An FMx-RIS and eigenvalue based angle of arrival estimation method and apparatus

Abstract

The present application relates to the technical field of wireless communication, especially to a kind of FMx-RIS and eigenvalue-based angle of arrival estimation method, device and computer program product, comprising: according to the phase offset of FMx-RIS, the reflection mode of FMx-RIS is set;Signal transmitted by user is received after being reflected by FMx-RIS, the phase of signal reflected by FMx-RIS is obtained;Based on the reflection mode of FMx-RIS, the wavelength of signal transmitted by user, the antenna interval of base station, the phase offset of FMx-RIS, the phase of signal reflected by FMx-RIS, wavelength and exit angle, the angle of arrival of signal from user to FMx-RIS is calculated.The present application establishes the internal relationship between the angle of arrival of signal from user to FMx-RIS and signal reflected by FMx-RIS, and improves the estimation accuracy of angle of arrival.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a method, apparatus, and computer program product for estimating angle of arrival based on FMx-RIS and eigenvalues. Background Technology

[0002] Reconfigurable Intelligent Surfaces (RIS) are a key technology in sixth-generation wireless communication systems. They enhance network coverage, spectral efficiency, and sensing capabilities by dynamically adjusting the propagation environment of electromagnetic waves. Especially in the millimeter-wave and terahertz bands, RIS can construct virtual line-of-sight links, compensating for the strong attenuation problem in high-frequency signal transmission. The Angle of Arrival (AoA) refers to the angle between the incident direction of a wireless signal and the receiver's reference coordinate system (such as the normal direction of the antenna array) as the signal propagates from the transmitter to the receiver. It is a core parameter describing the spatial propagation characteristics of a signal. By calculating the Angle of Arrival, spatial orientation information of the signal can be obtained, thereby supporting key applications such as positioning, communication optimization, and environmental sensing.

[0003] In traditional RIS architectures, estimating the angle of arrival typically involves the following methods:

[0004] (1) Use the MUSIC algorithm to extract the angle of arrival from the received signal. This method identifies the signal subspace and noise subspace by performing eigenvalue decomposition on the covariance matrix of the received signal, and then estimates the angle of arrival by searching the spectral peaks. However, the estimation accuracy is limited by the preset step size and the search time is too long.

[0005] (2) Multi-user direction-of-arrival estimation is performed using element sampling and sparse reconstruction, and the RIS element layout is optimized to minimize beam pattern sidelobes. This method provides an idea for direction-of-arrival estimation in multi-user scenarios. However, it relies on a complex sparse reconstruction algorithm, which has a large computational cost and is sensitive to channel conditions.

[0006] (3) Beamforming combined with maximum likelihood estimation is used to estimate the angle of arrival and angle of departure of the direct path between the base station (BS) or RIS and the user equipment (UE), but the beam training overhead is large.

[0007] (4) Use matrix augmentation and matrix pencil algorithm to estimate the angle of arrival and time of arrival of the reflection path, and use the time difference of arrival to locate the user equipment.

[0008] However, the inherent path ambiguity in traditional RIS architectures—where all reflection paths share the same frequency band, making it impossible to distinguish signals reflected from different RISs in the frequency domain—leads to indeterminacy in channel estimation and localization. In low signal-to-noise ratio environments, the accuracy of traditional angle-of-arrival (AOA) estimators drops significantly. Furthermore, methods based on covariance matrix factorization or sparse reconstruction require substantial snapshots and computational resources, resulting in high computational complexity and low computational efficiency, making them unsuitable for real-time estimation or computationally limited scenarios. Summary of the Invention

[0009] Therefore, the technical problem to be solved by the present invention is to overcome the problems of insufficient accuracy and low computational efficiency of angle of arrival estimation under low signal-to-noise ratio environment in the prior art.

[0010] To address the aforementioned technical problems, this invention provides an arrival angle estimation method based on FMx-RIS and eigenvalues, comprising:

[0011] In a communication system that includes users, FMx-RIS and base stations, the reflection mode of FMx-RIS is set according to the phase offset of FMx-RIS;

[0012] After the signal transmitted by the user is reflected by FMx-RIS and received by the base station, the phase of the signal reflected by FMx-RIS is obtained;

[0013] Based on the reflection mode of FMx-RIS, the arrival angle of the signal from the user to FMx-RIS is calculated using the wavelength of the signal transmitted by the user, the antenna spacing of the base station, the phase of the signal reflected by FMx-RIS, the phase offset of FMx-RIS, the wavelength of the signal after frequency adjustment by FMx-RIS, and the exit angle of the signal reflected from FMx-RIS to the base station.

[0014] Preferably, in a communication system including a user, an FMx-RIS, and a base station, the signal transmitted by the user is received by the base station after being reflected by the FMx-RIS;

[0015] The channel from the user to FMx-RIS is represented as follows:

[0016] ,

[0017] The channel from FMx-RIS to the base station is represented as follows:

[0018] ,

[0019] in, For the user's channel to the nth FMx-RIS, Let be the path loss coefficient of the channel from the user to the nth FMx-RIS. Let n be the line-of-sight channel vector between the user and the nth FMx-RIS. Let the angle of arrival of the signal from the user to the nth FMx-RIS be denoted as . The wavelength of the signal transmitted by the user. This refers to the number of reflective units in the FMx-RIS. For the nth FMx-RIS channel to the base station, Let be the path loss coefficient of the channel from the nth FMx-RIS to the base station. and Both are line-of-sight channel vectors between the base station and the nth FMx-RIS. Let be the angle of arrival of the signal reflected from the nth FMx-RIS to the base station. Let be the wavelength of the signal after frequency adjustment by the nth FMx-RIS. This refers to the number of antennas at the base station. Let be the emission angle of the signal reflected from the nth FMx-RIS to the base station.

[0020] Preferably, the method for setting the reflection mode of FMx-RIS according to the phase offset of FMx-RIS is as follows:

[0021] Set the reflection mode of FMx-RIS using the following formula:

[0022] ,

[0023] in, For the nth FMx-RIS reflection mode, This refers to the number of reflective units in the FMx-RIS. For the reflection unit index, Let be the phase offset of the i-th reflecting unit in the n-th FMx-RIS. Let n be the phase offset of the nth FMx-RIS. It is the imaginary unit.

[0024] Preferably, the method for obtaining the phase of the signal reflected by FMx-RIS is as follows:

[0025] Solve for the roots of the characteristic equation for angle estimation to obtain an estimate of the phase of the signal reflected by the FMx-RIS;

[0026] The characteristic equation for angle estimation is:

[0027] ,

[0028] in, For the complex exponential basis of the angle parameter, Let n be the phase of the signal reflected by the nth FMx-RIS; For normalized observation coefficients, Let be the line-of-sight channel vector between the base station and the nth FMx-RIS. Let be the angle of arrival of the signal reflected from the nth FMx-RIS to the base station. Let be the wavelength of the signal after frequency adjustment by the nth FMx-RIS. This refers to the number of antennas at the base station. For the noise-free signal reflected by the nth FMx-RIS, For transmission power, Let be the path loss coefficient of the channel from the user to the nth FMx-RIS. Let be the path loss coefficient of the channel from the nth FMx-RIS to the base station. It is a baseband signal; This represents the number of reflection units in the FMx-RIS.

[0029] Preferably, the method for solving the root of the angle estimation characteristic equation to obtain the estimated phase value of the FMx-RIS reflected signal is as follows: The root of the angle estimation characteristic equation is solved using the eigenvalue method to obtain the estimated phase value of the FMx-RIS reflected signal. Specific steps include:

[0030] make ,because If it is an irrelevant constant root of the characteristic equation for angle estimation, then... Decomposed into , For decomposition terms The root;

[0031] Constructing the matrix:

[0032] ,

[0033] in, ;for , ,but The root is a matrix eigenvalues;

[0034] Solve the matrix The eigenvalues ​​are used to obtain the matrix. eigenvalue set ;

[0035] Based on matrix eigenvalue set calculate effective roots :

[0036] ,

[0037] in, For matrix eigenvalue set Elements in;

[0038] based on The effective root is used to calculate the estimated phase of the signal reflected by the nth FMx-RIS. .

[0039] Preferably, based on the reflection mode of FMx-RIS, the arrival angle of the signal from the user to FMx-RIS is calculated using the wavelength of the signal transmitted by the user, the antenna spacing of the base station, the phase of the signal reflected by FMx-RIS, the phase offset of FMx-RIS, the wavelength of the signal after frequency adjustment by FMx-RIS, and the exit angle of the signal reflected from FMx-RIS to the base station. The formula is as follows:

[0040] ,

[0041] in, Let the angle of arrival of the signal from the user to the nth FMx-RIS be denoted as . The wavelength of the signal transmitted by the user. The antenna spacing of the base station. Let n be the phase of the signal reflected by the nth FMx-RIS. Let n be the phase offset of the nth FMx-RIS. Let be the wavelength of the signal after frequency adjustment by the nth FMx-RIS. Let be the emission angle of the signal reflected from the nth FMx-RIS to the base station.

[0042] Preferably, after calculating the angle of arrival of the signal from the user to the FMx-RIS, the method further includes:

[0043] Based on the arrival angle of the signal from the user to the FMx-RIS at the current time step, the phase offset of the FMx-RIS at the next time step is optimized, and then the reflection mode of the FMx-RIS at the next time step is adjusted according to the phase offset of the FMx-RIS at the next time step.

[0044] Preferably, the method for optimizing the phase offset of the FMx-RIS in the next time step based on the arrival angle of the signal from the user to the FMx-RIS in the current time step is as follows:

[0045] The phase shift of FMx-RIS at the next time step is calculated using the following formula:

[0046] ,

[0047] in, Let n be the phase offset of the nth FMx-RIS at time step t+1. The antenna spacing of the base station. Let be the wavelength of the signal after frequency adjustment by the nth FMx-RIS. Let be the emission angle of the signal reflected from the nth FMx-RIS to the base station. The wavelength of the signal transmitted by the user. Let t be the angle of arrival of the signal from the user to the nth FMx-RIS.

[0048] The present invention also provides an arrival angle estimation device based on FMx-RIS and eigenvalues, comprising:

[0049] The reflection mode setting module is used to set the reflection mode of FMx-RIS according to the phase offset of FMx-RIS in a communication system including users, FMx-RIS and base stations.

[0050] The reflected signal phase estimation module is used to obtain the phase of the signal reflected by the FMx-RIS after the signal transmitted by the user is reflected by the FMx-RIS and received by the base station.

[0051] The angle of arrival calculation module is used to calculate the angle of arrival of the signal from the user to the FMx-RIS based on the reflection mode of the FMx-RIS, using the wavelength of the signal transmitted by the user, the antenna spacing of the base station, the phase of the signal reflected by the FMx-RIS, the phase offset of the FMx-RIS, the wavelength of the signal after frequency adjustment by the FMx-RIS, and the emission angle of the signal reflected from the FMx-RIS to the base station.

[0052] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the above-described method for estimating the angle of arrival based on FMx-RIS and eigenvalues.

[0053] Compared with the prior art, the above-described technical solution of the present invention has the following advantages:

[0054] The present invention discloses an angle of arrival estimation method based on FMx-RIS and eigenvalues. Based on the characteristic that FMx-RIS can introduce frequency shift in the reflected signal to identify different propagation paths, the method establishes an intrinsic relationship between the angle of arrival of the signal from the user to the FMx-RIS and the signal reflected by the FMx-RIS in a communication system containing FMx-RIS, so as to solve the path ambiguity problem of multiple RIS and improve the estimation accuracy of the angle of arrival of the signal from the user to the FMx-RIS.

[0055] Furthermore, this invention utilizes the constructed angle estimation characteristic equation to solve for the estimated phase of the FMx-RIS reflected signal, replacing the spectral peak search or covariance matrix decomposition in traditional methods with the characteristic root solution method. This effectively reduces the computational complexity of solving for the phase of the FMx-RIS reflected signal, improves estimation efficiency, and is suitable for real-time signal processing.

[0056] Furthermore, the present invention also utilizes the calculated angle of arrival to iteratively optimize the setting of the reflection mode of FMx-RIS, so that the phase setting of FMx-RIS can gradually maximize the signal-to-noise ratio in practical applications, improve the estimation accuracy of the angle of arrival, and achieve stable and high-quality calculation of the angle of arrival even in low signal-to-noise ratio environments. Attached Figure Description

[0057] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein:

[0058] Figure 1 This is a flowchart of an arrival angle estimation method based on FMx-RIS and eigenvalues ​​according to the present invention;

[0059] Figure 2 This is a schematic diagram of a single-input multiple-output communication system assisted by FMx-RIS;

[0060] Figure 3 This is a graph showing the performance results of the algorithm of this invention for angle of arrival estimation;

[0061] Figure 4 This is a graph showing the effect of the number of reflection units in FMx-RIS on the estimation accuracy;

[0062] Figure 5 This is a schematic diagram showing the convergence results of the algorithm iteration of this invention under different numbers of FMx-RIS reflector units and transmit power. Detailed Implementation

[0063] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0064] To overcome the path ambiguity problem of RIS, researchers proposed Frequency-MixingRIS (FMx-RIS), which introduces frequency offset into the reflected signal to identify different propagation paths, while also having the phase modulation function of traditional RIS, thus supporting channel decoupling and parallel estimation.

[0065] Therefore, this invention proposes an angle-of-arrival estimation method based on FMx-RIS and eigenvalues ​​for a single-input multiple-output communication system assisted by FMx-RIS, comprising:

[0066] S1: In a communication system including users, FMx-RIS and base stations, the reflection mode of FMx-RIS is set according to the phase offset of FMx-RIS;

[0067] S2: After the signal transmitted by the user is reflected by FMx-RIS and received by the base station, the phase of the signal reflected by FMx-RIS is obtained;

[0068] S3: Based on the reflection mode of FMx-RIS, the arrival angle of the signal from the user to FMx-RIS is calculated using the wavelength of the signal transmitted by the user, the antenna spacing of the base station, the phase of the signal reflected by FMx-RIS, the phase offset of FMx-RIS, the wavelength of the signal after frequency adjustment by FMx-RIS, and the exit angle of the signal reflected from FMx-RIS to the base station.

[0069] A schematic diagram of a single-input multiple-output communication system assisted by FMx-RIS is shown below. Figure 2 As shown, the number of FMx-RIS in this communication system is N, and each FMx-RIS includes One reflector unit; the base station is equipped with a uniform linear array of M antennas for communication with users who have a single antenna.

[0070] Establish a Cartesian coordinate system for the communication system, with the base station located at the origin and its first antenna corresponding to the coordinates. The coordinates of user equipment randomly distributed within the coverage area. The coordinates of the nth FMx-RIS are determined by... It means that among them This is the index number of the FMx-RIS, corresponding to the nth of the N FMx-RIS.

[0071] In the communication system described herein, the present invention considers a far-field millimeter-wave scenario, and channel propagation only considers the reflection channel.

[0072] Assuming a uniform linear array is used at the receiver, the line-of-sight channel between the receiver and the transmitter can be modeled as a directional vector, expressed as:

[0073] ,

[0074] in, For line-of-sight channel vectors, To reach the angle, For carrier wavelength, For the number of antennas, This refers to the antenna spacing.

[0075] In a communication system including users, FMx-RIS, and base stations, for the channel formed after reflection by the nth FMx-RIS, due to their similar spatial structure, the cascaded model of user equipment-RIS-base station can be expressed as:

[0076] ,

[0077] in, The channel formed by the nth FMx-RIS reflection, For the user's channel to the nth FMx-RIS, For the nth FMx-RIS channel to the base station, For the nth FMx-RIS reflection mode, The standard symbol for representing the set of complex numbers in mathematics. This refers to the number of antennas at the base station.

[0078] The channel from the user to FMx-RIS is represented as follows:

[0079] ;

[0080] The channel from FMx-RIS to the base station is represented as follows:

[0081] ;

[0082] in, Let be the path loss coefficient of the channel from the user to the nth FMx-RIS. Let n be the line-of-sight channel vector between the user and the nth FMx-RIS. Let the angle of arrival of the signal from the user to the nth FMx-RIS be denoted as . The wavelength of the signal transmitted by the user. This refers to the number of reflective units in the FMx-RIS. Let be the path loss coefficient of the channel from the nth FMx-RIS to the base station. and Both are line-of-sight channel vectors between the base station and the nth FMx-RIS. Let be the angle of arrival of the signal reflected from the nth FMx-RIS to the base station. Let be the wavelength of the signal after frequency adjustment by the nth FMx-RIS. For carrier frequency, This represents the frequency offset of the nth FMx-RIS. This refers to the number of antennas at the base station. Let be the emission angle of the signal reflected from the nth FMx-RIS to the base station.

[0083] The reflection mode of the nth FMx-RIS is ,in This is the phase offset of the i-th reflecting unit in the n-th FMx-RIS. Therefore, the equivalent baseband signal reflected from the n-th FMx-RIS is:

[0084] ,

[0085] in, The equivalent baseband signal reflected by the nth FMx-RIS is... For transmission power, For baseband signals, The equivalent baseband signal reflected by the nth FMx-RIS at frequency Additive white Gaussian noise at a given location, whose elements follow the rules of... distributed.

[0086] The overall received signal of the base station, obtained from N FMx-RIS reflection paths, can be expressed as:

[0087] ,

[0088] in, For the overall received signal reflected by N FMx-RIS, This is the overall equivalent channel vector. It is an overall additive Gaussian white noise.

[0089] Because of the decoupling characteristics of FMx-RIS, the frequency shift uniquely associated with the nth FMx-RIS can be utilized. This allows us to distinguish signals from different channels, thus enabling us to extract signals from a single channel for analysis.

[0090] This invention utilizes the following lemma for analysis:

[0091] Given a length of , in the form of The guiding vector can be obtained as follows:

[0092] ,

[0093] in, , , and There are three arbitrary variables. When At that time, the corresponding norm reaches its maximum value. .

[0094] The proof of this lemma is as follows:

[0095] about The formula can be obtained directly by summing a geometric series. The amplitude bound is derived from the triangle inequality, as follows:

[0096] ,

[0097] The equation holds if and only if all complex exponents In phase, that is Furthermore, At the limit Established at that time, at the same time exist This holds strictly at the time, indicating that the maximum value is... Place.

[0098] Based on the above lemma, a specific reflection mode structure can be set. In this embodiment, the reflection mode of the FMx-RIS is set according to the phase offset of the FMx-RIS, which can be expressed as:

[0099] ,

[0100] in, For the nth FMx-RIS reflection mode, This refers to the number of reflective units in the FMx-RIS. For the reflection unit index, Let be the phase offset of the i-th reflecting unit in the n-th FMx-RIS, and assign a specific structure to the cascaded channel of the reflected signal. Let n be the phase offset of the nth FMx-RIS. It is the imaginary unit.

[0101] Therefore, a linear phase advance can be applied to the FMx-RIS device to efficiently extract angle information. This characteristic can be specifically stated by the following theorem:

[0102] Under ideal noise-free conditions, follow the reflection mode settings. Angle of arrival of the signal from the user to the FMx-RIS Based on the reflection mode of FMx-RIS, the formula can be obtained using the wavelength of the signal transmitted by the user, the antenna spacing of the base station, the phase of the signal reflected by FMx-RIS, the phase offset of FMx-RIS, the wavelength of the signal after frequency adjustment by FMx-RIS, and the exit angle of the signal reflected from FMx-RIS to the base station. The formula is as follows:

[0103] ,

[0104] in, Let the angle of arrival of the signal from the user to the nth FMx-RIS be denoted as . The wavelength of the signal transmitted by the user. The antenna spacing of the base station. Let n be the phase of the signal reflected by the nth FMx-RIS. Let n be the phase offset of the nth FMx-RIS. Let be the wavelength of the signal after frequency adjustment by the nth FMx-RIS. Let be the emission angle of the signal reflected from the nth FMx-RIS to the base station;

[0105] Characteristic equation for angle estimation The root;

[0106] in, For the complex exponential basis of the angle parameter; For normalized observation coefficients, Let be the line-of-sight channel vector between the base station and the nth FMx-RIS. Let be the angle of arrival of the signal reflected from the nth FMx-RIS to the base station. This refers to the number of antennas at the base station. For the noise-free received signal reflected by the nth FMx-RIS, For transmission power, Let be the path loss coefficient of the channel from the user to the nth FMx-RIS. Let be the path loss coefficient of the channel from the nth FMx-RIS to the base station. For baseband signals, This represents the number of reflection units in the FMx-RIS.

[0107] The proof of the above theorem is as follows:

[0108] Known base station Under these conditions, utilize the corresponding steering vector We can obtain:

[0109] ,

[0110] Among them, in the above formula The above formula is obtained by representing the channel from the user to the FMx-RIS and the channel from the FMx-RIS to the base station. The above lemma can be used in conjunction with the reflection mode configuration of FMx-RIS. Obtain. Let... and After some calculations, the above equation can be rearranged into the characteristic equation for angle estimation.

[0111] According to Lemma 1, the complete phase relationship at the receiver is:

[0112] ,

[0113] Based on this phase relationship, the angle of arrival of the signal from the user to the FMx-RIS can be obtained. The calculation formula.

[0114] This theorem shows that, given the reflection mode structure of FMx-RIS In noise-free, geometry-based channel environments, angles can be accurately estimated by solving one-dimensional higher-order equations. This result demonstrates that the proposed method overcomes the inherent accuracy limitations of codebook-based and MUSIC-based angle estimation methods.

[0115] Based on the above theorem, in one embodiment of the present invention, the method for obtaining the phase of the signal reflected by the FMx-RIS is as follows: by solving the root of the angle estimation characteristic equation, an estimated value of the phase of the signal reflected by the FMx-RIS is obtained. Then, the angle of arrival of the signal from the user to the FMx-RIS is calculated based on the estimated value of the phase of the signal reflected by the FMx-RIS.

[0116] Preferably, this embodiment also provides a robust method for solving the polynomial-complexity angle estimation characteristic equation using eigenvalues ​​to obtain an estimate of the phase of the FMx-RIS reflected signal, as follows:

[0117] make ,because If it is an irrelevant constant root of the characteristic equation for angle estimation, then... Decomposed into , For decomposition terms The root;

[0118] Constructing the matrix:

[0119] ,

[0120] in, ;for , ,but The root is a matrix eigenvalues;

[0121] Solve the matrix The eigenvalues ​​are used to obtain the matrix. eigenvalue set ;

[0122] Based on matrix eigenvalue set calculate effective roots :

[0123] ,

[0124] in, For matrix eigenvalue set Elements in;

[0125] based on The effective root is used to calculate the estimated phase of the signal reflected by the nth FMx-RIS. .

[0126] The eigenvalue-based solution method provides an efficient numerical approach for solving the characteristic equation of angle estimation.

[0127] However, real-world communication systems operate in noisy environments, where additive white Gaussian noise permeates the root lookup process, introducing estimation errors. To mitigate these noise-induced estimation errors, this invention utilizes the conclusion of the aforementioned lemma, namely, that when the FMx-RIS configuration ensures that the reflected signal at the receiver is coherent and its phase is accurate. At this point, the optimal signal-to-noise ratio can be achieved. This requirement for phase coherence is fundamentally different from previous work, which only focused on arbitrary phase alignment to maximize received power. Recalling the above theorem, where the input-output phase relationship is given by the complete phase relationship at the receiver, then based on the angle of arrival... The optimal phase configuration for FMx-RIS, which maximizes the signal-to-noise ratio, is optimized by adjusting the phase offset:

[0128] ,

[0129] in, The optimal phase offset for the nth FMx-RIS. The antenna spacing of the base station. Let be the wavelength of the signal after frequency adjustment by the nth FMx-RIS. Let be the emission angle of the signal reflected from the nth FMx-RIS to the base station. The wavelength of the signal transmitted by the user. The angle of arrival of the signal from the user to the nth FMx-RIS.

[0130] The reflection mode of FMx-RIS is updated based on the optimized phase offset. This can maximize the signal-to-noise ratio.

[0131] Due to the angle of arrival Since it is an unknown quantity, the optimal phase offset cannot be directly calculated in practical applications. According to the above theorem, the reflection configuration structure Phase offset at the initial time step Phase estimation can be achieved for any value, but signal quality cannot be guaranteed. An estimate of the arrival angle at the initial time step can be obtained under this reflection mode setting. Thus, the estimated angle of arrival is utilized. Reconfigure the phase offset for the next time step Therefore, this embodiment achieves convergence step by step by iteratively calculating the arrival angle of the signal from the user to the FMx-RIS and optimizing the phase offset of the FMx-RIS.

[0132] Preferably, after calculating the angle of arrival of the signal from the user to the FMx-RIS, the method further includes:

[0133] Based on the arrival angle of the signal from the user to the FMx-RIS at the current time step, the phase offset of the FMx-RIS at the next time step is optimized, and then the reflection mode of the FMx-RIS at the next time step is adjusted according to the phase offset of the FMx-RIS at the next time step.

[0134] Based on the arrival angle of the signal from the user to the FMx-RIS at the current time step, the phase offset of the FMx-RIS at the next time step is optimized using the following formula:

[0135] ,

[0136] in, Let n be the phase offset of the nth FMx-RIS at time step t+1. The antenna spacing of the base station. Let be the wavelength of the signal after frequency adjustment by the nth FMx-RIS. Let be the emission angle of the signal reflected from the nth FMx-RIS to the base station. The wavelength of the signal transmitted by the user. Let t be the angle of arrival of the signal from the user to the nth FMx-RIS.

[0137] The key to this iterative theory is that each estimation provides information to improve the stage configuration of the reflection mode, which in turn improves the quality of subsequent angle estimations. and With gradual refinement, the phase of the signal reflected by FMx-RIS It will gradually approach 0, and this improvement will gradually converge through continuous updates and iterations.

[0138] In summary, the FMx-RIS-based angle of arrival estimation method described in this invention leverages the characteristic of FMx-RIS to introduce frequency offsets into reflected signals, enabling the identification of different propagation paths. It establishes an intrinsic relationship between the angle of arrival of the signal from the user to the FMx-RIS and the signal reflected from the FMx-RIS in a communication system containing FMx-RIS, thereby solving the path ambiguity problem of multiple RISs and improving the estimation accuracy of the angle of arrival of the signal from the user to the FMx-RIS.

[0139] Furthermore, this invention utilizes the constructed angle estimation characteristic equation to solve for the estimated phase of the FMx-RIS reflected signal, replacing the spectral peak search or covariance matrix decomposition in traditional methods with the characteristic root solution method. This effectively reduces the computational complexity of solving for the phase of the FMx-RIS reflected signal, improves estimation efficiency, and is suitable for real-time signal processing.

[0140] Furthermore, the present invention also utilizes the calculated angle of arrival to iteratively optimize the setting of the reflection mode of FMx-RIS, so that the phase setting of FMx-RIS can gradually maximize the signal-to-noise ratio in practical applications, improve the estimation accuracy of the angle of arrival, and achieve stable and high-quality calculation of the angle of arrival even in low signal-to-noise ratio environments.

[0141] To verify the accuracy of the method of the present invention, this embodiment uses simulation for verification. In the simulation experiment, this embodiment considers an area of ​​200×200 square meters, in which the base station is located... Equipped with A uniform linear array of antennas, with the carrier frequency set to... Antenna spacing is The path loss model used is... ,in Indicates the distance between links. For reference distance, path loss index Set to 2.

[0142] In the simulation experiment, the number of iterations k is used to replace the time step t in the actual reference. The simulation iteration algorithm used is as follows:

[0143] Input: Number of antennas for the base station Number of reflective units The emission angle of the signal reflected from FMx-RIS to the base station Random initial phase offset Initial estimate of the phase of the signal reflected by FMx-RIS Number of iterations Smaller positive threshold ;

[0144] Output: An estimated angle of arrival of the signal from the user to the FMx-RIS after several iterations. ;

[0145] step:

[0146] 1: while do;

[0147] 2: ;

[0148] 3: ;

[0149] 4: Configuration for ;

[0150] 5: Receive Time signal ;

[0151] 6: Solve the root of the characteristic equation for angle estimation using the eigenvalue method to obtain an estimate of the phase of the signal reflected by FMx-RIS. ;

[0152] 7: ;

[0153] 8: end while

[0154] 9: .

[0155] The performance of the algorithm in this invention is evaluated using mean squared error, defined as follows: ,in and These represent the estimated and actual values ​​of the angle of arrival, respectively.

[0156] Figure 3 The graph shows the performance results of the algorithm of this invention for angle of arrival estimation, where the mean square error of estimation is used as the metric and the CRB is used as the theoretical benchmark. First, it can be seen that the algorithm of this invention can stably approach the CRB in the low to medium signal-to-noise ratio range. This superior performance can be attributed to the algorithm's ability to achieve optimal coherent phase alignment, i.e. This maximizes the received signal power. More importantly, the estimation accuracy exhibits a significant angle dependence, achieving excellent accuracy close to π / 2. Angle variations mean that angle-based positioning algorithms may exhibit spatially non-uniform accuracy.

[0157] Figure 4 The resulting graph shows the impact of the number of reflective units in the FMx-RIS on the estimation accuracy. As expected, it can be observed from Om that with... The increase in ... Increasing the value from 100 to 200 improves the estimation accuracy by approximately an order of magnitude. This result highlights the advantages of deploying large-scale RIS for high-precision sensing applications, but at the cost of increased computational complexity using eigenvalue-based methods.

[0158] Figure 5 This diagram illustrates the convergence results of the algorithm iteration of this invention under different numbers of FMx-RIS reflector units and transmit powers. It can be seen that, under high signal-to-noise ratio conditions, the algorithm of this invention achieves convergence at relatively high power levels. At higher signal-to-noise ratios (SNRs), more iterations are required for convergence. This phenomenon may be due to the introduction of additional local minima by higher-order polynomials, thus hindering efficient convergence to the optimal solution. Conversely, under low SNR conditions, the algorithm converges faster with larger SNR configurations because more RIS reflectors provide higher beamforming gain, improving signal quality and mitigating the noise impact of eigenvalue-based solutions. Therefore, although the algorithm of this invention converges more slowly under high SNR conditions, its superior robustness in noisy environments has been verified.

[0159] Based on the aforementioned method for estimating angle of arrival (AHA) based on FMx-RIS and eigenvalues, this invention also provides an AHA estimation apparatus based on FMx-RIS and eigenvalues, comprising:

[0160] The reflection mode setting module is used to set the reflection mode of FMx-RIS according to the phase offset of FMx-RIS in a communication system including users, FMx-RIS and base stations.

[0161] The reflected signal phase estimation module is used to obtain the phase of the signal reflected by the FMx-RIS after the signal transmitted by the user is reflected by the FMx-RIS and received by the base station.

[0162] The angle of arrival calculation module is used to calculate the angle of arrival of the signal from the user to the FMx-RIS based on the reflection mode of the FMx-RIS, using the wavelength of the signal transmitted by the user, the antenna spacing of the base station, the phase of the signal reflected by the FMx-RIS, the phase offset of the FMx-RIS, the wavelength of the signal after frequency adjustment by the FMx-RIS, and the emission angle of the signal reflected from the FMx-RIS to the base station.

[0163] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the above-described method for estimating the angle of arrival based on FMx-RIS and eigenvalues.

[0164] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0165] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0166] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0167] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0168] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for estimating the angle of arrival based on FMx-RIS and eigenvalues, characterized in that, include: In a communication system including users, FMx-RIS, and base stations, the reflection mode of FMx-RIS is set according to the phase offset of FMx-RIS. The method is as follows: The reflection mode of FMx-RIS is set using the following formula: ； in, For the nth FMx-RIS reflection mode, This refers to the number of reflective units in the FMx-RIS. For the reflection unit index, Let be the phase offset of the i-th reflecting unit in the n-th FMx-RIS. Let n be the phase offset of the nth FMx-RIS. The imaginary unit; After the signal transmitted by the user is reflected by FMx-RIS and received by the base station, the phase of the signal reflected by FMx-RIS is obtained; Based on the reflection mode of FMx-RIS, the arrival angle of the signal from the user to FMx-RIS is calculated using the wavelength of the signal transmitted by the user, the antenna spacing of the base station, the phase of the signal reflected by FMx-RIS, the phase offset of FMx-RIS, the wavelength of the signal after frequency adjustment by FMx-RIS, and the exit angle of the signal reflected from FMx-RIS to the base station.

2. The method for estimating the angle of arrival based on FMx-RIS and eigenvalues ​​according to claim 1, characterized in that, In a communication system that includes users, FMx-RIS and base stations, the signal transmitted by the user is reflected by the FMx-RIS and then received by the base station. The channel from the user to FMx-RIS is represented as follows: ； The channel from FMx-RIS to the base station is represented as follows: ； in, For the user's channel to the nth FMx-RIS, Let be the path loss coefficient of the channel from the user to the nth FMx-RIS. Let n be the line-of-sight channel vector between the user and the nth FMx-RIS. Let the angle of arrival of the signal from the user to the nth FMx-RIS be denoted as . The wavelength of the signal transmitted by the user. This refers to the number of reflective units in the FMx-RIS. For the nth FMx-RIS channel to the base station, Let be the path loss coefficient of the channel from the nth FMx-RIS to the base station. and Both are line-of-sight channel vectors between the base station and the nth FMx-RIS. Let be the angle of arrival of the signal reflected from the nth FMx-RIS to the base station. Let be the wavelength of the signal after frequency adjustment by the nth FMx-RIS. This refers to the number of antennas at the base station. Let be the emission angle of the signal reflected from the nth FMx-RIS to the base station.

3. The method for estimating the angle of arrival based on FMx-RIS and eigenvalues ​​according to claim 1, characterized in that, The method for obtaining the phase of the signal reflected by FMx-RIS is as follows: Solve for the roots of the characteristic equation for angle estimation to obtain an estimate of the phase of the signal reflected by the FMx-RIS; The characteristic equation for angle estimation is: ； in, For the complex exponential basis of the angle parameter, Let n be the phase of the signal reflected by the nth FMx-RIS; For normalized observation coefficients, Let be the line-of-sight channel vector between the base station and the nth FMx-RIS. Let be the angle of arrival of the signal reflected from the nth FMx-RIS to the base station. Let be the wavelength of the signal after frequency adjustment by the nth FMx-RIS. This refers to the number of antennas at the base station. For the noise-free signal reflected by the nth FMx-RIS, For transmission power, Let be the path loss coefficient of the channel from the user to the nth FMx-RIS. Let be the path loss coefficient of the channel from the nth FMx-RIS to the base station. It is a baseband signal; This represents the number of reflection units in the FMx-RIS.

4. The method for estimating the angle of arrival based on FMx-RIS and eigenvalues ​​according to claim 3, characterized in that, The method for solving the root of the angle estimation characteristic equation to obtain the phase estimate of the FMx-RIS reflected signal is as follows: The root of the angle estimation characteristic equation is solved using the eigenvalue method to obtain the phase estimate of the FMx-RIS reflected signal. Specific steps include: make ,because If it is an irrelevant constant root of the characteristic equation for angle estimation, then... Decomposed into , For decomposition terms The root; Constructing the matrix: ； in, ;for , ,but The root is a matrix eigenvalues; Solve the matrix The eigenvalues ​​are used to obtain the matrix. eigenvalue set ; Based on matrix eigenvalue set calculate effective roots : ； in, For matrix eigenvalue set Elements in; based on The effective root is used to calculate the estimated phase of the signal reflected by the nth FMx-RIS. .

5. The method for estimating the angle of arrival based on FMx-RIS and eigenvalues ​​according to claim 1, characterized in that, Based on the reflection mode of FMx-RIS, the arrival angle of the signal from the user to the FMx-RIS is calculated using the wavelength of the signal transmitted by the user, the antenna spacing of the base station, the phase of the signal reflected by the FMx-RIS, the phase offset of the FMx-RIS, the wavelength of the signal after frequency adjustment by the FMx-RIS, and the exit angle of the signal reflected from the FMx-RIS to the base station. The formula is as follows: ； in, Let the angle of arrival of the signal from the user to the nth FMx-RIS be denoted as . The wavelength of the signal transmitted by the user. The antenna spacing of the base station. Let n be the phase of the signal reflected by the nth FMx-RIS. Let n be the phase offset of the nth FMx-RIS. Let be the wavelength of the signal after frequency adjustment by the nth FMx-RIS. Let be the emission angle of the signal reflected from the nth FMx-RIS to the base station.

6. The method for estimating the angle of arrival based on FMx-RIS and eigenvalues ​​according to claim 5, characterized in that, After calculating the angle of arrival of the signal from the user to the FMx-RIS, the following is also included: Based on the arrival angle of the signal from the user to the FMx-RIS at the current time step, the phase offset of the FMx-RIS at the next time step is optimized, and then the reflection mode of the FMx-RIS at the next time step is adjusted according to the phase offset of the FMx-RIS at the next time step.

7. The method for estimating the angle of arrival based on FMx-RIS and eigenvalues ​​according to claim 6, characterized in that, The method for optimizing the phase offset of the FMx-RIS in the next time step based on the arrival angle of the signal from the user to the FMx-RIS at the current time step is as follows: The phase shift of FMx-RIS at the next time step is calculated using the following formula: ； in, Let n be the phase offset of the nth FMx-RIS at time step t+1. The antenna spacing of the base station. Let be the wavelength of the signal after frequency adjustment by the nth FMx-RIS. Let be the emission angle of the signal reflected from the nth FMx-RIS to the base station. The wavelength of the signal transmitted by the user. Let t be the angle of arrival of the signal from the user to the nth FMx-RIS.

8. An arrival angle estimation device based on FMx-RIS and eigenvalues, characterized in that, include: The reflection mode setting module is used to set the reflection mode of the FMx-RIS based on the phase offset of the FMx-RIS in a communication system including users, FMx-RIS, and base stations. The method is as follows: the reflection mode of the FMx-RIS is set using the following formula: ； in, For the nth FMx-RIS reflection mode, This refers to the number of reflective units in the FMx-RIS. For the reflection unit index, Let be the phase offset of the i-th reflecting unit in the n-th FMx-RIS. Let n be the phase offset of the nth FMx-RIS. The imaginary unit; The reflected signal phase estimation module is used to obtain the phase of the signal reflected by the FMx-RIS after the signal transmitted by the user is reflected by the FMx-RIS and received by the base station. The angle of arrival calculation module is used to calculate the angle of arrival of the signal from the user to the FMx-RIS based on the reflection mode of the FMx-RIS, using the wavelength of the signal transmitted by the user, the antenna spacing of the base station, the phase of the signal reflected by the FMx-RIS, the phase offset of the FMx-RIS, the wavelength of the signal after frequency adjustment by the FMx-RIS, and the emission angle of the signal reflected from the FMx-RIS to the base station.

9. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of an arrival angle estimation method based on FMx-RIS and eigenvalues ​​as described in any one of claims 1 to 7.

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