Channel Estimation and Waveform Optimization Method for DPSS Near-Field ISAC System

Abstract

The present invention discloses a method for channel estimation and waveform optimization of a DPSS-based near-field ISAC system, including: establishing a near-field ISAC channel and a signal model; designing a channel estimation scheme; designing a joint communication and sensing optimization problem; based on the designed joint communication and sensing optimization problem, designing a joint optimization algorithm under a full-digital architecture; and then based on the designed joint communication and sensing optimization problem, designing a joint optimization algorithm under a hybrid beamforming architecture. Compared with the DFT codebook and spherical codebook structures, the present invention can have stronger energy concentration and lower inter-column correlation, can effectively reduce energy leakage, improve the sparsity of the channel, and significantly improve the channel estimation accuracy. In addition, the DPSS structure is more adaptable to the near-field propagation characteristics. Combining with the compressed sensing method, high-precision channel estimation can be achieved under limited pilot resources, thereby improving communication and sensing performance in the near-field ISAC system.

Description

Technical Field

[0001] The present invention relates to a method for channel estimation and waveform optimization of a DPSS near-field ISAC system, belonging to the technical field of wireless communication and sensing integration. Background Art

[0002] With the rapid development of the sixth-generation mobile communication technology (6G), traditional wireless communication systems are gradually evolving towards integrated sensing and communication (ISAC) systems. By simultaneously achieving high-quality communication and high-precision sensing tasks on shared spectrum resources and hardware platforms, ISAC systems can effectively improve spectrum utilization, system integration, and service diversity, and have become an important research direction for the next-generation wireless communication systems.

[0003] In an ISAC system, obtaining accurate channel state information (CSI) is a key prerequisite for achieving communication reliability and sensing accuracy. However, most of the existing channel estimation methods are based on far-field propagation models, assuming that the signal wavefront received by each antenna element of the receiving array is a plane wave and only related to angle parameters. This modeling method is more applicable in traditional far-field communication scenarios. However, in typical 6G applications such as large-scale antenna arrays, millimeter-wave / terahertz communication bands, and close-range target detection, the system will inevitably enter the near-field propagation paradigm, where electromagnetic waves exhibit spherical wave characteristics, and the channel response depends on both angle and distance parameters. Under these conditions, far-field modeling will lead to serious performance degradation, including problems such as beam energy leakage, sparsity loss, and upper limit of estimation error, thus affecting the overall performance of communication and sensing.

[0004] To address the above problems, existing research has attempted to introduce spherical wave models and high-resolution codebooks to improve near-field channel estimation, but there are still problems such as severe oversampling, high inter-column correlation, and high computational complexity. Discrete Prolate Spheroidal Sequences (DPSS) are introduced to construct a sparse beam codebook due to their good spectral energy concentration and low cross-correlation, and have better near-field channel representation ability and estimation accuracy.

[0005] On the other hand, the ISAC system also faces the problem of waveform joint design, that is, maximizing the sensing accuracy under the premise of meeting the communication performance constraints. Traditional communication system design emphasizes throughput and channel capacity, while the sensing system pays more attention to beam directivity and delay resolution ability. There are significant conflicts between the performance indicators of the two when resources are limited. Therefore, an efficient communication-sensing collaborative waveform optimization strategy is urgently needed. In addition, the currently widely used hybrid beamforming architecture reduces the hardware complexity while introducing the non-convex constraint problem of signal design, further increasing the technical difficulty of waveform joint optimization. Therefore, a solution with efficient near-field channel modeling, low-complexity estimation, and communication-sensing collaborative optimization capabilities is needed to promote the application of the ISAC system in actual complex near-field environments. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method for channel estimation and waveform optimization of a DPSS near-field ISAC system. Through the DPSS codebook construction technology, two-stage near-field channel estimation algorithm, joint waveform optimization modeling and alternating iteration algorithm, the dual goals of ensuring communication performance and improving sensing accuracy are achieved, and it is applicable to near-field ISAC application scenarios under all-digital and hybrid beamforming architectures.

[0007] The present invention adopts the following technical solutions to solve the above technical problems:

[0008] A method for channel estimation and waveform optimization of a DPSS near-field ISAC system, the near-field ISAC system includes a base station with a uniform linear array equipped with antenna elements, communication users, and a sensing target. The system operates in the millimeter wave band. The method includes the following steps:

[0009] Step 1, establish a near-field ISAC system model, including the channels of each communication user, the channel of the sensing target, the transmission signal of the base station under the near-field all-digital architecture, and the transmission signal model of the base station under the near-field hybrid beam architecture;

[0010] Step 2, introduce a sparse representation of the channel models of each communication user, introduce a compensation matrix to construct a DPSS codebook, and use the orthogonal matching pursuit algorithm to estimate the channels of each communication user to obtain the near-field channel estimation values of each communication user;

[0011] Step 3, calculate the overall channel estimation error of all communication users based on the near-field channel estimation values of each communication user, and construct a waveform optimization problem for joint communication and sensing based on the overall channel estimation error of all communication users and the lower limit of the estimation error of the sensing target;

[0012] Step 4, under the near-field all-digital architecture, an alternating optimization method is used to solve the waveform optimization problem of joint communication and sensing constructed in Step 3 to achieve waveform optimization;

[0013] Step 5, under the near-field hybrid beam architecture, the alternating direction method of multipliers is used to solve the waveform optimization problem of joint communication and sensing constructed in Step 3 to achieve waveform optimization.

[0014] Compared with the prior art, the present invention adopts the above technical solutions and has the following technical effects:

[0015] 1. The present invention introduces a sparse modeling method based on discrete prolate spheroidal sequences (DPSS), which can effectively improve the accuracy of channel estimation. Especially in the near-field ISAC system, through the optimization of the DPSS codebook, the energy leakage and inter-column correlation are significantly reduced, thereby improving the reconstruction performance of channel estimation.

[0016] 2. The present invention adopts the compressive sensing theory and combines it with the DPSS sparse modeling method. While ensuring the accuracy of channel estimation, it effectively reduces the required pilot resource overhead. This technical advantage enables the system to complete high-precision channel estimation with a lower pilot overhead, greatly improving the spectral efficiency.

[0017] 3. In terms of waveform optimization, the present invention introduces a joint optimization framework for communication and sensing functions, which solves the non-convexity and coupling problems of traditional methods in high-dimensional parameter spaces. By adopting the alternating optimization and alternating direction method of multipliers algorithms, more efficient resource allocation can be achieved, optimizing the balance between communication rate and sensing accuracy, and improving the overall performance of the system.

[0018] 4. Under near-field conditions, the present invention improves the traditional far-field plane wave model. By combining the DPSS codebook with the near-field channel model, it can more accurately represent the distance and angle information of the target, thus overcoming the limitations of traditional methods that cannot adapt to the propagation characteristics of near-field waves. Description of the Drawings

[0019] Figure 1 is a model diagram of the near-field ISAC system of the present invention;

[0020] Figure 2 is a flowchart of the present invention;

[0021] Figure 3 is a graph showing the variation of the channel estimation NMSE of the DPSS codebook of the present invention with the DFT and spherical wave codebooks versus the pilot signal-to-noise ratio;

[0022] Figure 4 is a trade-off curve of the single-user single-target communication rate and the sensing error (RCRB);

[0023] Figure 5 It is a sparse representation diagram of the near-field channel under different codebooks;

[0024] Figure 6 It is a comparison curve of the root of the Cramer-Rao lower bound (RCRB) for distance estimation between the all-digital architecture and the hybrid architecture;

[0025] Figure 7 It is a comparison curve of the root of the Cramer-Rao lower bound (RCRB) for angle estimation between the all-digital architecture and the hybrid architecture;

[0026] Figure 8 It is the near-field channel estimation error and compression ratio under different codebooks and the performance ratio diagram of iterations;

[0027] Figure 9 It is the near-field channel estimation error and codebook oversampling rate under different codebooks and the performance ratio diagram of iterations. Detailed implementation manners

[0028] The following details the implementation manners of the present invention. Examples of the implementation manners are shown in the accompanying drawings. The implementation manners described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention and should not be construed as limiting the present invention.

[0029] As Figure 1 and Figure 2 shown, the present invention proposes a method for joint optimization of near-field ISAC system channel estimation and waveform based on the DPSS codebook. The near-field ISAC system based on the DPSS codebook includes a base station (Base Station, BS) equipped with uniform linear array elements, and is simultaneously equipped with communication users and 1 sensing target respectively. The system operates in the millimeter-wave frequency band with a working frequency of , corresponding to a wavelength of , and the element spacing is , then the array length is ; the position coordinate of the th antenna element in the array is , the polar coordinates of the communication user's position are , and the corresponding rectangular coordinates are , the polar coordinates of the sensing user's position are , and the corresponding rectangular coordinates are ; the distance between the communication user and the th antenna element is , the channel of the communication user is , and the channel of the sensing target is ; in the near-field all-digital architecture, at time The transmitted signal is , and the corresponding transmit covariance matrix is ; In the near-field hybrid beamforming architecture, the transmitted signal of the BS at time is , and the corresponding transmit covariance matrix is .

[0030] The specific process of the method is as follows:

[0031] Step 1, establish the near-field ISAC channel and signal model;

[0032] The position coordinates of the th antenna element in the array are expressed as , , and the rectangular coordinates of the positions of the communication user and the sensing user are respectively expressed as , ; The distance between the communication user and the th antenna element is , and the channel corresponding to this user is expressed as , where is the complex attenuation coefficient, and the near-field channel vector of user is expressed as , where is the near-field array response vector; The channel of the sensing target can be expressed as , where is the target complex scattering coefficient, is the near-field array response vector.

[0033] In the ISAC near-field all-digital architecture, the transmitted signal of the BS at time is , where is the beamforming vector of user , is the communication signal of user , satisfying , is the transmitted signal for sensing, and the corresponding transmit covariance matrix is , where is the sensing signal covariance matrix.

[0034] In the ISAC near-field hybrid beamforming architecture, the transmitted signal of the BS at time is , where is the analog precoding matrix, satisfying the constant modulus constraint , where is the digital precoding vector, is the baseband domain sensing signal, and the covariance is ; The transmit covariance matrix is .

[0035] Step 2, design a channel estimation scheme;

[0036] Step 2.1. The user vector in the near field contains distance and angle information. Introduce a sparse representation channel model , is a near-field sparse codebook constructed based on DPSS, is the sparse coefficient vector, represents the set of complex numbers, is the Gaussian noise vector. The goal is to reconstruct under the condition of limited pilot resources, which is expressed as:

[0037] ,

[0038] where is the received observation matrix, is the pilot measurement matrix, is the coefficient for controlling sparsity;

[0039] Step 2.2. Introduce a compensation matrix:

[0040] ,

[0041] where is the reference distance on the axis, is the position of the th array element; According to multiple near-field angle sampling points in the system, generate the phase-compensated channel response matrix

[0042] ,

[0043] Perform eigenvalue decomposition on and extract the first principal eigenvectors to construct the DPSS codebook:

[0044] ;

[0045] Step 2.3. In the coarse estimation stage, use the traditional spherical wave codebook to construct a polar coordinate network , and for each grid point , calculate the matching energy index:

[0046] ,

[0047] Select the largest The corresponding grid point is used as a rough position estimate for the local search range in the fine estimation stage;

[0048] Step 2.4. In the fine estimation stage, based on the constructed DPSS codebook, the OMP compressive sensing algorithm is used to solve:

[0049] ,

[0050] Use the prior rough estimation result to continuously iterate and correct until the reconstruction error converges to a predetermined threshold, and then construct an accurate channel .

[0051] Step 3. Design the joint communication and sensing optimization problem;

[0052] Step 3.1. Through the two-stage DPSS estimation, the near-field channel estimation value of the th communication user is , and its normalized mean square error (NMSE) can be expressed as:

[0053] ,

[0054] After using compressive sensing algorithms such as OMP to recover , the estimated channel can be obtained, and the overall channel estimation error is written as:

[0055] ,

[0056] The error will directly affect the effectiveness of communication beamforming and the accuracy of the Fisher information matrix of the sensing link, so it should be included in the overall optimization objective;

[0057] Step 3.2. It is necessary to ensure the quality of service (QoS) of all communication users, with the lower limit of the communication rate as the index. In the all-digital architecture, the transmit beam can be freely set, and the communication rate is:

[0058] ,

[0059] where represents the noise vector of the channel of the th communication user; for simplification and solution, this rate constraint can be transformed into the form of a second-order cone constraint (SOC):

[0060] ,

[0061] where is the minimum signal-to-noise ratio threshold;

[0062] Step 3.3. The target performance of the sensing link is evaluated by the lower bound of the target positioning error (CRB). According to the Cramer-Rao lower bound theory, the lower bound of the estimation error of the sensing target is:

[0063] ,

[0064] where the Fisher information matrix is defined as:

[0065] ,

[0066] where the parameter ; the signal model depends on the sensing signal covariance and the echo channel ; and are linearly related, and minimizing the CRB is a convex function optimization problem with respect to ;

[0067] Step 3.4. Introduce a weighting factor to control the trade-off between communication and sensing performance, and construct a joint optimization objective function expressed as:

[0068] ,

[0069] where the first term of the optimization objective ensures the minimization of the channel estimation error, and the second term ensures the reduction of the CRB.

[0070] Step 4. Based on the designed joint communication and sensing optimization problem, design a joint optimization algorithm for the full digital architecture;

[0071] Step 4.1. In the full digital architecture, the optimization variables include the transmit beam vector of each user, the sensing signal covariance matrix , the channel estimation result obtained by the OMP method. To solve this non-convex problem, the alternating optimization method is adopted to iteratively optimize , , respectively;

[0072] Step 4.2. Perform channel coefficient reconstruction. For each user , fix the pilot observation matrix , the observation matrix , the codebook , and solve the sparse function:

[0073] ,

[0074] The OMP algorithm can be used to quickly solve and restore the channel ;

[0075] Step 4.3. Fix the channel and the sensing covariance , optimize the beam vector , and perform communication beam optimization. The communication rate constraint is:

[0076] ,

[0077] Introduce auxiliary variables, and this constraint can be transformed into the following SOC form:

[0078] ,

[0079] The optimization objective is a quadratic function and can be transformed into:

[0080] ,

[0081] The problem is a standard second-order cone programming (SOCP) problem;

[0082] Step 4.4. Fix the channel and the beam vector , optimize the sensing covariance , and the optimization problem is transformed into:

[0083] ,

[0084] where the Fisher information matrix and are linearly related, and the problem is a convex function minimization, that is, a standard semi-definite programming (SDP) problem.

[0085] Step 5. Based on the designed joint communication and sensing optimization problem, design a hybrid beamforming architecture joint optimization algorithm.

[0086] Step 5.1. In the hybrid beamforming architecture, the transmitted signal of the base station is expressed as:

[0087] ,

[0088] In this architecture, the joint optimization problem is transformed into:

[0089] ,

[0090] Since and the product of them forms the beam vector, resulting in non-convex coupling. Therefore, introduce auxiliary variables:

[0091] ,

[0092] The optimization objective is transformed into a block form with equality constraints using the Alternating Direction Method of Multipliers (ADMM):

[0093] ,

[0094] where is the Lagrange multiplier variable introduced in ADMM, which is used to update the consistency error term, is the penalty factor in the ADMM iteration, which is used to control the variable update amplitude and the convergence speed; the augmented Lagrangian function is expressed as:

[0095] ;

[0096] Step 5.2. For each user , fix the analog beamforming and auxiliary variables, and update the digital precoder , and the optimization objective is transformed into:

[0097] ,

[0098] This optimization problem is a standard least squares problem, and the closed-form solution can be directly obtained:

[0099] ;

[0100] Step 5.3. Fix the digital beamforming and auxiliary variables, and update the analog beamforming matrix , to make it closest to the target matrix under the constant modulus constraint, and construct the auxiliary matrix as:

[0101] ,

[0102] This problem is a projection problem with a constant modulus constraint and can be updated element by element:

[0103] ;

[0104] Step 5.4. Fix the analog beamforming and digital beamforming, and update the auxiliary variable , and the goal is to optimize the trade-off between the communication error and the consistency error. The optimization problem is transformed into:

[0105] ,

[0106] This problem is a weighted quadratic function, and the closed-form solution is:

[0107] ;

[0108] Step 5.5. Update the Lagrange multiplier , and adjust the multiplier to make the variable constraint satisfy:

[0109] ,

[0110] If the gap between the current variables is large, increase the multiplier; if they have tended to be consistent, the change of the multiplier tends to be stable.

[0111] Step 5.6. After fixing all beams, update the sensing covariance , to minimize the CRB:

[0112] ,

[0113] The problem is transformed into an SDP problem.

[0114] The following takes an embodiment for simulation, and the parameter settings of the embodiment are as follows: The transmitter uses 192 transmit antennas, the number of communication users , the user distance is , the user angle is , the base station operating frequency , the corresponding wavelength , the element spacing , the total transmit power budget , the minimum communication rate requirement for each user .

[0115] Figure 3 is the change diagram of the channel estimation NMSE of the present invention, DFT and spherical codebooks with respect to the pilot signal-to-noise ratio. The three curves in the figure: the blue curve represents the DFT codebook; the red curve represents the spherical codebook; the yellow curve represents the DPSS codebook. It can be seen from the figure that at low signal-to-noise ratios, noise dominates the error, and the estimation performances of the three codebooks converge. In the high signal-to-noise ratio region, due to model mismatch, the DFT codebook will have energy leakage, and OMP cannot accurately represent the spherical wave channel with a single DFT beam even in the absence of noise, resulting in a higher error floor; the spherical wave codebook has no mismatch but has column correlation, and OMP may misselect or require multiple atoms to represent the same path, which will also bring errors; the DPSS codebook approximately optimally compresses the channel subspace within the design range, greatly reducing leakage and correlation, and thus has a lower error floor.

[0116] Figure 4 is the trade-off curve between the single-user single-target communication rate and the sensing error (RCRB) obtained by simulation verification. It can be seen from the figure that in the single-user single-target scenario, the RCRB of near-field beamforming and traditional far-field beamforming changes with the communication rate. It can be seen that the far-field design reaches performance saturation at low rates and it is difficult to ensure both a high communication rate and high sensing accuracy simultaneously; the near-field design provides a better Pareto compromise, maintaining a lower RCRB while meeting the user rate requirements.

[0117] Figure 5 It is the sparse representation diagram of the near-field channel under different codebooks obtained by simulation verification. It can be seen from the figure the channel sparse representation forms of the DFT codebook, the spherical wave codebook, and the proposed codebook. The traditional DFT codebook has serious energy leakage problems in the near-field region, while the spherical wave codebook can improve this problem to a certain extent through polar domain sampling. At the same time, the proposed DPSS-based feature codebook shows the sparsest representation form among the three codebooks. In addition, different from the DFT and spherical wave codebooks, the non-zero components of the sparse representation of the proposed codebook are mainly concentrated in the first few index positions because singular value decomposition (SVD) always preferentially arranges non-zero singular values.

[0118] Figure 6 and Figure 7 is the comparison curve of the root of the Cramér-Rao lower bound (RCRB) of the full-digital architecture and the hybrid architecture in distance and angle estimation obtained by simulation verification. It can be seen from the figure that the RCRB increases with the increase of the minimum communication rate, which indicates that there is a trade-off between sensing and communication performance. However, it is worth noting that even when the minimum rate becomes quite high, the RCRB still remains at a low level, which confirms the effectiveness of combining near-field sensing and communication. In addition, at the same communication rate, compared with the full-digital architecture, the hybrid architecture reduces the sensing performance, but its power consumption is much lower.

[0119] Figure 8 is the performance ratio diagram of the near-field channel estimation error and the compression ratio under different codebooks obtained by simulation verification and the number of iterations, and the codebook oversampling rate is set to 1, and the compression ratio keeps the sizes of the three considered codebooks the same. It can be seen from the figure that the reconstruction accuracy increases with increasing; when , since the coarse positioning is regarded as one iteration, the method proposed in the present invention shows the same performance as the spherical wave method; the slight performance degradation at is also due to the sudden codebook switching in the second step of the proposed CE scheme; starting from , due to the excellent ability to sparsify the near-field channel using mutually orthogonal codewords, the proposed DPSS-based feature codebook is much better than the baseline and converges to the lowest NMSE among the considered codebooks.

[0120] Figure 9 is the performance ratio diagram of the near-field channel estimation error and the codebook oversampling rate under different codebooks obtained by simulation verification and the number of iterations, and the compression ratio , and the oversampling rate . It can be seen from the figure that by increasing , the performance of all the schemes has been significantly improved, and the DPSS-based codebook proposed by the present invention still achieves the highest reconstruction accuracy within sufficient iterations; however, the performance improvement of the DFT and spherical codebooks comes at the cost of a larger codebook size; The increase only affects the positioning accuracy of the first step of the proposed CE scheme. The CE performance achieved by the DPSS-based codebook is much better than the two baselines, even though the codebook size is much smaller.

[0121] Based on the same inventive concept, an embodiment of the present application provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the aforementioned DPSS-based near-field ISAC system channel estimation and waveform optimization method are implemented.

[0122] Based on the same inventive concept, an embodiment of the present application provides a computer-readable storage medium. The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the aforementioned DPSS-based near-field ISAC system channel estimation and waveform optimization method are implemented.

[0123] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) containing computer-usable program code.

[0124] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be realized by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for realizing the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0125] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means, and the instruction means realizes the functions in the processFigure 1 one process or multiple processes and / or blocks Figure 1 the functions specified in one block or multiple blocks

[0126] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks

[0127] The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. Any modification made on the basis of the technical solution according to the technical idea proposed by the present invention falls within the protection scope of the present invention.

Claims

1. Channel Estimation and Waveform Optimization Method for DPSS Near-Field ISAC System. The near-field ISAC system includes a base station with a uniform linear array of N T antenna elements, K communication users, and a sensing target. The system operates in the millimeter-wave band, and is characterized in that The method includes the following steps: Step 1, establish a near-field ISAC system model, including the channels of each communication user, the channels of the sensing targets, the transmitted signals of the base station under the near-field all-digital architecture, and the transmitted signal model of the base station under the near-field hybrid beam architecture; the specific process is as follows: Near-field channel vector h of communication user k in the near field k It is expressed as: h k = β k a(r k , θ k ), k = 1, 2, …, K, Among them, β k is the complex attenuation coefficient, a(r k , θ k ) is the near-field array response vector, (r k , θ k ) are the polar coordinates of the position of communication user k, r k is the distance between communication user k and the transmitting antenna, θ k is the angle between communication user k and the transmitting antenna, n = 1, 2,..., N T , λ is the wavelength, h n,k (r k , θ k ) is the channel between communication user k and the nth antenna element, j is the imaginary unit, d n,k (r k , θ k ) is the distance between communication user k and the nth antenna element, d is the antenna element spacing; The channel g of the sensing target is expressed as: g = α s a(r s , θ s )a H (r s , θ s ), where α s is the target complex scattering coefficient, a(r s , θ s ) is the near-field array response vector, and H represents the conjugate transpose; Under the ISAC near-field all-digital architecture, the transmitted signal x of the base station at time t FD (t) is as follows: where, w k is the beamforming vector of communication user k, c k (t) is the communication signal of communication user k, satisfying denotes the mathematical expectation, s(t) is the transmitted signal for sensing, x FD (t) corresponds to the transmit covariance matrix where is the covariance matrix of the sensing signal part; Under the ISAC near-field hybrid beamforming architecture, the transmitted signal x of the base station at time t HB (t) is as follows: Among them, W RF is the analog beamforming matrix, satisfying the constant modulus constraint [W RF x,y is the element in W RF , w BB,k is the digital precoder, is the baseband domain sensing signal with covariance R s,BB , denotes the complex Gaussian distribution; x HB (t) corresponds to the transmit covariance matrix ​ Step 2, introduce a channel model that sparsely represents each communication user, introduce a compensation matrix to construct a DPSS codebook, and use the orthogonal matching pursuit algorithm to estimate the channels of each communication user to obtain the near-field channel estimation values of each communication user; Step 3, calculate the overall channel estimation error of all communication users based on the near-field channel estimation values of each communication user, and construct a waveform optimization problem for joint communication and sensing based on the overall channel estimation error of all communication users and the lower limit of the estimation error of the sensing target; Step 4, under the near-field all-digital architecture, use the alternating optimization method to solve the waveform optimization problem for joint communication and sensing constructed in Step 3 to achieve waveform optimization; Step 5, under the near-field hybrid beam architecture, use the alternating multiplier method to solve the waveform optimization problem for joint communication and sensing constructed in Step 3 to achieve waveform optimization.

2. The method for channel estimation and waveform optimization of the DPSS near-field ISAC system according to claim 1, wherein The specific process of Step 2 is as follows: Step 2.1, introduce a channel model that sparsely represents each communication user: h k = Ψ k α k + n k , Among them, Ψ k is a near-field sparse codebook constructed based on DPSS, α k is a sparse coefficient vector, and n k is a Gaussian noise vector; Reconstruct h k The objective function is as follows: Among them, γ k is the signal-to-noise ratio of communication user k, y k is the received observation matrix, P is the pilot measurement matrix, and λ1 is the coefficient for controlling the sparsity; Step 2.2, introduce a compensation matrix C: where d ref is the reference distance on the y-axis, and x n is the position of the nth antenna element; according to the preset near-field angle sampling points in the system, generate the phase-compensated channel response matrix H aug , and construct the autocorrelation matrix R H as follows: Perform eigenvalue decomposition on R H to obtain M eigenvectors corresponding to all eigenvalues Construct a DPSS codebook: D k = C·[v1,…,v M ; Step 2.3, using the spherical wave codebook Ψ grid Construct a polar coordinate network (r, θ). For each grid point (r i , θ j ) on (r, θ), calculate the matching energy index: Ψ grid (i, j) is the spherical wave codebook of the grid point (r i , θ j ). Select the grid point corresponding to the maximum E i,j as the rough position estimate for the local search range in the fine estimation stage; Step 2.4, Fine Estimation Phase: Based on the DPSS codebook D constructed in Step 2.2 k , the orthogonal matching pursuit algorithm is used to solve and iteratively correct the estimated sparse coefficient vector. When the reconstruction error converges to a preset threshold, the iteration stops. The communication user channel is reconstructed using the estimated sparse coefficient vector obtained in the last iteration, i.e., where the estimated sparse coefficient vector is expressed as:

3. The channel estimation and waveform optimization method for the DPSS near-field ISAC system according to claim 2, wherein In Step 3, the objective function of the waveform optimization problem for joint communication and sensing is as follows: where ω is the weighting factor, ω ∈ [0, 1], is the overall channel estimation error of all communication users, Tr(J -1 ) is the lower bound of the estimation error of the sensing target, P max is the maximum transmit power of the base station, R s is the covariance matrix of the sensing signal, is the lower bound of the communication rate; Let \(J\) be the Fisher information matrix, and the elements \(J_{ ij}\) in \(J\) are as follows: ij as follows: where \(p(y_0)\) is the probability density function of the random variable \(y_0\), \(\eta\) i and \(\eta\) j are the \(i\)-th and \(j\)-th components of the parameter vector \(\eta\) to be estimated; R k is the communication rate of communication user k, and: where, w l is the beamforming vector of communication user l, and σ k is the noise vector of the channel of communication user k.

4. The method for channel estimation and waveform optimization of the DPSS near-field ISAC system according to claim 3, wherein The specific process of Step 4 is as follows: Step 4.1, for communication user k, fix the pilot observation matrix Observation matrix Near-field sparse codebook Ψ k , and use the orthogonal matching pursuit algorithm to solve the following sparse function for channel coefficient reconstruction: Restore the channel according to the reconstructed channel coefficients Step 4.2, fix the channel estimation result and the covariance matrix R of the sensing signal s , optimize the beamforming vector w k , and the waveform optimization problem of joint communication and sensing constructed in Step 3 is transformed into the following second-order cone programming problem: Solve the above second-order cone programming problem to obtain the optimal to minimize the overall channel estimation error of all communication users; Step 4.3, fix the channel estimation result and the beamforming vector w k , optimize the sensing signal covariance matrix R s , and the waveform optimization problem for joint communication and sensing constructed in Step 3 is transformed into the following semidefinite programming problem: Solve the above semi-definite programming problem to obtain the optimal lower limit of the sensing target estimation error.

5. The channel estimation and waveform optimization method for the DPSS near-field ISAC system according to claim 3, wherein The specific process of Step 5 is as follows: Step 5.1, under the near-field hybrid beam architecture, the waveform optimization problem for joint communication and sensing constructed in Step 3 is transformed into: Among them, R x is the transmit power matrix; Introduce an auxiliary variable Z k = W RF w BB,k , and use the alternating multiplier method to transform the optimization objective into a block form with equality constraints: where ρ is the penalty factor and Λ k is the Lagrange multiplier variable; Step 5.2, for communication user k, fix the analog beamforming matrix W RF and the auxiliary variable Z k , update the digital precoder w BB,k , and the optimization objective is transformed into a least squares problem: Solve the above least squares problem to obtain a closed-form solution: wherein, is the digital precoder of communication user k in the (t + 1)-th iteration, is the auxiliary variable in the t-th iteration, is the Lagrange multiplier in the t-th iteration; Step 5.3, fix the digital precoder w BB,k and the auxiliary variable Z k , update the analog beam matrix W RF , construct the auxiliary matrix The optimization objective is transformed into a projection problem with a constant modulus constraint, and W RF is updated element by element: [W RF x,y For W RF is an element in is an element in;​ Step 5.4, fix the analog beamforming matrix W RF and the digital precoder w BB,k , update the auxiliary variable Z k , and the optimization objective is transformed into a weighted quadratic function: Solve the above weighted quadratic function to obtain a closed-form solution: Step 5.5, if ||Z k -W RF w BB,k || < ε k , where ε k is the error tolerance threshold, then update the Lagrange multiplier through the following formula and return to Step 5.2 for the (t + 1)-th iteration: wherein, is the Lagrange multiplier variable of communication user k at the (t + 1)-th iteration, is the auxiliary variable at the (t + 1)-th iteration, is the analog beamforming matrix at the (t + 1)-th iteration; Otherwise, no longer update the Lagrange multiplier variable, and the iteration ends; Step 5.6, after the iteration ends, update the perceptual signal covariance matrix R using the following formula s : Minimize the lower limit of the estimation error of the sensing target.

6. A computer device, comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the DPSS-based near-field ISAC system channel estimation and waveform optimization method according to any one of claims 1 to 5.

7. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the DPSS-based near-field ISAC system channel estimation and waveform optimization method according to any one of claims 1 to 5.

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