Method for estimating arrival angle of user assisted by intelligent reflecting surface in multi-carrier ISAC system

Abstract

The invention discloses an intelligent reflector assisted user arrival angle estimation method in a multi-carrier ISAC system. In the method, a plurality of users send pilot signals, and each IRS reflects the user signals to a remote radio access unit (RRH). The RRH uploads the received signal to a centralized baseband processing unit pool (BBU) through a forward link; the BBU performs joint processing on the received signals on the plurality of RRHs, and the observation dimension is increased by constructing the frequency domain snapshot observation matrix of the pilot signals on the plurality of subcarriers, so that the estimation precision of the arrival angle from the user to the IRS path is improved. According to the method, frequency domain snapshot information brought by pilot frequency subcarriers is fully utilized, and the angle estimation resolution and robustness are improved. By adopting the scheme of the invention, high-precision user positioning can be realized in a complex environment.

Description

Technical Field

[0001] This invention relates to the field of multi-carrier ISAC system technology, and specifically to a method for estimating the angle of arrival of users with intelligent reflectors in a multi-carrier ISAC system. Background Technology

[0002] With the increasing demand for high-precision environmental perception capabilities from emerging applications such as intelligent manufacturing, connected vehicles, and unmanned systems, ISAC technology is gradually becoming a core function of next-generation wireless systems. The C-RAN architecture achieves unified scheduling of communication and sensing resources through a centralized baseband unit (BBU) and distributed remote radio units (RRH), enabling large-scale deployment. However, the high pressure and complex structure of the fronthaul link in C-RAN systems limit their scalability in sensing tasks.

[0003] To enhance the spatial perception performance of the system, this invention introduces intelligent reflective surfaces (IRS) as relay sensing nodes. As a novel technology that is low-cost, low-power, and easy to deploy, IRS can intelligently reconstruct the signal propagation path by adjusting the phase of its passive reflective units, thereby enhancing signal coverage and mitigating occlusion while improving the system's ability to distinguish target directions. Summary of the Invention

[0004] This invention relates to a multi-carrier ISAC system, which, in the context of cloud access networks, enables the location of target users with the assistance of intelligent reflectors. In particular, it is a high-resolution sensing algorithm that constructs multiple snapshot observations in the frequency domain and combines one-dimensional and two-dimensional atomic norm minimization techniques to estimate the DOA of a user in the direction of the IRS.

[0005] This invention addresses a typical scenario: a user is located in an RRH (Redirect Route Hedge) obstruction area and actively transmits a known multi-carrier OFDM pilot signal; the IRS (Infrastructure Reception Controller) reflects the signal to multiple sensing RRHs via a LOS (Line of Attachment) link. Since the geometric position and line-of-sight direction between the IRS and the RRHs are known, the system's primary sensing task is to estimate the DOA (Direction of Alignment) angle between the user and the IRS.

[0006] The technical solution of the present invention is as follows:

[0007] A method for estimating the angle of arrival (Angle of Arrival) of users with intelligent reflectors in a multi-carrier ISAC system is proposed. U users to be estimated transmit known OFDM pilot signals. The BBU pool processes the received signals from each receiving RRH. By utilizing the shared angle information across all subcarriers and employing the atomic norm minimization method, the Angle of Arrival of the users to each IRS is estimated. The specific steps are as follows:

[0008] 1.1) The IRS-assisted user angle-of-arrival estimation system of the multi-carrier communication sensing integrated system includes a BBU pool, P RRHs, and J IRSs. Information is transmitted between the BBU pool and each RRH via a wired fronthaul link. Each receiving RRH is equipped with N... B A uniform linear antenna array (ULA) consisting of N antennas is responsible for sensing the target user's angle information. A passive IRS consists of N... I It consists of several reflection units. The BBU pool is known to receive the location information of the line-of-sight (LOS) channel from RRH to IRS. The user and RRH are blocked, and there are non-line-of-sight (NLOS) channels between the user and IRS and between IRS and RRH.

[0009] 1.2) Each frame is divided into two parts: the first T... P One time slot constitutes the uplink pilot subframe, dedicated to acquiring angle information, while the remaining TT... p Time slots constitute downlink subframes for data transmission. A comb pilot pattern is applied for uplink angle estimation. Specifically, the total bandwidth is divided into K subcarriers, each with an index set. K P Subcarriers are selected for pilot transmission. Where Δ = K / K p This represents the pilot subcarrier spacing. On each pilot subcarrier, the user transmits different pilot symbols to achieve frequency domain distinctiveness. Simultaneously, the reflection coefficient of the intelligent reflector (IRS) is time-domain modulated in each pilot time slot, and the phase of the reflection matrix changes independently within each time slot.

[0010] 1.3) In the system, user number u has an uplink connection with the Intelligent Reflective Surface (IRS) with an L-shaped path. UI Multipath components. Considering the sparsity of millimeter-wave channels, the UE-IRS channel frequency response of the k-th subcarrier of the u-th user at the J-th IRS. The p-th received RHH comes from the IRS-BS channel frequency response at the j-th IRS. As shown below:

[0011]

[0012] Accordingly, the downlink between the IRS and the Receive Remote Radio Unit (RRH) has L IB There are multiple path routes. Among them, the first... The path from the user to the IRS is determined by the path fading coefficient. Path delay and the angle of arrival The characterization, with a sampling frequency of f s (l UI =1,2,...,LUI (j = 1, 2, ..., J).

[0013] In the IRS to RRH link, the line-of-sight (LOS) path parameters are as follows: and These represent the fading coefficient, delay, angle of arrival (AOA), and angle of departure (AOD) of the IRS to the receiving RRH line-of-sight (LOS) channel.

[0014] In addition, the l IB The non-line-of-sight (NLOS) path parameters from IRS to RRH are as follows: and These are the lth channels from the IRS to the received RRH channel. IB Fading coefficient, delay, AOA and AOD of each path IB =2,...,L IB ;j=1,2,...,J). and The number of antennas representing the response vector of the array are N and N respectively. B and N I .

[0015] The array response vector (j = 1, 2, ..., J) from the u-th user to the j-th IRS angle of arrival is:

[0016]

[0017] in This represents the angle of arrival from user u to the IRS j.

[0018] 1.4) In the IRS-BS channel, where It is the lth IB The fading coefficient from the j-th IRS to the p-th RRH under a non-line-of-sight path, (l IB =2,...,L IB )

[0019] The array response vectors for the p-th RRH arrival angle and the j-th IRS departure angle are:

[0020]

[0021] Where, d RRH d represents the distance between two adjacent antennas of RRH. IRS λ represents the distance between two adjacent reflective elements of the IRS; λ represents the carrier wavelength. and Let these represent the departure angle and arrival angle from the j-th IRS to the p-th RRH, respectively; where Let represent the reflection coefficient matrix of the IRS in time slot t, where and Let represent the phase shift of the i-th reflection unit in the t-th time slot. The pilot signals transmitted by u users in the t-th time slot are defined as follows: at last It is additive white Gaussian noise, σ 2 Indicates IRS noise power. It is the identity matrix;

[0022] 1.5) The signal of the k-th subcarrier received in the p-th RRH of the t-th time slot

[0023]

[0024] in This represents the channel length s of the k-th subcarrier along the path from the u-th user to the j-th IRS. u,t This represents the pilot signal transmitted by the u-th user in the t-th time slot, v k,t H represents the noise generated by the signal in the k-th subcarrier of the t-th time slot. IB,j,p,k It includes the line-of-sight and non-line-of-sight paths of the signal reaching the RRH after reflection from the IRS, and is expressed in the following form:

[0025]

[0026] The entire system can be uniformly modeled as follows:

[0027]

[0028] In the system and Let represent the NLOS and LOS channel matrices of the j-th IRS to p-th RRH on the k-th subcarrier, respectively. All receiving remote radio units (RRHs) synchronously transmit their received signals to the baseband processing unit (BBU) pool via a wired fronthaul link in each time slot to achieve centralized signal processing. Specifically, for the t-th time slot, the k-th subcarrier, and the u-th user, the globally stacked signal received by the BBU pool is denoted as . It can be represented as:

[0029]

[0030] Furthermore, in the IRS-assisted user angle of arrival estimation of a multi-carrier communication sensing integrated system, the BBU knows the location information of the IRS and the receiving RRH, so the angle information, i.e., the RRH angle of arrival, is known in the LOS channel from the IRS to the RRH. Angle of departure from IRS We need to estimate the angle of arrival from all users to all IRSs.

[0031] The specific steps are as follows:

[0032] 2.1) First, the NLOS path from IRS to RRH and the user-to-IRS path are extracted separately to form a concatenated channel. The statement is as follows:

[0033]

[0034] Transformation of cascaded channels

[0035]

[0036] Where ⊙ represents the Khatri Rao product, Represents the Kronecker product. It is N B Line N B The identity matrix of columns, and Let represent the reflection coefficient matrix of the t-th time slot IRS, where This indicates that in the t-th time slot, the 1st, ..., Nth time slot... I The phase shift of each element and the channel fading coefficient can be combined into

[0037]

[0038] ο j,p The definition of

[0039]

[0040] Next, we define the composition Z. 2D,j,p Atom set A 2D,j,p (j=1,2…,J; p=1,2…,P), Z 2D,j,p It is composed of two-dimensional atom set A 2D,j,p A linearly combined matrix, where all pilot subcarriers share the same angular information, has the following expression:

[0041]

[0042] in This represents the portion required to form the 2D atomic norm, excluding the known parts.

[0043]

[0044] The non-line-of-sight cascaded channel where the user sends a signal to the IRS and the IRS reflects it to the RRH can be written as the following expression, where let

[0045]

[0046] 2.2) The LOS path portion of the cascaded channel from the reflector to the receiving RRH, where... This represents the concatenated channel of the LOS path from the reflector to the receiving RRH, which is represented as follows:

[0047]

[0048] The BBU has known the location information of the IRS and the base station. The known information of the channel can be represented as follows:

[0049]

[0050] Define composition Z 1D,j Atom set A 1D,j (j = 1, 2, ..., J), This represents the portion required to form the 1D atomic norm, excluding the known components.

[0051]

[0052]

[0053] The cascaded channel from the user sending a signal to the IRS, and the IRS reflecting it to the RRH line-of-sight path, can be written as the following expression:

[0054]

[0055] 2.3) In order to estimate the received signal The angle in the middle Formulas It can be rewritten as:

[0056]

[0057] In the formula In the middle, Γ j,p,t and W j,t These are all known, and they only relate to the angular information of the LOS path between the active IRS and the sensing RRH. This leads to the following optimization problem:

[0058]

[0059] Where x 1,j and x 2,j,p These are variables to be optimized. and The matrix to be optimized is T. To represent the 1D atomic norm using a semidefinite programming (SDP) problem, a Hermitian Tolliterz matrix is ​​used. 1D,j It is a dimension N I ×N I Topulitz matrix, T 1D It can be written as:

[0060]

[0061] in T 2D,j,p It is a second-order Toplitz matrix, which can be composed of Hermitian Toplitz matrices and Toplitz matrices.

[0062]

[0063] Where T 1D,0 Denotes the Hermitian matrix for i = 1, 2, ..., N B -1,T 1D,i Let represent the Toeplitz matrix. The above DOA estimation problem is modeled as an SDP, whose objective function and constraints are convex, and therefore can be efficiently solved using standard convex optimization tools (such as the CVX framework). 2.4) After obtaining the optimal solution, the user's angle of incidence (DOA) information can be extracted by eigenvalue decomposition or spectral estimation of the optimal Toeplitz matrix. Commonly used methods include: Vandermonde structure decomposition or the Root-MUSIC algorithm, which estimates the DOA by finding the roots of the null space polynomial of the optimal Toeplitz matrix.

[0064] The design concept of this invention is as follows:

[0065] This invention involves multiple users transmitting pilot signals, with each IRS reflecting the user signals to a Remote Radio Access Unit (RRH). The RRH then transmits the received signals to a centralized baseband processing unit (BBU) via a fronthaul link. The BBU jointly processes the received signals from multiple RRHs, constructing a frequency-domain snapshot observation matrix of the pilot signals across multiple subcarriers. This increases the observation dimension and improves the accuracy of the angle of arrival (AHA) estimation from the user to the IRS. This invention fully utilizes the frequency-domain snapshot information provided by the pilot subcarriers, enhancing the angle estimation resolution and robustness. Using this invention, high-precision user positioning can be achieved in complex environments.

[0066] The beneficial effects of this invention are as follows:

[0067] This invention utilizes OFDM pilot structures to construct a multi-snapshot observation model by selecting several pilot subcarriers in the frequency domain, and proposes a DOA estimation method combining one-dimensional and two-dimensional atomic norm minimization. Specifically, the user-to-IRS path is modeled as a sparse combination on a one-dimensional atomic set, while the IRS-to-RRH non-line-of-sight path is modeled as a sparse combination on a two-dimensional atomic set. This formalizes the DOA estimation problem into a hybrid ANM optimization problem, which is solved using semidefinite programming (SDP). This method does not require complete IRS-RRH channel state information, offers high estimation accuracy, and exhibits strong algorithm robustness. It is suitable for user localization and direction awareness tasks in complex obstruction and multipath environments. Compared with other algorithms, this invention has smaller errors and higher accuracy, demonstrating promising engineering application prospects. Attached Figure Description

[0068] Figure 1 This is a schematic diagram of the system model;

[0069] Figure 2 These are mean squared error plots under different algorithms, comparing the following schemes: L1 norm algorithm, among which...

[0070] Detailed Implementation

[0071] The present invention will be further described below with reference to the accompanying drawings.

[0072] A method for estimating the angle of arrival (Angle of Arrival) of users with intelligent reflectors in a multi-carrier ISAC system is proposed. U users to be estimated transmit known OFDM pilot signals. The BBU pool processes the received signals from each receiving RRH. By utilizing the shared angle information across all subcarriers and employing the atomic norm minimization method, the Angle of Arrival of the users to each IRS is estimated. The specific steps are as follows:

[0073] 1.1) As Figure 1 As shown, the IRS-assisted user angle-of-arrival estimation system of the multi-carrier communication sensing integrated system includes a BBU pool, P RRHs, and J IRSs. Information is transmitted between the BBU pool and each RRH via a wired fronthaul link. Each receiving RRH is equipped with N... B A uniform linear antenna array (ULA) consisting of N antennas is responsible for sensing the target user's angle information. A passive IRS consists of N... I It consists of several reflection units. The BBU pool is known to receive the location information of the line-of-sight (LOS) channel from RRH to IRS. The user and RRH are blocked, and there are non-line-of-sight (NLOS) channels between the user and IRS and between IRS and RRH.

[0074] 1.2) Each frame is divided into two parts: the first T... POne time slot constitutes the uplink pilot subframe, dedicated to acquiring angle information, while the remaining TT... p Time slots constitute downlink subframes for data transmission. A comb pilot pattern is applied for uplink angle estimation. Specifically, the total bandwidth is divided into K subcarriers, each with an index set. K P Subcarriers are selected for pilot transmission. Where Δ = K / K p This represents the pilot subcarrier spacing. On each pilot subcarrier, the user transmits different pilot symbols to achieve frequency domain distinctiveness. Simultaneously, the reflection coefficient of the intelligent reflector (IRS) is time-domain modulated in each pilot time slot, and the phase of the reflection matrix changes independently within each time slot.

[0075] 1.3) In the system, user number u has an uplink connection with the Intelligent Reflective Surface (IRS) with an L-shaped path. UI Multipath components. Considering the sparsity of millimeter-wave channels, the UE-IRS channel frequency response of the k-th subcarrier of the u-th user at the J-th IRS. The p-th received RHH comes from the IRS-BS channel frequency response at the j-th IRS. As shown below:

[0076]

[0077] Accordingly, the downlink between the IRS and the Receive Remote Radio Unit (RRH) has L IB There are multiple path routes. Among them, the lth path... UI The path from the user to the IRS is determined by the path fading coefficient. Path delay and the angle of arrival The characterization, with a sampling frequency of f s (l UI =1,2,...,L UI (j = 1, 2, ..., J).

[0078] In the IRS to RRH link, the line-of-sight (LOS) path parameters are as follows: and These represent the fading coefficient, delay, angle of arrival (AOA), and angle of departure (AOD) of the IRS to the receiving RRH line-of-sight (LOS) channel.

[0079] In addition, the l IB The non-line-of-sight (NLOS) path parameters from IRS to RRH are as follows: and These are the lth channels from the IRS to the received RRH channel.IB Fading coefficient, delay, AOA and AOD of each path IB =2,...,L IB ;j=1,2,...,J). and The number of antennas representing the response vector of the array are N and N respectively. B and N I .

[0080] The array response vector (j = 1, 2, ..., J) from the u-th user to the j-th IRS angle of arrival is:

[0081]

[0082] in This represents the angle of arrival from user u to the IRS j.

[0083] 1.4) In the IRS-BS channel, where It is the lth IB The fading coefficient from the j-th IRS to the p-th RRH under a non-line-of-sight path, (l IB =2,...,L IB )

[0084] The array response vectors for the p-th RRH arrival angle and the j-th IRS departure angle are:

[0085]

[0086] Where, d RRH d represents the distance between two adjacent antennas of RRH. IRS λ represents the distance between two adjacent reflective elements of the IRS; λ represents the carrier wavelength. and Let these represent the departure angle and arrival angle from the j-th IRS to the p-th RRH, respectively; where Let represent the reflection coefficient matrix of the IRS in time slot t, where and Let represent the phase shift of the i-th reflection unit in the t-th time slot. The pilot signals transmitted by u users in the t-th time slot are defined as follows: at last It is additive white Gaussian noise, σ 2 Indicates IRS noise power. It is the identity matrix;

[0087] 1.5) The signal of the k-th subcarrier received in the p-th RRH of the t-th time slot

[0088]

[0089] in This represents the channel length s of the k-th subcarrier along the path from the u-th user to the j-th IRS. u,t This represents the pilot signal transmitted by the u-th user in the t-th time slot, v k,t H represents the noise generated by the signal in the k-th subcarrier of the t-th time slot. IB,j,p,k It includes the line-of-sight and non-line-of-sight paths of the signal reaching the RRH after reflection from the IRS, and is expressed in the following form:

[0090]

[0091] The entire system can be uniformly modeled as follows:

[0092]

[0093] In the system and Let represent the NLOS and LOS channel matrices of the j-th IRS to p-th RRH on the k-th subcarrier, respectively. All receiving remote radio units (RRHs) synchronously transmit their received signals to the baseband processing unit (BBU) pool via a wired fronthaul link in each time slot to achieve centralized signal processing. Specifically, for the t-th time slot, the k-th subcarrier, and the u-th user, the globally stacked signal received by the BBU pool is denoted as . It can be represented as:

[0094]

[0095] In IRS-assisted user angle of arrival estimation for a multi-carrier communication sensing integrated system, the BBU knows the location information of the IRS and the receiving RRH. Therefore, the angle information, i.e., the RRH angle of arrival, is known in the LOS channel from the IRS to the RRH. Angle of departure from IRS We need to estimate the angle of arrival from all users to all IRSs. The specific steps are as follows:

[0096] 2.1) First, the NLOS path from IRS to RRH and the user-to-IRS path are extracted separately to form a concatenated channel. The statement is as follows:

[0097]

[0098] Transformation of cascaded channels

[0099]

[0100] Where ⊙ represents the Khatri Rao product, Represents the Kronecker product. It is N B Line N B The identity matrix of columns, and Let represent the reflection coefficient matrix of the t-th time slot IRS, where This indicates that in the t-th time slot, the 1st, ..., Nth time slot... I The phase shift of each element and the channel fading coefficient can be combined into

[0101]

[0102] ο j,p The definition of

[0103]

[0104] Next, we define the composition Z. 2D,j,p Atom set A 2D,j,p (j=1,2…,J; p=1,2…,P), Z 2D,j,p It is composed of two-dimensional atom set A 2D,j,p A linearly combined matrix, where all pilot subcarriers share the same angular information, has the following expression:

[0105]

[0106] in This represents the portion required to form the 2D atomic norm, excluding the known parts.

[0107]

[0108]

[0109] The non-line-of-sight cascaded channel where the user sends a signal to the IRS and the IRS reflects it to the RRH can be written as the following expression, where let

[0110]

[0111] 2.2) The LOS path portion of the cascaded channel from the reflector to the receiving RRH, where... This represents the concatenated channel of the LOS path from the reflector to the receiving RRH, which is represented as follows:

[0112]

[0113] The BBU has known the location information of the IRS and the base station. The known information of the channel can be represented as follows:

[0114]

[0115] Define composition Z 1D,j Atom set A 1D,j (j = 1, 2, ..., J), This represents the portion required to form the 1D atomic norm, excluding the known components.

[0116]

[0117] The cascaded channel from the user sending a signal to the IRS, and the IRS reflecting it to the RRH line-of-sight path, can be written as the following expression:

[0118]

[0119] 2.3) In order to estimate the received signal The angle in the middle Formulas It can be rewritten as:

[0120]

[0121] In the formula In the middle, Γ j,p,t and W j,t These are all known, and they only relate to the angular information of the LOS path between the active IRS and the sensing RRH. This leads to the following optimization problem:

[0122]

[0123] Where x 1,j and x 2,j,p These are variables to be optimized. and The matrix to be optimized is T. To represent the 1D atomic norm using a semidefinite programming (SDP) problem, a Hermitian Tolliterz matrix is ​​used. 1D,j It is a dimension N I ×N I Toplitz matrix, T 1D It can be written as:

[0124]

[0125] in T 2D,j,p It is a second-order Toplitz matrix, which can be composed of Hermitian Toplitz matrices and Toplitz matrices.

[0126]

[0127] Where T 1D,0Denotes the Hermitian matrix for i = 1, 2, ..., N B -1,T 1D,i Let represent the Toeplitz matrix. The above DOA estimation problem is modeled as an SDP, whose objective function and constraints are convex, and therefore can be efficiently solved using standard convex optimization tools (such as the CVX framework). 2.4) After obtaining the optimal solution, the user's angle of incidence (DOA) information can be extracted by eigenvalue decomposition or spectral estimation of the optimal Toeplitz matrix. Commonly used methods include: Vandermonde structure decomposition or the Root-MUSIC algorithm, which estimates the DOA by finding the roots of the null space polynomial of the optimal Toeplitz matrix.

[0128] like Figure 2 As shown, the algorithm of this invention significantly outperforms the L1 norm method under different signal-to-noise ratios and different numbers of pilots. Especially under low signal-to-noise ratios and fewer pilots, the algorithm of this invention still maintains a low RMSE, demonstrating higher robustness and estimation accuracy. This indicates that the algorithm of this invention represents a significant technological advancement in DOA estimation, has lower dependence on system pilot resources, and is more suitable for applications in complex real-world environments.

Claims

1. A method for estimating the angle of arrival (Angle of Arrival) of users with intelligent reflectors in a multi-carrier ISAC system, characterized in that: U users to be estimated transmit known OFDM pilot signals; the BBU pool processes the received signals from each receiving RRH; the angle of arrival of the users to each IRS is estimated by utilizing the shared angle information of all subcarriers and then by using the atomic norm minimization method; the specific steps are as follows: 1.1) The IRS-assisted user angle-of-arrival estimation system of the multi-carrier communication sensing integrated system includes a BBU pool, P RRHs, and J IRSs; information is transmitted between the BBU pool and each RRH via a wired fronthaul link, and each receiving RRH is equipped with N... B A uniform linear antenna array (ULA) consisting of N antennas is responsible for sensing the target user's angle information; a passive IRS consists of N I It consists of a reflection unit; the BBU pool is known to receive the location information of the line-of-sight (LOS) channel from RRH to IRS. The user and RRH are blocked, and there are non-line-of-sight (NLOS) channels between the user and IRS and between IRS and RRH. 1.2) Each frame is divided into two parts: the first T... P One time slot constitutes the uplink pilot subframe, dedicated to acquiring angle information, while the remaining TT... p Time slots constitute downlink subframes for data transmission; a comb pilot pattern is applied for uplink angle estimation. Specifically, the total bandwidth is divided into K subcarriers, which have an index set. K P Subcarriers are selected for pilot transmission, where Δ = K / K p Indicates the pilot subcarrier spacing; On each pilot subcarrier, the user transmits different pilot symbols to achieve frequency domain identification. Meanwhile, the reflection coefficient of the intelligent reflector surface IRS is time-domain tuned in each pilot time slot, and the phase of the reflection matrix changes independently in each time slot. 1.3) In the system, the user ID is u, and there is an uplink L between the user and the intelligent reflective surface IRS. UI Multipath components; considering the sparsity of millimeter-wave channels, the UE-IRS channel frequency response of the k-th subcarrier of the u-th user at the J-th IRS. The p-th received RHH comes from the IRS-BS channel frequency response at the j-th IRS. As shown below: Accordingly, the downlink between the IRS and the receiving remote radio unit RRH has L IB Multiple paths; Among them, the lth UI The path from the user to the IRS is determined by the path fading coefficient. Path delay and the angle of arrival The characterization, sampling frequency is f s (L UI < 1,2,...,L UI (j)1,2,...,J); In the IRS to RRH link, the line-of-sight (LOS) path parameters are as follows: and These represent the fading coefficient, delay, angle of arrival (AOA), and angle of departure (AOD) of the line-of-sight (LOS) channel from the IRS to the receiving RRH. In addition, the l IB The non-line-of-sight NLOS path parameters from IRS to RRH are as follows: and These are the lth channels from the IRS to the received RRH channel. IB Fading coefficient, delay, AOA and AOD of each path IB =2,...,L IB ;j=1,2,...,J); where and The number of antennas representing the response vector of the array are N and N respectively. B and N I ; The array response vector (j = 1, 2, ..., J) from the u-th user to the j-th IRS angle of arrival is: in This represents the angle of arrival from user u to the IRS j. 1.4) In the IRS-BS channel, where It is the lth IB The fading coefficient from the j-th IRS to the p-th RRH under a non-line-of-sight path, (l IB =2,...,L IB ); The array response vectors for the p-th RRH arrival angle and the j-th IRS departure angle are: Where, d RRH d represents the distance between two adjacent antennas of RRH. IRS λ represents the distance between two adjacent reflective elements of the IRS; λ represents the carrier wavelength. and Let these represent the departure angle and arrival angle from the j-th IRS to the p-th RRH, respectively; where Let represent the reflection coefficient matrix of the IRS in time slot t, where and The phase shift of the i-th reflection unit in the t-th time slot is represented; the pilot signals transmitted by u users in the t-th time slot are defined as... at last It is additive white Gaussian noise, σ 2 Indicates IRS noise power. It is the identity matrix; 1.5) The signal of the k-th subcarrier received in the p-th RRH of the t-th time slot: in This represents the channel length s of the k-th subcarrier along the path from the u-th user to the j-th IRS. u,t This represents the pilot signal transmitted by the u-th user in the t-th time slot, v k,t H represents the noise generated by the signal in the k-th subcarrier of the t-th time slot. IB,j,p,k It includes the line-of-sight and non-line-of-sight paths of the signal reaching the RRH after reflection from the IRS, and is expressed in the following form: The entire system is modeled as follows: In the system and Let represent the NLOS and LOS channel matrices of the j-th IRS to p-th RRH on the k-th subcarrier, respectively; all receiving remote radio units (RRHs) synchronously transmit the received signals to the baseband processing unit (BBU) pool via a wired fronthaul link in each time slot to achieve centralized signal processing; specifically, for the t-th time slot, the k-th subcarrier, and the u-th user, the global stacked signal received by the BBU pool is denoted as . Represented as:

2. The method for estimating the angle of arrival of a user with an intelligent reflector-assisted method in a multi-carrier ISAC system according to claim 1, characterized in that, In the IRS-assisted user angle of arrival estimation system of the multi-carrier communication sensing integrated system, the BBU knows the location information of the IRS and the receiving RRH, so the angle information, i.e., the RRH angle of arrival, is known in the LOS channel from the IRS to the RRH. Angle of departure from IRS We need to estimate the angle of arrival from all users to all IRSs. The specific steps are as follows: 2.1) First, the NLOS path from IRS to RRH and the user-to-IRS path are extracted separately to form a concatenated channel. The statement is as follows: Transform the cascaded channel: Where ⊙ represents the Khatri Rao product, Represents the Kronecker product. It is N B Line N B The identity matrix of columns, and Let represent the reflection coefficient matrix of the t-th time slot IRS, where This indicates that in the t-th time slot, the 1st, ..., Nth time slot... I The phase shift of each element and the channel fading coefficient are combined into ο j,p The definition of is: Next, we define the composition Z. 2D,j,p Atom set A 2D,j,p (j=1,2…,J; p=1,2…,P), Z 2D,j,p It is composed of two-dimensional atom set A 2D,j,p A linearly combined matrix, where all pilot subcarriers share the same angular information, has the following expression: in This represents the portion required to form the 2D atomic norm, excluding the known portion. The non-line-of-sight cascaded channel where the user sends a signal to the IRS and the IRS reflects it to the RRH can be expressed as follows, where let 2.2) The LOS path portion of the cascaded channel from the reflector to the receiving RRH, where... This represents the concatenated channel of the LOS path from the reflector to the receiving RRH, which is represented as follows: The BBU has known the location information of the IRS and the base station. The known information of the channel is represented as follows: Define composition Z 1D,j Atom set A 1D,j (j = 1, 2, ..., J), This represents the portion required to form the 1D atomic norm, excluding the known components. The cascaded channel from the user sending a signal to the IRS, and the IRS reflecting it to the RRH line-of-sight path, can be written as the following expression: 2.3) In order to estimate the received signal The angle in the middle Formula Rewritten as: In the formula In the middle, Γ j,p,t and W j,t All of these are known, and they only relate to the active IRS reflection matrix and the angular information of the LOS path between the active IRS and the sensing RRH; this leads to the following optimization problem: Where x 1,j and x 2,j,p These are variables to be optimized. and The matrix to be optimized is T. To represent the 1D atomic norm using the semidefinite programming problem SDP, a Hermitian Tolliterz matrix is ​​used. 1D,j It is a dimension N I ×N I Toplitz matrix, T 1D Written as: in T 2D,j,p It is a second-order Toplitz matrix, which consists of a Hermitian Toplitz matrix and a Toplitz matrix: Where T 1D,0 Denotes the Hermitian matrix for i = 1, 2, ..., N B -1,T 1D,i Represents the Toplitz matrix; The above DOA estimation problem is modeled as an SDP, whose objective function and constraints are convex, and therefore can be solved efficiently using standard convex optimization tools. 2.4) After obtaining the optimal solution, the user's angle of incidence (DOA) information can be extracted by eigenvalue decomposition or spectral estimation of the optimal Toeplitz matrix.

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