090] Step 4: Construct the equivalent channel matrix: Based on the known RIS phase control matrix v and the RIS-to-receiver channel matrix G, construct the equivalent channel matrix S;

[0091] Step 5: Perform low-bit quantization on the received signal: Use a low-precision analog-to-digital converter to perform low-bit quantization on the received signal matrix Y to obtain the quantized signal matrix Z;

[0092] Step 6: Estimate angle parameters based on LQANM algorithm: Use the atomic norm minimization algorithm under low bit quantization to transform the angle estimation problem into a semi-positive definite programming problem for the quantization matrix Z, and solve it to obtain the Topletz matrix and the optimization variable X;

[0093] Step 7: Obtain DOA and DOD estimation results: Perform Vandermonde decomposition on the estimated Toplez matrix to obtain the estimated angles, use the optimization variable X to perform angle matching, and finally obtain the DOA and DOD estimation results for K targets.

[0094] Specifically, step 1, the specific steps for the transmitting array antenna to transmit signals are as follows:

[0095] The system employs a MIMO array. The transmitter is a uniform linear array with M antennas, the RIS is a uniform linear array with Q elements, and the receiver is a uniform linear array with N antennas. The spacing between the transmitting antenna arrays and the spacing between the RIS elements are equal to the base spacing, i.e., d. T =d Q =d. Let be the signal wavelength. Assume there are K incoherent targets within the same range gate of the radar system, and the transmission steering vector... This represents the direction vector between the transmitter and the k-th target. This represents the transpose of the matrix. For the k-th target, its DOD (Difference of Departure) is denoted as... DOA (receiving angle) is denoted as .

[0096] Specifically, step 2, the specific steps for the RIS to reflect the target echo signal are as follows:

[0097] As a reconfigurable smart metasurface that can be adjusted in real time, the RIS can be adjusted so that the echo signal scattered by the target is reflected by the RIS and directed to the receiving antenna.

[0098] The channel matrix from RIS to the receiver is as follows: This represents the channel phase correspondence between the receiving array antenna and the RIS array elements. The phase control signal of the RIS is... There are L configurations, representing the active control of the RIS array elements by each snapshot. The target radar cross-section (RCS) coefficient remains constant across snapshots. It remains unchanged. (Among them) Represents the RCS amplitude. Represents the RCS phase. Receive direction vector. .

[0099] Specifically, step 3, the specific steps for receiving signals from the receiving array antenna, are as follows:

[0100] By reflecting the signal through the RIS (Radio Reflector) to the receiving antenna array, a complete signal link is established: "Transmitter—Target—RIS—Receiver". The signal received by the receiving array antenna is as follows:

[0101] (1)

[0102] in The noise level is the channel noise within the l-th snapshot.

[0103] Specifically, step 4, constructing the RIS channel matrix, involves the following steps:

[0104] Using the known channel matrix G of the RIS and receiving antenna, and the phase control signal v, construct the RIS channel relationship matrix. In the noise-free case, first define the channel correlation component:

[0105] (2)

[0106] Utilizing the associativity of the Kronecker product:

[0107] (3)

[0108] The receive vector can be transformed into:

[0109] (4)

[0110] Extract the channel matrix portion outside the accumulation terms and rename it to a new matrix vector:

[0111] (5)

[0112] Collect L snapshots to obtain the complete received signal:

[0113] (6)

[0114] However, to extract the channel component from the received signal vector, the received signal vector needs to be vectorized:

[0115] (7)

[0116] Define the channel matrix

[0117] (8)

[0118] The vectorized signal model is then:

[0119] (9)

[0120] In summary, we only need to use G and v to construct the complete channel matrix vector:

[0121] (10) (11)

[0122] (12)

[0123] Specifically, step 5, low-bit quantization of the received signal, involves the following steps:

[0124] At the receiver, each RF link uses a pair of real quantizers to quantize the real and imaginary parts of the received signal:

[0125] (13)

[0126] (14)

[0127] in For quantization function,

[0128] (15)

[0129] For quantization interval, Take the minimum value. Round up.

[0130] (16)

[0131] b is the number of quantization bits. When b = 1 to 4, it is low-bit quantization. Z is the received signal after low-bit quantization.

[0132] Specifically, step 6, the LQANM algorithm for solving the target direction vector, involves the following steps:

[0133] Signal model analysis shows that,

[0134] (17)

[0135] (18)

[0136] By constructing an equivalent channel matrix S as an auxiliary, the angle estimation problem is transformed into a convex optimization problem; and optimization variables are set. Construct the matching matrix U.

[0137] (19)

[0138] Make the matching matrix U approximate the quantized received signal Z, and satisfy the quantization constraints during the iteration process:

[0139] (20)

[0140] The objective optimization function is:

[0141] (twenty one)

[0142] The constraints are:

[0143] (twenty two)

[0144] In the formula Given two one-dimensional Toeplitz matrices, Indicates that it is from its first line A defined Toeplitz matrix. Similarly, the specific representation is as follows:

[0145] (twenty three)

[0146] (twenty four)

[0147] In the formula The incoherence coefficient;

[0148] The optimization variable X is:

[0149] (25)

[0150] The convex optimization problem was solved using the CVX toolbox in Matlab, and the results were obtained. .

[0151] Utilizing the special structure of the Topletz matrix, a one-dimensional Vandermonde decomposition is performed on the Topletz matrix. The angle is then obtained. and However, the angle order does not match the true order value. Therefore, we use the X estimated by the algorithm to perform angle matching. The steps are as follows:

[0152] First, construct the direction vector using the estimated angle results. and We use exhaustive enumeration to list all possible permutations and combinations.

[0153] Then, using the Kronecker product property: Construct the estimation result matrix

[0154] (26)

[0155] Calculate the residual with X, and take the result corresponding to the smallest residual value as the matching result.

[0156] Algorithm: Low-bit Quantization Atom Norm Minimization Algorithm (LQANM) Input: Quantized signal matrix Z, RIS phase control matrix v, RIS backward channel matrix G, number of transmit antennas M, number of receive antennas N, number of RIS elements Q. Output: Target estimated value. Step S1: Construct the channel vector S in equation (8) using G and v. Step S2: Use S as an auxiliary variable to input into the optimization function to transform the problem from an angle estimation problem into a convex optimization problem. Step S3: Solve the convex optimization problem using MATLAB's CVX toolbox, with constraints in equations (20) and (22), to obtain... , Step S4: Using the eigenvalue decomposition method, decompose equations (23) and (24) into... and Performing Vandermonde decomposition, we obtain and Step S5: Using the vector relationship obtained from equation (25), X can be matched with the estimated angle result, and the final output is the corresponding angle. and .

[0157] Specifically, step 7, obtaining the target DOD and DOA estimation results, involves the following steps:

[0158] The angle estimation results are obtained by using the LQANM algorithm, which yields the target's DOD and DOA estimation results.

[0159] This invention innovatively combines the path manipulation capabilities of reconfigurable intelligent metasurfaces (RIS) with an efficient atomic norm minimization (ANM) algorithm to achieve high-precision, low-complexity joint direction of arrival (DOA) and direction of departure (DOD) estimation in non-line-of-sight environments. Specific objectives include:

[0160] Targeted compensation for quantization error: By constructing an enhanced signal transmission path using RIS, the quality of the received signal is improved from the source, thereby effectively offsetting the signal-to-noise ratio loss caused by low-bit quantization. The aim is to stabilize the RMSE of DOA estimation below -15dB over a wide range of SNR ≥ -20dB, overcoming the defect of existing methods that suffer from drastic performance degradation at low signal-to-noise ratios.

[0161] Significantly reduced computational complexity: By designing a convex optimization model that does not require the introduction of additional complex regularization terms and using RIS to simplify the channel model, the goal is to control the average running time of the algorithm to less than 0.5 seconds when the number of snapshots L=100, achieving a computational efficiency one order of magnitude higher than the "Low-Precision DOA Estimation via Atomic Norm Minimization" method, thus meeting the requirements of real-time processing.

[0162] Enhance robustness under conditions of few snapshots: Optimize the solution process for minimizing the atomic norm to ensure that angle estimation still maintains high success rate and high accuracy under a very small number of snapshots (e.g., L=10), and solve the estimation failure problem caused by the superposition of noise and error in the "Low-Precision DOA Estimation via Atomic Norm Minimization" method when there are few snapshots.

[0163] This invention is not a simple improvement on existing technologies in the background art, but a systematic innovation. It solves the signal quality degradation problem under low-bit quantization with the aid of RIS, achieves high-efficiency solution through an optimized ANM algorithm, and ultimately significantly outperforms the existing technology represented by the prior art in terms of computational complexity, estimation accuracy, and environmental robustness.

[0164] Example

[0165] To verify the actual effect of the present invention, the following simulation experiments were conducted using Matlab.

[0166] 1. Radar system parameter settings

[0167] The radar has 8 transmitting antennas (M) and 12 receiving antenna elements (N).

[0168] 2. Experimental parameter settings

[0169] The signal frequency of the transmitted signal is set to Hz, the spacing between each array antenna and RIS array element is uniformly set to 1 Hz. m / s, c is the speed of light in vacuum, and λ is the signal wavelength. RCS parameters are set to... .

[0170] Example 1: Target Recovery Performance Simulation

[0171] Experimental settings for signal-to-noise ratio Quick shot number This is used to verify the target robustness of the proposed algorithm.

[0172] Angle estimation error is measured by the root mean square error (RMSE), calculated as follows:

[0173]

[0174] in Where is the number of Monte Carlo experiments, and K is the number of targets. The smaller the RMSE, the closer the estimated value is to the true value, and the smaller the estimation error. This represents the angle estimation result of the k-th target in the i-th Monte Carlo experiment.

[0175] Suppose there are four targets (K = 4) with wave-away azimuth (DOD) angles of 32.293°, 69.82°, 9°, and 54.0032°, respectively, and wave-arrival azimuth (DOA) angles of 46.64°, 79°, 23.984°, and 36.5°, respectively.

[0176] Experimental results are as follows Figure 2 Experimental results show that the RMSE of DOD estimation is -12.86dB and the RMSE of DOA estimation is -17.85dB. Even in non-line-of-sight environments and under low bit quantization conditions, the proposed algorithm can still maintain good angle estimation performance, indicating that it has high angle estimation accuracy and can effectively address the non-line-of-sight target estimation problem under low bit quantization and low signal-to-noise ratio conditions.

[0177] To further verify the reliability of the algorithm, a target recovery experiment was conducted in a noise-free environment, and the results are as follows: Figure 3 , Figure 4 As shown, the results indicate that in the absence of noise, low-bit quantization leads to a decrease in estimation performance due to quantization noise; however, when the number of quantization bits is increased, the algorithm can still achieve high-precision estimation, thus proving the reliability of the algorithm.

[0178] Example 2: Target recovery performance and algorithm complexity vary with the number of sampling snapshots

[0179] To investigate the impact of the number of snapshots on algorithm performance, other parameters were kept constant, controlling for a single variable. The computational complexity was measured using the average running time, which is the time difference between the start and end of each algorithm iteration. A longer average running time indicates higher algorithm complexity.

[0180] Fixed signal-to-noise ratio , number of RIS array elements Set the number of Monte Carlo experiments Four targets were set up (K=4), with wave departure azimuth (DOD) angles of 32.293°, 69.82°, 9°, and 54.0032°, and wave arrival azimuth (DOA) angles of 46.64°, 79°, 23.984°, and 36.5°, respectively.

[0181] The number of snapshots varies from 4 to 40, increasing in increments of 4, as shown in the following results. Figures 5-7 .Depend on Figure 5 and 6 It is evident that the estimation accuracy of non-line-of-sight targets gradually improves with the increase in the number of snapshots. Furthermore, the higher the number of quantization bits, the better the overall estimation accuracy. Figure 7 This indicates that increasing the number of snapshots leads to an increase in the average running time of the algorithm, while the number of quantization bits has virtually no impact on the running time.

[0182] Example 3: Target recovery performance and algorithm complexity as a function of signal-to-noise ratio

[0183] Fixed number of snapshots , number of RIS array elements Set the number of Monte Carlo experiments Four incoherent targets (K=4) are set up, with wave-away azimuth (DOD) angles of 32.293°, 69.82°, 9°, and 54.0032°, respectively; and wave-arrival azimuth (DOA) angles of 46.64°, 79°, 23.984°, and 36.5°, respectively.

[0184] The SNR range was set to -10 to 40 dB, with increments of 5 dB. The experimental results are as follows: Figures 8-9 Experimental results show that the target estimation performance of the algorithm is significantly improved as the signal-to-noise ratio increases.

[0185] Example 4: Target recovery performance and algorithm complexity as a function of the number of RIS array elements

[0186] Fixed signal-to-noise ratio Signal-to-noise ratio Set the number of Monte Carlo experiments Four incoherent targets (K=4) are set up, with wave-away azimuth (DOD) angles of 32.293°, 69.82°, 9°, and 54.0032°, respectively; and wave-arrival azimuth (DOA) angles of 46.64°, 79°, 23.984°, and 36.5°, respectively.

[0187] The number of elements in the RIS array was set to range from 18 to 36, increasing in increments of 6. Experimental results are as follows: Figures 10-12 . Figure 10 , 11 This indicates that as the number of RIS array elements increases, the estimation error generally decreases, and the algorithm's estimation performance gradually improves. Figure 12 The results show that increasing the number of RIS array elements gradually increases the average running time of the algorithm.

[0188] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0189] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for estimating the DOA of a low-bit quantized array non-line-of-sight signal source with intelligent metasurface assistance, characterized in that, Includes the following steps: Step 1: Transmitting signals from the transmitting array antenna: The M-element transmitting antenna array transmits M mutually orthogonal unit power waveforms to initialize the azimuth of arrival (DOA) and azimuth of departure (DOD) information of K incoherent targets within the observable area; Step 2: RIS reflects the target echo signal: RIS consists of Q reflection units. The reflection coefficient of each unit is adjusted in real time by the phase control matrix v to reflect the echo signal scattered by the target in a directional manner, thus constructing a complete "transmitter-target-RIS-receiver" non-line-of-sight signal transmission link. Step 3: Receive signal from the receiving array antenna: The N-element receiving antenna array receives the RIS reflected signal, and accumulates L snapshots to construct the received signal matrix Y; Step 4: Construct the equivalent channel matrix: Based on the known RIS phase control matrix v and the RIS-to-receiver channel matrix G, construct the equivalent channel matrix S; Step 5: Perform low-bit quantization on the received signal: Use a low-precision analog-to-digital converter to perform low-bit quantization on the received signal matrix Y to obtain the quantized signal matrix Z; Step 6: Estimate angle parameters based on LQANM algorithm: Use the atomic norm minimization algorithm under low bit quantization to transform the angle estimation problem into a semi-positive definite programming problem for the quantization matrix Z, and solve it to obtain the Topletz matrix and the optimization variable X; Step 7: Obtain DOA and DOD estimation results: Perform Vandermonde decomposition on the estimated Toplez matrix to obtain the estimated angles, use the optimization variable X to perform angle matching, and finally obtain the DOA and DOD estimation results for K targets.

2. The method for DOA estimation of a low-bit quantization array non-line-of-sight signal source assisted by a smart metasurface according to claim 1, characterized in that, In step 1, the system uses a MIMO array. The transmitter is a uniform linear array with M antennas, the RIS is a uniform linear array with Q elements, and the receiver is a uniform linear array with N antennas. The spacing between the transmitter antenna arrays and the spacing between the RIS elements are equal to the base spacing, i.e., d. T =d Q =d; Let be the signal wavelength; assume there are K incoherent targets within the same range gate of the radar system, and the transmission steering vector is... This represents the direction vector between the transmitter and the k-th target; The transpose of the matrix is ​​represented; for the k-th target, its emission angle DOD is denoted as... The receiving angle DOA is denoted as .

3. The method for DOA estimation of a low-bit quantization array non-line-of-sight signal source assisted by a smart metasurface according to claim 1, characterized in that, In step 2, the RIS, as a reconfigurable smart metasurface that can be adjusted in real time, directs the echo signal scattered by the target to the receiving antenna after reflection by the RIS; the channel matrix from the RIS to the receiver is as follows. This represents the channel phase correspondence between the receiving array antenna and the RIS array elements; the phase control signal of the RIS is... There are L configurations, representing the active control of the RIS array elements by each snapshot; the target radar cross section (RCS) coefficient remains unchanged between snapshots. Remain unchanged; among which Represents the RCS amplitude. Represents RCS phase; receive direction vector .

4. The method for DOA estimation of a low-bit quantization array non-line-of-sight signal source assisted by a smart metasurface according to claim 1, characterized in that, In step 3, the RIS reflects the signal to the receiving antenna array, establishing a complete signal link of "transmitter—target—RIS—receiver"; the signal received by the receiving array antenna is: in The noise level is the channel noise within the l-th snapshot.

5. The method for DOA estimation of a low-bit quantization array non-line-of-sight signal source assisted by a smart metasurface according to claim 1, characterized in that, In step 4, the RIS channel relationship matrix is ​​constructed using the known channel matrix G of the RIS and the receiving antenna, and the phase control signal v. In the noise-free case, the channel correlation part is first defined: Utilizing the Kronecker product's associativity: ; The receive vector is transformed into: ; Extract the channel matrix portion outside the accumulation terms and rename it to a new matrix vector: Collect L snapshots to obtain the complete received signal: To extract the channel component from the received signal vector, the received signal vector needs to be vectorized: Define the channel matrix The vectorized signal model is then: Finally, the complete channel matrix vector is constructed using G and v: 。 6. The method for DOA estimation of a low-bit quantization array non-line-of-sight signal source assisted by a smart metasurface according to claim 1, characterized in that, In step 5, each RF link at the receiving end uses a pair of real-value quantizers to quantize the real and imaginary parts of the received signal: in For quantization function, ; For quantization interval, Take the minimum value. Round up; b is the number of quantization bits. When b = 1 to 4, it is low-bit quantization; Z is the received signal after low-bit quantization.

7. The method for DOA estimation of a low-bit quantization array non-line-of-sight signal source assisted by a smart metasurface according to claim 1, characterized in that, In step 6, the signal model analysis yields the following results: By constructing an equivalent channel matrix S as an auxiliary, the angle estimation problem is transformed into a convex optimization problem; and optimization variables are set. Construct the matching matrix U. ； Make the matching matrix U approximate the quantized received signal Z, and satisfy the quantization constraints during the iteration process: The objective optimization function is: The constraints are: In the formula Given two one-dimensional Toeplitz matrices, Indicates that it is from its first line A defined Toeplitz matrix. Similarly, the specific representation is as follows: In the formula The incoherence coefficient; The optimization variable X is: The convex optimization problem was solved using the CVX toolbox in Matlab, and the results were obtained. .

8. The method for DOA estimation of a low-bit quantization array non-line-of-sight signal source assisted by a smart metasurface according to claim 7, characterized in that, Utilizing the special structure of the Topletz matrix, a one-dimensional Vandermonde decomposition is performed on the Topletz matrix; the angle is obtained. and However, the angle order does not match the true order value. Therefore, we use the X estimated by the algorithm to perform angle matching. The steps are as follows: First, construct the direction vector using the estimated angle results. and Use exhaustive search to list all possible permutations and combinations; Then, using the Kronecker product property: Construct the estimation result matrix Calculate the residual with X, and take the result corresponding to the smallest residual value as the matching result.

9. The method for DOA estimation of a low-bit quantization array non-line-of-sight signal source assisted by a smart metasurface according to claim 1, characterized in that, In step 7, the LQANM algorithm is used to process the angle estimation results, that is, the DOA and DOD estimation results of the target are obtained.

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