Reconfigurable intelligent surface assisted direction of arrival estimation method for MISO system

Abstract

The application belongs to the technical field of target positioning, and particularly relates to a 2D-DOA estimation method of a reconfigurable intelligent surface assisted MISO system. The method establishes a far-field signal model of the RIS assisted MISO system, and the far-field signal model is composed of M RIS panels, K target signals and a receiving end. According to the far-field signal model, a receiving data expression is constructed, a meshless sparse reconstruction is performed by using an atomic norm, and a sparse reconstruction signal is obtained. The obtained sparse reconstruction signal is expressed in the form of a Hankel matrix, singular value decomposition is performed on the Hankel matrix, and a signal subspace and a noise subspace are obtained. In combination with a MUSIC algorithm, the azimuth and the elevation of the target are obtained by using spectral peak search.

Description

Technical Field

[0001] This invention belongs to the field of target localization technology, specifically relating to a method for estimating the direction of arrival of a reconfigurable intelligent surface-assisted MISO system. Background Technology

[0002] A key problem in array signal processing is direction-of-arrival (DOA) estimation. Existing DOA estimation methods mainly include traditional Fourier spectrum estimation methods and subspace estimation methods. Among them, the multiple signal classification (MUSIC) algorithm and the rotation-invariant subspace (ESPRIT) algorithm based on subspace theory have rapidly become the theoretical foundation of array direction finding since their introduction. To achieve DOA estimation of target signals, existing direction finding systems typically require multiple receiving channels, resulting in high costs and complex structures. In recent years, reconfigurable smart surfaces (RIS) have attracted widespread attention in wireless communication, signal processing, and radar. RIS can reflect signals and change the amplitude or phase of the received signal, thereby achieving signal control. Based on this characteristic, virtual line-of-sight (LoS) links can be constructed using RIS to avoid obstacles between transceivers, enabling direction estimation with only one receiving channel. Summary of the Invention

[0003] Therefore, a 2D-DOA estimation method for a reconfigurable smart surface (RIS)-assisted MISO system is needed. In the far field, this method uses RIS to estimate the azimuth and elevation angles of the target signal. Compared with existing DOA estimation methods, this method has better estimation performance.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] A method for estimating the direction of arrival (DOA) of a reconfigurable smart surface-assisted MISO system includes the following steps:

[0006] A far-field signal model for a reconfigurable intelligent surface-assisted MISO system is established, consisting of M RIS panels, K target signals, and a receiver. Based on the far-field signal model, a received data expression is constructed, and meshless sparse reconstruction is performed using the atomic norm to obtain the sparse reconstructed signal.

[0007] The obtained sparse reconstructed signal is represented in the form of a Hankel matrix, and singular value decomposition is performed on it to obtain the signal subspace and noise subspace. Combined with the MUSIC algorithm, the azimuth and elevation angles of the target signal are obtained by spectral peak search.

[0008] A further optimization of this technical solution is as follows: The method for constructing the expression for receiving data is as follows:

[0009] In the far-field signal model, M RIS panels are placed in a uniform planar array in the yoz plane, and each RIS panel contains N = N y N z N elements y N represents the number of elements along the y-direction. z This represents the number of elements along the z-direction, where the spacing between RIS panels is... The element spacing of the RIS panel is d, and the wavelength is λ. d can be taken as half a wavelength, i.e. Assuming the line-of-sight (LoS) paths between K target signals and the receiver are blocked by obstacles, meaning there is only the reflection path from the target signal to the RIS panel and from the RIS panel back to the receiver, with the lower left corner of the first RIS panel as the origin of the three-dimensional Cartesian coordinate system, the steering vector from the target to the RIS is defined as:

[0010]

[0011] in Azimuth θ k Let k be the angle between the target k and the yoz plane, and let the pitch angle be the angle between the target k and the Let k be the angle between the target k and the z-axis, and let... symbol This represents the Kronecker product operation.

[0012] The array manifold matrix can be represented as

[0013]

[0014] Where matrices C and A y A z They are respectively denoted as The symbol ⊙ represents the Khatri-Rao product operation.

[0015] Measurement Matrix Defined as

[0016]

[0017] Where P represents the number of measurements. α p,mn and υp,mn These represent the amplitude and phase of the RIS reflection units in P different time slots, respectively. This paper considers implementing a passive RIS element using PIN diodes; therefore, the measurement matrix must satisfy... That is, by using the RIS to provide a reflection path and appropriately adjusting the phase of its components, the incident signal is reflected to the receiving end;

[0018] Assume all reflected signals are at If the signal is received in the direction of the signal, then in the Pth time slot, the K received signals at the receiver can be represented as...

[0019]

[0020] The signal vector is defined as The term is additive white Gaussian noise and follows a distribution. σ 2 Let its variance be denoted as 'variance'.

[0021] This technical solution is further optimized, and the steps for sparse signal reconstruction are as follows:

[0022] First, the atomic decomposition of the output signal can be expressed as:

[0023]

[0024] Using the atomic decomposition formula given in equation (5), the atomic set of the two-dimensional signal is:

[0025]

[0026] The two-dimensional zero-atom norm of the output signal is

[0027]

[0028] Since the l0 atomic norm is an NP-hard problem, considering its convex relaxation, the corresponding atomic norm can be re-expressed as:

[0029]

[0030] Based on the definition of the atomic norm above, the sparse reconstruction problem, which reconstructs a sparse signal x from a received signal r, can be expressed as follows:

[0031]

[0032] Where β is the regularization parameter, used to balance sparsity and reconstruction accuracy; β can be taken as...

[0033] Then, the sparse signal x can be reconstructed by solving a semidefinite programming method, i.e., the following equation. Using the expression for the atomic norm, the atomic norm minimization problem can be rewritten as follows:

[0034]

[0035] In the formula, Tr(·) represents the trace operation. It is a double Hermitian Toeplitz matrix with respect to h, specifically defined as follows:

[0036]

[0037] each corresponding block matrix is expressed as

[0038]

[0039] where i=1,2,…,M.

[0040] The above semidefinite programming problem, namely formula (10), can be solved using the CVX optimization package in MATLAB, so as to obtain the sparse reconstructed signal x.

[0041] In a further optimization of the technical solution, the steps for obtaining the azimuth angle and elevation angle of the target signal are as follows:

[0042] First, fix a positive integer L satisfying K≤L<MN-K+1, and construct a Hankel matrix H:

[0043]

[0044] Singular value decomposition is performed on matrix H to obtain

[0045] H=UDV H (14)

[0046] where D=diag(σ1,σ2,…,σ K ,0,…,0) is a diagonal matrix composed of singular values, U is the left singular matrix, V is the right singular matrix, the noise subspace is a space composed of vectors in the left singular matrix U1 corresponding to small singular values, and the signal subspace consists of vectors corresponding to non-zero singular values, so as to obtain a two-dimensional MUSIC spatial spectral function:

[0047]

[0048] Finally, the azimuth angle and elevation angle of the target signal can be estimated by using peak search.

[0049] In a further optimization of the technical solution, the RIS element is a PIN diode.

[0050] Different from the prior art, the beneficial effects of the above technical solution are: the above direction-of-arrival estimation method for a reconfigurable intelligent surface-assisted MISO system can accurately estimate the azimuth angle and elevation angle of the target signal when the line-of-sight (LOS) link is blocked in an actual scenario. Meanwhile, in the parameter estimation process, a method based on atomic norm is adopted, which avoids the problem of off-grid deviation existing in traditional compressed sensing methods. Compared with existing algorithms, the method of the present invention has better estimation performance. Description of Drawings

[0051] Figure 1 This is a schematic diagram of the far-field signal model of the present invention;

[0052] Figure 2 This is a two-dimensional spatial spectrum of the target signal obtained using the method of the present invention. Detailed Implementation

[0053] To explain in detail the technical content, structural features, objectives, and effects of the technical solution, the following description is provided in conjunction with specific embodiments and accompanying drawings.

[0054] Example: A method for estimating the direction of arrival (DOA) of a reconfigurable smart surface-assisted MISO system, the method comprising:

[0055] A far-field signal model for a RIS-assisted MISO system is established, consisting of M RIS panels, K target signals, and a receiver. Based on the far-field signal model, a received data expression is constructed, and meshless sparse reconstruction is performed using the atomic norm to obtain the sparsely reconstructed signal.

[0056] The obtained sparse reconstructed signal is represented in the form of a Hankel matrix, and singular decomposition is performed on it to obtain the signal subspace and noise subspace. Combined with the MUSIC algorithm, spectral peak search is used to obtain estimated parameters such as the target's azimuth and elevation angles.

[0057] The specific methods for constructing the received data expression based on the far-field signal model include:

[0058] In the far-field signal model, M RIS panels are placed in a uniform planar array (UPA) in the yoz plane, and each RIS panel contains N = N y N z N elements y N represents the number of elements along the y-direction. z This represents the number of elements along the z-direction, where the spacing between RIS panels is... The element spacing of the RIS panel is d, and the wavelength is λ. d can be taken as half a wavelength, i.e. Assume that the line-of-sight (LoS) paths between K target signals and the receiver are blocked by obstacles, meaning there is only the reflection path from the target signal to the RIS panel and from the RIS panel back to the receiver. Taking the lower-left corner of the first RIS panel as the origin of the three-dimensional Cartesian coordinate system, the steering vector from the target to the RIS is defined as:

[0059]

[0060] Where the azimuth angle θ k Let k be the angle between the target k and the yoz plane, and let k be the pitch angle. Let k be the angle between the target k and the z-axis. symbol This represents the Kronecker product operation.

[0061]

[0062] and These represent the steering vectors of a single RIS panel along the y and z directions, respectively. This represents the guide vector corresponding to the M panels along the y-direction.

[0063] The array manifold matrix can be represented as

[0064]

[0065] Where matrices C and A y A z They are respectively denoted as

[0066] The symbol ⊙ represents the Khatri-Rao product operation.

[0067] Measurement Matrix Defined as

[0068]

[0069] Where P represents the number of measurements. α p,mn and υp,mn These represent the amplitude and phase of the RIS reflection units in P different time slots, respectively. This paper considers implementing a passive RIS element using PIN diodes; therefore, the measurement matrix must satisfy... That is, the RIS provides a reflection path and the phase of its components is adjusted appropriately to reflect the incident signal to the receiving end.

[0070] Assume all reflected signals are at If the signal is received in the direction of the signal, then in the Pth time slot, the K received signals at the receiver can be represented as...

[0071]

[0072] The signal vector is defined as The term is additive white Gaussian noise and follows a distribution. σ 2 Let its variance be denoted as 'variance'.

[0073] The specific methods for obtaining the estimated azimuth and elevation angles of the target signal include:

[0074] By employing an atomic norm-based approach, efficient DOA estimation is achieved in a low-cost RIS system.

[0075] First, the atomic decomposition of the output signal can be expressed as:

[0076]

[0077] Using the atomic decomposition formula given in equation (20), the atomic set of the two-dimensional signal is:

[0078]

[0079] The two-dimensional l0 atomic norm of the output signal is

[0080]

[0081] Since the l0 atomic norm is an NP-hard problem, considering its convex relaxation, the corresponding atomic norm can be re-expressed as:

[0082]

[0083] Based on the definition of the atomic norm above, the sparse reconstruction problem, which reconstructs a sparse signal x from a received signal r, can be expressed as follows:

[0084]

[0085] Where β is the regularization parameter, used to balance sparsity and reconstruction accuracy; β can be taken as...

[0086] Then, the sparse signal x can be reconstructed by solving a semidefinite programming (SDP) method, i.e., the following equation. Using the expression for the atomic norm, the atomic norm minimization (ANM) problem can be rewritten as...

[0087]

[0088] In the formula, Tr(·) represents the trace operation. It is a double Hermitian Toeplitz matrix with respect to h, specifically defined as follows:

[0089]

[0090] Each corresponding block matrix Represented as

[0091]

[0092] Where i = 1, 2, ..., M.

[0093] The above SDP problem, namely formula (25), can be solved using the CVX optimization package in MATLAB, so as to obtain the sparsely reconstructed signal x, then perform spatial spectrum estimation through the MUSIC method, and estimate the DOA of the target signal by using spectral peak search. First, fix a positive integer L satisfying K≤L<MN-K+1, and construct a Hankel matrix H:

[0094]

[0095] Singular value decomposition (SVD) is performed on matrix H to obtain

[0096] H=UDV H (29)

[0097] where D=diag(σ1,σ2,…,σ K ,0,…,0) is a diagonal matrix composed of singular values, U is the left singular matrix, V is the right singular matrix, the noise subspace is the space composed of vectors in the left singular matrix U1 corresponding to small singular values, and the signal subspace is the vectors corresponding to non-zero singular values. The two-dimensional MUSIC spatial spectrum function is obtained as:

[0098]

[0099] Finally, the azimuth angle and elevation angle of the target signal can be estimated by using spectral peak search.

[0100] Example: Assume there are two far-field target signals, whose azimuth angle and elevation angle parameters are incident on 4 RIS panels, and each panel contains 16 elements. Set SNR to 30dB, and the included angle between the receiving end and the RIS panel is θ R =0 ° , the result is as shown in Figure 2 . It can be seen from the figure that the estimated parameters of the two target signals can be correctly estimated and paired.

[0101] 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 terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Unless otherwise specified, an element defined by the phrase "comprising..." or "including..." does not exclude the presence of additional elements in the process, method, article, or terminal device that includes said element. Additionally, in this document, "greater than," "less than," "exceeding," etc., are understood to exclude the stated number; "above," "below," "within," etc., are understood to include the stated number.

[0102] Although the above embodiments have been described, those skilled in the art, once they understand the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the above descriptions are merely embodiments of the present invention and do not limit the scope of patent protection of the present invention. Any equivalent structural or procedural transformations made using the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A method for estimating the direction of arrival (DOA) of a reconfigurable smart surface-assisted MISO system, characterized in that, Includes the following steps, A far-field signal model for a reconfigurable intelligent surface-assisted MISO system is established. The far-field signal model consists of M RIS panels, K target signals, and a receiver. A received data expression is constructed based on the far-field signal model, and meshless sparse reconstruction is performed using the atomic norm to obtain a sparse reconstructed signal. In the far-field signal model, the M RIS panels are placed in a uniform planar array in the yoz plane. The obtained sparse reconstructed signal is represented in the form of a Hankel matrix, and singular value decomposition is performed on it to obtain the signal subspace and noise subspace. Combined with the MUSIC algorithm, the azimuth and elevation angles of the target signal are obtained by spectral peak search. In the far-field signal model, M RIS panels are placed in a uniform planar array in the yoz plane, and each RIS panel contains One element, This represents the number of elements along the y-direction. This represents the number of elements along the z-direction, where the spacing between RIS panels is... The element spacing of the RIS panel is d, and the wavelength is d is taken as half wavelength, that is Assuming the line-of-sight paths between K target signals and the receiver are blocked by obstacles, meaning there is only the reflection path from the target signal to the RIS panel and from the RIS panel back to the receiver, and taking the lower left corner of the first RIS panel as the origin of the three-dimensional Cartesian coordinate system, the steering vector from the target to the RIS is defined as: (2) in , , azimuth Let k be the angle between the target k and the yoz plane, and let k be the pitch angle. Let k be the angle between the target k and the z-axis, and let... , , ,symbol This represents the Kronecker product operation; The array manifold matrix is ​​represented as (3) Where the matrix They are respectively denoted as , , ,symbol This represents the Khatri-Rao product operation; Measurement Matrix Defined as (4) Where P represents the number of measurements. , and These represent the amplitude and phase of the RIS reflection units in P different time slots, respectively. A passive RIS element is implemented using PIN diodes; therefore, the measurement matrix must satisfy... That is, by using RIS to provide a reflection path and appropriately adjusting the phase of its components, the incident signal is reflected to the receiving end; Assume all reflected signals are at If the signal is received in the direction of the signal, then in the P-th time slot, the K received signals at the receiver are represented as follows: (5) The signal vector is defined as , The term is additive white Gaussian noise and follows a distribution. , Let its variance be denoted as 'variance'.

2. The direction-of-arrival estimation method for a reconfigurable smart surface-assisted MISO system as described in claim 1, characterized in that, The steps for reconstructing the sparse signal are as follows: The atomic decomposition of the output signal is first expressed as: (6) Using the atomic decomposition formula given in equation (5), the atomic set of the two-dimensional signal is: (7) Two-dimensional output signal atomic norm is (8) because The atomic norm is an NP-hard problem, therefore, considering its convex relaxation, the corresponding atomic norm is re-expressed as: (9) Based on the above definition of atomic norm, by receiving signals Reconstructing sparse signals The sparse reconstruction problem is represented as (10) in This is a regularization parameter used to balance sparsity and reconstruction accuracy. Take as ; Then, the sparse signal is reconstructed by solving a semidefinite programming-based method, namely the following equation. Using the expression for the atomic norm, the atomic norm minimization problem is rewritten as follows: (11) In the formula This represents the trace operation. It is about The dual Hermitian Toeplitz matrix is ​​specifically defined as follows: (12) Each corresponding block matrix Represented as (13) in ; The above semidefinite programming problem, i.e., equation (10), is solved using the CVX optimization package in MATLAB to obtain the sparse reconstructed signal. .

3. The direction-of-arrival estimation method for a reconfigurable smart surface-assisted MISO system as described in claim 2, characterized in that, The steps for obtaining the azimuth and elevation angles of the target signal are as follows: First, fix a positive integer L, satisfying Construct a Hankel matrix : (14) For matrix Singular value decomposition yields (15) in It is a diagonal matrix composed of singular values. It is a left singular matrix. It is a right singular matrix, and the noise subspace is the left singular matrix corresponding to the smaller singular values. The space composed of vectors in the vector space, where the signal subspace is the vector corresponding to the non-zero singular values, yields the two-dimensional MUSIC space spectrum function: (15) Finally, the azimuth and elevation angles of the target signal are estimated by using spectral peak search.

4. The direction-of-arrival estimation method for a reconfigurable smart surface-assisted MISO system as described in claim 1, characterized in that, The RIS element is a PIN diode.

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