A method and apparatus for optimizing beamforming, an electronic device, and a storage medium

Abstract

Embodiments of the application disclose a beamforming optimization method and device, electronic equipment and storage medium, and relate to the technical field of wireless communication and radar perception, wherein the method comprises: constructing a multi-stream transmission signal model, establishing a communication user signal-to-interference-and-noise ratio expression and a low-altitude target echo signal model, performing vector stacking on echo observation to construct an equivalent perception matrix, using partial derivatives of each to-be-estimated parameter to construct a Fisher information matrix, taking the trace of the inverse matrix thereof as an optimization target, under power and communication constraints, introducing a semi-positive definite relaxation to replace the outer product of the beam vector with a semi-positive definite matrix variable, introducing an auxiliary matrix variable and converting the matrix inverse constraint into a linear matrix inequality through a Shur complement transformation, solving by a solver, performing eigenvalue decomposition on the output semi-positive definite matrix, and restoring each beamforming vector. The application solves the problems that the evaluation index in the prior art is difficult to guide fine beam design and lacks collaborative optimization of communication and perception.

Description

Technical Field

[0001] This invention relates to the fields of wireless communication and radar sensing technology, and in particular to a beamforming optimization method, apparatus, electronic device, and storage medium. Background Technology

[0002] With the booming development of the low-altitude economy, low-altitude applications such as drone logistics, urban air traffic, and emergency rescue are rapidly being implemented, leading to a surge in the number of low-altitude aircraft and increasingly complex airspace. Low-altitude communication and sensing capabilities have become core technological supports for ensuring low-altitude flight safety and achieving efficient airspace management. Integrated communication and sensing, as a key technology direction for future wireless networks, can integrate communication data transmission and target sensing functions on a unified hardware platform, sharing spectrum and antenna resources, thus becoming an effective way to address communication assurance and target monitoring needs in low-altitude scenarios. Against this backdrop, how to simultaneously serve communication users and sensing targets through beamforming technology has become a core issue in the design of integrated low-altitude communication and sensing systems.

[0003] However, existing beamforming methods for integrated low-altitude communication and sensing still face many limitations. Traditional solutions typically use radar receiver signal-to-noise ratio (SNR), signal-to-interference-plus-noise ratio (SINR), or beam pattern matching error as performance evaluation indicators. While these indicators can reflect the strength of target echo energy or beam pointing effect, their physical meaning is concentrated at the energy level, making it difficult to intuitively characterize the actual estimation accuracy of multi-dimensional parameters such as azimuth, elevation, range, and velocity of low-altitude targets. In multi-target, multi-parameter joint sensing scenarios, there is coupling between different target echoes and correlation between different parameters. Relying solely on SNR indicators cannot accurately characterize multi-dimensional parameter estimation errors, nor can it guide the system in refined beam design under limited power and antenna degrees of freedom. Furthermore, low-altitude targets typically exhibit three-dimensional maneuvering characteristics, with their position and velocity changing rapidly over time, placing high demands on the system's angle, range, and velocity resolution capabilities. Traditional energy-oriented beam design methods are insufficient to meet the high-precision sensing requirements.

[0004] Meanwhile, in integrated communication and sensing systems, communication data streams and sensing detection streams share the same transmit power and array spatial degrees of freedom. Improving communication service quality typically reduces the resources available to the sensing target, leading to a decrease in sensing accuracy, and a significant resource competition exists between communication and sensing. Traditional methods lack a system framework for synergistic optimization of both, making it difficult to effectively improve sensing performance while ensuring communication quality.

[0005] Therefore, there is an urgent need for a beamforming optimization method that integrates communication and sensing, is guided by the accuracy of sensing parameter estimation, takes into account the constraints of communication service quality, and is applicable to low-altitude multi-target scenarios. Summary of the Invention

[0006] The embodiments of this invention provide a beamforming optimization method to address the problems of existing technology evaluation indicators being insufficient to guide refined beam design and lacking coordinated optimization of communication and sensing. The technical solution is as follows: According to one aspect of the present invention, a beamforming optimization method is provided, the method comprising: spatially weighting OFDM transmit symbol vectors using a beamforming matrix to form a multi-antenna transmit signal; each column of the beamforming matrix corresponds to a beamforming vector of a data stream on a certain subcarrier; the data stream includes sensing and communication data streams; independently applying a beamforming vector to each data stream, establishing a signal-to-interference-plus-noise ratio (SINR) expression with the power of the desired communication beam signal arriving at the user in the received signal as the numerator and the sum of the interference power and noise power of all other data streams arriving at the user in the received signal as the denominator; converting the round-trip propagation delay determined by the target distance into the time delay phase on each subcarrier, converting the Doppler frequency shift determined by the target radial velocity into the Doppler phase between each OFDM symbol, determining the spatial phase between each element of the uniform array using the target azimuth and elevation angles, and establishing mapping relationships with corresponding target parameters respectively; multiplying the time delay phase, Doppler phase, and spatial phase to obtain a complex exponential phase factor, and multiplying the phase factor sequentially by the target dispersion... The transmitted signal and base station transmitted signal are additively superimposed with received noise to obtain a single-target echo signal model with azimuth, elevation, range, and velocity as parameters to be estimated. Based on the single-target echo signal model, equivalent sensing matrices are constructed by vector stacking of sensing echo observations from multiple subcarriers, multiple OFDM symbols, and multiple array elements. Based on the multi-stream transmitted signal model and the equivalent sensing matrix, a Cramer-Rao lower bound matrix is ​​constructed to obtain the optimization target. Target constraints are constructed based on the signal-to-interference-plus-noise ratio expression and the beamforming matrix. The target constraints are transformed into trace form with respect to the semi-definite matrix variables by introducing positive semi-definite matrix variables to replace the beam vector cross product. The optimization target is transformed into a linear matrix inequality by introducing auxiliary matrix variables and Schur complement transformation. The linear matrix inequality is numerically solved using a semi-definite programming solver to obtain the positive semi-definite matrices corresponding to each data stream of each subcarrier. The positive semi-definite matrices are then decomposed into eigenvalues, and the largest eigenvalue and corresponding eigenvector are used to recover the beamforming vectors. These are combined to obtain the beamforming matrix for each subcarrier.

[0007] In one embodiment, the equivalent sensing matrix is ​​constructed by vector stacking of sensing echo observations from multiple subcarriers, multiple OFDM symbols, and multiple array elements based on the single-target echo signal model through the following steps: The single-target echo signal corresponding to each low-altitude sensing target is treated as an independent target unit, arranged sequentially according to the target order. Each target unit contains all observation data of the target on all subcarriers, all symbols, and all array elements, resulting in a target block. Within each target block, the echo observation data on all subcarriers are arranged in subcarrier order, and the echo observation data on all OFDM symbols are arranged in symbol order, so that the time delay phase is arranged along the subcarrier direction and the Doppler phase is arranged along the symbol direction to form a matrix block. In the observation data corresponding to each subcarrier and each symbol, the echo signals received by all array elements are arranged in array element order, so that the spatial phase is arranged along the array element direction, carrying azimuth and elevation angle information. The target blocks and matrix blocks are combined to construct an equivalent sensing matrix.

[0008] In one embodiment, the optimization objective is obtained by constructing a Cramer-Rao lower bound matrix based on each parameter to be estimated according to the multi-stream transmitted signal model and the equivalent sensing matrix through the following steps: The partial derivatives of the parameters to be estimated are obtained by taking the partial derivatives of the equivalent sensing matrix; the partial derivative matrices are multiplied and traced with the target scattering coefficient matrix and the transmitted signal correlation matrix respectively, and then summed to obtain the Fischer information matrix; the parameters to be estimated include the azimuth, elevation, range, and radial velocity of each target; the Fischer information matrix is ​​inverted to obtain the Cramer-Rao lower bound matrix; the sum of all diagonal elements of the Cramer-Rao lower bound matrix is ​​taken as the optimization objective; the diagonal elements of the Cramer-Rao lower bound matrix correspond to the theoretical lower bound of the estimation error of each parameter to be estimated.

[0009] In one embodiment, a target constraint is constructed based on the signal-to-interference-plus-noise ratio (SINR) expression and the beamforming matrix. This target constraint is transformed into a trace form with respect to the SINR by introducing positive semi-definite matrix variables to replace the beam vector cross product. An auxiliary matrix variable and a Schur complement transformation are then introduced to transform the optimization objective into a linear matrix inequality. This is achieved through the following steps: the total transmit power of the base station is expressed as the sum of the squares of the Frobenius norms of the beamforming matrices on all subcarriers, with a power constraint of not exceeding the maximum transmit power; the SINR of each communication user on each subcarrier is not lower than a preset threshold, with the beamforming matrix as the variable. The original optimization problem is constructed; the outer product of each beamforming vector and its conjugate transpose is replaced with a positive semi-definite matrix variable and the rank-one constraint is removed. The power constraint is transformed into the sum of the traces of all positive semi-definite matrix variables not being greater than the maximum transmit power. The communication constraint is transformed into an inequality between the traces of the product of the channel matrix and the corresponding positive semi-definite matrix variable. A first auxiliary matrix variable is introduced, and the optimization objective is replaced by the positive semi-definite constraint of the Fischer information matrix and the first auxiliary matrix variable. A second auxiliary matrix variable is introduced, and the optimization objective is transformed into minimizing the trace of the second auxiliary matrix by using the Schur complement transformation.

[0010] In one embodiment, the linear matrix inequality is numerically solved using a semidefinite programming solver to obtain the positive semidefinite matrix corresponding to each data stream on each subcarrier. The positive semidefinite matrix is ​​then subjected to eigenvalue decomposition, and the largest eigenvalue and its corresponding eigenvector are used to recover the beamforming vectors of each subcarrier. The beamforming matrix of each subcarrier is obtained by combining these vectors through the following steps: the linear matrix inequality is input into the semidefinite programming solver for numerical iterative calculation, ensuring that the solver minimizes the trace of the second auxiliary matrix while satisfying the power constraints, communication constraints, and positive semidefinite constraints. The solver then outputs the beamforming matrix for each data stream on each subcarrier. The optimal solution for the corresponding positive semidefinite matrix variable is obtained; each optimal solution is decomposed into an eigenvalue matrix, an eigenvalue diagonal matrix, and the product of the conjugate transpose of the eigenvectors, and the maximum eigenvalue and its corresponding eigenvector are extracted. The square root of the maximum eigenvalue is multiplied by the eigenvector to recover the physical transmittable beamforming vectors of the corresponding subcarrier and data stream; the beamforming vectors recovered from all data streams on the same subcarrier are arranged in the order of data stream index and combined to form the complete beamforming matrix of the corresponding subcarrier; the beamforming matrix is ​​used by the base station to perform amplitude and phase weighting on the transmitted signals of each antenna.

[0011] According to one aspect of the present invention, a beamforming optimization apparatus includes: a system model building module, configured to perform beamforming matrix weighting on OFDM transmit symbol vectors using a uniform array antenna to construct a multi-stream transmit signal model including sensing and detection symbols and communication data symbols; establish a signal-to-interference-plus-noise ratio (SINR) expression based on the communication user channel response; and establish a single-target echo signal model based on echo delay phase, Doppler phase, and spatial phase; and a sensing index construction module, configured to construct an equivalent sensing matrix by vector stacking of sensing echo observations of multiple subcarriers, multiple OFDM symbols, and multiple array elements based on the single-target echo signal model; and construct an equivalent sensing matrix based on the multi-stream transmit signal model and the equivalent sensing matrix using various parameters to be estimated. The optimization objective is obtained by constructing a Cramer-Rao lower bound matrix. An optimization problem transformation module is used to construct target constraints based on the signal-to-interference-plus-noise ratio (SINR) expression and the beamforming matrix. The target constraints are transformed into trace form with respect to the SINR matrix variables by introducing positive semi-definite matrix variables to replace the beam vector cross product. An auxiliary matrix variable and a Schur complement transformation are introduced to transform the optimization objective into a linear matrix inequality. A beam matrix recovery module is used to numerically solve the linear matrix inequality using a semi-definite programming solver to obtain the positive semi-definite matrix corresponding to each data stream of each subcarrier. Eigenvalue decomposition is performed on the positive semi-definite matrix, and the largest eigenvalue and corresponding eigenvector are taken to recover each beamforming vector. These are then combined to obtain the beamforming matrix for each subcarrier.

[0012] According to one aspect of the present invention, an electronic device includes at least one processor and at least one memory, wherein computer-readable instructions are stored in the memory; the computer-readable instructions are executed by one or more of the processors to cause the electronic device to implement the beamforming optimization method as described above.

[0013] According to one aspect of the invention, a storage medium stores computer-readable instructions thereon, which are executed by one or more processors to implement the beamforming optimization method as described above.

[0014] The beneficial effects of the technical solution provided by this invention are: In the above technical solution, this invention first constructs a multi-stream transmitted signal model containing sensing and detection symbols and communication data symbols by using a beamforming matrix weighting method on the OFDM transmitted symbol vectors in the system modeling stage, during which the signal-to-interference-plus-noise ratio (SINR) expression for communication users and the low-altitude target echo signal model are established, providing a model foundation for subsequent sensing-coordinated optimization. Based on this, an equivalent sensing matrix is ​​constructed by stacking the echo observations of multiple subcarriers, multiple OFDM symbols, and multiple array elements based on the single-target echo signal model. The Fisher information matrix is ​​constructed using the partial derivatives of the equivalent sensing matrix with respect to each parameter to be estimated. The trace of its inverse matrix, i.e., the Cramer-Rao lower bound matrix, is used as the sensing performance optimization target, achieving sensing accuracy-oriented optimization target modeling. Then, under the constraints of base station transmit power and communication user communication, the beam vector outer product is replaced with a semi-definite matrix variable by introducing a positive semidefinite relaxation variable, unifying the constraints into trace form. An auxiliary matrix variable is then introduced, and the inverse matrix constraint is transformed into a linear matrix inequality through Schur complement transformation, forming a standard semidefinite programming problem. Finally, a semidefinite programming solver is used for numerical solution. The output positive semidefinite matrix is ​​decomposed into eigenvalues, and the beamforming vectors of each subcarrier are recovered by taking the largest eigenvalue and the corresponding eigenvector. The beamforming matrix of each subcarrier is then obtained by combining them. This invention uses the Cramer-Rao lower bound as the sensing performance evaluation index, and directly incorporates the estimation accuracy of multi-dimensional parameters such as target azimuth, elevation, range, and velocity into the beamforming optimization process. Compared with the traditional energy-based index mainly based on signal-to-noise ratio, it can more accurately characterize the lower bound of parameter estimation error. At the same time, through positive semidefinite relaxation, Shure complement transformation, and eigenvalue recovery, the original non-convex problem is transformed into a solvable convex optimization form. Under the premise of ensuring the quality of service for communication users, the sensing parameter estimation error is minimized. This effectively solves the problems of existing technologies that cannot characterize the multi-dimensional parameter estimation accuracy with energy-based indexes and lack a collaborative optimization framework for sensing resource competition. It significantly improves the joint sensing accuracy and sensing collaboration capability of the low-altitude communication sensing integrated system under multi-dimensional parameters such as target azimuth, elevation, range, and velocity. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0016] Figure 1 This is a flowchart illustrating a beamforming optimization method according to an exemplary embodiment; Figure 2 This is a schematic diagram of a low-altitude integrated sensing system in an application scenario; Figure 3 yes Figure 2 A flowchart of beamforming optimization methods in the corresponding application scenarios; Figure 4 This is a schematic diagram illustrating the effectiveness verification of a beamforming system in another application scenario; Figure 5 yes Figure 4 A schematic diagram showing the relationship between the estimated RCRB and transmit power for each parameter in the corresponding application scenario; Figure 6 yes Figure 4 A schematic diagram showing the relationship between the estimated RCRB of each parameter and the communication signal-to-noise ratio constraint threshold in the corresponding application scenario; Figure 7 This is a block diagram illustrating a beamforming optimization apparatus according to an exemplary embodiment; Figure 8 This is a hardware structure diagram of an electronic device according to an exemplary embodiment; Figure 9 This is a block diagram illustrating an electronic device according to an exemplary embodiment. Detailed Implementation

[0017] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0018] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this disclosure means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or wireless coupling. The term “and / or” as used herein includes all or any units and all combinations of one or more associated listed items.

[0019] This invention provides a beamforming optimization method that drives beamforming optimization through the Cramer-Rao lower bound. It directly uses the estimation accuracy of multi-dimensional parameters such as azimuth, elevation, range, and velocity of low-altitude targets as the optimization objective, achieving a precise improvement in sensing performance under communication service quality constraints. This solves the problems of traditional methods, where energy-based indicators cannot characterize parameter estimation accuracy and where there is a lack of a collaborative optimization framework for sensing resource competition. This beamforming optimization method is applicable to beamforming optimization devices, which can be electronic devices. The beamforming optimization method in this invention can be applied to various scenarios, such as integrated beamforming optimization for low-altitude communication and sensing.

[0020] Uniform Planar Array (UPA) antennas are antenna array systems formed by arranging multiple antenna elements in a plane at equal intervals. Simply put, it involves arranging many small antennas, like chess pieces, evenly and neatly in both the horizontal and vertical directions on a plane. A "3×3 uniform planar array" represents 3 horizontal and 3 vertical antennas, for a total of 9 antennas. It is used to achieve three-dimensional beam pointing: unlike linear arrays which can only swing horizontally, planar arrays have degrees of freedom in both the horizontal (azimuth) and vertical (elevation) directions. This is crucial for monitoring low-altitude aircraft, as drones may be either horizontally to the side of the base station or diagonally above it; it also provides spatial phase difference: when the transmitted signal reaches a low-altitude target, due to the different positions of the target relative to each antenna in the array, the echo will generate a fixed spatial phase difference between different array elements. This phase difference contains the target's azimuth and elevation angle information.

[0021] OFDM Transmitted Symbol Vector: In an Orthogonal Frequency Division Multiplexing (OFDM) system, the transmitted symbol vector is a complex numerical array consisting of multiple parallel data streams at a specific time (within one OFDM symbol period) and on a specific subcarrier.

[0022] Frequency domain resource block: OFDM systems divide the entire bandwidth into a large number of orthogonal subcarriers. A data symbol can be transmitted independently on each subcarrier. Simultaneously, the time domain is divided into multiple OFDM symbols. Therefore, the transmitted signal is a three-dimensional resource block (subcarrier × time symbol × antenna). Used to achieve integrated sensing and communication: Traditional systems either transmit data or probe waves. This invention concatenates sensing and communication symbols into the same vector, enabling a single transmission to both transmit information and detect targets—the foundation for achieving "integration."

[0023] Establishing a time-delay-frequency mapping: The target's distance causes a delay in echo arrival time, which in OFDM translates into a linear phase difference between subcarriers (time-delay phase); the target's velocity (Doppler shift) translates into a phase difference between OFDM symbols (Doppler phase). Therefore, this vector is constructed to subsequently use phase information to deduce the target's distance and velocity.

[0024] The beamforming matrix acts like a "signal distributor," assigning different amplitudes and phases to each data stream in the OFDM symbol vector (e.g., probe stream 1, communication stream 2), and then mapping it onto each antenna of the array. In this way, the final synthesized electromagnetic wave beam simultaneously meets the needs of communication and sensing in three dimensions: space (pointing to the target), frequency (for subcarriers), and time (for symbols).

[0025] Please see Figure 1 This invention provides a beamforming optimization method applicable to electronic devices.

[0026] In the following method embodiments, for ease of description, the execution subject of each step of the method is an electronic device, but this does not constitute a specific limitation.

[0027] like Figure 1 As shown, the method may include the following steps: Step 110: The OFDM transmitted symbol vector is weighted by beamforming matrix through a uniform array antenna to construct a multi-stream transmitted signal model containing sensing and detection symbols and communication data symbols. The signal-to-interference-plus-noise ratio expression is established based on the communication user channel response. The single-target echo signal model is established based on the echo delay phase, Doppler phase and spatial phase.

[0028] In one possible implementation, the OFDM transmit symbol vector is spatially weighted by a beamforming matrix to form a multi-antenna transmit signal. A beamforming vector is applied independently to each data stream. The signal-to-interference-plus-noise ratio (SINR) expression is established by using the power of the desired communication beam signal arriving at the user in the received signal as the numerator and the sum of the interference power and noise power of all other data streams arriving at the user in the received signal as the denominator.

[0029] In one possible implementation, the round-trip propagation delay is determined by the target distance and converted into the time delay phase on each subcarrier; the Doppler frequency shift is determined by the target radial velocity and converted into the Doppler phase between each OFDM symbol; the spatial phase between each element of the uniform array is determined by the target azimuth and elevation angles, and mapping relationships with the corresponding target parameters are established respectively; the time delay phase, Doppler phase, and spatial phase are multiplied to obtain a complex exponential phase factor; the phase factor is multiplied by the target scattering coefficient and the base station transmitted signal in sequence, and then the received noise is additively superimposed to obtain a single-target echo signal model with azimuth, elevation angle, distance, and velocity as the parameters to be estimated.

[0030] Each column of the beamforming matrix corresponds to the beamforming vector of a data stream on a certain subcarrier; the data stream includes sensing and communication data streams.

[0031] Specifically, the base station uses an OFDM signaling system for downlink transmission, configured with uniform array antennas. The total number of antennas is the product of the number of array elements in both directions, and the element spacing is half a wavelength to avoid grating lobes. The base station's transmit symbol vector on each subcarrier and each OFDM symbol consists of multiple sensing and detection symbols and multiple communication data symbols. The total number of data streams is the sum of the number of sensing and detection streams and the number of communication data streams. The transmit symbol vectors are spatially weighted using a beamforming matrix to form a multi-antenna transmit signal; each column of the beamforming matrix corresponds to the beamforming vector of one data stream on a certain subcarrier. This model establishes the beamforming vector as the core variable for subsequent optimization, enabling the same transmit signal to simultaneously carry communication data and sensing / detection functions.

[0032] Furthermore, for each communication user, there is an equivalent downlink channel vector on each subcarrier, representing the propagation characteristics between the base station's antennas and the user. The received signal of this user includes not only the desired communication data stream, but also other communication data streams and all sensing and detection streams. These undesired data streams will all cause co-channel interference to this user. Using the signal power of the desired communication beam reaching the user as the numerator, and the sum of the interference power and noise power of all other data streams reaching the user as the denominator, a signal-to-interference-plus-noise ratio (SINR) expression is established. This expression quantifies the quality of service into mathematical constraints that can be substituted into the optimization solution, and is used to construct subsequent constraint conditions.

[0033] Furthermore, for each low-altitude sensing target, the round-trip propagation delay is determined by the target distance and converted into the time delay phase on each subcarrier; the Doppler frequency shift is determined by the target radial velocity and converted into the Doppler phase between each OFDM symbol; and the spatial phase between each element of the uniform array is determined by the target azimuth and elevation angles. Mapping relationships between these three phases and their corresponding target parameters are established. The time delay phase, Doppler phase, and spatial phase are multiplied to obtain a complex exponential phase factor, which is then multiplied sequentially by the target scattering coefficient and the base station transmitted signal, and finally additively superimposed with the received noise. This yields a single-target echo signal model with azimuth, elevation, distance, and velocity as the parameters to be estimated. Through this modeling, the target's physical parameters are uniformly mapped to the phase characteristics of the echo signal.

[0034] In the above process, the embodiments of the present invention unify communication and sensing within the OFDM transmission signal framework, enabling a single beamforming matrix to simultaneously carry communication data and sensing detection functions, providing a system model foundation for integrated communication and sensing, and realizing the mathematical descriptivity of subsequent optimization problems.

[0035] Step 120: Based on the single-target echo signal model, construct an equivalent sensing matrix by vector stacking of sensing echo observations of multiple subcarriers, multiple OFDM symbols, and multiple array elements. Based on the multi-stream transmitted signal model and the equivalent sensing matrix, construct the Cramer-Rao lower bound matrix based on each parameter to be estimated to obtain the optimization target.

[0036] In one possible implementation, the single-target echo signal corresponding to each low-altitude sensing target is treated as an independent target unit, arranged sequentially according to the target order. Each target unit contains all observation data of the target on all subcarriers, all symbols, and all array elements, resulting in target blocks. Within each target block, the echo observation data on all subcarriers are arranged in subcarrier order, and the echo observation data on all OFDM symbols are arranged in symbol order, so that the time delay phase is arranged along the subcarrier direction and the Doppler phase is arranged along the symbol direction to form matrix blocks. In one possible implementation, in the observation data corresponding to each subcarrier and each symbol, the echo signals received by all array elements are arranged in array element order, so that the spatial phase is arranged along the array element direction, carrying azimuth and elevation angle information, and the target block and matrix block are combined to construct an equivalent sensing matrix.

[0037] In one possible implementation, the partial derivatives of the parameters to be estimated are obtained by taking the partial derivatives of the equivalent sensing matrix. The partial derivative matrices are then multiplied and traced with the target scattering coefficient matrix and the transmitted signal correlation matrix, respectively, and summed to obtain the Fischer information matrix. The Fischer information matrix is ​​then inverted to obtain the Cramer-Rao lower bound matrix. The sum of all diagonal elements of the Cramer-Rao lower bound matrix is ​​taken as the optimization objective.

[0038] In this context, the diagonal elements of the Cramerlow lower bound matrix correspond to the theoretical lower bounds of the estimation errors of each parameter to be estimated; the parameters to be estimated include the azimuth, elevation, range, and radial velocity of each target, etc., which are not specified here.

[0039] Specifically, the echo signal of each low-altitude sensing target is treated as an independent target unit, arranged sequentially according to target order. Each target unit contains all observation data of that target across all subcarriers, all symbols, and all array elements, resulting in target blocks. Within each target block, the echo data on all subcarriers are arranged in subcarrier order, with the time delay phase aligned along the subcarrier direction; the echo data on all OFDM symbols are arranged in symbol order, with the Doppler phase aligned along the symbol direction. In the observation data corresponding to each subcarrier and each symbol, the echo signals received by all array elements are arranged in array element order, with the spatial phase aligned along the array element direction, carrying azimuth and elevation angle information. Through the sequential stacking of these three dimensions, a complete equivalent sensing matrix containing observation data of all targets, all subcarriers, all symbols, and all array elements is constructed, integrating the scattered time-domain, frequency-domain, and spatial-domain observation data into a unified structured mathematical object.

[0040] Furthermore, partial derivative matrices are obtained by taking the partial derivatives of the equivalent sensing matrix for each parameter to be estimated, including the azimuth, elevation, range, and radial velocity of each target. Each partial derivative matrix is ​​then multiplied and traced with the target scattering coefficient matrix and the transmitted signal correlation matrix, respectively, and summed to obtain the Fischer information matrix. The transmitted signal correlation matrix is ​​formed by stacking the multi-stream transmitted signals on each subcarrier, and the transmitted signal is obtained by multiplying the beamforming matrix by the transmitted symbol vector. Therefore, the Fischer information matrix is ​​directly related to the beamforming matrix; that is, changes in the beamforming matrix directly affect the value of the Fischer information matrix, thus affecting the sensing accuracy.

[0041] Furthermore, matrix inversion is performed on the Fischer information matrix to obtain the Cramer-Rao lower bound matrix. The diagonal elements of this matrix correspond to the theoretical lower bounds of the estimation errors of each parameter to be estimated, while the off-diagonal elements reflect the degree of coupling between different parameters. The sum of all diagonal elements of the Cramer-Rao lower bound matrix is ​​taken as the optimization objective; the smaller this value, the smaller the lower bound of the joint estimation error of all parameters to be estimated, and the higher the sensing accuracy. Compared to traditional energy-based indicators such as signal-to-noise ratio, the Cramer-Rao lower bound can directly characterize the estimation accuracy of multi-dimensional parameters. Using this indicator as the optimization objective transforms beamforming design from simply enhancing the echo energy in the target direction to a systematic optimization oriented towards the joint estimation accuracy of multi-dimensional parameters.

[0042] In the above process, the embodiments of the present invention use the Cramer-Rao lower bound of the joint estimation of multi-dimensional parameters as a measure of sensing performance, so that beamforming optimization shifts from traditional energy enhancement to optimization directly aimed at the accuracy of parameter estimation, providing an optimization target oriented towards sensing accuracy, and realizing the joint accuracy characterization of target azimuth, elevation, range and velocity.

[0043] Step 130: Construct target constraints based on the signal-to-interference-plus-noise ratio expression and beamforming matrix. Transform the target constraints into trace form with respect to the positive semi-definite matrix variables by introducing positive semi-definite matrix variables to replace the beam vector cross product. Transform the optimization objective into a linear matrix inequality by introducing auxiliary matrix variables and Schur complement transformation.

[0044] In one possible implementation, the total transmit power of the base station is expressed as the sum of the squares of the Frobenius norms of the beamforming matrices on all subcarriers. The maximum transmit power is used as a power constraint, and the signal-to-interference-plus-noise ratio (SIR) of each communication user on each subcarrier is not lower than a preset threshold as a communication constraint. The original optimization problem is constructed with the beamforming matrix as a variable.

[0045] In one possible implementation, the outer product of each beamforming vector and its conjugate transpose is replaced with a positive semi-definite matrix variable and the rank-one constraint is removed. The power constraint is transformed into the sum of the traces of all positive semi-definite matrix variables not being greater than the maximum transmit power, and the communication constraint is transformed into an inequality between the traces of the product of the channel matrix and the corresponding positive semi-definite matrix variables.

[0046] In one possible implementation, a first auxiliary matrix variable is introduced, and the optimization objective is replaced by the positive semidefinite constraint of the Fischer information matrix and the first auxiliary matrix variable. A second auxiliary matrix variable is introduced, and the optimization objective is transformed into minimizing the trace of the second auxiliary matrix by using the Schur complement transformation to construct a linear matrix inequality, thus forming a linear matrix inequality.

[0047] Specifically, the total transmit power of the base station is expressed as the sum of the squares of the Frobenius norms of the beamforming matrices on all subcarriers, with a power constraint of not exceeding the maximum transmit power; the signal-to-interference-plus-noise ratio (SIR) of each communication user on each subcarrier is not lower than a preset threshold, as a communication constraint. The original optimization problem is constructed with the objective of minimizing the trace of the Cramer-Rao lower bound matrix and the beamforming matrix as the variable. The core of this optimization problem is to minimize the theoretical error of the sensing parameter estimation by designing the beamforming matrix while satisfying the quality of service. However, this original problem is a non-convex optimization problem due to the presence of quadratic terms in the beam vector, the SIR expression structure, and matrix inverse operations, making it difficult to solve directly.

[0048] Furthermore, the outer product of each beamforming vector and its conjugate transpose is replaced with a positive semi-definite matrix variable, and the rank-one constraint is temporarily removed, relaxing the non-convex feasible region into a convex set. The power constraint is transformed into the sum of the traces of all positive semi-definite matrix variables not exceeding the maximum transmit power; the communication constraint is transformed into an inequality relationship between the traces of the product of the channel matrix and the corresponding positive semi-definite matrix variables; the transmit signal correlation terms in the Fischer information matrix are also transformed into linear combinations of each positive semi-definite matrix variable through the above substitution. All constraints are unified into a linear trace form with respect to positive semi-definite matrix variables, transforming the original non-convex problem into the prototype of a convex optimization problem.

[0049] Furthermore, a first auxiliary matrix variable is introduced, with the same dimension as the Fischer information matrix. The constraint that the first auxiliary matrix variable is a positive semi-definite matrix is ​​constructed by subtracting this constraint from the Fischer information matrix. Based on the inversion property of positive definite matrices, the trace of the Cramero lower bound matrix is ​​indirectly minimized by minimizing the trace of the inverse matrix of the first auxiliary matrix variable. A second auxiliary matrix variable is introduced, and the block linear matrix inequality constructed using the Schur complement transformation is equivalent to the second auxiliary matrix variable being no less than the inverse of the first auxiliary matrix variable. The trace of the second auxiliary matrix variable is used as the objective function. After these two transformations, the original non-convex optimization problem is transformed into a standard semi-definite programming problem.

[0050] In the above process, the embodiments of the present invention transform the non-convex problem into a convex semidefinite programming problem through positive semidefinite relaxation, and avoid the problem of solving matrix inverse operations in the objective function through Schur complement transformation. It provides a complete transformation path from the original non-convex problem to a solvable standard form, and realizes the computability of the perception performance optimization problem under the premise of ensuring the quality of communication services.

[0051] Step 140: Numerically solve the linear matrix inequalities using a semidefinite programming solver to obtain the positive semidefinite matrix corresponding to each data stream of each subcarrier. Perform eigenvalue decomposition on the positive semidefinite matrix, take the largest eigenvalue and the corresponding eigenvector to recover each beamforming vector, and combine them to obtain the beamforming matrix of each subcarrier.

[0052] In one possible implementation, the linear matrix inequality is input into a semidefinite programming solver for numerical iterative computation, so that the solver minimizes the trace of the second auxiliary matrix under the premise of satisfying power constraints, communication constraints and semidefinite constraints, and outputs the optimal solution of the semidefinite matrix variables corresponding to each data stream on each subcarrier.

[0053] In one possible implementation, each optimal solution is decomposed into an eigenvalue matrix, an eigenvalue diagonal matrix, and the product of the conjugate transpose of the eigenvectors. The largest eigenvalue and its corresponding eigenvector are extracted, and the square root of the largest eigenvalue is multiplied by the eigenvector to recover the physical transmittable beamforming vectors of the corresponding subcarriers and data streams.

[0054] In one possible implementation, the beamforming vectors recovered from all data streams on the same subcarrier are arranged sequentially according to the data stream index order and combined to form the complete beamforming matrix of the corresponding subcarrier; the beamforming matrix is ​​used by the base station to perform amplitude and phase weighting on the signals transmitted by each antenna.

[0055] Specifically, the semidefinite programming problem is input into a semidefinite programming solver for numerical iterative calculation. This allows the solver to minimize the trace of the second auxiliary matrix variable while satisfying power constraints, communication constraints, and all positive semidefinite constraints. The solver then outputs the optimal solution for the positive semidefinite matrix variable corresponding to each data stream on each subcarrier. This positive semidefinite matrix variable is a mathematical variable obtained in step three by relaxing the rank-one constraint. Its dimension is equal to the number of transmit antennas, but it is not physically usable as beam weights for base station transmission; actual transmission requires a vector form.

[0056] Furthermore, the optimal solution for each positive semi-definite matrix variable is decomposed into eigenvalues, which are then broken down into the product of an eigenvector matrix, an eigenvalue diagonal matrix, and the conjugate transpose of the eigenvectors. The largest eigenvalue and its corresponding eigenvector are extracted, and the square root of the largest eigenvalue is multiplied by the eigenvector to recover the physical transmittable beamforming vector for that subcarrier and that data stream. This recovery method is based on the fact that since the optimal solution of a positive semi-definite programming problem degenerates into the outer product of the beamforming vector and its conjugate transpose when the rank-one condition is satisfied, the eigenvector corresponding to the largest eigenvalue is the optimal beamforming direction, and its magnitude is determined by the square root of the largest eigenvalue.

[0057] Furthermore, the beamforming vectors recovered from all data streams on the same subcarrier are arranged sequentially according to the data stream index order and combined to form the complete beamforming matrix for that subcarrier. This matrix can be directly used by the base station to perform amplitude and phase weighting on the signals transmitted by each antenna, achieving optimal beam transmission for integrated communication and sensing.

[0058] In the above process, the embodiments of the present invention extract the maximum eigenvalue and the corresponding eigenvector from the semidefinite relaxation solution through eigenvalue decomposition to recover the physical beam, so that the mathematically optimal solution can be transformed into the actual transmittable beam weights without loss, providing an effective connection from theoretical optimization to engineering implementation, and realizing the deployability of the optimization results in the actual base station system.

[0059] Through the above process, this embodiment of the invention first constructs a multi-stream transmitted signal model in the system modeling stage, establishing the signal-to-interference-plus-noise ratio (SNR) expression for communication users and the echo signal model for low-altitude targets, providing a model foundation for sensing-sensing collaborative optimization. Based on this, an equivalent sensing matrix is ​​constructed by vector stacking of echo observations from multiple subcarriers, symbols, and array elements. The partial derivatives of this matrix with respect to each parameter to be estimated are used to construct a Fisher information matrix, and the trace of its inverse matrix is ​​used as the sensing performance optimization target, achieving sensing accuracy-oriented optimization target modeling. Then, under power and communication constraints, a positive semidefinite relaxation is introduced to replace the beam vector cross product with a positive semidefinite matrix variable. An auxiliary matrix variable is introduced, and the inverse matrix constraint is transformed into a linear matrix inequality through Schur complement transformation, forming a semidefinite programming problem. Finally, a solver is used to solve the problem, performing eigenvalue decomposition on the output positive semidefinite matrix and recovering each beamforming vector, combining them to obtain the beamforming matrix. This invention directly characterizes the accuracy of multidimensional parameter estimation using the Cramer-Rao lower bound. By minimizing the sensing error while ensuring communication quality through convex optimization transformation, it effectively solves the problems that traditional energy-type indicators cannot characterize parameter accuracy and lack a collaborative framework for competition of sensing resources. It significantly improves the joint sensing accuracy and sensing collaboration capability of low-altitude target azimuth, pitch, range and velocity.

[0060] like Figure 2 As shown, a system transceiver model in an application scenario is illustrated, in which an ISAC base station with a uniform array antenna simultaneously transmits downlink communication signals to communication users and transmits sensing and detection signals to low-altitude targets; the low-altitude targets generate scattered echoes from the incident signals, and the base station receives the echo signals and uses them for target parameter sensing.

[0061] The beamforming optimization method of this invention uses the Cramer-Rao lower bound as the sensing performance evaluation index. Under the conditions of satisfying the communication user service quality constraints and the base station transmit power constraints, the base station transmit beamforming matrix is ​​optimized, thereby improving the estimation accuracy of multi-dimensional parameters such as azimuth, elevation, range and velocity of low-altitude targets.

[0062] Figure 3 The flowchart illustrates the beamforming optimization process, which may include the following steps: Step 1. System Modeling Phase: Establish an integrated communication and sensing system model for low-altitude environments. The ISAC base station uses OFDM signaling for downlink transmission, transmitting signals that simultaneously include sensing and detection symbols and communication data symbols. The base station uses a uniform array antenna to beamform the transmitted signal, enabling it to serve multiple communication users while simultaneously illuminating low-altitude sensing targets and receiving their scattered echoes. Simultaneously, establish a communication user signal-to-interference-plus-noise ratio (SIR) model, a low-altitude target sensing echo model, and a multi-dimensional parameter joint sensing model for target azimuth, elevation, range, and velocity.

[0063] Step 2. Optimization Problem Formation and Transformation Stage: Based on the system model obtained in Step 1, a sensing performance evaluation index and a beamforming optimization problem are constructed. Specifically, sensing echo observations are stacked to establish an equivalent sensing matrix. Furthermore, a Fischer information matrix is ​​constructed based on the partial derivatives of the equivalent sensing matrix with respect to parameters such as target azimuth, elevation, range, and velocity. The inverse of the Fischer information matrix is ​​used as the Cramer-Rao lower bound matrix. The trace of the Cramer-Rao lower bound matrix is ​​used as the sensing performance optimization objective. Under the constraints of base station transmit power and minimum communication user communication, a beamforming optimization problem prioritizing sensing performance is formed. For the quadratic beam term and the signal-to-interference-plus-noise ratio (SIR) ratio in the original optimization problem, semi-definite relaxation variables are introduced to transform the beam vector outer product into a semi-definite matrix variable, thereby transforming the power constraint, communication constraint, and beam-related terms in the Fischer information matrix into trace form.

[0064] Step 3. In the optimization problem-solving stage, to address the issue that the Cramer-Rao lower bound matrix contains the inverse operation of the Fischer information matrix, making direct solution difficult, auxiliary matrix variables are introduced, and the Schur complement transformation is used to convert the matrix inverse constraint into a linear matrix inequality constraint. Thus, the original non-convex optimization problem, which includes communication constraints, power constraints, and sensing accuracy targets, is transformed into a solvable semidefinite programming problem, and the semidefinite programming solver is used to obtain the positive semidefinite matrix solutions corresponding to each subcarrier and each data stream.

[0065] Step 4. Beamforming Maximum Eigenvalue Recovery Stage: Based on the positive semi-definite matrix solution obtained in Step 3, the actual transmittable beamforming matrix is ​​recovered. Eigenvalue decomposition is performed on the obtained positive semi-definite matrix, and the beamforming vector is recovered by taking the maximum eigenvalue and its corresponding eigenvector. The beamforming matrix on the subcarrier is then composed of the beamforming vectors corresponding to each data stream.

[0066] Furthermore, in step 1, the base station in the... The subcarrier, the first The transmitted signal model on each OFDM symbol is: .

[0067] in, This indicates the multi-antenna transmitted signal after beamforming. Indicates the first Beamforming matrix corresponding to each subcarrier This represents the transmit symbol vector, which consists of sensing and detection symbols and communication data symbols. This indicates that the complex field, i.e., the signal, has complex values. This indicates the number of transmitting antennas (total number of array elements). This indicates that each antenna represents one signal, and K represents the total number of data streams (sensing data streams and communication data streams). The beamforming matrix can be represented as: .

[0068] in, Indicates the first On the subcarrier Beamforming vectors corresponding to the data streams, This represents the total number of sensing and detection streams and communication data streams, the number of transmitting antennas (total number of array elements), and one signal per antenna. In one specific implementation, the base station in the... The subcarrier, the first The transmit symbol vectors on each OFDM symbol are: .

[0069] in, Indicates the first Road sensing detection symbols, Indicates the first Road communication data symbols, Indicates the number of sensing probes. Indicates the number of communication data streams. The communication user in the first The signal-to-interference-plus-noise ratio (SIR) on each subcarrier can be expressed as: .

[0070] in, Indicates the first The communication user in the first Equivalent downlink channel vectors on each subcarrier Indicates the first Communication beamforming vectors corresponding to each communication user Indicates the first On the subcarrier Beamforming vectors corresponding to the data streams, This represents noise power. As shown in the model above, the received signal-to-interference-plus-noise ratio (SIR) of a communication user is not only related to their desired communication beam, but also influenced by other communication data streams and sensing / detection streams. Therefore, beamforming design needs to simultaneously consider both communication service quality and sensing / detection requirements.

[0071] Furthermore, in step 2, based on the communication signal model and sensing echo model established in step 1, sensing performance evaluation indicators and beamforming optimization problems are constructed. First, the sensing echo observations are stacked to obtain a unified sensing received signal model: .

[0072] in, For the equivalent perception matrix, This is the equivalent scattering coefficient vector for low-altitude targets. This is the stacked transmitted signal vector. Let be the noise vector. The vector of parameters to be estimated is defined as: .

[0073] in, , , and These represent the azimuth, elevation, range, and radial velocity vectors of the low-altitude target, respectively. Based on the aforementioned stacked observation model, and according to the equivalent sensing matrix... Construct the Fisher information matrix by relating the partial derivatives of the parameters to be estimated. Let: .

[0074] Then the Fisher information matrix The Line 1 Column elements can be represented as: .

[0075] in, For the correlation matrix of the transmitted signal, This represents the noise power. Therefore, the Fischer information matrix is ​​related to the transmitted signal correlation matrix, which is determined by the beamforming matrix. Thus, optimizing the beamforming matrix can improve the accuracy of sensing parameter estimation.

[0076] The lower bound matrix of Cramer-Rao is defined as: .

[0077] And its trace is used as an indicator for optimizing perception performance: .

[0078] Based on the above sensing performance indicators, a beamforming optimization problem prioritizing sensing performance is constructed: .

[0079] .

[0080] .

[0081] in, Indicates the maximum transmission power of the base station. Indicates the first The communication user in the first Minimum signal-to-interference-plus-noise ratio (SIR) threshold on each subcarrier. To address the beam quadratic term, the SIR expression structure, and the inverse operation of the Fischer information matrix in the above optimization problem, a semidefinite relaxation variable is introduced: .

[0082] By substituting this variable, the beam-related quadratic term can be transformed into trace form: .

[0083] in, Therefore, power constraints, communication constraints, and beam correlation terms in the Fischer information matrix can be uniformly transformed into semidefinite matrix variables. The trace expression provides a foundation for subsequent solutions using Schur complement transformation and semidefinite programming.

[0084] In step 3, the semidefinite relaxation optimization problem obtained in step 2 is further addressed by tackling the issue that the Cramero lower bound matrix contains the inverse operation of the Fischer information matrix, making it difficult to solve directly. Since the perception performance index can be expressed as... ,in The Fischer information matrix is ​​a matrix that contains positive semidefinite slack variables. Related. To avoid directly solving for the matrix inverse, an auxiliary matrix variable is introduced. and make them satisfied. The above constraints are used to establish a positive semi-definite relationship between the Fischer information matrix and the auxiliary matrix, thereby transforming the original Cramero lower bound objective into the optimization of the trace of the inverse of the auxiliary matrix.

[0085] Based on this, in order to further eliminate matrix inversion operations in the objective function, an auxiliary matrix variable is introduced. And using the Schur complement transformation, the following linear matrix inequality is constructed: .

[0086] in, It is an identity matrix.

[0087] Therefore, the original non-convex optimization problem formed in step 2 can be transformed into a semidefinite programming problem, with the objective function being: .

[0088] .

[0089] .

[0090] .

[0091] .

[0092] The above problem is a standard semidefinite programming problem, which can be solved using a semidefinite programming solver.

[0093] After solving, the positive semi-definite matrix solutions for each subcarrier and each data stream can be obtained: .

[0094] This serves as the basis for recovering the actual transmittable beamforming vector in the subsequent step 4.

[0095] Furthermore, in step 4, the actual transmittable beamforming matrix is ​​recovered based on the positive semi-definite matrix solution obtained in step 3. Then, eigenvalue decomposition is performed on it: .

[0096] Take the largest eigenvalue and its corresponding eigenvectors , restore the On the subcarrier Beamforming vectors corresponding to the data streams: .

[0097] The beamforming vectors corresponding to each data stream constitute the first... Beamforming matrix on each subcarrier: .

[0098] Through the above process, this invention adopts the Cramer-Rao lower bound as an evaluation index for low-altitude target perception performance, and integrates the estimation accuracy of multi-dimensional parameters such as target azimuth, elevation, range, and velocity into the beamforming optimization process. Compared with traditional perception performance evaluation methods based on received signal-to-noise ratio or beam energy distribution, this invention can more directly characterize the lower bound of parameter estimation error, enabling beamforming design to shift from simply enhancing target directional energy to optimizing parameter estimation accuracy, thereby improving the joint perception accuracy of multi-dimensional parameters for low-altitude targets. Under the premise of satisfying base station transmit power constraints and minimum communication constraints for communication users, this invention transforms the original non-convex beamforming optimization problem into a solvable semidefinite programming problem through semidefinite relaxation, trace form transformation, Shur complement transformation, and beam recovery methods, and further recovers the actual transmittable beamforming matrix. This method can improve perception performance while ensuring the quality of service for communication users, and is suitable for scenarios requiring collaborative communication and perception, such as low-altitude communication, UAV surveillance, and airspace monitoring, and has good engineering implementation value and scalability.

[0099] In an application scenario, simulation was used to verify the beneficial effects of the low-altitude communication sensing integrated beamforming optimization method provided by this invention. The simulation adopted a single-base station downlink OFDM-ISAC scenario, with the base station configured with a 3×3 uniform array antenna and the element spacing set to d=λ / 2 to avoid grating lobe generation and ensure good angular resolution. The system subcarrier spacing was set to Δf=80kHz, the number of subcarriers was M=32, the number of consecutive OFDM symbols was Ns=8, and the noise power was set to... On the communication side, Kc=2 ground communication users are set up with fixed locations and radial velocities of 1 m / s. A minimum communication constraint γm,k≥30dB is applied to each subcarrier to characterize the minimum quality of service requirements of the communication users. On the sensing side, a low-altitude target is set in the far-field region of the base station, and single-target and multi-target scenarios are considered to verify the performance of the proposed beamforming method in estimating multi-dimensional parameters such as target azimuth, elevation, range, and velocity. During the simulation, the trace of the Cramer-Rao lower bound matrix or its square root form RCRB is used as the sensing performance evaluation index. The impact of beamforming, beam optimization, transmit power budget, array size, and changes in the communication SINR threshold on the accuracy of multi-dimensional parameter estimation for low-altitude targets is analyzed in detail, thereby verifying the effectiveness and feasibility of the present invention in improving the accuracy of sensing parameter estimation under communication QoS constraints.

[0100] like Figure 4 As shown, Figure 4 (a) Figure 4 (b) Figure 4 (c) and Figure 4 Figure (d) in the figure presents the RCRB performance comparison results for four parameters—pitch angle, azimuth angle, range, and velocity—of low-altitude targets when using the CRB-driven beamforming (BF) method and when not using the beamforming method (NoBF). Figure 4 As can be seen, with the base station transmit power increasing from 20dBm to 40dBm, the RCRB corresponding to each parameter shows a significant decreasing trend. This indicates that increasing the transmit power can enhance the target echo signal quality, increase the Fischer information content, and thus reduce the lower bound of parameter estimation error. Further comparison of the BF and NoBF curves shows that, under the same transmit power conditions, the RCRB after beamforming is consistently lower than that without beamforming. This advantage remains consistent across the four parameters: elevation, azimuth, range, and velocity. This demonstrates that the beamforming method can effectively focus the transmitted energy towards the low-altitude target direction, improving the target echo gain and the accuracy of multi-dimensional parameter estimation.

[0101] like Figure 5 As shown, Figure 5 (a) Figure 5 (b) Figure 5 (c) and Figure 5Figure (d) shows the curves of RCRB variation with base station transmit power for four parameters: elevation angle, azimuth angle, range, and velocity of low-altitude targets. Figure 5 As can be seen, with the increase in transmit power from 20dBm to 40dBm, the RCRB corresponding to a single sensing user, sensing target 1, and sensing target 2 all show a continuous downward trend. This indicates that increasing the base station transmit power can enhance the target echo energy, improve the received observation signal-to-noise ratio and Fischer information content, thereby effectively reducing the lower bound of the multidimensional parameter estimation error. Further comparison of different curves shows that the RCRB in the single-sensing user scenario is consistently lower than that in the multi-target scenario. This indicates that when the system needs to simultaneously sense multiple low-altitude targets, the limited transmit power and spatial degrees of freedom need to be allocated among multiple target directions, resulting in a reduction in the effective sensing resources obtained by a single target and a corresponding decrease in parameter estimation accuracy. Meanwhile, the RCRB of sensing target 1 is generally lower than that of sensing target 2, indicating that the sensing difficulty varies for different targets due to differences in distance, spatial angle, or array response conditions. In summary, Figure 5 This indicates that increasing the transmit power can significantly improve the estimation accuracy of multi-dimensional parameters such as azimuth, elevation, range, and velocity of low-altitude targets. It also verifies the impact of beam resource allocation on sensing performance in multi-target scenarios.

[0102] like Figure 6 As shown, Figure 6 (a) Figure 6 (b) Figure 6 (c) and Figure 6 Figure (d) shows the RCRB curves of four parameters—pitch angle, azimuth angle, range, and velocity—as a function of the communication signal-to-noise ratio (SNR) constraint threshold for low-altitude targets. As can be seen from the figure, as the SNR threshold increases from 27 dB to 35 dB, the RCRB for each parameter generally shows an upward trend, indicating that the increased requirements for communication service quality put some pressure on sensing performance. This is because as the minimum SNR threshold required by communication users gradually increases, the base station needs to allocate more transmit power and spatial beam resources to the direction of communication users to meet the reliable transmission requirements of the communication link. This reduces the effective resources available for low-altitude target illumination and echo enhancement, leading to a decrease in Fischer information and an increase in the lower bound of parameter estimation error. Further comparison of different array sizes shows that the RCRB is lowest for the 5×5 array, followed by the 4×4 array, and highest for the 3×3 array, indicating that increasing the antenna array size can effectively alleviate the degradation of sensing performance under enhanced communication constraints. The reason is that a larger array size can provide more spatial degrees of freedom and higher array gain, so that while the system meets the communication SINR constraints, it can still retain a certain energy focusing capability and parameter identification capability for the sensing target. Figure 6Furthermore, it can be observed that in the higher SINR threshold region, some curves, especially those under the 3×3 array, show a more pronounced upward trend. This indicates that when antenna resources are limited and communication constraints are strict, the resource competition between communication and sensing becomes more prominent, and the degradation of sensing accuracy is more significant. In summary, this suggests a clear trade-off between the communication SINR threshold and the accuracy of multi-dimensional parameter estimation for low-altitude targets, and that increasing the array size can improve the system's sensing and communication coordination capabilities under strict communication constraints.

[0103] In summary, this invention addresses the challenge of simultaneously ensuring communication service quality and improving the accuracy of sensing parameter estimation in integrated low-altitude communication and sensing systems by proposing a beamforming optimization method based on CRB-driven beamforming. This method, grounded in an OFDM-ISAC system, utilizes spatial, frequency, and temporal information provided by uniform array antennas, subcarriers, and continuous OFDM symbols to jointly sense multi-dimensional parameters such as azimuth, elevation, range, and velocity of low-altitude targets, using RCRB as the sensing performance evaluation index. Simulation results show that, compared to schemes without beamforming, the proposed method significantly reduces the RCRB of various sensing parameters and improves the estimation accuracy of multi-dimensional parameters of low-altitude targets. As transmit power increases, target echo energy and Fischer information increase, leading to a continuous improvement in sensing performance. Furthermore, as the antenna array size increases, the system's spatial degrees of freedom and array aperture increase, further improving the estimation accuracy of parameters such as angle, range, and velocity. However, when the communication SINR threshold increases, the system needs to prioritize communication link quality, which somewhat compresses sensing performance; but larger array sizes can effectively mitigate this degradation trend. Therefore, this invention can effectively improve the accuracy of multi-dimensional parameter estimation for low-altitude targets while meeting the minimum quality of service constraints for communication users, demonstrating good communication sensing collaborative optimization capabilities and engineering application value.

[0104] The following are embodiments of the apparatus of the present invention, which can be used to execute the beamforming optimization method involved in the present invention. For details not disclosed in the embodiments of the apparatus of the present invention, please refer to the method embodiments of the beamforming optimization method involved in the present invention.

[0105] Please see Figure 7 This invention provides a beamforming optimization device 800.

[0106] The beamforming optimization device 800 includes, but is not limited to: a system model establishment module 810, a perception index construction module 830, an optimization problem transformation module 850, and a beam matrix recovery module 870.

[0107] Among them, the system model establishment module 810 is used to perform beamforming matrix weighting on the OFDM transmitted symbol vector through a uniform array antenna, construct a multi-stream transmitted signal model containing sensing and detection symbols and communication data symbols, establish a signal-to-interference-plus-noise ratio expression based on the communication user channel response, and establish a single-target echo signal model based on the echo delay phase, Doppler phase and spatial phase.

[0108] The sensing index construction module 830 is used to construct an equivalent sensing matrix by vector stacking of sensing echo observations of multiple subcarriers, multiple OFDM symbols and multiple array elements according to the single-target echo signal model. Based on the multi-stream transmitted signal model and the equivalent sensing matrix, the Cramer-Rao lower bound matrix is ​​constructed based on each parameter to be estimated to obtain the optimization target.

[0109] The optimization problem transformation module 850 is used to construct target constraints based on the signal-to-interference-plus-noise ratio expression and beamforming matrix. By introducing positive semi-definite matrix variables to replace the beam vector cross product, the target constraints are transformed into trace form with respect to positive semi-definite matrix variables. By introducing auxiliary matrix variables and Schur complement transformation, the optimization objective is transformed into a linear matrix inequality.

[0110] The beam matrix recovery module 870 is used to numerically solve the linear matrix inequality through a semidefinite programming solver to obtain the positive semidefinite matrix corresponding to each data stream of each subcarrier. The positive semidefinite matrix is ​​then decomposed into eigenvalues, and the beamforming vectors of each subcarrier are recovered by taking the largest eigenvalue and the corresponding eigenvector. The beamforming matrix of each subcarrier is then combined.

[0111] It should be noted that the beamforming optimization provided in the above embodiments is only illustrated by the division of the above functional modules. In actual applications, the above functions can be assigned to different functional modules as needed. That is, the internal structure of the beamforming optimization device will be divided into different functional modules to complete all or part of the functions described above.

[0112] Furthermore, the beamforming optimization apparatus and the beamforming optimization method provided in the above embodiments belong to the same concept, and the specific way in which each module performs its operation has been described in detail in the method embodiments, and will not be repeated here.

[0113] Figure 8 A schematic diagram of the structure of an electronic device according to an exemplary embodiment is shown.

[0114] It should be noted that this electronic device is merely an example adapted to the present invention and should not be construed as providing any limitation on the scope of use of the present invention. Furthermore, this electronic device should not be interpreted as requiring or depending on having... Figure 8 One or more components of the exemplary electronic device 2000 shown.

[0115] The hardware structure of electronic devices 2000 can vary significantly due to differences in configuration or performance, such as... Figure 8 As shown, the electronic device 2000 includes: a power supply 210, an interface 230, at least one memory 250, and at least one central processing unit (CPU) 270.

[0116] Specifically, power supply 210 is used to provide operating voltage for various hardware devices on electronic device 2000.

[0117] Interface 230 includes at least one wired or wireless network interface 231 for interacting with external devices. Of course, in other examples adapted to this invention, interface 230 may further include at least one serial-to-parallel conversion interface 233, at least one input / output interface 235, and at least one USB interface 237, etc. Figure 8 As shown, this does not constitute a specific limitation.

[0118] The memory 250 serves as a carrier for resource storage and can be a read-only memory, random access memory, disk, or optical disk, etc. The resources stored on it include the operating system 251, application programs 253, and data 255, etc., and the storage method can be temporary storage or permanent storage.

[0119] The operating system 251 is used to manage and control the various hardware devices and application programs 253 on the electronic device 2000, so as to enable the central processing unit 270 to perform calculations and processing on the massive data 255 in the memory 250. It can be Windows Server™, Mac OS X™, Unix™, Linux™, FreeBSD™, etc.

[0120] Application 253 is a computer-readable instruction based on operating system 251 that performs at least one specific task, and may include at least one module ( Figure 8 (Not shown), each module may contain computer-readable instructions for electronic device 2000. For example, the beamforming optimization device can be considered as application program 253 deployed on electronic device 2000.

[0121] Data 255 may be signal information, etc., and is stored in memory 250.

[0122] The central processing unit 270 may include one or more processors and is configured to communicate with the memory 250 via at least one communication bus to read computer-readable instructions stored in the memory 250, thereby performing operations and processing on massive amounts of data 255 stored in the memory 250. For example, a beamforming optimization method may be implemented by the central processing unit 270 reading a series of computer-readable instructions stored in the memory 250.

[0123] Furthermore, the present invention can also be implemented through hardware circuits or a combination of hardware circuits and software. Therefore, the implementation of the present invention is not limited to any specific hardware circuit, software, or combination thereof.

[0124] Please see Figure 9 This invention provides an electronic device 4000, which may include: a desktop computer, a laptop computer, a server, etc., with sensor recognition capabilities.

[0125] exist Figure 9 In this context, the electronic device 4000 includes at least one processor 4001 and at least one memory 4003.

[0126] The data interaction between the processor 4001 and the memory 4003 can be achieved through at least one communication bus 4002. This communication bus 4002 may include a path for transmitting data between the processor 4001 and the memory 4003. The communication bus 4002 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. The communication bus 4002 can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 9 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0127] Optionally, the electronic device 4000 may further include a transceiver 4004, which can be used for data interaction between the electronic device and other electronic devices, such as sending and / or receiving data. It should be noted that in practical applications, the transceiver 4004 is not limited to one type, and the structure of the electronic device 4000 does not constitute a limitation on the embodiments of the present invention.

[0128] Processor 4001 may be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this invention. Processor 4001 may also be a combination that implements computing functions, such as including one or more microprocessor combinations, a combination of a DSP and a microprocessor, etc.

[0129] The memory 4003 may be a ROM (Read Only Memory) or other type of static storage device capable of storing static information and instructions, RAM (Random Access Memory) or other type of dynamic storage device capable of storing information and instructions, or an EEPROM (Electrically Erasable Programmable Read Only Memory), CD-ROM (Compact Disc Read Only Memory) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program instructions or code in the form of instructions or data structures and accessible by the electronic device 4000, but not limited thereto.

[0130] The memory 4003 stores computer-readable instructions, and the processor 4001 can read the computer-readable instructions stored in the memory 4003 through the communication bus 4002.

[0131] The computer-readable instructions are executed by one or more processors 4001 to implement the beamforming optimization methods in the above embodiments.

[0132] Furthermore, this embodiment of the invention provides a storage medium storing computer-readable instructions, which are executed by one or more processors to implement the beamforming optimization method described above.

[0133] This invention provides a computer program product, which includes computer-readable instructions stored in a storage medium. One or more processors of an electronic device read the computer-readable instructions from the storage medium, load and execute the computer-readable instructions, thereby enabling the electronic device to implement the beamforming optimization method as described above.

[0134] Compared with related technologies, the beneficial effects of the present invention are: 1. This invention enables deep integration and resource sharing of communication and sensing functions. By using a uniform array antenna to perform beamforming matrix weighting on the transmitted symbol vector within a unified OFDM signal framework, this invention allows the same transmitted signal to simultaneously carry downlink data streams for communication users and sensing and detection streams for low-altitude targets. Without requiring additional dedicated sensing spectrum and independent hardware resources, a single system can simultaneously complete communication services and target sensing tasks, significantly improving spectrum utilization efficiency and reducing system deployment costs and energy consumption.

[0135] 2. This invention can directly improve the joint estimation accuracy of multi-dimensional parameters of low-altitude targets. By constructing an equivalent sensing matrix jointly determined by the target's azimuth, elevation, range, and velocity, and using the Cramer-Rao lower bound as a sensing performance evaluation index, this invention directly incorporates the theoretical estimation errors of the multi-dimensional parameters into the beamforming optimization objective function. Compared to traditional energy-based evaluation methods represented by receiver signal-to-noise ratio or beam pattern matching error, this invention can directly characterize the theoretical lower bounds of the estimation errors of each parameter and their mutual coupling relationships. This transforms beamforming design from simply enhancing the echo energy in the target direction to a systematic optimization oriented towards the joint estimation accuracy of multi-dimensional parameters, significantly improving the overall sensing accuracy of the four parameters: azimuth, elevation, range, and velocity of low-altitude targets.

[0136] 3. This invention can improve sensing performance while ensuring communication service quality. By simultaneously incorporating the total base station transmit power constraint and the minimum signal-to-interference-plus-noise ratio (SINR) threshold constraint for each communication user on each subcarrier into the optimization problem, and using the trace of the Cramer-Rao lower bound matrix as the optimization objective, this invention constructs a beamforming optimization framework for communication and sensing coordination. This framework can optimize the allocation of remaining power and spatial degrees of freedom resources to the low-altitude target sensing direction while ensuring the minimum service quality for all communication users. It achieves the optimal balance between communication assurance and improved sensing accuracy, effectively solving the technical problem of competition and compromise when communication and sensing share the same transmit power and array degrees of freedom.

[0137] 4. This invention possesses the complete transformation capability from non-convex optimization to a solvable standard form. By introducing positive semidefinite relaxation variables, this invention replaces the beam vector cross product with positive semidefinite matrix variables, relaxing the original non-convex optimization problem into a convex semidefinite programming problem. Furthermore, by introducing auxiliary matrix variables and utilizing the Schur complement transformation, the inverse operation of the Fischer information matrix in the objective function is converted into a linear matrix inequality constraint. Using the trace of the second auxiliary matrix variable as the objective function, a standard semidefinite programming problem is formed. This transformation process does not require additional approximation or suboptimal processing, ensuring the theoretical optimality of the solution. Moreover, the semidefinite programming solver has a mature and stable numerical implementation scheme, enabling efficient solution of practical problems at the engineering scale.

[0138] 5. This invention possesses the complete recovery capability from the theoretical optimal solution to an engineering-deployable scheme. This invention performs eigenvalue decomposition on the positive definite matrices of each subcarrier and data stream output from the semidefinite programming solution, extracts the largest eigenvalue and its corresponding eigenvector to recover each beamforming vector, and then combines them column-wise to form a complete beamforming matrix. This recovery method can accurately restore the optimal beamforming vector when the positive definite relaxation solution satisfies the rank-one condition, ensuring that the optimized solution is losslessly converted into physically transmittable actual beam weights. This allows the final subcarrier beamforming matrices to be directly deployed at the base station for actual transmission, achieving a seamless connection from theoretical optimization to engineering deployment. It should be understood that although the steps in the flowchart of the attached figures are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction for the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowchart of the attached figure may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. Their execution order is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0139] The above description is only a partial embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A beamforming optimization method, characterized in that, The method includes: The OFDM transmit symbol vector is spatially weighted by a beamforming matrix to form a multi-antenna transmit signal; each column of the beamforming matrix corresponds to the beamforming vector of a data stream on a certain subcarrier; the data stream includes sensing and communication data streams; By applying beamforming matrix weights to OFDM transmit symbol vectors using a uniform array antenna, a multi-stream transmit signal model containing sensing and detection symbols and communication data symbols is constructed. Beamforming vectors are applied independently to each data stream. The signal-to-interference-plus-noise ratio (SINR) expression is established with the power of the desired communication beam signal arriving at the user in the received signal as the numerator and the sum of the interference power and noise power of all other data streams arriving at the user in the received signal as the denominator. The round-trip propagation delay determined by the target distance is converted into the time delay phase on each subcarrier; the Doppler frequency shift determined by the target radial velocity is converted into the Doppler phase between each OFDM symbol; the spatial phase between each element of the uniform array is determined by the target azimuth and elevation angles, and mapping relationships with the corresponding target parameters are established respectively. The time delay phase, Doppler phase and spatial phase are multiplied to obtain a complex exponential phase factor. The phase factor is then multiplied by the target scattering coefficient and the base station transmitted signal in sequence, and the received noise is additively superimposed to obtain a single target echo signal model with azimuth angle, elevation angle, range and velocity as parameters to be estimated. Based on the single-target echo signal model, the sensing echo observations of multiple subcarriers, multiple OFDM symbols, and multiple array elements are vector-stacking to construct an equivalent sensing matrix. Based on the multi-stream transmit signal model and the equivalent sensing matrix, a Cramer-Rao lower bound matrix is ​​constructed based on each parameter to be estimated to obtain the optimization target. The target constraint is constructed based on the signal-to-interference-plus-noise ratio expression and the beamforming matrix. The target constraint is transformed into a trace form with respect to the positive semi-definite matrix variables by introducing positive semi-definite matrix variables to replace the beam vector cross product. The optimization objective is transformed into a linear matrix inequality by introducing auxiliary matrix variables and Schur complement transformation. The linear matrix inequalities are numerically solved using a semidefinite programming solver to obtain the positive semidefinite matrix corresponding to each data stream of each subcarrier. The positive semidefinite matrix is ​​then decomposed into eigenvalues, and the beamforming vectors of each subcarrier are recovered by taking the largest eigenvalue and the corresponding eigenvector. The beamforming matrix of each subcarrier is then obtained by combining these eigenvalues ​​and eigenvectors.

2. The beamforming optimization method as described in claim 1, characterized in that, The step of constructing an equivalent sensing matrix by vector stacking of sensing echo observations of multiple subcarriers, multiple OFDM symbols, and multiple array elements based on the single-target echo signal model includes: Each low-altitude sensing target's single-target echo signal is taken as an independent target unit and arranged sequentially according to the target order. Each target unit contains all the observation data of the target on all subcarriers, all symbols and all array elements, thus obtaining target blocks. Within each target block, the echo observation data on all subcarriers are arranged in subcarrier order, and the echo observation data on all OFDM symbols are arranged in symbol order, so that the time delay phase is arranged along the subcarrier direction and the Doppler phase is arranged along the symbol direction to form a matrix block; In the observation data corresponding to each subcarrier and each symbol, the echo signals received by all array elements are arranged in array element order, so that the spatial phase is arranged along the array element direction, carrying azimuth and elevation angle information, and the target block and matrix block are combined to construct an equivalent sensing matrix.

3. The beamforming optimization method as described in claim 1, characterized in that, The step of constructing a Cramer-Rao lower bound matrix based on each parameter to be estimated, according to the multi-stream transmitted signal model and the equivalent sensing matrix, to obtain the optimization objective includes: The partial derivatives of the parameters to be estimated are obtained by taking the partial derivatives of the equivalent sensing matrix. The partial derivative matrices are then multiplied and traced with the target scattering coefficient matrix and the transmitted signal correlation matrix, respectively, and summed to obtain the Fischer information matrix. The parameters to be estimated include the azimuth, elevation, range, and radial velocity of each target. The Fischer information matrix is ​​inverted to obtain the Cramer-Robber lower bound matrix. The sum of all diagonal elements of the Cramer-Robber lower bound matrix is ​​taken as the optimization objective. The diagonal elements of the Cramer-Robber lower bound matrix correspond to the theoretical lower bound of the estimation error of each parameter to be estimated.

4. The beamforming optimization method as described in claim 1, characterized in that, The step of constructing target constraints based on the signal-to-interference-plus-noise ratio expression and the beamforming matrix, transforming the target constraints into trace form with respect to positive semi-definite matrix variables by introducing positive semi-definite matrix variables to replace the beam vector outer product, and introducing auxiliary matrix variables and Schur complement transformation to transform the optimization objective into a linear matrix inequality includes: The total transmit power of the base station is expressed as the sum of the squares of the Frobenius norms of the beamforming matrices on all subcarriers. The maximum transmit power is used as the power constraint, and the signal-to-interference-plus-noise ratio of each communication user on each subcarrier is not lower than a preset threshold as the communication constraint. The original optimization problem is constructed with the beamforming matrix as the variable. Replace the outer product of each beamforming vector and its conjugate transpose with a positive semi-definite matrix variable and remove the rank-one constraint. Transform the power constraint into the sum of the traces of all positive semi-definite matrix variables not exceeding the maximum transmit power. Transform the communication constraint into an inequality between the traces of the channel matrix and the corresponding positive semi-definite matrix variable products. A first auxiliary matrix variable is introduced, and the optimization objective is replaced by the positive semidefinite constraint of the Fischer information matrix and the first auxiliary matrix variable. A second auxiliary matrix variable is introduced, and the optimization objective is transformed into minimizing the trace of the second auxiliary matrix by constructing a linear matrix inequality using the Schur complement transformation, thus forming a linear matrix inequality.

5. The beamforming optimization method as described in claim 4, characterized in that, The process involves numerically solving the linear matrix inequalities using a semidefinite programming solver to obtain the positive semidefinite matrix corresponding to each data stream of each subcarrier. Eigenvalue decomposition is then performed on the positive semidefinite matrix, and the largest eigenvalue and its corresponding eigenvector are used to recover the beamforming vectors of each subcarrier. These vectors are then combined to obtain the beamforming matrix for each subcarrier. The linear matrix inequality is input into a semidefinite programming solver for numerical iterative calculation, so that the solver minimizes the trace of the second auxiliary matrix under the premise of satisfying the power constraint, communication constraint and semidefinite constraint, and outputs the optimal solution of the semidefinite matrix variable corresponding to each data stream on each subcarrier; The optimal solutions are decomposed into eigenvalue matrices, eigenvalue diagonal matrices, and the product of the conjugate transpose of the eigenvectors. The maximum eigenvalue and the corresponding eigenvector are extracted. The square root of the maximum eigenvalue is multiplied by the eigenvector to recover the physical transmittable beamforming vectors of the corresponding subcarriers and data streams. The beamforming vectors recovered from all data streams on the same subcarrier are arranged sequentially according to the data stream index order and combined to form the complete beamforming matrix of the corresponding subcarrier; the beamforming matrix is ​​used by the base station to perform amplitude and phase weighting on the transmitted signals of each antenna.

6. A beamforming optimization device, characterized in that, The apparatus is applied to the beamforming optimization method according to claim 1, and the apparatus comprises: The system model building module is used to perform beamforming matrix weighting on the OFDM transmitted symbol vector through a uniform array antenna, construct a multi-stream transmitted signal model that includes sensing and detection symbols and communication data symbols, establish a signal-to-interference-plus-noise ratio expression based on the communication user channel response, and establish a single-target echo signal model based on echo delay phase, Doppler phase, and spatial phase. The sensing index construction module is used to construct an equivalent sensing matrix by vector stacking of the sensing echo observations of multiple subcarriers, multiple OFDM symbols and multiple array elements according to the single-target echo signal model, and to construct a Cramer-Rao lower bound matrix based on each parameter to be estimated according to the multi-stream transmitted signal model and the equivalent sensing matrix to obtain the optimization target. The optimization problem transformation module is used to construct target constraints based on the signal-to-interference-plus-noise ratio expression and the beamforming matrix. By introducing positive semi-definite matrix variables to replace the beam vector cross product, the target constraints are transformed into trace form with respect to positive semi-definite matrix variables. Auxiliary matrix variables and Schur complement transformation are introduced to transform the optimization objective into a linear matrix inequality. The beamforming matrix recovery module is used to numerically solve the linear matrix inequalities using a semidefinite programming solver to obtain the positive semidefinite matrix corresponding to each data stream of each subcarrier. The positive semidefinite matrix is ​​then decomposed into eigenvalues, and the largest eigenvalue and the corresponding eigenvector are taken to recover each beamforming vector. The combined vectors are then used to obtain the beamforming matrix of each subcarrier.

7. An electronic device, characterized in that, include: At least one processor and at least one memory, wherein, The memory stores computer-readable instructions; The computer-readable instructions are executed by one or more of the processors, causing the electronic device to implement the beamforming optimization method as described in any one of claims 1 to 5.

8. A storage medium having computer-readable instructions stored thereon, characterized in that, The computer-readable instructions are executed by one or more processors to implement the beamforming optimization method as described in any one of claims 1 to 5.

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