MIMO-OFDM integrated wireless sensing method based on tensor decomposition and flexible space-time-frequency optimization

Abstract

The application provides a MIMO-OFDM integrated sensing and communication wireless sensing method based on tensor decomposition and flexible space-time-frequency optimization, and establishes a single-station sensing model supporting flexible configuration of antenna positions, OFDM symbols and subcarriers in a MIMO-OFDM ISAC system, wherein a base station is provided with movable antennas to collect echo signals, and unknown parameters of a target are acquired within limited coherent time and signal bandwidth. Then, the target parameter estimation problem is modeled as a third-order tensor decomposition problem meeting a canonical multi-linear format, so that the target parameters are extracted from the corresponding factor matrices in the spatial, temporal and spectral dimensions in parallel. Based on the factor matrices after decomposition, in combination with the array geometry structure and the OFDM time-frequency resources, a globally optimal solution of the antenna positions, the subcarrier allocation and the OFDM symbol allocation is derived. The application significantly reduces the parameter estimation limit and the mean square error of the distance, the speed, the azimuth angle and the elevation angle and the like.

Description

Technical Field

[0001] This invention belongs to the field of wireless signal processing and integrated sensing communication (ISAC) technology, specifically relating to a MIMO-OFDM integrated sensing wireless sensing method based on tensor decomposition and flexible spatiotemporal frequency optimization. Background Technology

[0002] With the development of sixth-generation (6G) mobile communication technology, Integrated Sensing and Communication (ISAC) has received widespread attention as an important technology that simultaneously supports wireless communication and target perception. ISAC typically relies on multi-carrier modulation technologies such as Orthogonal Frequency Division Multiplexing (OFDM) and Multiple-Input Multiple-Output (MIMO) technology to multiplex communication signals into sensing signals, thereby improving spectrum utilization efficiency and realizing environmental perception functions.

[0003] MIMO technology improves spatial resolution and array gain by deploying multiple antenna elements, enabling systems to simultaneously support multi-user communication and multi-target sensing in complex environments. Existing research has proposed methods such as multi-beam design and joint optimization of waveform and receiver processing to strike a balance between communication and sensing performance.

[0004] However, existing integrated sensing communication systems using multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM ISAC systems) mostly employ fixed-position antenna arrays. This static array structure limits the full utilization of the spatial degrees of freedom of the wireless channel and makes it difficult to flexibly adapt to dynamic and complex sensing scenarios. As the requirements for sensing accuracy and flexibility increase, the adaptability of fixed arrays in future ISAC systems is gradually becoming limited.

[0005] To enhance the spatial freedom of a system, movable antenna (MA) technology has been proposed, allowing antenna elements to dynamically adjust their positions within a predefined area, thereby improving channel conditions and sensing performance. Existing research has shown that MA technology can be used in communication systems to reduce transmit power, improve energy efficiency, and jointly optimize beam and antenna positions; however, its systematic application in multi-parameter wireless sensing scenarios still requires further investigation.

[0006] On the other hand, tensor decomposition methods can characterize the structural properties of multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) signals in multiple dimensions such as space, time, and spectrum. In recent years, they have been widely used to reduce training overhead, improve parameter estimation accuracy, and reduce computational complexity. However, existing works are mostly aimed at cases where some parameters are known or a single sensing dimension is not enough to meet the need for joint high-precision estimation of multi-dimensional target parameters under conditions where all parameters are unknown.

[0007] Therefore, how to combine movable antennas with tensor decomposition modeling in a MIMO-OFDM ISAC system and achieve high-precision estimation of multidimensional target parameters through joint optimization of spatial-temporal-spectral resources remains a technical problem to be solved. Summary of the Invention

[0008] To address the problems of insufficient flexibility of fixed arrays, limited accuracy of multi-parameter sensing, and high complexity of high-dimensional channel estimation in existing MIMO-OFDM ISAC systems, this invention proposes a MIMO-OFDM integrated wireless sensing method based on tensor decomposition and flexible spatiotemporal frequency optimization.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: a MIMO-OFDM integrated wireless sensing method based on tensor decomposition and flexible spatiotemporal frequency optimization, comprising:

[0010] Step 1: Establish a single-station MIMO-OFDM ISAC wireless sensing model, collect the target echo signal within a limited coherence time and signal bandwidth, and flexibly configure the position of antenna elements, OFDM symbols used for sensing, and subcarrier resources according to sensing requirements.

[0011] Step 2: Based on the echo signal of the acquired target, construct a three-dimensional tensor representation model to describe the sensing observation data, so that the echo signal forms a structured observation signal tensor in the spatial, temporal and spectral dimensions;

[0012] Step 3: Perform canonical multilinear tensor decomposition on the three-dimensional tensor representation model describing the sensory observation data to obtain the factor matrix estimates corresponding to the spatial dimension, temporal dimension and spectral dimension, respectively;

[0013] Step 4: Utilize the structural correspondence of the factor matrices corresponding to the spatial dimension, time dimension, and spectral dimension in three dimensions to extract the parameters to be estimated of the target in parallel. The parameters to be estimated include azimuth or elevation angle, range, and velocity.

[0014] Step 5: Based on the parameter estimation vector, derive the corresponding Cramer-Rao bound and establish the relationship between the target parameter estimation accuracy and the antenna array geometry, OFDM symbol distribution, and subcarrier allocation method;

[0015] Step 6: Based on the Cramer-Rao boundary, jointly optimize the location of antenna elements, subcarrier allocation, and OFDM symbol allocation to obtain the optimal configuration of spatial-temporal-spectrum resources.

[0016] Compared with the prior art, this invention has at least the following advantages:

[0017] (1) This invention proposes a novel wireless sensing enhancement framework for MIMO-OFDM ISAC systems, and constructs a single-site MIMO-OFDM ISAC wireless sensing framework that supports flexible configuration of antenna position, OFDM symbols and subcarriers, which is beneficial to improve multi-parameter sensing performance under limited coherence time and bandwidth conditions.

[0018] (2) The present invention models the target perception problem as a tensor decomposition problem that satisfies the CP decomposition form, so that the joint estimation of the target parameters can be transformed into parallel estimation from the corresponding factor matrices in the spatial, temporal and spectral dimensions respectively;

[0019] (3) This invention derives the Cramer-Rao bound (CRB) for unknown target parameters and reveals that the estimation accuracy of azimuth or elevation angle, velocity and range fundamentally depends on the array geometry, OFDM symbol distribution and subcarrier allocation method; based on this, the global optimal solution of antenna position, subcarrier and OFDM symbol allocation is obtained to minimize the CRB;

[0020] (4) The superiority of the proposed method is verified by sufficient simulation experiments. The results show that the proposed method based on tensor decomposition and space-time-spectrum optimization is significantly better than the traditional tensor decomposition method and subspace class method in terms of performance, and the mean square error of the target parameter estimation is closer to CRB. Attached Figure Description

[0021] Figure 1 The diagram shows the MIMO-OFDM integrated sensing and communication system model proposed in this invention, illustrating the base station array, target scattering structure, and signal propagation path.

[0022] Figure 2 This is a schematic diagram of the three-dimensional received signal tensor structure constructed in this invention, illustrating how the signal is organized in the spatial, temporal, and frequency dimensions.

[0023] Figure 3 This is a schematic diagram of the optimal location distribution of the movable antenna proposed in this invention, showing the antenna spatial placement structure obtained through optimization within the receiving area.

[0024] Figure 4 This is a graph showing the root mean square error of pitch angle estimation as a function of signal-to-noise ratio, used to demonstrate the performance of the method in angle estimation.

[0025] Figure 5 This is a graph showing the root mean square error of the azimuth angle estimation of the present invention as a function of the signal-to-noise ratio, used to further illustrate the stability and superiority of the present invention in angle estimation.

[0026] Figure 6The graph shows the root mean square error of distance estimation as a function of signal-to-noise ratio, illustrating the performance of the method in the time delay estimation stage.

[0027] Figure 7 This is a graph showing the root mean square error of the Doppler frequency shift estimation of the present invention as a function of the signal-to-noise ratio, used to illustrate the accuracy improvement of the method of the present invention in velocity estimation.

[0028] Figure 8 The graph shows the normalized mean square error of the scattering coefficient estimation of this invention as a function of the signal-to-noise ratio, demonstrating the performance advantages of this invention in complex amplitude parameter estimation.

[0029] Figure 9 This is a graph showing the root mean square error of the time delay estimation in this invention as a function of the total number of subcarriers, used to illustrate the impact of the number of frequency domain training resources on the estimation performance.

[0030] Figure 10 This is a graph showing the change in the root mean square error of the Doppler frequency shift estimation of this invention as a function of the total number of frame structures, illustrating the impact of changes in the amount of training resources in the time dimension on performance.

[0031] Figure 11 This is a schematic diagram of a subcarrier optimization design, illustrating the optimal placement of training subcarriers when the number of subcarriers is even.

[0032] Figure 12 This is a schematic diagram of a subcarrier optimization design, illustrating the optimal placement of training subcarriers under an odd number of conditions. Detailed Implementation

[0033] It is readily understood that, based on the technical solution of this invention, various embodiments of the invention can be conceived by those skilled in the art without altering the essential spirit of the invention. Therefore, the following detailed embodiments and accompanying drawings are merely illustrative examples of the technical solution of this invention and should not be considered as the entirety of the invention or as limitations or restrictions on the technical solution of this invention. Rather, these embodiments are provided to enable those skilled in the art to gain a more thorough understanding of the invention. Preferred embodiments of the invention are described below in conjunction with the accompanying drawings, which form part of this application and, together with the embodiments of the invention, serve to illustrate the innovative concept of the invention.

[0034] A MIMO-OFDM integrated sensing wireless sensing method based on tensor decomposition and flexible spatiotemporal frequency optimization includes:

[0035] Step 1: Establish a single-station MIMO-OFDM ISAC wireless sensing model, collect the target echo signal within a limited coherence time and signal bandwidth, and flexibly configure the position of the antenna unit, the OFDM symbols used for sensing, and the subcarrier resources according to the sensing requirements.

[0036] In this embodiment, a single-site MIMO-OFDM ISAC wireless sensing system model is established. The single-site MIMO-OFDM ISAC wireless sensing system includes a base station, which is configured with a transmitting antenna array for transmitting OFDM-based wireless signals. Multiple movable antenna units are set up within a predefined movable area near the base station as sensing receivers to receive echo signals reflected from the sensing target. The positions of the movable antenna units can be flexibly adjusted in a two-dimensional plane, and their positions are determined by a two-dimensional position vector. Characterization.

[0037] A single-station MIMO-OFDM ISAC wireless sensing system operates within a limited coherent time interval and signal bandwidth; the set of all OFDM symbols contained in an OFDM frame (or multiple consecutive OFDM symbols) within the coherent time interval is denoted as . The set of all available subcarriers within the signal bandwidth is denoted as .from and Select the OFDM symbol index set for wireless sensing respectively. With subcarrier index set .

[0038] For the th selected OFDM symbol ∈ and the th selected subcarrier , the corresponding sensing echo channel matrix can be expressed as:

[0039]

[0040] Where, 𝑄 represents the number of perceived targets. Let be the complex scattering coefficient of the nth target. and These represent the target's azimuth and elevation angles, respectively. and These represent the round-trip time delay and Doppler shift of the target, respectively. and These are the array direction vectors for the receiver and transmitter, respectively. For subcarrier spacing, The duration of the OFDM symbol.

[0041] Given the transmit precoding vector corresponding to the nth OFDM symbol At that time, the echo received signal at the nth OFDM symbol and the nth subcarrier can be expressed as:

[0042]

[0043] in, The echo received signal vector, It is an additive white Gaussian noise vector;

[0044] Through the above process, the echo received signals acquired on the OFDM symbol index set 𝐹 and subcarrier index set 𝑇 provide an observation data basis for the subsequent construction of the third-order observation signal tensor and the estimation of multi-target parameters.

[0045] Step 2: Based on the acquired echo signals, construct a three-dimensional tensor representation model to describe the sensing observation data, so that the echo signals form a structured observation signal tensor in the spatial, temporal, and spectral dimensions;

[0046] Based on step 1, in the OFDM symbol index set for wireless sensing With subcarrier index set The echo received signal acquired above (wherein) The echo received signal is organized and rearranged according to the receiving antenna index, OFDM symbol index, and subcarrier index to construct a third-order observation signal tensor for describing the sensing observation data. .

[0047] Let the number of movable receiving antenna elements be... The selected OFDM symbol number is The number of selected subcarriers is The third-order observation signal tensor The dimension is Its three dimensions correspond to the spatial dimension (receiving antenna), the time dimension (OFDM symbol), and the spectrum dimension (subcarrier), respectively.

[0048] In a multi-target sensing scenario, the third-order observation signal tensor can be represented as a model satisfying the canonical multilinear decomposition (CP decomposition) structure:

[0049]

[0050] Wherein, the symbol “∘” represents the vector outer product, and 𝑄 represents the number of perceived targets. , and These are the feature vectors of the nth target in the spatial, temporal, and spectral dimensions, respectively. To and Noise tensors of the same dimension.

[0051] To facilitate subsequent tensor decomposition, the above CP model is further written in factor matrix form:

[0052]

[0053] in , , These are factor matrices representing the spatial, temporal, and spectral dimensions, respectively.

[0054] Through the above steps, the output of step 2 is the third-order observation signal tensor. The corresponding CP structure representation provides input for the tensor decomposition in step 3 and the parallel estimation of the target parameters in step 4.

[0055] Step 3: Perform canonical multilinear tensor decomposition on the three-dimensional tensor representation model describing the sensory observation data to obtain factor matrices corresponding to the spatial dimension, temporal dimension and spectral dimension respectively;

[0056] The alternating least squares (ALS) algorithm is used to perform CP decomposition on the observed signal tensor to estimate the factor matrices in the spatial, temporal and spectral dimensions. This achieves decoupled estimation of multi-objective parameters without adding extra hardware components or significantly increasing computational complexity.

[0057] In this embodiment, the Alternating Least Squares (ALS) algorithm is used to process the third-order observation signal tensor constructed in step 2. Perform canonical multilinear tensor decomposition (CP decomposition) to obtain factor matrices corresponding to the spatial, temporal, and spectral dimensions, respectively. , and .

[0058] To facilitate the solution, the tensor is... Expanding along the spatial, temporal, and spectral dimensions respectively yields the corresponding expanded matrices, denoted as follows: , and Initialize the factor matrices for spatial, temporal, and spectral dimensions. , , (For example, using random initialization or initialization based on singular value decomposition), and in the (x+1)th iteration, fixing two of the factor matrices and updating the remaining factor matrix, specifically including:

[0059] (1) When updating the spatial dimension factor matrix, fix and This is obtained by solving the following least squares problem. :

[0060]

[0061] (2) When updating the time dimension factor matrix, fix and This is obtained by solving the corresponding least squares problem. ;

[0062] (3) When updating the spectral dimension factor matrix, fix and This is obtained by solving the corresponding least squares problem. .

[0063] Here, the symbol "⊙" represents the Khatri–Rao product (or Kronecker product). This represents the Frobenius norm.

[0064] The ALS iteration process terminates when a preset termination condition is met. This termination condition includes reaching a preset maximum number of iterations and / or the change in tensor reconstruction error between two adjacent iterations being less than a preset threshold. After the iteration ends, the estimated values ​​of the factor matrices in the spatial, temporal, and spectral dimensions are output. , and The target parameters are used for parallel extraction in the subsequent step 4.

[0065] Step 4: Utilize the structural correspondence of the factor matrices corresponding to the spatial dimension, time dimension, and spectral dimension in three dimensions to extract the parameters to be estimated of the target in parallel. The parameters to be estimated include at least azimuth or elevation angle, range, and velocity.

[0066] In this embodiment, after performing canonical multilinear tensor decomposition on the observed signal tensor in step 3, factor matrix estimates corresponding to the spatial, temporal, and spectral dimensions are obtained.

[0067] , ,

[0068] Among them, the nth column of the three factor matrices corresponds to the same perceptual target in three dimensions.

[0069] Furthermore, let the factor vectors of the nth target in the spatial, temporal, and spectral dimensions be respectively...

[0070]

[0071] Based on the structural characteristics of the aforementioned factor vectors, the parameters of multiple targets are estimated in parallel, as detailed below.

[0072] (1) Angle parameter estimation (spatial dimension)

[0073] In the spatial dimension, for the azimuth and elevation angle parameters of the nth target, a spatial dictionary composed of the receiver array direction vectors is constructed. By maximizing the correlation between the spatial dictionary vectors and the spatial dimension factor vectors, the angle estimate of the nth target is obtained.

[0074]

[0075] Let represent the estimated azimuth and elevation angles of the nth target, respectively. represents the direction vector of the receiver array; 𝜃 and 𝜙 represent the azimuth and elevation angle variables to be searched, respectively.

[0076] (2) Doppler frequency shift estimation (time dimension)

[0077] In the time dimension, a time dictionary composed of Doppler feature vectors is constructed for the Doppler frequency shift parameters of the nth target. The estimated Doppler frequency shift of the nth target is obtained by maximizing the correlation between the time dimension factor vector and the time dictionary vector. :

[0078]

[0079] Represents the Doppler eigenvectors. This represents the set of OFDM symbol indices used for sensing, and 𝜔 represents the Doppler frequency shift variable to be searched.

[0080] (3) Delay estimation (spectral dimension)

[0081] In the spectral dimension, a spectral dictionary composed of delay feature vectors is constructed for the round-trip delay parameters of the *x*-th target. The delay estimate of the *x*-th target is obtained by maximizing the correlation between the spectral dimension factor vectors and the spectral dictionary vectors. :

[0082]

[0083] Represents the delay feature vector; represents the set of subcarrier indices used for sensing. This represents the round-trip time delay variable to be searched.

[0084] (4) Estimation of complex scattering coefficients and construction of parameter vectors

[0085] Based on the least squares criterion, the complex scattering coefficients of the nth target are estimated, and the estimation result can be expressed as:

[0086]

[0087] in, This represents the Moore–Penrose generalized inverse. Expand the matrix along the spectral dimension. This represents the time delay direction matrix composed of the time delay direction vectors of each target; vec(⋅) represents the vectorization operation, that is, rearranging the matrix into column vectors. ⊙ represents the Khatri–Rao product.

[0088] After obtaining the angle, Doppler frequency shift, and time delay estimates of the nth target, the corresponding spatial feature vector, temporal feature vector, and spectral feature vector are combined to form a rank-one structure vector.

[0089] From this, we can obtain the parameter estimation vector for the nth target:

[0090]

[0091] This enables parallel estimation of azimuth or pitch angle, range, and velocity parameters for multiple targets.

[0092] Step 5: Based on the parameter estimation vector, derive the corresponding Cramer-Rao bound and establish the relationship between the target parameter estimation accuracy and the antenna array geometry, OFDM symbol distribution, and subcarrier allocation method;

[0093] In this embodiment, the spatial dimension, temporal dimension, and spectral dimension factor matrices are obtained from the canonical multilinear decomposition of the observed signal tensor in step 3:

[0094]

[0095] Construct a global parameter vector η containing the target azimuth or elevation angle, time delay, and Doppler shift, and further calculate the range and velocity based on the time delay and Doppler shift; under given noise statistical characteristics, establish a likelihood function based on the parameterized model of the observed signal tensor, and thereby construct the Fisher information matrix corresponding to η.

[0096] Because the original target parameters are coupled in spatial, temporal, and spectral dimensions, the Fisher information matrix obtained directly from the original observation model is a high-dimensional coupling matrix, which is difficult to invert. Therefore, this invention establishes the Fisher information matrix of grouped parameters based on the factor matrix obtained from tensor decomposition, and further obtains the Cramer-Rao bound expressions for each parameter:

[0097]

[0098] in, Let represent the Fisher information matrix corresponding to the parameter vector η. The diagonal elements of the Cramer-Rao bound matrix correspond to the theoretical mean square error lower bounds of the target azimuth or elevation angle, Doppler frequency shift, and time delay parameter, respectively. The Cramer-Rao bounds for each parameter are specifically as follows:

[0099] (1) Relationship between the Cramer-Rao boundary of the angular parameter and the antenna geometry

[0100] Regarding the estimation accuracy of the angle parameters, based on the geometric distribution characteristics of the position vectors 𝑥 and 𝑦 of the movable receiving antenna in the two-dimensional plane, the Cramer-Rao boundary corresponding to the azimuth or elevation angle is expressed in a form related to the position distribution statistics, specifically:

[0101]

[0102]

[0103] in and Let Cramer-Rao boundaries represent the two angular parameters respectively. and The scaling factor is determined by the carrier wavelength, noise variance, and correlation factor matrix. and Let Variance and covariance be the vectors, respectively.

[0104] As can be seen from the above relationship, the estimation accuracy of the angle parameter is closely related to the geometric distribution characteristics of the movable antenna array.

[0105] (2) The relationship between time delay and the Cramer-Rao bound of Doppler parameters and time-frequency resource allocation

[0106] For the time delay and Doppler shift parameters, their estimation accuracy is related to the time-frequency distribution characteristics determined by the selected subcarrier index set 𝑇 and OFDM symbol index set 𝐹. The corresponding Cramer-Rao bound can be expressed in a form related to the dispersion of the index distribution, and the problem of minimizing the Cramer-Rao bound is transformed into the following equivalent optimization objective:

[0107]

[0108]

[0109] in and Cramer-Rao boundaries, representing time delay and Doppler shift respectively, and These are the mean values ​​of the subcarrier index and the OFDM symbol index, respectively.

[0110] The above analysis shows that the Cramer-Rao bound of the target parameters can be explicitly represented as a function of the resource allocation methods in the spatial, temporal, and spectral dimensions, providing a theoretical basis for subsequent joint optimization of antenna location, subcarrier allocation, and OFDM symbol allocation.

[0111] Step 6: Based on the Cramer-Rao bound, jointly optimize the location of antenna elements, subcarrier allocation, and OFDM symbol allocation to obtain the optimal configuration of spatial-temporal-spectrum resources, thereby including but not limited to reducing the Cramer-Rao bound of target parameter estimation and minimizing the mean square error of target parameter estimation.

[0112] In this embodiment, in order to enable the target parameter Cramer-Rao boundary obtained in step 5 to directly guide the spatial-temporal-spectrum resource allocation, the overall process of the MIMO-OFDM-ISAC wireless sensing method based on tensor decomposition and flexible spatiotemporal spectrum optimization described in this invention adopts a phased spatial-temporal-frequency resource allocation and target parameter estimation mechanism, which specifically includes the following two stages.

[0113] Phase 1: Joint Optimization of Space-Time-Frequency Resources

[0114] Given the number of sensing targets (r), noise statistics, system bandwidth, coherence time, and other system parameters, a comprehensive performance index function is constructed based on the Cramer-Rao bound expressions for the angle parameters, Doppler frequency shift parameters, and time delay parameters obtained in step 5. Specifically:

[0115]

[0116] in, represents the position vector of the movable receiving antenna element within a predefined movable area; represents the set of subcarrier indices used for sensing, and represents the set of OFDM symbol indices used for sensing; , and The Cramer-Rao bounds represent the angle, time delay, and Doppler parameters, respectively, determined by the receiving antenna geometry, subcarrier allocation method, and OFDM symbol distribution method. , , These are non-negative weighting coefficients;

[0117] The optimal allocation of spatial, temporal, and spectral resources can be obtained by solving the following joint optimization problem.

[0118]

[0119] This allows us to obtain the optimal position of the movable receiving antenna element. Optimal Subcarrier Index Set and the optimal OFDM symbol index set This achieves a joint reduction of the angle, time delay, and Doppler parameter estimation Cramer-Rao bound.

[0120] Phase Two: Target Parameter Estimation Based on Optimal Resource Allocation

[0121] Optimal resource allocation obtained in the first phase Under the conditions described, the base station collects echo observation data according to the optimal configuration: Corresponding OFDM symbols and The echo received signal is acquired on the corresponding subcarrier, and a corresponding third-order observation signal tensor is constructed based on the echo signal. Under noise-free conditions, the observed signal tensor can be expressed as:

[0122]

[0123] Considering the noise tensor When affected, the actual observed signal tensor is represented as:

[0124]

[0125] Subsequently, the observed signal tensor Perform canonical multilinear tensor decomposition to obtain factor matrix estimates in the spatial, temporal, and spectral dimensions. , , Following the parallel parameter extraction method described in step 4, the factor matrix is ​​mapped to the parameter estimation results for each objective:

[0126]

[0127] in, Including the Parameters of a target, such as azimuth or elevation angle, time delay, velocity, and complex scattering coefficient. This represents the mapping relationship for estimating target parameters based on the factor matrix.

[0128] Through the above-described space-time-frequency resource allocation and target parameter estimation process based on Cramer-Rao bound optimization, high-precision parallel estimation of multiple target parameters can be achieved under optimized resource conditions.

[0129] The following examples are only used to illustrate the technical effects of the present invention and do not constitute a limitation on the scope of protection of the present invention.

[0130] Example 1

[0131] This invention uses computer simulation to verify the proposed MIMO-OFDM integrated sensing (ISAC) wireless sensing method based on tensor decomposition. All experiments were completed in the MATLAB (Matrix Labs software) environment.

[0132] Considering base station configuration Root antenna, among which , Deployed in a predefined mobile area near the base station One movable receiving antenna element (MA). The carrier frequency is... GHz, bandwidth GHz, of which , The duration of the cyclic prefix in a single OFDM symbol is ,in , Base station detection For each target, the reflection coefficient and path gain are set to... .

[0133] The arrival angle (degrees) and departure angle (degrees) are set as follows: , ;distance (meters) are set as follows: Target movement speed (meters per second) is set as follows: The negative sign indicates the direction opposite to the positive direction. The signal-to-noise ratio is defined as: .parameter The RMSE is defined as follows: ,in Indicates the number of Monte Carlo trials. Indicates the first The second test One estimated parameter, one true parameter , .

[0134] Reflectance coefficient In the The estimation performance on OFDM symbols is measured by the normalized mean square error, defined as: .

[0135] Step 1: Establish a single-site MIMO-OFDM ISAC wireless sensing model, deploy movable antenna units for sensing at the base station, collect the echo signal of the target within a limited coherence time and signal bandwidth, and flexibly configure the position of the antenna units, the OFDM symbols used for sensing, and the subcarrier resources according to the sensing requirements.

[0136] The base station is deployed with transmitting antennas arranged in a uniform rectangular array within a movable area near the base station. A movable receiving antenna, whose position on a two-dimensional plane is represented by vectors 𝑥 and 𝑦. The system operates under constraints of finite coherence time and system bandwidth: from the set of OFDM symbols available within the coherence time interval and the set of subcarriers available within the system bandwidth, an OFDM symbol index set 𝐹 and a subcarrier index set 𝑇 are selected for sensing. For the 𝑚-th selected OFDM symbol and the 𝑘-th selected subcarrier, its sensing channel matrix is ​​represented as:

[0137]

[0138] in, Let be the complex scattering coefficient of the nth target. and These are the receiving and transmitting direction vectors, determined by the position of the movable receiving antenna, the structure of the transmitting array, and the target azimuth and elevation angles, respectively. and These represent the round-trip time delay and Doppler shift of the target, respectively. and Functions related to the selected subcarrier and OFDM symbol index, For subcarrier spacing, Duration of a single OFDM symbol;

[0139] Given the set of OFDM symbol indices *x* and the set of subcarrier indices *k* for the *n*th sensing (or training) term, the precoding vector corresponding to each symbol... At that time, the echo received signal under this symbol and subcarrier can be written as

[0140]

[0141] in, For dimension The received signal vector, Let be an additive white Gaussian noise vector; substituting the above channel matrix, the specific expression for the echo received signal can be obtained as follows:

[0142]

[0143] The MIMO-OFDM-ISAC system adopts a downlink communication and wireless sensing architecture based on signal sharing: the base station transmits pre-designed training precoding vectors on a selected subcarrier index set 𝑇 and OFDM symbol index set 𝐹. During the downlink channel training phase, it provides communication channel estimation for multiple users simultaneously and provides echo signals required for target sensing for single-station wireless sensing receivers.

[0144] For the _i_th user, its downlink training received signal on the _i_th selected OFDM symbol and the _i_th selected subcarrier can be expressed as:

[0145]

[0146] in, The received signal vector used for communication channel estimation. This is a downlink communication MIMO channel matrix that includes parameters such as azimuth or elevation angle, range, and velocity. To summarize the overall parameter vector of the above target and channel parameters, It is an additive white Gaussian noise vector;

[0147] The single-station wireless sensing receiver receives signals from the same training precoding vector on the same subcarrier index set 𝑇 and OFDM symbol index set 𝐹. The sensing channel matrix of the excited echo signal is denoted as... It has the same parameterization form as the downlink communication channel matrix, thus satisfying

[0148]

[0149] This allows the communication channel and the sensing channel to be characterized by the exact same mathematical model, enabling the sharing of the same MIMO-OFDM sensing (or training) waveform for downlink communication channel estimation and wireless sensing tasks without adding extra pilot and time-frequency resource overhead.

[0150] Step 2: Based on the acquired echo signals, construct a three-dimensional tensor representation model to describe the sensing observation data, so that the echo signals form a structured observation signal tensor in the spatial, temporal, and spectral dimensions;

[0151] By selecting K subcarriers for sensing (or training) and K OFDM symbols for sensing (or training), the corresponding echo received signals are organized and rearranged according to the receiving antenna index, OFDM symbol index, and subcarrier index, constructing a dimension-based system. The third-order observation signal tensor ,in Let the number of receiving antenna elements be R, and the number of sensing targets be R; the joint estimation problem of target parameters is expressed as an optimization problem of minimizing tensor reconstruction error.

[0152]

[0153] in, and Let be the position vector of the movable receiving antenna, and let and represent the subcarrier and OFDM symbol index sets, respectively. , , , , These are the azimuth or elevation angle, Doppler frequency shift, round-trip time delay, and complex scattering coefficient of the nth target, respectively. , and These are the direction vectors related to the spatial, temporal, and spectral dimensions, respectively.

[0154] Based on the above modeling, the observed signal tensor can be rewritten as a third-order signal tensor model that satisfies the canonical multilinear decomposition form.

[0155]

[0156] in, For noise tensors of the same dimension, These are factor matrices in the spatial, temporal, and spectral dimensions, respectively, and the i-th column corresponds to the feature vector of the i-th target in the corresponding dimension.

[0157] The rank of the third-order observation signal tensor in the sense of CP decomposition corresponds one-to-one with the number of sensing targets, i.e., each target corresponds to a rank-one component in the tensor model.

[0158] For the The feature vectors of each target in the spatial, temporal, and spectral dimensions are denoted as follows:

[0159]

[0160] The rank-one signal tensor component corresponding to the target is defined as follows:

[0161]

[0162] in, The outer product of vectors is represented; the rank-tensor components corresponding to all n targets are superimposed to obtain the noise-free observation signal tensor.

[0163]

[0164] And add a noise tensor to this. This constitutes the tensor of the actual observed signal;

[0165] Under the above definition, the CP rank of the noiseless observation signal tensor satisfies ;

[0166] The corresponding factor matrix can be written as

[0167]

[0168] The factor matrix of the first Column and rank tensor components The one-to-one correspondence allows for parallel estimation of parameters such as azimuth or elevation angle, velocity, and range of n targets when using the factor matrix for parameter estimation, without the need for additional decoupling steps.

[0169] Step 3: Based on the third-order observation signal tensor 𝑌 constructed in Step 2, the observation signal tensor is subjected to canonical multilinear tensor decomposition (CP decomposition) to represent it as a linear superposition of multiple rank tensor components, thereby obtaining factor matrices corresponding to the spatial dimension, time dimension and spectral dimension respectively.

[0170] Specifically, the third-order observation signal tensor Expanding along the receiver antenna dimension (first dimension), OFDM symbol dimension (second dimension), and subcarrier dimension (third dimension) respectively, the corresponding expanded matrices are denoted as follows: , and .

[0171] The observed signal tensor is decomposed into CP by the Alternating Least Squares (ALS) algorithm. In each iteration, two factor matrices are fixed and the least squares problem is solved for the remaining factor matrix. The factor matrices corresponding to the spatial dimension, time dimension and spectral dimension are iteratively updated until the preset convergence condition is met.

[0172] Through the above CP decomposition process, the corresponding factor matrix estimates in the spatial, temporal, and spectral dimensions can be obtained, denoted as follows: , Under the condition of allowing permutation uncertainty and scale uncertainty, the factor vectors of each objective in different dimensions maintain a consistent column correspondence in the three sets of factor matrices, thus providing a foundation for subsequent parallel estimation of objective parameters based on multidimensional structure.

[0173] Step 4: Based on the multidimensional structural characteristics of the factor matrices corresponding to the spatial, temporal, and spectral dimensions, extract the parameters to be estimated for the target in parallel. The parameters to be estimated include at least azimuth or elevation angle, range, and velocity.

[0174] After performing CP decomposition on the observed signal tensor in step 3, the factor matrix estimates corresponding to the spatial, temporal, and spectral dimensions can be obtained, respectively. , , Under conditions where permutation uncertainty and scale uncertainty are permissible, the factor vectors of the same objective in different dimensions maintain a consistent column correspondence in the three sets of factor matrices.

[0175] Based on the aforementioned column consistency characteristic, each column of factor vectors can be mapped to the observed features of the same target in different dimensions, thereby enabling parallel extraction of parameters for multiple targets. Specifically, for the nth target, its factor vectors in the spatial, temporal, and spectral dimensions are denoted as follows: And parameter estimation is achieved by maximizing the correlation with the dictionary of directional vectors in each dimension;

[0176] In terms of spatial dimension, regarding the first For each target, the azimuth or elevation angle parameters are used to construct a spatial dictionary composed of the receiver's direction vectors. By solving

[0177] Get the first Estimate the azimuth or elevation angle of a target;

[0178] In terms of time dimension, for the first The Doppler frequency shift parameters of each target are used to construct a time dictionary composed of Doppler direction vectors. ,in

[0179]

[0180] By solving

[0181]

[0182] Get the first Doppler shift estimation for each target;

[0183] In the spectral dimension, for the first The time delay parameters of each target are used to construct a spectrum dictionary composed of time delay direction vectors. By solving

[0184]

[0185] Get the first Time delay estimation for each target;

[0186] In obtaining Then, the above estimation results are combined with the factor vectors of each dimension to estimate the _th_ ... Complex scattering coefficients of a target Thus, the first The complete parameter estimation vector of the target

[0187]

[0188] By utilizing the structural characteristics of the three-dimensional factor matrix, parallel estimation of azimuth or pitch angles, range, and velocity parameters of multiple targets can be achieved.

[0189] Step 5: For the target parameters to be estimated, derive the corresponding Cramer-Rao bounds, and establish the relationship between the target parameter estimation accuracy and the antenna array geometry, OFDM symbol distribution, and subcarrier allocation method;

[0190] Based on the observation signal tensor model established in step 2 and the target parameter set obtained in step 4, a global parameter vector 𝜂 is constructed, containing the target azimuth or elevation angle, time delay (or range), Doppler shift (or velocity), and complex scattering coefficients. Given the statistical characteristics of the noise (e.g., additive white Gaussian noise), a Fisher information matrix corresponding to 𝜂 is established. The Cramer-Rao bound matrix estimated by its parameters is:

[0191]

[0192] in, The diagonal blocks correspond to the theoretical lower bound of the mean square error of parameters such as target azimuth or elevation angle, Doppler frequency shift, and time delay;

[0193] Regarding the estimation accuracy of the angle parameters, based on the receiving antenna position vector and The distribution characteristics allow the Cramer-Rao boundary of azimuth or elevation angles to be expressed in a form related to the position variance and covariance, for example...

[0194]

[0195]

[0196] in and Let Cramer-Rao boundaries represent the two angular parameters respectively. and The scaling factor is determined by the carrier wavelength, noise variance, and correlation factor matrix. and Let Variance and Covariance of the vector be represented respectively.

[0197] For the time delay and Doppler parameters, based on the time-frequency distribution determined by the subcarrier index set 𝑇 and the OFDM symbol index set 𝐹, the corresponding Cramer-Rao bound can be expressed as a form related to the index variance. The problem of minimizing the CRB for each parameter is rewritten as a problem of maximizing the variance of the antenna position and the time-frequency index, specifically:

[0198]

[0199]

[0200] in and Cramer-Rao boundaries, representing time delay and Doppler shift respectively, and These are the mean values ​​of the subcarrier index and the OFDM symbol index, respectively.

[0201] Through the above derivation and equivalent transformation, the relationship between the target parameter estimation accuracy and the antenna array geometry, OFDM symbol distribution and subcarrier allocation method is established, providing a basis for the joint optimization of space-time-frequency resources in the subsequent step 6.

[0202] Step 6: Based on the Cramer-Rao bound, jointly optimize the location of antenna elements, subcarrier allocation, and OFDM symbol allocation to obtain the optimal configuration of spatial-temporal-spectrum resources, thereby including but not limited to reducing the Cramer-Rao bound of target parameter estimation and minimizing the mean square error of target parameter estimation.

[0203] In the MIMO-OFDM-ISAC wireless sensing method based on tensor decomposition and flexible spatiotemporal spectrum optimization described in this invention, in order to execute step 6 above and enable the Cramer-Rao bound obtained in step 5 to directly guide the spatiotemporal-frequency resource allocation, the overall processing flow adopts a phased spatiotemporal-frequency resource allocation and target parameter estimation mechanism, specifically including a first-stage joint resource optimization and a second-stage parameter estimation based on optimal resource allocation:

[0204] The first stage is the space-time-frequency resource optimization stage. Given the number of sensing targets (r) and system parameters such as noise variance, a comprehensive performance index function is constructed based on the Cramer-Rao bound of the target azimuth or elevation angle, time delay, and Doppler frequency shift. For example:

[0205]

[0206] Where, 𝑟 represents the location variable (or set of location variables) of the movable receiving antenna element within a predefined movable area, 𝑇 represents the subcarrier index set used for sensing, and 𝐹 represents the OFDM symbol index set used for sensing. These are non-negative weighting coefficients.

[0207] The optimal allocation of spatial-temporal-spectrum resources is obtained by solving the following joint optimization problem:

[0208]

[0209] To achieve the joint minimization of the Cramer-Rao bounds for parameters such as angle, distance, and velocity;

[0210] The second stage is the target parameter estimation stage, which utilizes the optimal movable receiving antenna position obtained in the first stage. and the optimal set of indices Next, the training precoding vector is emitted according to the methods described in steps 1 to 4. The echo received signal was acquired, and the corresponding third-order observation signal tensor was constructed. It satisfies the following in the absence of noise.

[0211]

[0212] Adding noise tensor The tensor of the actual observed signal was then obtained. And perform CP decomposition on it to obtain the factor matrix estimate. , , Finally, the estimated vectors of each target parameter are obtained through a pre-designed parameter estimation algorithm.

[0213]

[0214] in, Including the Parameters of a target, such as azimuth or elevation angle, time delay, velocity, and complex scattering coefficient. This represents the mapping relationship of target parameters estimated based on the factor matrix, thereby achieving high-precision estimation of multiple target parameters under optimized spatial-temporal-spectral resource allocation.

[0215] Based on the above simulation conditions, the simulation graphics are shown in the attached figures in the instruction manual.

[0216] Simulation 1: 100 Monte Carlo experiments were conducted. The system settings included: a 6×6 36-element URA base station, 36 movable antennas (MA) at the receiver, a carrier frequency of 28 GHz, a bandwidth of 0.1 GHz, 128 OFDM subcarriers, 16 training subcarriers, 64 OFDM symbols, and 16 training symbols. The system sensed three targets, with their angle, distance, and velocity parameters configured according to the initial parameters given in the example (see attached figures). Under different signal-to-noise ratio conditions, the traditional CPD algorithm, the traditional subspace algorithm (MUSIC / MF), and the proposed flexible space-time-frequency joint optimization CPD algorithm were used to compare their azimuth and elevation angle estimation performance, obtaining the correspondence between RMSE and SNR, as shown in Figures 4 and 5.

[0217] Experimental results show that the angle estimation accuracy of each algorithm improves with increasing SNR; however, in the low to medium SNR range, the traditional subspace-based algorithms have large errors and significant fluctuations, and the traditional CPD method still has significant biases; in contrast, the method of this invention maintains the minimum RMSE in the entire SNR range, and its estimation performance is close to the lower bound of CRB under medium to high SNR conditions, which is better than the comparison methods overall.

[0218] Simulation 2: Under the same system parameters and experimental configuration as Simulation 1, the performance of different algorithms in delay parameter estimation is further compared. By using the traditional matched filtering (MF) algorithm, the traditional CPD method, and the proposed flexible space-time-frequency optimization algorithm, the trend of delay RMSE with SNR is obtained, as shown in Figure 6.

[0219] Experimental results show that the traditional MF method basically fails under low SNR conditions and exhibits a significant error floor in the medium-to-high SNR region; although the traditional CPD method shows improvement, it is still limited under high-dimensional coupling parameters; the method of this invention can significantly reduce the CRB of delay estimation by jointly optimizing space-time-frequency resources, enabling the algorithm to maintain stable and high-precision delay estimation across the entire SNR range, with a significantly lower RMSE than the traditional method, and close to the theoretical optimal performance in the high SNR region.

[0220] Simulation 3: Maintaining the same experimental conditions as the first two simulations, compare the performance of Doppler parameter estimation under different algorithms. The RMSE versus SNR curve is obtained through Monte Carlo simulation, as shown in Figure 7.

[0221] Experimental results show that the traditional MF method is sensitive to noise and fails in Doppler estimation under low to medium SNR conditions; the traditional CPD method is relatively stable, but still has an error floor under high SNR conditions; the space-time-frequency optimized CPD method proposed in this invention exhibits stronger robustness across the entire SNR region, with the estimation error decreasing rapidly as SNR increases, eventually approaching the lower bound of the CRB. Its advantage stems from the fact that this invention improves the discriminability of the Doppler direction vector in the frequency domain by optimizing the frame structure and subcarrier configuration, thereby enhancing estimation accuracy.

[0222] Simulation 4: Under the same experimental settings, the estimation performance of different algorithms for target scattering intensity (reflection coefficient) is compared. Since the estimation of reflection coefficient depends on the estimation accuracy of angle, time delay, and Doppler parameters, this simulation can reflect the overall performance of the algorithm in a multi-parameter joint estimation scenario. The relationship between its NMSE and the changes of SNR, total number of subcarriers, and total number of frame structures are shown in Figures 8 to 10, respectively.

[0223] Simulation results show that traditional methods for estimating reflection coefficients have large errors and are unstable; the traditional CPD method can improve performance to some extent, but it is still affected by the uncertainty of factor matrix scaling and permutation, resulting in an error floor at high SNR; the method of this invention can significantly reduce NMSE and achieve near-optimal estimation performance under medium-to-high SNR conditions. This is because the proposed optimal time-frequency resource allocation and MA spatial layout can reduce the CRB of each parameter, thereby improving the accuracy and stability of reflection coefficient estimation.

Claims

1. A MIMO-OFDM integrated wireless sensing method based on tensor decomposition and flexible spatiotemporal frequency optimization, characterized in that, include: Step 1: Establish a single-station MIMO-OFDM ISAC wireless sensing model, collect the target echo signal within a limited coherence time and signal bandwidth, and flexibly configure the position of antenna elements, OFDM symbols used for sensing, and subcarrier resources according to sensing requirements. Step 2: Based on the echo signal of the acquired target, construct a three-dimensional tensor representation model to describe the sensing observation data, so that the echo signal forms a structured observation signal tensor in the spatial, temporal and spectral dimensions; Step 3: Perform canonical multilinear tensor decomposition on the three-dimensional tensor representation model describing the sensory observation data to obtain the factor matrix estimates corresponding to the spatial dimension, time dimension and spectral dimension, respectively; Step 4: Utilize the structural correspondence of the factor matrices corresponding to the spatial dimension, time dimension, and spectral dimension in three dimensions to extract the parameters to be estimated of the target in parallel. The parameters to be estimated include azimuth or elevation angle, range, and velocity. Step 5: Based on the parameter estimation vector, derive the corresponding Cramer-Rao bound and establish the relationship between the target parameter estimation accuracy and the antenna array geometry, OFDM symbol distribution, and subcarrier allocation method; Step 6: Based on the Cramer-Rao boundary, jointly optimize the location of antenna elements, subcarrier allocation, and OFDM symbol allocation to obtain the optimal configuration of spatial-temporal-spectrum resources.

2. The MIMO-OFDM integrated wireless sensing method based on tensor decomposition and flexible spatiotemporal frequency optimization according to claim 1, characterized in that, The single-station MIMO-OFDM ISAC wireless sensing system includes a base station and a sensing receiver set up in a predefined movable area near the base station. The base station is equipped with a transmitting antenna array for transmitting OFDM-based wireless signals. The sensing receiver includes multiple movable antenna elements for receiving echo signals reflected by the sensing target. The single-station MIMO-OFDM ISAC wireless sensing system operates within a limited coherence time interval and signal bandwidth.

3. The MIMO-OFDM integrated wireless sensing method based on tensor decomposition and flexible spatiotemporal frequency optimization according to claim 1, characterized in that, Given the transmit precoding vector corresponding to the nth OFDM symbol At that time, the echo received signal at the nth OFDM symbol and the nth subcarrier is specifically as follows: in, The echo received signal vector, It is an additive white Gaussian noise vector. Let the sensing echo channel matrix be the one corresponding to the nth OFDM symbol and the nth subcarrier; whereby the sensing echo channel matrix is ​​specifically: Where, 𝑄 represents the number of perceived targets. Let be the complex scattering coefficient of the nth target. and These represent the target's azimuth and elevation angles, respectively. and These represent the round-trip time delay and Doppler shift of the target, respectively. and These are the array direction vectors for the receiver and transmitter, respectively. For subcarrier spacing, The duration of the OFDM symbol.

4. The MIMO-OFDM integrated wireless sensing method based on tensor decomposition and flexible spatiotemporal frequency optimization according to claim 1, characterized in that, The constructed three-dimensional tensor representation model for describing the sensory observation data is as follows: Where ∘ represents the vector outer product, and 𝑄 represents the number of perceived targets. , and These are the feature vectors of the nth target in the spatial, temporal, and spectral dimensions, respectively. To and Noise tensors of the same dimension; The three-dimensional tensor representation model in factor matrix form is as follows: in , , These are factor matrices representing the spatial, temporal, and spectral dimensions, respectively.

5. The MIMO-OFDM integrated wireless sensing method based on tensor decomposition and flexible spatiotemporal frequency optimization according to claim 1, characterized in that, The specific method for performing canonical multilinear tensor decomposition on the three-dimensional tensor representation model describing the sensory observation data to obtain the factor matrix estimates corresponding to the spatial, temporal, and spectral dimensions is as follows: tensor Expanding along the spatial, temporal, and spectral dimensions respectively yields the corresponding expanded matrices, denoted as follows: , and Initialize the factor matrices for spatial, temporal, and spectral dimensions. , , ; In the (n+1)th iteration, two factor matrices are fixed, and the remaining factor matrix is ​​updated, specifically including: (1) When updating the spatial dimension factor matrix, fix and This is obtained by solving the following least squares problem. : (2) When updating the time dimension factor matrix, fix and This is obtained by solving the corresponding least squares problem. ; (3) When updating the spectral dimension factor matrix, fix and This is obtained by solving the corresponding least squares problem. Where ⊙ represents the Khatri–Rao product, Denotes the Frobenius norm; The iteration ends when the preset maximum number of iterations is reached and / or the change in tensor reconstruction error between two adjacent iterations is less than a preset threshold. The factor matrices of the spatial, temporal, and spectral dimensions of the last iteration are the estimated values ​​of the factor matrices of the spatial, temporal, and spectral dimensions. , and .

6. The MIMO-OFDM integrated wireless sensing method based on tensor decomposition and flexible spatiotemporal frequency optimization according to claim 1, characterized in that, By utilizing the three-dimensional structural correspondence of factor matrices corresponding to spatial, temporal, and spectral dimensions, the parameters to be estimated for the target are extracted in parallel, including: Angle parameter estimation: In the spatial dimension, for the azimuth and elevation angle parameters of the nth target, a spatial dictionary composed of the receiver array direction vectors is constructed. By maximizing the correlation between the spatial dictionary vectors and the spatial dimension factor vectors, the angle estimate of the nth target is obtained. In the formula, Let represent the estimated azimuth and elevation angles of the nth target, respectively. This represents the direction vector of the receiver array; 𝜃 and 𝜙 represent the azimuth and elevation angle variables to be searched, respectively; Doppler frequency shift estimation: In the time dimension, for the Doppler frequency shift parameters of the nth target, a time dictionary composed of Doppler feature vectors is constructed. By maximizing the correlation between the time dimension factor vector and the time dictionary vector, the estimated Doppler frequency shift value of the nth target is obtained. : Represents the Doppler eigenvectors. This represents the set of OFDM symbol indices used for sensing, and 𝜔 represents the Doppler frequency shift variable to be searched; Delay estimation: In the spectral dimension, for the round-trip delay parameters of the nth target, a spectral dictionary composed of delay feature vectors is constructed. By maximizing the correlation between the spectral dimension factor vector and the spectral dictionary vector, the delay estimate of the nth target is obtained. : Represents the delay feature vector; represents the set of subcarrier indices used for sensing. This represents the round-trip time delay variable to be searched; Complex scattering coefficient estimation: Based on the least squares criterion, the complex scattering coefficients of the nth target are estimated, and the estimation result can be expressed as: in, This represents the Moore–Penrose generalized inverse. Expand the matrix along the spectral dimension. vec(⋅) represents the time delay direction matrix composed of the time delay direction vectors of each target; vec(⋅) represents the vectorization operation, that is, rearranging the matrix into column vectors; ⊙ represents the Khatri-Rao product. Construct the parameter estimation vector for the nth objective: 。 7. The MIMO-OFDM integrated wireless sensing method based on tensor decomposition and flexible spatiotemporal frequency optimization according to claim 1, characterized in that, Based on the parameter estimation vector, the corresponding Cramer-Rao bound is derived, and the relationship between the target parameter estimation accuracy and the antenna array geometry, OFDM symbol distribution, and subcarrier allocation method is established, specifically including: Relationship between the Cramer-Rao boundary of the angular parameters and the antenna geometry: Regarding the estimation accuracy of the angle parameters, based on the geometric distribution characteristics of the position vectors 𝑥 and 𝑦 of the movable receiving antenna in the two-dimensional plane, the Cramer-Rao boundary corresponding to the azimuth or elevation angle is expressed in a form related to the position distribution statistics, specifically: in and Let Cramer-Rao boundaries represent the two angular parameters respectively. and The scaling factor is determined by the carrier wavelength, noise variance, and correlation factor matrix. and Let Variance and Covariance of the vector be represented respectively. The relationship between time delay and the Cramer-Rao bound of Doppler parameters and time-frequency resource allocation: For the time delay parameter and the Doppler frequency shift parameter, their estimation accuracy is related to the time-frequency distribution characteristics determined by the selected subcarrier index set 𝑇 and OFDM symbol index set 𝐹. The corresponding Cramer-Rao bound can be expressed in a form related to the dispersion of the index distribution, and the problem of minimizing the Cramer-Rao bound is transformed into the following equivalent optimization objective: in and Cramer-Rao boundaries, representing time delay and Doppler shift respectively, and These are the mean values ​​of the subcarrier index and the OFDM symbol index, respectively.

8. The MIMO-OFDM integrated wireless sensing method based on tensor decomposition and flexible spatiotemporal frequency optimization according to claim 1, characterized in that, Based on the Cramer-Rao boundary, the specific method for jointly optimizing the location of antenna elements, subcarrier allocation, and OFDM symbol allocation to obtain the optimal configuration of spatial-temporal-spectrum resources is as follows: Given the number of sensing targets (r), noise statistics, system bandwidth, coherence time, and other system parameters, a comprehensive performance index function is constructed based on the Cramer-Rao bound expression for angle parameters, Doppler frequency shift parameters, and time delay parameters. Specifically: in, represents the position vector of the movable receiving antenna element within a predefined movable area; represents the set of subcarrier indices used for sensing, and represents the set of OFDM symbol indices used for sensing; , and The Cramer-Rao bounds represent the angle, time delay, and Doppler parameters, respectively, determined by the receiving antenna geometry, subcarrier allocation method, and OFDM symbol distribution method. , , These are non-negative weighting coefficients; The optimal configuration of the spatial-temporal-spectrum resources of the mobile receiving antenna element is obtained by solving the following joint optimization problem: This allows us to obtain the optimal position of the movable receiving antenna element. Optimal Subcarrier Index Set and the optimal OFDM symbol index set ; The base station collects echo observation data according to the optimal configuration of spatial-temporal-spectrum resources of the mobile receiving antenna elements: In Corresponding OFDM symbols and The echo received signal is acquired on the corresponding subcarrier, and a corresponding third-order observation signal tensor is constructed based on the echo signal. Under noise-free conditions, the observed signal tensor is represented as: Considering the noise tensor When affected, the actual observed signal tensor is represented as: For the observed signal tensor Perform canonical multilinear tensor decomposition to obtain factor matrix estimates in the spatial, temporal, and spectral dimensions. , , Following the parallel parameter extraction method described in step 4, the factor matrix is ​​mapped to the parameter estimation results for each objective: in, Including the Parameters of a target, such as azimuth or elevation angle, time delay, velocity, and complex scattering coefficient. This represents the mapping relationship for estimating target parameters based on the factor matrix.

Images