L-shaped array of OFDM integrated target parameter estimation method based on coupling tensor decomposition

Abstract

This invention discloses a target parameter estimation method for an L-shaped array OFDM integrated sensing system based on Coupled Tensor Decomposition (CPD). The method includes: constructing an OFDM integrated sensing system model using an L-shaped receiving array, which consists of two sets of mutually orthogonal uniform linear arrays; establishing corresponding third-order tensor signal models based on the received echo signals along the horizontal and vertical axes, and constructing a coupled tensor that satisfies typical multilinear decomposition; transforming the multi-target parameter estimation problem into a coupled CPD solution problem, designing a two-stage coupled CPD parameter estimation algorithm, and sequentially extracting target azimuth, elevation, Doppler frequency shift, time delay, and complex reflection coefficient information from the estimated coupling factor matrix; and finally completing the joint estimation of multi-target parameters. This invention has stronger target parameter estimation capabilities and can improve the reliability and accuracy of target parameter estimation while reducing array hardware complexity.

Description

Technical Field

[0001] This invention belongs to the field of wireless sensing and communication fusion technology, specifically a target parameter estimation method for an L-shaped array OFDM based on coupled tensor decomposition. Background Technology

[0002] With the rapid development of sixth-generation (6G) mobile communication technology, communication systems are placing higher demands on spectrum utilization, hardware reuse, and environmental awareness capabilities. Integrated Sensing and Communication Architecture (ISAC), by simultaneously implementing wireless communication and target sensing functions on a unified hardware platform, can effectively improve the system's spectrum efficiency, hardware efficiency, and energy efficiency, and is therefore widely considered one of the key supporting technologies for future 6G wireless networks. This technology has broad application prospects in fields such as autonomous driving, low-altitude economy, smart cities, and smart homes.

[0003] Among various ISAC waveform systems, Orthogonal Frequency Division Multiplexing (OFDM) has become a relatively ideal ISAC waveform due to its good compatibility with high-speed wireless communication systems and its strong fine sensing capabilities. OFDM signals have a multi-carrier structure, and their frequency-domain orthogonality facilitates the separation of target delay and Doppler-induced phase changes in the frequency and time domains, thus providing convenience for estimating target parameters such as range and velocity. Therefore, OFDM has been widely used in practical wireless communication standards and has become an important foundation for target parameter estimation research in OFDM ISAC systems.

[0004] However, existing methods generally still have the following shortcomings: First, many methods rely on relatively accurate communication channel state information, which limits their applicability in actual integrated communication and sensing deployments; second, to achieve two-dimensional angle estimation, it is usually necessary to configure large-scale multi-antenna arrays or multiple-input multiple-output architectures, which leads to high array hardware complexity and system cost; third, some methods adopt decoupled processing or matrix modeling, which fails to fully explore the multi-dimensional coupling structure of the received signal in the spatial, frequency, and time domains, thus resulting in problems such as insufficient estimation robustness, high computational complexity, and limited parameter recovery capability.

[0005] In recent years, tensor signal processing methods have been increasingly introduced into the fields of ISAC and target parameter estimation due to their ability to explicitly characterize the intrinsic structural relationships of multidimensional observation data in spatial, temporal, and frequency dimensions. Existing research has proposed channel estimation and target parameter estimation methods based on tensor decomposition, which have improved multidimensional parameter processing capabilities to some extent. However, most existing methods are designed for uniform linear array scenarios or are only applicable to two-dimensional angle estimation problems. For OFDM ISAC systems with L-shaped array structures, while some studies have considered the two-dimensional angular domain characteristics of the array, they are usually limited to narrowband scenarios, partial target parameter recovery, or specific array structure conditions, making it difficult to reliably jointly estimate target parameters such as time delay, Doppler, azimuth, and elevation angles within a unified framework.

[0006] Therefore, in OFDM integrated sensing systems, how to fully utilize the inherent coupling relationship of the received echo signal in different dimensions for L-shaped receiving array structure, and achieve high-precision and reliable joint estimation of parameters such as target distance, velocity and two-dimensional angle under conditions of low array hardware complexity, remains a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0007] In response to the current state of research, this invention proposes a target parameter estimation method based on coupled tensor decomposition for L-shaped array OFDM inductive integrated systems. This method addresses the problems of high array hardware cost, insufficient parameter identification capability, and limited estimation accuracy in the joint estimation of target distance, velocity, and two-dimensional angular domain in existing inductive integrated systems based on OFDM waveforms.

[0008] The technical solution to achieve the objective of this invention is: a method for estimating target parameters of an L-shaped array OFDM with integrated sensing based on coupled tensor decomposition, comprising:

[0009] Step 1: For the L-shaped array OFDM integrated sensing system, construct a target sensing model, which includes the transmitted signal and echo signal of the integrated sensing system;

[0010] Step 2: Establish a communication transmission model, which includes downlink OFDM communication user terminal received signal and frequency selective multipath channel model, used to characterize the transmission mechanism and channel structure characteristics of communication link and sensing link under unified OFDM resource grid;

[0011] Step 3: Based on the base station's L-shaped receiver array shaft and The discrete-time echo signal corresponding to the axial uniform linear array is used to construct the corresponding third-order tensor model along the OFDM symbol dimension, the receiving radio frequency link dimension and the subcarrier dimension, respectively. Based on this, the structural characteristics of the horizontal axis and vertical axis echo tensors sharing the time delay correlation factor in the subcarrier dimension are used to construct the coupled tensor that satisfies the typical multilinear decomposition of coupling, and the coupled tensor decomposition sensing problem is transformed into the corresponding optimization problem.

[0012] Step 4: Design a two-stage coupled CPD parameter estimation algorithm for the coupled tensor. Estimate the corresponding factor matrix by solving the coupled tensor decomposition problem, and extract the target direction cosine, Doppler frequency shift, time delay and complex reflection coefficient information sequentially based on the estimated coupling factor matrix. Further recover the azimuth and elevation parameters of each target, thereby completing the joint estimation of the azimuth, elevation, Doppler frequency shift, time delay and complex reflection coefficient of multiple targets.

[0013] Compared with the prior art, the significant features of this invention are:

[0014] (1) The OFDM integrated sensing target parameter estimation method based on L-shaped array and coupled tensor decomposition proposed in this invention can improve the accuracy, stability and reliability of multi-target parameter estimation compared with traditional parameter estimation methods;

[0015] (2) This invention makes full use of the coupling structure of the L-shaped array receiving signals in two orthogonal directions, which can realize the joint modeling and unified solution of multi-dimensional parameters such as target angle, time delay and Doppler, and has a strong parameter identification capability.

[0016] (3) The present invention adopts an L-shaped array structure and a coupled tensor decomposition model, which is relatively simple in structure, easy to implement, and can complete multi-objective parameter estimation with low hardware complexity.

[0017] The objects and other advantages of the present invention can be realized and obtained by means of the structures particularly pointed out in the written description, claims and drawings. Attached Figure Description

[0018] Figure 1 This is a system model diagram of an integrated target parameter estimation method for an L-shaped array OFDM based on coupled tensor decomposition proposed in this invention.

[0019] Figure 2 This is a comparison chart of the three-dimensional target localization results of the algorithm proposed in this invention and the traditional algorithm.

[0020] Figure 3 This is a comparison chart of the target azimuth and elevation angle estimation results of the algorithm proposed in this invention and the traditional algorithm.

[0021] Figure 4This is a comparison chart of the target distance and velocity estimation results of the algorithm proposed in this invention and the traditional algorithm.

[0022] Figure 5 This is a graph showing the cumulative distribution function results of the RMSE performance of the algorithm proposed in this invention and the traditional algorithm relative to the azimuth angle.

[0023] Figure 6 This is a graph showing the cumulative distribution function results of the RMSE performance of the algorithm proposed in this invention and the traditional algorithm relative to the pitch angle.

[0024] Figure 7 This is a graph showing the cumulative distribution function of the RMSE performance of the algorithm proposed in this invention and the traditional algorithm relative to the distance.

[0025] Figure 8 This is a graph showing the cumulative distribution function of the RMSE performance of the algorithm proposed in this invention and the traditional algorithm relative to speed. Detailed Implementation

[0026] 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.

[0027] A method for estimating target parameters of an L-shaped array OFDM with integrated sensing based on coupled tensor decomposition is described below:

[0028] Step 1: For the L-shaped array OFDM sensing system, construct a target perception model, which includes the transmitted signal and echo signal of the base station of the sensing system.

[0029] In a further embodiment, the OFDM inductive integrated system of the L-shaped receiver array includes an inductive integrated transmitter and an inductive integrated receiver, wherein the inductive integrated transmitter transmits OFDM waveforms to simultaneously achieve communication transmission and monitoring of the surrounding environment. For target perception, the integrated sensing receiver employs a spatially separated L-shaped array to receive the target's reflected echo signal; the L-shaped array consists of two mutually orthogonal uniform linear arrays, including those along... The shaft is set with A uniform linear array of antennas and along The shaft is set with A uniform linear array of antennas; to balance power consumption and hardware cost, each uniform linear array adopts a hybrid merging architecture: Axial uniform linear arrays are connected via a fully connected phase shifter network. One radio frequency link, Axial uniform linear arrays are connected via a fully connected phase shifter network. One radio frequency link, and satisfying , ; shaft and The receiver combining matrices of the axial uniform linear array are respectively expressed as: .

[0030] Build bandwidth And spanning the continuous OFDM transmit signal model of OFDM symbol, the first OFDM symbol The complex baseband time-domain transmitted signal corresponding to each OFDM symbol is represented as follows:

[0031]

[0032] in, Indicates the first The first OFDM symbol Transmitted complex symbols on each subcarrier, This represents the total number of subcarriers in a single OFDM symbol, with a subcarrier spacing of . The duration of a single OFDM symbol is ,in For the duration of the effective symbol, For the duration of the loop prefix, a rectangular window function exist The value is 1 at any given time and 0 at all other times.

[0033] In continuous During the duration of one OFDM symbol, the complex baseband transmitted signal is represented as follows:

[0034]

[0035] The complex baseband transmit signal is up-converted to the radio frequency band to obtain the radio frequency transmit signal.

[0036]

[0037] in, Indicates the carrier frequency;

[0038] Suppose that there exists in three-dimensional space The target point, the first The parameters corresponding to each target include distance. radial velocity Azimuth and pitch angle ; during a duration of Within a coherent processing time, the first The round-trip propagation time delay of a target varies with the radial motion of the target, and its expression is as follows:

[0039]

[0040] in, Indicates the round-trip propagation delay. Represents the speed of light;

[0041] remember Axial uniform linear array and The radio frequency echo signals received by the axial uniform linear array are respectively and Under the far-field plane wave assumption, the two sets of radio frequency echo signals are respectively expressed as:

[0042]

[0043]

[0044] in, Indicates the first The complex reflection coefficient of a target, and These represent the propagation noise terms corresponding to the two sets of uniform linear arrays, respectively.

[0045] Establish a corresponding array manifold model for the L-shaped array, where, Axial uniform linear array and The guiding vectors of the axially uniform linear array are respectively expressed as:

[0046]

[0047] The response of a standard uniform linear array is expressed as:

[0048]

[0049] In the formula, Indicates the spacing between array elements. The carrier wavelength is represented; the direction cosine is defined as to characterize the three-dimensional angle parameters.

[0050]

[0051] The received radio frequency echo signal is down-converted to remove the carrier term. Then, through the hybrid merging matrix respectively and The two sets of echoes are combined to obtain the baseband echo signal.

[0052]

[0053]

[0054] in, Indicates the effective reflection coefficient. Indicates the round-trip Doppler frequency shift. and This represents the noise term after merging; Under the condition of, an approximate relationship is adopted. .

[0055] After removing the cycle prefix, at the 1st Sampling is performed within each OFDM symbol to obtain the base station end. shaft and The discrete-time echo signals corresponding to the axial uniform linear array are as follows:

[0056]

[0057]

[0058] in, and These represent the corresponding discrete noise terms. .

[0059] Step 2: Establish a communication transmission model, which includes downlink OFDM communication user terminal received signal and a frequency-selective multipath channel model, used to characterize the transmission mechanism and channel structure characteristics of the communication link and sensing link under a unified OFDM resource grid.

[0060] In the OFDM inductive integrated system, considering the downlink communication transmission model, the base station transmitter adopts a single-antenna structure and broadcasts OFDM symbols in the downlink direction. The communication user terminal, after removing the cyclic prefix and performing a fast Fourier transform, transmits the OFDM symbol at the... The first OFDM symbol The received signal on each subcarrier is represented as

[0061]

[0062] in, Indicates the first Frequency domain downlink channel coefficients on each subcarrier Indicates the first The OFDM symbol of the first Transmitted symbols on each subcarrier This represents additive noise that follows a complex Gaussian distribution. .

[0063] A frequency-selective multipath channel model is used to model a single-input single-output downlink communication link, wherein the first... The channel response corresponding to each subcarrier is represented as a superposition of multipath components, i.e.

[0064]

[0065] in, and They represent the first Complex gain and delay of each propagation path, Indicates the number of resolvable multipath components. This indicates the subcarrier spacing.

[0066] Step 3: Based on the base station's L-shaped receiver array shaft and For the discrete-time echo signal corresponding to the axial uniform linear array, construct corresponding third-order tensor models along the OFDM symbol dimension, the received radio frequency link dimension, and the subcarrier dimension, respectively. Based on this, utilize the structural characteristic that the horizontal and vertical axis echo tensors share a time delay correlation factor in the subcarrier dimension to construct a coupled tensor that satisfies the Coupled Typical Multilinear Decomposition (CPD). The coupled tensor decomposition sensing problem is transformed into a corresponding optimization problem. The specific steps are as follows:

[0067] Performing a Fast Fourier Transform on the discrete-time echo signal yields the result from... Axial uniform linear array and The frequency domain echo signals observed by the axially uniform linear array are represented as follows:

[0068]

[0069]

[0070] in, for Frequency domain echo signal measured by a uniform linear array of axes. for Frequency domain echo signal observed from an axially uniform linear array. and for Axial uniform linear array and Noise term corresponding to axial uniform linear array.

[0071] To facilitate tensor-based signal processing, after removing the influence of training symbols at the receiver, the echo signal is represented as...

[0072]

[0073]

[0074] in, , This represents the noise term after removing the training symbols.

[0075] To explicitly separate the receiver array response from the echo signal, the effective receiver spatial characteristics are defined as follows:

[0076]

[0077]

[0078] Shift the Doppler frequency at The phase progression relationships on each OFDM symbol are respectively represented as follows: shaft and Time steering vector corresponding to the axis

[0079]

[0080]

[0081] in, and Characterization shaft and The axis may have array-related calibration errors and scale differences, ideally... and Both are 1.

[0082] For each subcarrier ,Will Observation signal on OFDM symbol and Reconstructed into data matrices indexed by subcarriers

[0083]

[0084]

[0085] Each row corresponds to an OFDM symbol index. Each column corresponds to the combined observation value of the radio frequency link on the corresponding receiving axis.

[0086] Substituting the echo signal after removing the training symbols into the data matrix, the echo observations on each subcarrier satisfy the rank of... The bilinear decomposition form, i.e.

[0087]

[0088]

[0089] in, and This is the corresponding noise matrix.

[0090] set up One subcarrier is used for target sensing, and the representation delay is defined in the... The range-dependent subcarrier steering vector that causes the phase progression relationship on each subcarrier is:

[0091]

[0092] Through the The echo observations on each subcarrier are collected and combined. shaft and The signals received by the axial uniform linear array are reconstructed into two third-order tensors, denoted as follows: Among them, the first of the two third-order tensors Each forward slice is respectively and , .

[0093] In rank Under the model, the received tensor and The following third-order tensor models (CPDs) are respectively satisfied:

[0094]

[0095]

[0096] in, Represents the cross product of vectors. and This corresponds to the noise tensor.

[0097] Due to the structural characteristic that the horizontal and vertical axis echo tensors share a time delay correlation factor in the subcarrier dimension, a coupled tensor representation satisfying the typical multilinear decomposition of coupling is constructed, and the factor matrix corresponding to the coupled tensor is constructed as follows.

[0098]

[0099]

[0100]

[0101]

[0102]

[0103] in, and Through the shared subcarrier factor matrix To achieve coupling, the shared subcarrier factor matrix The spatial factor matrix characterizes the time-delay-dependent cross-subcarrier phase progression characteristic shared by the two receiving axes. and These correspond to different array manifolds in two orthogonal directions.

[0104] Based on the aforementioned coupled tensor, the coupled tensor decomposition perception problem is constructed as the following optimization problem:

[0105]

[0106] Set of target parameters to be estimated Embedded in the factor matrix, after obtaining the factor matrix estimate, by and Recover the direction cosine respectively and ,Depend on and Restoring Doppler frequency shift , from the shared factor matrix Recover the time delay parameters and complex reflection coefficient.

[0107] Step 4: Design a two-stage coupled CPD parameter estimation algorithm for the coupled tensor. This involves solving the coupled tensor decomposition problem to estimate the corresponding factor matrix, and then extracting the target direction cosine, Doppler shift, time delay, and complex reflection coefficient information based on the estimated coupling factor matrix. This further recovers the azimuth and elevation parameters of each target, thus completing the joint estimation of azimuth, elevation, Doppler shift, time delay, and complex reflection coefficients for multiple targets.

[0108] Based on the constructed coupling tensor and By solving the coupled least squares fitting problem, the factor matrix is... To make an estimate, that is

[0109]

[0110] The coupled least squares fitting problem is solved iteratively using the alternating least squares (ALS) method, denoted as... and Represent tensors respectively and The Modular expansion matrix, in the first In this iteration, the remaining factor matrices are fixed, and each individual factor matrix is ​​minimized and updated to obtain...

[0111]

[0112]

[0113]

[0114]

[0115]

[0116] For the least squares problem Its optimal solution is Therefore, the closed-form update expression for each factor matrix is ​​obtained as follows:

[0117]

[0118]

[0119]

[0120]

[0121]

[0122] in, , The factor matrix estimate is obtained by iteratively solving until convergence. .

[0123] Since the CPD decomposition involves permutation ambiguity and scale ambiguity, the factor matrix estimation results satisfy...

[0124]

[0125]

[0126]

[0127]

[0128]

[0129] in, Represents the common permutation matrix, , , , and Represents the diagonal scaling matrix. Let represent the estimated error term, and satisfy . .

[0130] set up and They represent and The List, and They represent and The List, express The List.

[0131] For angle parameter estimation, direction cosine and Embedded in the receiving space factor matrix respectively and In the equation, the estimated column vector satisfies

[0132]

[0133] in, and For unknown multiscalar quantity, and To decompose the error term, the cosine of the target direction is estimated using least-squares fitting. and ,Right now

[0134]

[0135]

[0136] This is further equivalently transformed into a relevance-maximizing search, i.e.

[0137]

[0138]

[0139] Based on the estimated direction cosine, the target azimuth and elevation angles are calculated as follows:

[0140] .

[0141] For Doppler frequency shift parameter estimation, the Doppler steering vector is defined as follows:

[0142]

[0143] Then the first Each time factor satisfies

[0144]

[0145] in, and For unknown multiscalar quantity, and The residual error term is used; the Doppler frequency shift is estimated by jointly fitting two time factors. ,Right now

[0146]

[0147] This is further equivalently transformed into a relevance-maximizing search, i.e.

[0148]

[0149] For time delay parameter estimation, the distance-related steering vector is defined as follows:

[0150]

[0151] Then the first A shared subcarrier factor satisfies

[0152]

[0153] in, For unknown multiscalar quantity, The residual error term is used; the time delay is estimated through least squares fitting, i.e.

[0154]

[0155] This is further equivalently transformed into a relevance-maximizing search, i.e.

[0156]

[0157] After obtaining the time delay estimation results, the target complex reflection coefficients are further estimated by combining the two coupling tensors. Complex reflection coefficient vector The estimation is performed using the following joint least squares problem:

[0158]

[0159] in, , , .

[0160] Its closed-form solution is

[0161]

[0162] in, , Finally, the joint estimation results of the multi-objective parameters are obtained. .

[0163] Example 1

[0164] This embodiment uses computer simulation to verify the proposed method for estimating target parameters of an L-shaped array OFDM based on coupled tensor decomposition. All steps and conclusions have been verified to be correct on the MATLAB platform.

[0165] In this embodiment, the receiver employs an L-shaped array with a hybrid beamforming architecture. The total number of receiving antennas in the L-shaped receiver array is... , among which along axis and along The two orthogonal uniform linear arrays of the axis are respectively set as and There are [number] antennas; the total number of RF links at the receiver is [number]. ,in shaft and The axes correspond to and One radio frequency link. Receiver merging matrix. and Each element is generated randomly and uniformly from the unit circle.

[0166] The simulation parameters are set as follows: carrier frequency GHz, OFDM signal bandwidth MHz, total number of subcarriers The duration of the loop prefix is ​​set to ,in, Subcarrier spacing; noise power spectral density set to -174dBm / Hz; base station pairs The system senses individual targets; the communication data load uses QAM modulation.

[0167] The target parameters are set as follows: azimuth angles of each target. and pitch angle In the intervals and Randomly generated within the range; target distance and speed are respectively within the range and Uniformly distributed within, among which m, m, maximum speed m / s. The complex reflection coefficients of each target are generated according to the following formula:

[0168]

[0169] in, Indicates the base station and the first The distance between the targets To represent the target's radar cross section, take... , To conform to a uniform distribution The random phase.

[0170] This embodiment uses the root mean square error (RMSE) as the performance index for estimating the target parameter, and its expression is:

[0171]

[0172] in, and They represent the first The estimated and actual values ​​of each target parameter. Meanwhile, the standard CPD method, the MUSIC method, and the OMP method were selected as comparative methods.

[0173] like Figure 2 As shown, this is at the transmit power Comparison of 3D target localization results using different methods under dB conditions. Figure 2 As can be seen, the target location estimation result obtained by the coupled CPD method proposed in this invention highly coincides with the true target coordinates, while the positioning results of the ordinary CPD method, MUSIC method, and OMP method have a large degree of dispersion and obvious bias. This result demonstrates that the method of this invention can be combined with... shaft and The inherent coupling relationship between the two receiving tensors of the axis enables the automatic association of multi-target parameters, thereby improving the three-dimensional positioning accuracy of the target.

[0174] like Figure 3 As shown, this is at the transmit power A comparison of azimuth and elevation estimation results using different methods under dB conditions. Figure 3 As can be seen, the angle estimation results obtained by the coupled CPD method proposed in this invention are more concentrated near the true angle position, while the ordinary CPD method, MUSIC method, and OMP method have large angle offsets. This indicates that the present invention, by coupling and modeling the echo tensors in two orthogonal directions through a shared subcarrier factor, can better preserve the multidimensional structural information of the signal, thereby improving the accuracy of angle parameter estimation.

[0175] like Figure 4 As shown, this is at the transmit power A comparison of distance and velocity estimation results from different methods under dB conditions. Figure 4 As can be seen, the coupled CPD method proposed in this invention can accurately recover the range and velocity parameters of each target, and the parameter correspondence is correct; while the estimation errors of the ordinary CPD method, the MUSIC method, and the OMP method are larger and more prone to outliers. This result shows that the method of this invention achieves reliable joint estimation of range and velocity parameters by jointly utilizing echo information from two spatial dimensions and constraining the range correlation factor by using a shared subcarrier mode.

[0176] like Figure 5 The figure shows the empirical cumulative distribution function (CDF) curve of the azimuth angle estimation RMSE, where the number of training subcarriers is... OFDM symbol count .Depend on Figure 5 As can be seen, the CDF curve corresponding to the coupled CPD method proposed in this invention is located on the far left and rises faster, indicating that this method has a higher probability of obtaining a smaller azimuth estimation error and the error distribution is more concentrated. In contrast, the ordinary CPD method has a more obvious large error tail, while the MUSIC method and OMP method accumulate significantly in the high error region, indicating that they are more susceptible to noise and multi-target interference under the L-shaped array measurement model.

[0177] like Figure 6 The figure shows the empirical cumulative distribution function (CDF) curve of the pitch angle estimation RMSE, where the number of training subcarriers is... OFDM symbol count .Depend on Figure 6 As can be seen, the coupled CPD method proposed in this invention still exhibits the best performance, with its CDF curve located on the far left, indicating that it also has higher accuracy and stronger robustness in pitch angle estimation. The error distribution of the ordinary CPD method is relatively dispersed, while the MUSIC method and OMP method are concentrated in a larger RMSE region, indicating that their pitch angle estimation performance is significantly reduced under conditions of limited snapshot count and multi-target coupling.

[0178] like Figure 7 The figure shows the empirical cumulative distribution function (CDF) curve for the distance estimation RMSE, where the number of training subcarriers is... OFDM symbol count .Depend on Figure 7 As can be seen, the coupled CPD method proposed in this invention has lower error and more concentrated distribution characteristics. This is because this invention uniformly characterizes the cross-subcarrier delay phase progression by sharing a subcarrier factor, supported by two received tensors, thereby achieving multi-subcarrier information fusion and suppressing estimation fluctuations caused by noise. Therefore, it has higher reliability in distance estimation.

[0179] like Figure 8 The figure shows the empirical cumulative distribution function (CDF) curve for the velocity estimation RMSE, where the number of training subcarriers is... OFDM symbol count .Depend on Figure 8As can be seen, the coupled CPD method proposed in this invention exhibits the leftmost CDF curve throughout the entire probability interval, indicating that its velocity estimation error is smaller and its estimation stability is better. In contrast, the ordinary CPD method shows obvious right shift and heavy-tailed phenomena, and the MUSIC and OMP methods perform even worse, indicating that they are more prone to estimation failure under limited data and noise conditions.

[0180] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto.

[0181] Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this invention should be included within the protection scope of this invention.

[0182] It should be understood that, in order to simplify the present invention and help those skilled in the art understand its various aspects, in the above description of exemplary embodiments of the present invention, various features of the present invention are sometimes described in a single embodiment or with reference to a single figure. However, the present invention should not be construed as including all features in the exemplary embodiments as essential technical features of the claims of this patent.

Claims

1. A method for estimating target parameters of an L-shaped array OFDM sensor based on coupled tensor decomposition, characterized in that, The specific steps are as follows: Step 1: For the L-shaped array OFDM integrated sensing system, construct a target sensing model, which includes the transmitted signal and echo signal of the integrated sensing system; Step 2: Establish a communication transmission model, which includes downlink OFDM communication user terminal received signal and frequency selective multipath channel model, used to characterize the transmission mechanism and channel structure characteristics of communication link and sensing link under unified OFDM resource grid; Step 3: Based on the base station's L-shaped receiver array shaft and For the discrete-time echo signal corresponding to the axial uniform linear array, a third-order tensor model is constructed along the OFDM symbol dimension, the receiving radio frequency link dimension, and the subcarrier dimension. Taking advantage of the structural characteristics of the horizontal and vertical axis echo tensors sharing the time delay correlation factor in the subcarrier dimension, a coupled tensor that satisfies the typical multilinear decomposition of coupling is constructed, and the coupled tensor decomposition sensing problem is transformed into the corresponding optimization problem. Step 4: Design a two-stage coupled CPD parameter estimation algorithm for the coupled tensor. Estimate the corresponding factor matrix by solving the coupled tensor decomposition problem, and extract the target direction cosine, Doppler frequency shift, time delay and complex reflection coefficient information in sequence based on the estimated coupling factor matrix to recover the azimuth and elevation parameters of each target, thereby completing the joint estimation of the azimuth, elevation, Doppler frequency shift, time delay and complex reflection coefficient of multiple targets.

2. The method for estimating target parameters of an L-shaped array OFDM integrated sensing system based on coupled tensor decomposition according to claim 1, characterized in that, The L-shaped receiver array OFDM inductive integrated system includes an inductive integrated transmitter and an inductive integrated receiver. The inductive integrated transmitter transmits OFDM waveforms to simultaneously achieve communication transmission and monitoring of the surrounding environment. For target perception, the integrated sensing receiver employs a spatially separated L-shaped array to receive the target's reflected echo signal; the L-shaped array consists of two mutually orthogonal uniform linear arrays, including those along... The shaft is set with A uniform linear array of antennas and along The shaft is set with A uniform linear array of antennas; Axial uniform linear arrays are connected via a fully connected phase shifter network. One radio frequency link, Axial uniform linear arrays are connected via a fully connected phase shifter network. One radio frequency link, and satisfying , .

3. The method for estimating target parameters of an L-shaped array OFDM integrated sensing system based on coupled tensor decomposition according to claim 1, characterized in that, The specific transmitted signal of the integrated sensing system is as follows: ； In the formula, , Indicates the carrier frequency. Indicates the first The first OFDM symbol Transmitted complex symbols on each subcarrier, This represents the total number of subcarriers in a single OFDM symbol. For the total number of symbols, For subcarrier spacing, the duration of a single OFDM symbol is... ,in For the duration of the effective symbol, For the duration of the loop prefix, a rectangular window function exist The value is 1 at any given time, and 0 at all other times. ; The echo signal of the integrated sensing system is from the base station. shaft and The discrete-time echo signals acquired by the axially uniform linear array are as follows: ； ； in, and They represent shaft and The discrete noise term corresponding to the axis, For the target number, the first The parameters corresponding to each target include distance. radial velocity Azimuth and pitch angle , Indicates the effective reflection coefficient. Indicates the round-trip Doppler frequency shift. They are respectively shaft and The receiving and merging matrix of the axis. Indicates the round-trip propagation delay. Representing the speed of light, discrete sampling is performed within the OFDM symbol. , The guiding vector of the axial uniform linear array is and The guiding vector of the axial uniform linear array is , This is the conjugate transpose of the matrix.

4. The method for estimating target parameters of an L-shaped array OFDM integrated sensing system based on coupled tensor decomposition according to claim 1, characterized in that, The specific method for establishing the communication transmission model is as follows: In the OFDM integrated sensing system, the base station transmitter adopts a single-antenna structure and broadcasts OFDM symbols in the downlink direction. After removing the cyclic prefix and performing a fast Fourier transform, the communication user end obtains the... The first OFDM symbol Received signal on each subcarrier Specifically, it is expressed as: in, Indicates the first Frequency domain downlink channel coefficients on each subcarrier Indicates the first The OFDM symbol of the first Transmitted symbols on each subcarrier This represents additive noise that follows a complex Gaussian distribution; A frequency-selective multipath channel model is used to model a single-input single-output downlink communication link, wherein the first... The channel response corresponding to each subcarrier is represented as a superposition of multipath components, i.e. ； in, and They represent the first Complex gain and delay of each propagation path, Indicates the number of resolvable multipath components. Indicates the subcarrier spacing. .

5. The method for estimating target parameters of an L-shaped array OFDM integrated sensing system based on coupled tensor decomposition according to claim 1, characterized in that, According to the base station L-shaped receiving array shaft and The specific method for constructing a third-order tensor model of the discrete-time echo signal corresponding to an axially uniform linear array along the OFDM symbol dimension, the received radio frequency link dimension, and the subcarrier dimension is as follows: Perform a Fast Fourier Transform on the discrete-time echo signal to obtain Axial uniform linear array and Frequency domain echo signal observed from an axially uniform linear array; At the receiving end, the influence of training symbols on the frequency domain echo signal is removed to obtain the echo signal after removing training symbols: ； ； in, for Frequency domain echo signal observed from an axially uniform linear array. for Frequency domain echo signal observed from an axially uniform linear array. For the first The OFDM symbol of the first Transmitted symbols on each subcarrier The conjugate; The effective reception space characteristics are defined as follows: in, for The receiving and merging matrix of the axis. for The receiving and merging matrix of the axis. for The direction cosine of the axis, for The direction cosine of the axis, for Spatial eigenvectors of axes for Spatial eigenvectors of axes for Number of receiver array antennas along the axial direction for Number of receiver array antennas along the axial direction for The guiding vector of an axially uniform linear array. for The guiding vector of an axially uniform linear array; Shift the Doppler frequency at The phase progression relationships on each OFDM symbol are respectively represented as follows: shaft and The time steering vector corresponding to the axis: in, and They represent shaft and The axis may have array-related calibration errors and scale differences. Indicates round-trip Doppler frequency shift, The total number of OFDM symbols, Duration of a single OFDM symbol; For each subcarrier ,Will Observation signal on OFDM symbol and Reconstructed into data matrices indexed by subcarriers: Each row corresponds to an OFDM symbol index. Each column corresponds to the combined observation value of the radio frequency link on the corresponding receiving axis; Substituting the echo signal after removing the training symbols into the data matrix indexed by the subcarriers, we obtain the echo observations on each subcarrier that satisfy the rank of... The bilinear decomposition form, i.e. ； ； in, and For the corresponding noise matrix, Indicates the effective reflection coefficient. Indicates the round-trip propagation delay. Subcarrier spacing; set up Each subcarrier is used for target sensing, defining the representation delay in... The range-dependent subcarrier steering vector that causes the phase progression relationship on each subcarrier is: ； Through the The echo observations on each subcarrier are collected and combined. shaft and The signals received by the axial uniform linear array are reconstructed into two third-order tensors, denoted as follows: Among them, the first of the two third-order tensors Each forward slice is respectively and , ; In rank Under the model, the receiving tensor and Each of the following third-order tensor models satisfies: ； ； in, Represents the cross product of vectors. and For the corresponding noise tensor, for Axial time dimension factor matrix, for The spatial dimension factor matrix of the axis, for The time dimension factor matrix of the axis, for Axial space dimension factor matrix, For subcarrier dimension factor matrix, and That is, the constructed third-order tensor model.

6. The method for estimating target parameters of an L-shaped array OFDM integrated sensing system based on coupled tensor decomposition according to claim 5, characterized in that, Utilizing the structural characteristic that the horizontal and vertical axis echo tensors share a time delay correlation factor in the subcarrier dimension, a coupled tensor satisfying the typical multilinear decomposition of coupling is constructed. The factor matrix corresponding to the coupled tensor is: in, and They are respectively shaft and The time steering vector corresponding to the axis, for Spatial eigenvectors of axes for Spatial eigenvectors of axes Indicates the effective reflection coefficient. For distance-dependent subcarrier steering vectors, for Axial time dimension factor matrix, for The spatial dimension factor matrix of the axis, for The time dimension factor matrix of the axis, for Axial space dimension factor matrix, This is the subcarrier dimension factor matrix; and Through the shared subcarrier factor matrix To achieve coupling, the shared subcarrier factor matrix The spatial factor matrix characterizes the time-delay-dependent cross-subcarrier phase progression characteristic shared by the two receiving axes. and These correspond to different array manifolds in two orthogonal directions.

7. The method for estimating target parameters of an L-shaped array OFDM integrated sensing system based on coupled tensor decomposition according to claim 6, characterized in that, The coupled tensor decomposition perception problem is transformed into a corresponding optimization problem, specifically: 。 8. The method for estimating target parameters of an L-shaped array OFDM integrated sensing system based on coupled tensor decomposition according to claim 7, characterized in that, A two-stage coupled CPD parameter estimation algorithm is designed for the coupled tensor, and the corresponding factor matrix is ​​estimated by solving the coupled tensor decomposition problem: Based on the constructed shaft and Coupled tensor of the received signal of the axial uniform linear array and By solving the coupled least squares fitting problem, the factor matrix is... To make an estimate, that is ； Factor matrix The estimated value.

9. The method for estimating target parameters of an L-shaped array OFDM integrated sensing system based on coupled tensor decomposition according to claim 8, characterized in that, Based on the estimated coupling factor matrix, the target direction cosine, Doppler frequency shift, time delay, and complex reflection coefficient information are extracted sequentially to recover the azimuth and elevation parameters of each target. The specific method for jointly estimating the azimuth, elevation, Doppler frequency shift, time delay, and complex reflection coefficient of multiple targets is as follows: The coupled least squares fitting problem is solved iteratively using the alternating least squares (ALS) method, specifically as follows: and Represent tensors respectively and The Modular expansion matrix, in the first In this iteration, the remaining factor matrices are fixed, and each individual factor matrix is ​​minimized and updated to obtain... ； in, for Time dimension factor matrix of the axis The The result of the second iteration for Spatial dimension factor matrix of axes The The result of the second iteration for Time dimension factor matrix of the axis The The result of the second iteration for Spatial dimension factor matrix of axes The The result of the second iteration Represented as a subcarrier dimension factor matrix The The result of the second iteration Represented as the Khatri-Rao product; For the least squares problem The optimal solution is Therefore, the closed-form update expression for each factor matrix is ​​obtained as follows: in, , The factor matrix estimate is obtained by iteratively solving until convergence. ; set up and They represent and The List, and They represent and The List, express The List; For angle parameter estimation, direction cosine and Embedded in the spatial dimension factor matrix and In the equation, the estimated column vector satisfies in, and For unknown multiscalar quantity, for Spatial eigenvectors of axes for Spatial eigenvectors of axes and To decompose the error term; Estimate by least squares fitting respectively Cosine estimate of the target direction along the axis and Cosine estimate of the target direction along the axis ,Right now Calculate the target azimuth estimate based on the obtained direction cosine. and pitch angle estimates for ； For Doppler frequency shift parameter estimation, the Doppler steering vector is defined as: in, Indicates Doppler frequency shift, The total number of OFDM symbols, Duration of a single OFDM symbol; Then the first Each time factor satisfies in, and For unknown multiscalar quantity, and The residual error term is used; the Doppler frequency shift estimate is obtained by jointly fitting two time factors. ,Right now ； For time delay parameter estimation, the distance-related steering vector is defined as follows: in, Indicates the propagation delay. For subcarrier spacing, Let be the number of subcarriers used for target sensing; then the th A shared subcarrier factor satisfies in, For unknown multiscalar quantity, The residual error term; the time delay estimate is obtained by least-squares fitting. ,Right now ； After obtaining the time delay estimation results, the target complex reflection coefficients are further estimated by combining the two coupling tensors: complex reflection coefficient vector. The estimation is performed using the following joint least squares problem: in, For reconstruction Axial time dimension factor matrix, For reconstruction The spatial dimension factor matrix of the axis, For reconstruction The time dimension factor matrix of the axis, For reconstruction Axial space dimension factor matrix, For the reconstructed subcarrier dimension factor matrix, For tensor The vectorization result, For tensor The vectorized result; The closed-form solution of the complex reflection coefficient vector is in, , ; Finally, the joint estimation results of the multi-objective parameters are obtained. .

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