A RIS-Assisted DOA Estimation Method for a Single Receive Antenna

Abstract

The present invention discloses a RIS-assisted single-receive-antenna DOA estimation method, which realizes single-antenna DOA estimation in a non-line-of-sight (NLOS) scenario by using a reconfigurable intelligent surface (RIS). It includes: in the first stage, uniformly divided phase shift vectors are selected at the RIS side to reflect the signal, and the power of the signal is analyzed at the receiving end to obtain a rough DOA range; in the second stage, the RIS divides the phase shift vectors again within the obtained rough range to reflect the signal again. The total least squares (TLS) idea is adopted to overcome the RIS phase shift error problem existing in practical applications, an optimization problem is constructed and simplified by Lanczos bidiagonalization projection, then the truncated SVD algorithm is used to realize robust covariance matrix reconstruction, and finally the classical MUSIC algorithm is used to estimate the DOA of the target through the covariance matrix. The model of the present invention has a high universality and is applicable to various communication transmission environments. Moreover, the algorithm effectively avoids high-dimensional matrix decomposition and inverse operations and has good computational efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of DOA estimation of array signals, and in particular to a DOA estimation method for a single receiving antenna assisted by RIS. Background Art

[0002] A Reconfigurable Intelligent Surface (RIS) is a tiny intelligent surface composed of many passive elements. It has the ability to adjust the propagation characteristics of electromagnetic waves and can achieve control of interference, reflection, and diffraction of incident signals. The reconfigurable intelligent surface can enhance the signal transmission effect of a wireless communication system, and can adjust the amplitude, phase, and direction of reflected and scattered signals in real time according to the environment and user requirements, optimizing the signal transmission quality, coverage, and capacity. By controlling the intensity, direction, and delay of the reflected signal, the reconfigurable intelligent surface can improve the coverage and deep coverage ability of a wireless network. It can assist signals to penetrate obstacles, reduce signal attenuation, improve signal quality and connection stability. At the same time, by adjusting the phase and amplitude of the reflected signal, interference control between different users can be achieved. It can concentrate signals on specific user devices, reduce interference, and improve system capacity and efficiency. By changing the direction and intensity of the reflected signal, the reconfigurable intelligent surface can be used for indoor positioning and navigation. It can provide more accurate and reliable indoor position information, supporting applications such as smart home, indoor navigation, and area monitoring.

[0003] So far, DOA estimation methods customized for different application scenarios have been comprehensively studied. Representative methods include Multiple Signal Classification (MUSIC) based on subspace and Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT), as well as other solutions such as Compressive Sensing (CS) and methods based on covariance matrix analysis. However, all of these methods are directly designed for Line-of-Sight (LOS) propagation scenarios, and their drawbacks are: when performing DOA estimation, their computational efficiency is low, and the signal positioning and tracking capabilities are poor. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a DOA estimation method for a single receiving antenna that is different from the sensor array method, which has a low computational cost and can handle the phase shift error problem generated by RIS in practical applications, improving the signal positioning and tracking capabilities.

[0005] The technical solution adopted by the present invention is a DOA estimation method for a single receiving antenna assisted by RIS, and the method includes the following steps:

[0006] Step 1: Establish a signal model: In a non-line-of-sight scenario, assume that L user devices are from {θ1, θ2,..., θL Transmit L far - field narrow - band signals in a certain direction. The L far - field narrow - band signals pass through the RIS side. The RIS side consists of M reflecting elements with a uniform spacing of d. After being reflected by the RIS side, the signals are received by the base station;

[0007] Step 2: Uniformly divide the angles within the range of [-90°, 90°] at the RIS side and form a phase - shift vector u p , and according to the phase - shift vector u p Obtain the average power p of the received signal at the base station g , and estimate the rough range of DOA by searching for the maximum value of the average power of the received signal;

[0008] Step 3: Re - uniformly divide the angles within the rough range of the DOA and form a phase - shift vector According to the phase - shift vector Obtain the power matrix of the received signal at the base station According to the power matrix Use the total least - squares method to construct an optimization problem where E represents the phase - shift error matrix. Simplify the optimization problem through Lanczos bidiagonalization projection. According to the simplified optimization problem, use the truncated SVD algorithm to reconstruct the covariance matrix of the received signal at the RIS side, perform singular - value decomposition on the covariance matrix, and use the classical MUSIC algorithm to estimate the DOA of the target.

[0009] Preferably, in Step 1, the signal received by the m - th reflecting element of the RIS side during the p - th measurement is expressed as: where s l,p represents the l - th signal transmitted by the user during the p - th measurement, λ and ω p represent the carrier wavelength and additive white Gaussian noise respectively; the signal received by the single - antenna of the base station during the p - th measurement is expressed as: where, x p = As l,p + w, A = [α(θ1),..., α(θ L )], u p represents the phase - shift vector formed by the RIS side during the p - th measurement, represents the phase - shift amount of the M - th reflecting element of the RIS during the p - th measurement, φ M,p represents the phase - shift of the M - th reflecting element of the RIS during the p - th measurement, s l,p represents the signal transmitted by the l - th user equipment during the p - th measurement, s l,p represents the signal transmitted by the l - th user equipment during the p - th measurement, α(θ L) represents the steering vector of the far-field narrowband signals transmitted by L users, θ l represents the direction angle of the signal transmitted by the l-th user equipment, x m,p represents the signal received by the m-th reflecting element at the RIS end during the p-th measurement, ω M represents the additive white Gaussian noise generated during the reflection process of the M-th reflecting element; the P received signals collected by the base station are represented by a vector as: where, Since the signals sent by the users are assumed to be narrowband signals, the time required for the signals to pass through the array length should be much less than the coherence time of the signals, and the signal envelope changes little during the propagation time of the antenna array. It can be considered that s l = s l,1 ≈ s l,2 ≈ s l,P , so

[0010] Preferably, the specific process of step 2 includes the following steps:

[0011] (2.1) Uniformly divide the angle within the range of [-90°, 90°] at the RIS end to form the phase shift amount According to the phase shift amount φ m,p form the phase shift vector

[0012] (2.2) According to the phase shift vector u p obtain the average power p of the received signal at the base station g , and the average power of the received signal at the base station is expressed as: where,

[0013] R represents the covariance matrix of the received signals at the RIS end, represents the received power of the l-th signal, represents the noise power of the l-th signal; the covariance matrix R after P measurements is expressed as: Estimate the rough range of DOA by searching for the maximum value of the average received power of the received signal The rough range of the DOA is expressed as:

[0014] where p is obtained by averaging the power of the row vectors of y.

[0015] Preferably, the specific process of step 3 includes the following steps:

[0016] (3.1) Uniformly extract G angles within the rough range of DOA obtained in step (2.2) and form the phase shift vector According to the phase shift vector obtain the average power of the received signal of the base station where r = vec(R); according to the average power of the received signal of the base station obtain the received power matrix as: where

[0017] (3.2) Estimate the vector form r of the covariance matrix of the received signal of the base station using the total least squares criterion, and construct an exact matrix equation based on r. The exact matrix equation is expressed as: where E represents the phase shift error matrix, and r represents the error vector; solve the exact matrix equation to minimize the phase shift error matrix and the error vector, and use the constrained optimization problem describe the solution process of the exact matrix equation;

[0018] (3.3) Perform Lanczos bidiagonalization on to obtain where U k+1 and V k represent the left and right Lanczos matrices of dimensions G×(k + 1) and M 2 ×k respectively, B k represents the (k + 1)×k lower bidiagonal matrix, and V k = [v1, v2,..., v k ;

[0019] (3.4) Project the optimization problem onto the subspaces of V k and U k+1 to obtain an equivalent expression of : where and simplify the equivalent expression to obtain a simplified expression:

[0020]

[0021] (3.4) Perform truncated singular value decomposition on (B k , β1e1) in the simplified expression:

[0022] where have dimensions k×k, k×1, 1×k, 1×1 respectively; obtain the decomposition result expression through decomposition: According to the decomposition result expression, the vector form r of the covariance matrix of the received signal of the base station is estimated as: For Obtained by inverse quantization The reconstructed covariance matrix obtained is

[0023] (3.5) For the reconstructed covariance matrix Perform singular value decomposition to obtain the M×(M - L)-dimensional noise subspace U n , according to the fact that the received power is maximum when the DOA is orthogonal to the noise subspace U n Estimate the final DOA through the MUSIC spectral function, that is:

[0024] Compared with the prior art, the beneficial effects of the present invention are: A new DOA estimation method in the RIS-assisted NLOS scenario is proposed. In the presence of phase shift errors, an efficient two-stage method for RIS phase shift and spatial covariance matrix reconstruction based on the total least squares (TLS) criterion is proposed. Using the reconstructed spatial covariance matrix, the DOA is estimated by using the traditional MUSIC algorithm. This method does not require a very fine RIS phase shift grid, thus avoiding high-dimensional matrix decomposition and inverse operations, and thus obtaining a solution with high computational efficiency. The simulation results show that this method has good performance. Description of the drawings

[0025] Figure 1 It is a schematic diagram of the signal model of a RIS-assisted single-receive-antenna DOA estimation method of the present invention;

[0026] Figure 2 It is a flowchart of a RIS-assisted single-receive-antenna DOA estimation method of the present invention;

[0027] Figure 3 It is a schematic diagram showing the relationship between the performance and the signal-to-noise ratio when comparing the method of the present invention with DLT;

[0028] Figure 4 It is a schematic diagram showing the relationship between the RMSE and the signal-to-noise ratio when comparing the method of the present invention with the DLP method after changing the number of phase shifts. Detailed implementation manners

[0029] The following further describes the invention with reference to the accompanying drawings and in combination with specific implementation manners, so that those skilled in the art can implement it according to the description in the specification. The protection scope of the present invention is not limited to this specific implementation manner.

[0030] Those skilled in the art should understand that in the disclosure of the present invention, the orientation or positional relationships indicated by the terms "longitudinal", "transverse", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. are based on the orientation or positional relationships shown in the drawings. These are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the above terms should not be construed as limiting the present invention.

[0031] The present invention provides a single-receiving antenna DOA estimation method different from the sensor array method. This method uses the phase shift adjustment of the RIS to achieve multiple measurements of the reflected signal, thereby realizing low-cost DOA estimation with a single antenna. In this configuration, a two-stage method for efficient RIS phase shift and robust covariance matrix reconstruction with phase shift errors is proposed. It has a low computational cost and can handle the phase shift error problem generated by the RIS in practical applications, improving the signal positioning and tracking capabilities.

[0032] The present invention relates to a RIS-assisted single-receiving antenna DOA estimation method, which includes the following steps:

[0033] Step 1: Establish a signal model: In a non-line-of-sight scenario, assume that L user equipments transmit L far-field narrowband signals from {θ1, θ2,..., θ L}. The L far-field narrowband signals pass through the RIS end, and the RIS end is composed of M reflection elements with a uniform spacing of d. After being reflected by the RIS end, the signals are received by the base station;

[0034] Step 2: Uniformly divide the angles within the range of [-90°, 90°] at the RIS end and form a phase shift vector u p According to the phase shift vector u p Obtain the average power p of the received signal at the base station g Estimate the rough range of DOA by searching for the maximum value of the average power of the received signal;

[0035] Step 3: Re-uniformly divide the angles within the rough range of the DOA and form a phase shift vector According to the phase shift vector Obtain the power matrix of the received signal at the base station According to the power matrix Construct an optimization problem using the total least squares method Among them, E represents the phase shift error matrix. The optimization problem is simplified by Lanczos bidiagonalization projection. According to the simplified optimization problem, the truncated SVD algorithm is used to reconstruct the covariance matrix of the received signal at the RIS side, the covariance matrix is subjected to singular value decomposition, and the classical MUSIC algorithm is used to estimate the DOA of the target.

[0036] In step 1, the signal received by the m-th reflecting element at the RIS side during the p-th measurement is expressed as: where s l,p represents the l-th signal transmitted by the user during the p-th measurement, and λ and ω p represent the carrier wavelength and additive white Gaussian noise respectively; the signal received by the single antenna at the base station during the p-th measurement is expressed as: where, x p = As l,p + w, A = [α(θ1),..., α(θ L )], u p represents the phase shift vector formed at the RIS side during the p-th measurement, represents the phase shift amount of the M-th reflecting element of the RIS during the p-th measurement, φ M,p represents the phase shift of the M-th reflecting element of the RIS during the p-th measurement, s l,p represents the signal transmitted by the l-th user equipment during the p-th measurement, s l,p represents the signal transmitted by the l-th user equipment during the p-th measurement, α(θ L ) represents the steering vector of the far-field narrowband signals transmitted by L users, θ l represents the direction angle of the signal transmitted by the l-th user equipment, x m,p represents the signal received by the m-th reflecting element at the RIS side during the p-th measurement, ω M represents the additive white Gaussian noise generated during the reflection process of the M-th reflecting element; the P received signals collected by the base station are represented by a vector as: where, Since the signals sent by the users are assumed to be narrowband signals, the time required for the signals to pass through the array length should be much less than the coherence time of the signals, and the signal envelope does not change much during the propagation time of the antenna array. It can be considered that s l = s l,1 ≈ s l,2 ≈ s l,P , so

[0037] In step 2, angles are evenly divided at the RIS side to form phase shift vectors. The narrowband signal passes through the RIS reflection elements to obtain the reflected signal. By utilizing the property that the average power of the signal is large near the divided angles, the power of the signal is analyzed at the receiving end to obtain the approximate DOA range. This stage is a rough estimation process. Although there are RIS errors, they do not affect the estimation result. The specific process includes the following steps:

[0038] (2.1) Evenly divide the angles within the range of [-90°, 90°] at the RIS side to form phase shift amounts According to the phase shift amount φ m,p Form phase shift vectors

[0039] (2.2) According to the phase shift vector u p Obtain the average power p of the received signal of the base station g , the average power of the received signal of the base station is expressed as: Among them,

[0040] R represents the covariance matrix of the received signal at the RIS side, represents the received power of the l-th signal, represents the noise power of the l-th signal; the covariance matrix R after P measurements is expressed as: Estimate the rough range of DOA by searching for the maximum value of the average received power of the received signal The rough range of the DOA is expressed as:

[0041] Among them, p is obtained by averaging the power of the row vectors of y;

[0042] In step 3, the signal is reflected again by dividing the phase shift vectors. The idea of total least squares (TLS) is adopted to overcome the phase shift error problem existing in the RIS. An optimization problem is constructed and the optimization problem is simplified by Lanczos bidiagonalization projection. Then, the truncated SVD algorithm is used to realize the robust covariance matrix reconstruction, and the classical MUSIC algorithm is used to estimate the DOA of the target. The specific process includes the following steps:

[0043] (3.1) Evenly extract G angles within the rough range of DOA obtained in step (2.2) And form phase shift vectors According to the phase shift vector Obtain the average power of the received signal of the base station

[0044] Among them, r = vec(R); according to the average power of the received signal of the base station The received power matrix obtained is as follows: Among them,

[0045]

[0046] (3.2) Considering the phase shift error problem that may occur in practical applications, the vector form r of the covariance matrix of the base station received signal is estimated using the total least squares (TLS) criterion, and an accurate matrix equation is constructed based on r. The accurate matrix equation is expressed as: Among them E represents the phase shift error matrix, and r represents the error vector; solving the accurate matrix equation makes both the phase shift error matrix and the error vector as small as possible. This solution idea can be described by the constrained optimization problem for description;

[0047] (3.3) Perform Lanczos bidiagonalization on to obtain Among them, U k+1 and V k respectively represent the left and right Lanczos matrices of dimensions G×(k + 1) and M 2 ×k, B k represents the (k + 1)×k lower bidiagonal matrix, and V k = [v1, v2,..., v k ; The aforementioned V k , U k+1 and B k are obtained from the k - th Lanczos iteration process. The k - th Lanczos iteration process is expressed as: Among them,

[0048] (3.4) Project the aforementioned optimization problem onto the subspaces of V k and U k+1 to obtain the equivalent form of : Among them, and simplify the aforementioned equivalent form to obtain the simplified form:

[0049]

[0050] (3.4) Perform truncated singular value decomposition on (B k , β1e1) in the aforementioned simplified form:

[0051] Among them, Their dimensions are k×k, k×1, 1×k, and 1×1 respectively; through decomposition, the decomposition result expression is obtained: According to the decomposition result expression, the vector form r of the covariance matrix of the base station received signal is estimated as: For Inverse quantization gives The reconstructed covariance matrix obtained is

[0052] (3.5) For the reconstructed covariance matrix Perform singular value decomposition to obtain the M×(M - L)-dimensional noise subspace U n , according to the fact that the received power is maximum when the DOA is orthogonal to the noise subspace U n , and the final DOA is estimated through the MUSIC spectral function, that is:

[0053] Next, through simulation experiments, the computational effectiveness of a RIS-assisted single-receive-antenna DOA estimation method proposed in an embodiment of the present invention is analyzed, and the simulation process is all carried out through MATLAB software.

[0054] Simulation experiment: The method proposed in an embodiment of the present invention is used to verify the effectiveness of the proposed method through numerical simulation. Three independent, equal-power source signals are transmitted from directions -17°, 22°, and 44° to a RIS with 16 equally spaced reflecting elements, the phase shift error is 0.02 degrees, and the normalized mean square error of the covariance matrix Select the root mean square error (RMSE) of the DOA estimation (in radians) obtained from 300 Monte-Carlo trials as two performance evaluation indicators.

[0055] In the first simulation, the relationship between performance and signal-to-noise ratio was studied and compared with the diagonal loading method (DLT). The simulation results are as Figure 3 shown, where P = 150, G = 20, and the signal-to-noise ratio is from -15 dB to 5 dB. It can be seen that when the signal-to-noise ratio < -10 dB, the NMSE and RMSE of DLT are smaller. However, as the signal-to-noise ratio increases, due to the influence of phase shift error and the dual constraints of relatively few measurements and G, the performance of DLT becomes worse or reaches a saturation point, and there is no further improvement in reducing the error. While the performance of the method of the present invention improves significantly as the signal-to-noise ratio increases. The estimation error of the comparison method decreases sharply, and after reaching a certain threshold, as the signal-to-noise ratio increases, the estimation error continues to decrease slowly.

[0056] In the second simulation, while keeping the method unchanged, we increased the G value of DLT from 20 to 30, and other simulation conditions were the same as those in the first simulation. From Figure 4It can be seen that compared with the RMSE of the first simulation, the increase in G of DLT leads to an improvement in its performance. However, since P is still limited to 150, the final performance cannot reach the optimal level. In contrast, although G is only set to 20, due to the design of the two-stage RIS phase shift strategy, the method of the present invention can provide better performance.

Claims

1. A RIS-assisted DOA estimation method for a single receiving antenna, characterized in that: The method includes the following steps: Step 1: Establish a signal model: In a non-line-of-sight scenario, assume that L user equipments transmit L far-field narrowband signals from directions {θ1, θ2,..., θ L}. The L far-field narrowband signals pass through the RIS side, and the RIS side consists of M reflection elements with a uniform spacing of d. After being reflected by the RIS side, the signals are received by the base station; Step 2: Uniformly divide the angles within the range of [-90°, 90°] at the RIS side and form the phase shift vector u p , according to the phase shift vector u p obtain the average power p of the received signal of the base station g , estimate the rough range of DOA by searching for the maximum value of the average power of the received signal; Step 3: Re-uniformly divide the angles within the rough range of the DOA and form a phase shift vector According to the phase shift vector Obtain the power matrix of the received signal of the base station According to the power matrix Use the total least squares method to construct an optimization problem Where E represents the phase shift error matrix, simplify the optimization problem through Lanczos bidiagonalization projection. According to the simplified optimization problem, use the truncated SVD algorithm to reconstruct the covariance matrix of the received signal at the RIS end, perform singular value decomposition on the covariance matrix, and use the classical MUSIC algorithm to estimate the DOA of the target.

2. The RIS-assisted DOA estimation method for a single receiving antenna according to claim 1, characterized in that: In step 1, the signal received by the m-th reflecting element at the RIS side during the p-th measurement is expressed as: where s l,p represents the l-th signal transmitted by the user during the p-th measurement, and λ and ω p represent the carrier wavelength and additive white Gaussian noise respectively; the signal received by the single antenna of the base station during the p-th measurement is expressed as: where, x p = As l,p + w, A = [α(θ1),..., α(θ L )] u p represents the phase shift vector formed at the RIS side during the p-th measurement, represents the phase shift amount of the M-th reflecting element of the RIS during the p-th measurement, φ M,p represents the phase shift of the M-th reflecting element of the RIS during the p-th measurement, s l,p represents the signal transmitted by the l-th user equipment during the p-th measurement, s l,p represents the signal transmitted by the l-th user equipment during the p-th measurement, α(θ L ) represents the steering vector of the far-field narrowband signals transmitted by L users, θ l represents the direction angle of the signal transmitted by the l-th user equipment, x m,p represents the signal received by the m-th reflecting element of the RIS side during the p-th measurement, ω M represents the additive white Gaussian noise generated during the reflection process of the M-th reflecting element; the P received signals collected by the base station are represented by a vector as: where, Since s l = s l,1 ≈ s l,2 ≈ s l,P , then we get:

3. The RIS-assisted DOA estimation method for a single receiving antenna according to claim 2, characterized in that: The specific process of step 2 includes the following steps: (2.1) Uniformly divide the angle within the range of [-90°, 90°] at the RIS end to form the phase shift amount According to the phase shift amount φ m,p Form the phase shift vector (2.2) Obtain the average power p of the received signal of the base station according to the phase shift vector u p The average power p of the received signal of the base station is obtained g The average power of the received signal of the base station is expressed as: Wherein, R represents the covariance matrix of the received signals at the RIS side, represents the received power of the l-th signal, represents the noise power of the l-th signal; the covariance matrix R is expressed as after P measurements: The rough range of DOA is estimated by searching for the maximum value of the average received power of the received signals The rough range of the said DOA is expressed as: Among them, p is obtained by averaging the power of the row vectors of y.

4. The RIS-assisted DOA estimation method for a single receiving antenna according to claim 3, characterized in that: The specific process of step 3 includes the following steps: (3.1) Uniformly extract G angles within the rough range of the DOA obtained in step (2.2) and form a phase shift vector According to the phase shift vector obtain the average power of the received signal of the base station where r = vec(R); according to the average power of the received signal at the base station the received power matrix is obtained as follows: where (3.2) Estimate the vector form r of the covariance matrix of the base station received signal using the total least squares criterion, and construct an exact matrix equation based on r. The exact matrix equation is expressed as: where E represents the phase shift error matrix, and r represents the error vector; solve the exact matrix equation to minimize the phase shift error matrix and the error vector, and use the constrained optimization problem to describe the solution process of the exact matrix equation. (3.3), perform Lanczos bidiagonalization on to obtain where U k+1 and V k represent the left and right Lanczos matrices of dimensions G×(k + 1) and M 2 ×k respectively, and B k represents the (k + 1)×k lower bidiagonal matrix. V k = [v1, v2,..., v k , (3.4) Project the optimization problem onto the subspaces of V k and U k+1 to obtain an equivalent expression of : where and simplify the equivalent expression to obtain a simplified expression: (3.4) Truncate the singular value decomposition of (B k , β1e1) in the simplified formula: Among them, The dimensions of are k×k, k×1, 1×k, 1×1 respectively; the decomposition result expression is obtained through decomposition: According to the decomposition result expression, the vector form r of the base station received signal covariance matrix is estimated as: For Inverse quantization gives The reconstructed covariance matrix obtained is (3.5) For the reconstructed covariance matrix perform singular value decomposition to obtain the M×(M-L)-dimensional noise subspace U n , according to the fact that the received power is maximum when the DOA is orthogonal to the noise subspace U n , estimate the final DOA through the MUSIC spectral function, that is:

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