High resolution time delay estimation method based on multi-subband OFDM signals and density clustering

Abstract

The application provides a high-resolution time delay estimation method based on a multi-subband OFDM signal and density clustering, and belongs to the technical field of distributed sensing and communication integration. The method comprises the following steps: a multi-band channel frequency response model is constructed, and a global optimization problem is constructed in combination with a frequency domain discrete received signal; a time delay coarse estimation vector of a subsystem and an equivalent complex amplitude are estimated by combining multiple coherent subbands in the subsystem; a non-coherent deviation compensation between subsystems is performed based on a line-of-sight path mechanism, so that a compensated global coherent multi-band channel frequency response column vector is obtained; a multi-band joint sparse fine estimation in the system is performed by limiting a search domain according to a coarse estimation, so that accurate complex amplitudes and high-precision time delay estimation results are obtained. The application breaks the dependence of a traditional subspace algorithm on continuous frequency bands, successfully overcomes serious false peak interference caused by cross-sparse frequency bands, and avoids huge calculation overhead caused by global high-precision grid division, so that a good compromise between calculation complexity and resolution is achieved.

Description

Technical Field

[0001] This invention belongs to the field of distributed sensing technology, and particularly relates to a high-resolution time delay estimation method based on multi-subband OFDM signals and density clustering. Background Technology

[0002] Integrated Sensing and Communication (ISAC) aims to achieve both wireless communication and environmental sensing using the same hardware and spectrum, and has become a core trend for 6G and future Wi-Fi. In practical systems, to achieve deep integration of communication and radar, Orthogonal Frequency Division Multiplexing (OFDM) waveforms, which have a wide deployment base, are reused to extract target information, integrating sensing capabilities into existing networks at a lower cost. This technology is currently widely used in areas such as UAV surveillance, smart cities, and the low-altitude economy.

[0003] In real-world communication scenarios, the available spectrum allocated by the system is often scarce and fragmented due to limitations such as multi-user access and interference avoidance. Since sensing distance resolution is proportional to available bandwidth, traditional single-subband sensing, limited by narrow local bandwidth, cannot achieve high-precision resolution. Although multi-band sensing technology can aggregate discontinuous frequency bands to construct ultra-large virtual bandwidth, it faces two major challenges in actual cross-band coherent fusion: spectrum fragmentation disrupts the complete coherent structure of the signal, significantly increasing the difficulty of global optimization and easily leading to serious estimation errors. Limited by hardware independence, the local oscillators of each distributed subsystem inevitably exhibit frequency drift and initial phase randomness, introducing asynchronous interference such as timing offset (TO), carrier frequency offset (CFO), and random phase offset (RPO) into the link. These asynchronicities hinder the realization of full-band coherent combination.

[0004] For high-precision time delay estimation in multi-subband systems, existing technologies can be mainly divided into the following two categories:

[0005] Subspace-based algorithms estimate parameters by utilizing the multiple shift-invariant structures within the channel state information of continuous frequency bands. This algorithm leverages the rotation invariance of the signal subspace to directly analyze the time delay by solving for generalized eigenvalues, eliminating the need for global spectral peak search. However, this algorithm places extremely stringent requirements on the continuity of the frequency band and the equally spaced array structure, making it unable to directly traverse sparse frequency band gaps. Furthermore, it typically does not consider incoherent error compensation between multiple systems, making it difficult to apply in fragmented spectrum.

[0006] Algorithms based on compressed sensing theory address discrete, discontinuous frequency band scenarios by aggregating discrete frequency bands to construct large apertures, thus handling the problem of multi-band channel reconstruction with large spans and sparse bandwidth. They also attempt to utilize link paths to correct incoherence between systems. However, when dealing with highly fragmented frequency bands, the sparse bandwidth leads to extremely high cross-correlation in the column vectors of the sensing dictionary matrix, making direct cross-band reconstruction highly susceptible to strong spurious sidelobe interference. Furthermore, performing high-precision grid partitioning and search across the entire domain presents enormous computational complexity, making it difficult to achieve a good trade-off between complexity and sensing performance. Summary of the Invention

[0007] The purpose of this invention is to provide a high-resolution time delay estimation method based on multi-subband OFDM signals and density clustering, so as to solve the technical problems in the prior art that are prone to generating spurious peaks when processing incoherent and sparse frequency bands, have high dependence on continuous frequency bands, and have huge computational complexity.

[0008] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:

[0009] A high-resolution time delay estimation method based on multi-subband OFDM signals and density clustering, the method comprising the following steps:

[0010] Step S1: Construct a multi-band channel frequency response model and combine it with the discrete received signal in the frequency domain to construct a global optimization problem;

[0011] Step S2: Combine multiple coherent subbands within the subsystem to estimate the coarse time delay vector and equivalent complex amplitude of the subsystem;

[0012] Step S3: Perform incoherent offset compensation between subsystems based on the reference path mechanism to obtain the compensated global coherent multi-band channel frequency response column vector;

[0013] Step S4: Based on the compensated global coherent multi-band channel frequency response column vector, perform coarse estimation of the prior-constrained search domain and joint sparse fine estimation of the multi-band channels within the system to obtain accurate complex amplitude and high-precision time delay estimation results.

[0014] Further, step S2 includes the following steps:

[0015] Step S21: Construct a joint optimization problem for each subsystem to solve the coarse time delay set and the equivalent complex amplitude set of the target multipath;

[0016] Step S22: Solve the time delay independently using the local equal-interval characteristics of a single subband: Solve on a single continuous subband, split the joint optimization problem into each subband, and obtain a coarse estimate set of time delay for each subband;

[0017] Step S23: Joint fusion in the parameter domain by density clustering: After obtaining the coarse time delay estimate set of all single subbands, density clustering is used to fuse the time delay estimate results of multiple coherent subbands, and the fused time delay is used as the coarse time delay estimate vector of the subsystem. After obtaining the coarse time delay estimate vector, the equivalent complex amplitude is calculated.

[0018] Further, step S3 includes the following steps:

[0019] Step S31: Construct an optimization problem for relative phase offset and relative timing offset estimation;

[0020] Step S32: Based on the coarse estimation vector of the time delay of each subsystem, calculate the initial estimate of the relative timing offset of each subsystem based on the reference path;

[0021] Step S33: Use the interior point method to solve the optimization problem of relative phase offset and relative timing offset estimation, and obtain the relative timing offset estimate and relative phase offset estimate of each subsystem;

[0022] Step S34: Full-band incoherent compensation: After obtaining the relative timing offset estimate and relative phase offset estimate of each subsystem, the channel frequency response of each sub-band is compensated to obtain the compensated global coherent multi-band channel frequency response column vector.

[0023] Further, step S4 includes the following steps:

[0024] Step S41: Construct a discrete reconstruction model in the sparse frequency domain: reconstruct the compensated global coherent multi-band channel frequency response column vector into a linear sparse reconstruction model;

[0025] Step S42: Local search interval establishment: Based on the coarse delay estimation vector of the reference subsystem, the local search interval is determined with the delay resolution corresponding to the shortest sub-band in the subsystem as the interval, so as to include the true delay with the highest probability.

[0026] Step S43: OMP Joint Fine Estimation: Based on full-band incoherent compensation, the multi-band joint fine estimation of the linear sparse reconstruction model is transformed into solving the OMP sparse optimization problem within a given reconstruction error tolerance, to obtain accurate complex amplitude and high-precision time delay estimation results.

[0027] Compared with the prior art, the present invention has the following beneficial technical effects:

[0028] 1) High robustness and spurious peak suppression: By introducing DBSCAN density clustering (combined with CRB adaptive radius) in the parameter domain, the dependence of traditional subspace algorithms on continuous frequency bands is broken, and the serious spurious peak interference caused by cross-sparse frequency bands is successfully overcome.

[0029] 2) Achieving a good trade-off between complexity and performance: In the global OMP reconstruction, a search strategy based on minimum subband constraints is introduced, which avoids the huge computational overhead brought about by global high-precision mesh partitioning and greatly reduces computational complexity.

[0030] 3) Significantly improves ranging accuracy and target resolution: Simulation results show that, under the spectrum configuration of irregular fragments (System 1), compared with the existing HiSAC algorithm, the average root mean square error (RMSE) of the present invention is reduced by about 42.75%, and the target resolution ratio (FRT) is increased by 52.05%, which greatly improves the accuracy of high-resolution sensing.

[0031] 4) In addition to distributed sensing integration (ISAC) systems in 6G and Wi-Fi networks, this invention can also be applied to dense UAV vehicle-mounted network radar, distributed passive radar detection, high-precision indoor wireless positioning (such as high-precision UWB or meter-level Wi-Fi positioning), sonar array signal processing, and radar satellite large-aperture sparse synthesis (delay calibration for SAR imaging). Applications in these fields can effectively solve the problems of false multi-target sidelobes and high computational overhead caused by hardware asynchrony and spectrum fragmentation, achieving super-resolution distance and position awareness. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 This is a schematic diagram of the full-band system and subsystems of the present invention.

[0034] Figure 2 This is a schematic diagram of the OFDM multi-band sensing of the present invention.

[0035] Figure 3 This is a schematic diagram of clustering fusion according to the present invention.

[0036] Figure 4 This is a schematic diagram comparing the average RMSE and FRT of different algorithms under different systems in this invention.

[0037] Figure 5 This diagram illustrates the variation of RMSE with SNR for different algorithms under different systems in this invention.

[0038] Figure 6 This is a schematic diagram illustrating the variation of FRT with SNR for different algorithms under different systems in this invention. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0040] This invention proposes a high-resolution time delay estimation method based on multi-subband OFDM signal and density clustering. Addressing the discontinuous and fragmented frequency band issues caused by multi-user access in communication systems, as well as the asynchrony issues between multiple hardware subsystems, this invention designs a cascaded processing architecture of "local coarse estimation—error compensation—joint fine estimation." The method includes the following steps:

[0041] Step S1: Construct a multi-band channel frequency response model and combine it with the discrete received signal in the frequency domain to construct a global optimization problem.

[0042] Considering the full-band bandwidth of an OFDM-based communication system is The starting frequency is The subcarrier spacing is The total number of subcarriers is The index is The system has The subsystem, for the first subsystem Each subsystem contains The nth continuous sub-band, the nth Individual band ( The starting discrete index in the full frequency band is denoted as . Suppose that the subband contains One "actually available subcarrier" for sensing, with a local index of . Therefore, the actual number of available subcarriers in a single subsystem and the entire system are respectively... and In practical estimation, whether the subsystem utilizes part or all of the bandwidth depends on the specific sensing frequency band. In subsequent processing, it is assumed that the subcarrier spacing of all subbands is constant. .

[0043] In the target perception process, it is assumed that the signal passes through Each target reflects light along a Line-of-Sight (LoS) path to the receiver. Since each subsystem's hardware is independent, to establish a unified framework for multi-band joint estimation, we take the first subsystem (…) as an example. (This is) used as a reference subsystem. The non-reference subsystem inevitably exhibits relative TO with respect to the reference system. (Relative timing offset) and relative PO (Relative Phase Offset) (including CFO (Carrier Frequency Offset) and RPO (Random Phase Offset)). After OFDM demodulation, the... The first subsystem Within the first generation Discrete frequency-domain received signal on each subcarrier It can be represented as:

[0044] (1)

[0045] In the formula, Indicates the first Relative phase shift of each subsystem; Indicates the subcarrier spacing; Indicates the first Relative timing offset of each subsystem; Indicates the total number of transmission paths; The complex amplitude, i.e., the path, takes into account the combined effects of propagation loss and target scattering. The complex amplitude, For path Physical delay; For the first The first subsystem Within the first generation Pilot symbol sequence transmitted in the frequency domain of each subcarrier For the first The first subsystem Within the first generation Additive complex white Gaussian noise with zero mean for each subcarrier.

[0046] Constructing a multi-band channel frequency response model: The first... The first subsystem Within the first generation of the belt The theoretical channel frequency response (CFR) of each subcarrier, including the target physical parameters and system asynchronous errors, is defined as follows:

[0047] (2)

[0048] in, Indicates the first The first subsystem Within the first generation Ideal channel frequency response for each subcarrier.

[0049] Substituting equation (2) into equation (1), the frequency domain discrete received signal can be expressed as:

[0050] (3)

[0051] Based on the aforementioned multi-band channel frequency response model, the goal of multi-band joint sensing is to receive signals discretely in the frequency domain. Solve for the multipath delay set of the target. Complex amplitude set and the set of relative timing offsets of the non-reference subsystems relative to the reference system. ( ) and relative phase offset set ( The estimation of the above four sets of parameters can be modeled as the following global optimization problem:

[0052] (4)

[0053] Since the parameters to be estimated are all contained in the channel frequency response, the known pilot symbol sequence can be used. By decoupling the transmitted symbols through zero-forcing equalization, an estimate of the ideal channel frequency response is obtained. ,in For the first The first subsystem Within the first generation The equivalent noise of each subcarrier. At this point, the multi-band channel frequency response model can be rewritten as:

[0054] (5)

[0055] Indicates the first The first subsystem Within the first generation Ideal channel frequency response of each subcarrier The estimated value. When the total effective bandwidth of the system is less than 20% of the carrier center frequency, the complex amplitude... It can be considered constant. The theoretical full-band time delay resolution is... The Channel Impulse Response (CIR) can be obtained by the inverse discrete Fourier transform (IDFT) of the channel frequency response.

[0056] The first Within each subsystem All of the individual belts By concatenating the estimates from the available subcarriers, the channel frequency response estimate vector for that single subband can be obtained. :

[0057] (6)

[0058] in, Indicates the first Within each subsystem The channel frequency response vector of each sub-band.

[0059] Furthermore, the channel frequency response vectors of all available sub-bands of all subsystems are globally concatenated to construct the complete system channel frequency response estimation vector. :

[0060] (7)

[0061] Through this mapping transformation, the global optimization problem is equivalently transformed into an estimation of the system-complete channel frequency response vector. Parameter optimization problem:

[0062] (8)

[0063] in, This is the channel frequency response reconstructed based on the parameters to be estimated.

[0064] Step S2: Estimate the coarse time delay vector and equivalent complex amplitude of the subsystem from multiple coherent subbands within the joint subsystem.

[0065] Step S21: Construct a joint optimization problem for each subsystem to solve the coarse time delay set and the equivalent complex amplitude set of the target multipath.

[0066] In the Within each subsystem, the hardware offset is consistent across all subbands due to the shared RF front-end. Therefore, local parameter estimation utilizes only the subsystem's parameters. Internal observation dataset (containing) (a series of continuous sub-bands), to solve for the coarse time delay set of the target multipath. and equivalent complex amplitude set ; Indicates the first A rough set of time delays for each subsystem; Indicates the first The equivalent complex amplitude set of each subsystem; Indicates the first Path of each subsystem The approximate time delay for solving; Indicates the first Path of each subsystem The equivalent complex amplitude is obtained by solving for it.

[0067] Will and The parameter estimation is modeled as the following least squares joint optimization problem:

[0068] (9)

[0069] in, Indicates the first Path of each subsystem The estimated equivalent complex amplitude; Indicates the first Path of each subsystem The estimated latency; Indicates the first The set of estimated time delays for each subsystem; Indicates the first The set of equivalent complex amplitudes to be estimated for each subsystem.

[0070] However, directly solving this joint optimization problem faces two major challenges: first, sparse frequency bands disrupt the continuous coherent structure, and direct cross-band reconstruction easily generates strong spurious peaks; second, high-resolution subspace algorithms heavily rely on equally spaced array structures, requiring each sub-band to have the same number of subcarriers and spacing, which is difficult to meet the needs of actual fragmented spectrum. To solve this problem, this invention proposes a coarse estimation algorithm based on density clustering fusion, including the following steps: Step S21 independently solves the time delay using the local equally spaced characteristics of a single sub-band without forcibly performing signal-level splicing; Step S22 performs joint fusion in the parameter domain through density clustering.

[0071] Step S22: Solve the time delay independently using the local equal interval characteristics of a single sub-band: Solve on a single continuous sub-band, split the joint optimization problem of formula (9) into each sub-band, and obtain a coarse estimate set of time delay for a single sub-band.

[0072] (10)

[0073] in, and For the first Subsystem The time delay estimation set and the equivalent complex amplitude estimation set for each sub-band; Indicates the first Subsystem Path of sub-band The estimated equivalent complex amplitude; Indicates the first Subsystem Path of sub-band The estimated latency; Indicates the first Subsystem The set of estimated time delays for each sub-band; Indicates the first Subsystem The set of equivalent complex amplitudes to be estimated for each sub-band.

[0074] In its implementation, the ESPRIT algorithm is used to estimate the delay of each sub-band. First, the delay of each sub-band is constructed separately. Subsystem Hankel matrix of sub-bands , The relevant window length is usually taken as... The Hankel matrix, number 1. Line number Column elements are ; Indicates the first Subsystem Within the first generation The initial channel frequency response of each subcarrier. Ignoring the noise term, the multi-band channel frequency response model of equation (5) is rewritten as:

[0075] (11)

[0076] in Integrating complex amplitude, absolute initial frequency offset phase, and relative phase shift, it is considered as an equivalent composite complex amplitude, i.e., the first... Subsystem Sub-path The equivalent composite complex amplitude.

[0077] The channel frequency response can be seen after rewriting as follows: A superposition of complex sinusoidal signals. Due to the equal spacing of local subcarriers in OFDM, adjacent signal components differ only in phase by a fixed rotation factor. Constructing the Hankel matrix After that, the Hankel matrix It naturally possesses a Vandermonde rotation-invariant structure. Regarding the Hankel matrix... Singular value decomposition is performed to obtain the signal subspace, and the order of the Hankel matrix is ​​determined jointly based on the MDL criterion and the AIC criterion. Subsequently, the rotational invariance of the ESPRIT algorithm is used to solve the generalized eigenvalue equations, obtaining eigenvalues ​​containing multipath phase shift information. ( ), eigenvalues This is a coarse estimation of the time delay. Therefore, there is no need for a global spectral peak search; the local time delay parameters can be resolved by directly extracting the phase of the eigenvalues.

[0078] (12)

[0079] in, Indicates the first Subsystem The first A rough estimate of the time delay can be obtained from this; thus, the first delay can be efficiently obtained. Subsystem A set of coarse time delay estimates for each sub-band .

[0080] Step S23: Joint fusion in the parameter domain by density clustering: After obtaining the coarse time delay estimate set of all single subbands, density clustering is used to fuse the time delay estimate results of multiple coherent subbands, and the fused time delay is used as the coarse time delay estimate vector of the subsystem. After obtaining the coarse time delay estimate vector, the equivalent complex amplitude is calculated.

[0081] After obtaining the coarse delay estimates for all single subbands, these coarse delay estimates are often accompanied by random noise and local error values ​​due to the single subband bandwidth bottleneck. The DBSCAN density clustering algorithm is introduced to divide the coarse delay estimates and extract the statistical consensus of multi-band observations by finding high-density estimate clusters in the parameter domain.

[0082] The DBSCAN density clustering algorithm forms clusters (representing the target time delay) by finding high-density clustering regions in the time delay data space and removing outliers. Its effectiveness depends on two core parameters: ① Cluster neighborhood radius. ② Minimum number of points within a cluster. To ensure that multipath estimates are grouped into the same cluster, the cluster neighborhood radius... The Gaussian error range must be included. Since the ESPRIT error approximately follows a zero-mean Gaussian distribution and its variance approximates the Cramér-Rao Bound (CRB), this invention utilizes the theoretical CRB to quantify error fluctuations to guide the cluster neighborhood radius. Design. For OFDM signal arrival time estimation in an additive white Gaussian noise channel, the CRB is derived and presented:

[0083] (13)

[0084] in, This represents the variance of the estimation error. The receiver signal-to-noise ratio (SNR) is used. The effective bandwidth of the signal is defined as the second moment of the frequency domain energy distribution; This represents the Cramer-Rao lower bound. This invention defines the effective bandwidth of the signal. Equivalent to the longest subband bandwidth in the subsystem And by omitting the coefficients in the denominator, a simplified empirical formula is obtained. The radius R of the cluster is set to three standard deviations, therefore the... Cluster neighborhood radius of each subsystem It is expressed as follows:

[0085] (14)

[0086] in, Indicates the first Cluster neighborhood radius of each subsystem; Indicates the first The longest subband bandwidth of each subsystem.

[0087] In practical engineering, the prior signal-to-noise ratio required by formula (14) The power of the OFDM signal can be quickly estimated using the ratio of the received power of the preamble or pilot subcarrier to the noise power on the idle subcarrier. Meanwhile, to ensure system robustness, the minimum number of included points in each cluster of the DBSCAN algorithm is specified to be at least half the number of available subbands within that subsystem. The first... 1 effective cluster After (including) (a coarse estimation point), calculate the sample mean to smooth the noise, and obtain the first... The final subsystem Coarse estimate of path delay:

[0088] (15)

[0089] in, Indicates the first The final subsystem Coarse estimate of path delay; Indicates the first Subsystem One effective cluster; No. Subsystem A rough estimate of the number of points in each effective cluster; This represents the time delay estimate belonging to this cluster.

[0090] Suppose that the subsystem ultimately determines through clustering. Multiple paths constitute the first Coarse estimation vector of time delay of each subsystem Obtain the coarse delay estimation vector. Then, Equation (9) contains a joint optimization problem of a highly nonlinear channel with unknown complex exponential terms, which degenerates into a problem of solving a linear overdetermined set of equations about the path complex amplitude.

[0091] The first The channel frequency response observation data of all available subbands within each subsystem are concatenated into an observation vector. and to coarsely estimate the vector Construct the corresponding guiding vector matrix The first of the matrix Column guide vector Corresponding to the first Delay of a physical path Frequency phase shift sequences generated on all available subcarriers of this subsystem. To be used in conjunction with the subsystem's observation vectors. Alignment, this guiding vector can be formed by concatenating the local phase shift sub-vectors of each sub-band: the first... Column guide vector It is formed by concatenating the phase shift sub-vectors of each local sub-band, i.e. ,in, Indicates the first Subsystem The number of sub-band phase shift vectors, expanded as At this time, the first The equivalent complex amplitude set of each subsystem ; Indicates the estimated first Subsystem Path Equivalent complex amplitude; set of equivalent complex amplitudes The solution is transformed into a least squares optimization problem. The optimal analytical solution can be directly obtained using the generalized inverse of a matrix. .

[0092] The local parameter extraction is now complete. For subsequent error compensation, the channel frequency response needs to be extended and reconstructed to include... A full-band grid of subcarriers. Define the full-band reconstructed channel frequency response vector. No. Subcarrier elements (full-band index) Expanded as:

[0093] (16)

[0094] Note that since the relative time-frequency offset between different subsystems has not yet been eliminated, the local parameters actually include the relative timing offset. This means reconstructing the channel frequency response vector. The phase still implies asynchronous errors between systems. This provides data preparation for establishing a joint phase compensation model among multiple subsystems.

[0095] Invention Point 1: Adaptive Error Boundary Density Clustering Fusion Mechanism. Traditional algorithms require strict continuous frequency bands and a consistent number of subcarriers; this invention breaks this limitation. The core innovation of this invention lies in the fact that the cluster neighborhood radius of density clustering is not an empirically fixed value, but is adaptively calculated and set based on the Cramer-Rao lower bound (CRB) and the channel signal-to-noise ratio (SNR). This mechanism enables the cluster radius to accurately encompass the Gaussian error range of local estimates, effectively extracting the "statistical consensus" of multi-subband observations, adaptively eliminating outliers caused by local noise, and significantly improving the robustness of coarse estimation.

[0096] Step S3: Compensation for incoherent deviations between subsystems based on the reference path mechanism.

[0097] Step S31: Construct an optimization problem for relative phase offset and relative timing offset estimation.

[0098] After obtaining the local parameters of each subsystem, the asynchrony deviation caused by hardware independence must be eliminated. This invention constructs an alignment mechanism based on a reference path. In communication-sensing integration, it is usually assumed that a Loss-of-Sight (LoS) path exists and that the signal power is significantly higher than that of the scattering path. When the LoS path does not exist, a static strong reflection path can be used as a substitute. By comparing the full-band channel frequency response estimated by different subsystems with that of the reference subsystem, the estimation of relative phase offset and relative timing offset can be transformed into the following optimization problem:

[0099] (17)

[0100] in, Indicates the first Estimated relative timing offset of each subsystem; Indicates the first Estimates of relative phase offset of each subsystem.

[0101] This optimization problem is nonlinear, nonconvex, and high-dimensional. Leveraging the characteristic that all subsystems share the same channel, the optimization problem is simplified by directly comparing it with the reference path. The process consists of three steps: Step S32: Initial estimation of the deviation based on the reference path; Step S33: Relative deviation optimization solution based on the interior-point method; Step S34: Full-band coherent compensation.

[0102] Step S32: Based on the coarse estimation vector of the time delay of each subsystem, calculate the initial estimate of the relative timing offset of each subsystem based on the reference path.

[0103] In the Coarse estimation vector of time delay of each subsystem In the process, extract the delay of the first path with the earliest arrival time. The first The difference in delay between the first path of the first subsystem and the reference subsystem is defined as the time delay of the first subsystem. Initial estimates of the relative timing offset of each subsystem: .

[0104] Step S33: Use the interior point method to solve the optimization problem of relative phase offset and relative timing offset estimation, and obtain the relative timing offset estimate and relative phase offset estimate of each subsystem.

[0105] In the optimization problem of relative phase offset and relative timing offset estimation, the relative timing offset is an unconstrained variable, while the relative phase offset has physical boundary constraints. The interior-point method is used to solve the problem, transforming the hard boundary into a penalty term. Let the first... Vector of parameters to be estimated for each subsystem Basic objective function Defined as:

[0106] (18)

[0107] Since the relative phase offset has a defined physical boundary, for this non-convex optimization problem with inequality constraints, a logarithmic barrier function is introduced to construct an augmented objective function, transforming the boundary constraints into penalty terms. The algorithm then proceeds to the next step. Initial parameter vector of each subsystem Using the initial values ​​and given the barrier parameters, the parameter vector is updated along the gradient descent direction using Newton's method. By gradually decaying the barrier parameters, it efficiently converges to the relative timing offset estimate of the inter-system relative deviation. Relative phase offset estimate .

[0108] Step S34: Full-band incoherent compensation: After obtaining the relative timing offset estimates of each subsystem... and relative phase offset estimates Then, the channel frequency response of each sub-band is compensated to obtain the compensated global coherent multi-band channel frequency response column vector.

[0109] The full-band incoherent compensation method is as follows:

[0110] (19)

[0111] in, Indicates the first The first subsystem Within the first generation The channel frequency response after compensation for each subcarrier.

[0112] After compensation, hardware incoherence between different subsystems is eliminated. Referring to the sequence concatenation logic of multi-band fusion, the effective sub-band observations of all systems after coherent alignment are concatenated sequentially according to their frequency indices to construct a globally coherent multi-band channel frequency response column vector. This global vector will directly serve as the unified observation input for subsequent joint fine-grained estimation.

[0113] (20)

[0114] in, This represents the column vector of the global coherent multi-band channel frequency response, which is the observation input. This indicates the total number of available subcarriers.

[0115] Step S4: Intra-system multi-band joint sparse fine estimation based on coarse prior constraint search domain.

[0116] After eliminating cross-band incoherence, given the superior computational efficiency and convergence of the OMP algorithm in handling sparse channel reconstruction, it is widely used in channel estimation. This invention employs the OMP algorithm to achieve global parameter reconstruction. However, due to the fragmented nature of the spectrum, the column vectors of the dictionary matrix exhibit extremely high cross-correlation, making global grid search prone to falling into spurious sidelobes caused by spectrum gaps. Furthermore, extremely fine grid division incurs significant computational overhead. Therefore, instead of blindly searching the entire domain, a fine scan is performed within the small neighborhood where the real target might exist, centered on the coarse estimation result. This strategy physically isolates most of the phase ambiguity regions, fully leveraging the resolution gain from multi-band aggregation while effectively avoiding the sidelobe interference caused by the reduction in sparse frequency bands, achieving higher resolution and accuracy in time delay estimation. The solution process can be divided into the following two key steps: Step S41: Constructing a discrete reconstruction model in the sparse frequency domain; Step S42: Joint fine estimation using OMP.

[0117] Step S41: Construct a discrete reconstruction model in the sparse frequency domain: Reconstruct the compensated global coherent multi-band channel frequency response column vector into a linear sparse reconstruction model.

[0118] Discretize the continuous time delay space within the time delay estimation range into Dense grid points , Indicates the first The time delay corresponding to each discrete grid point is defined as the column vector of the channel impulse response to be estimated. (Elements are non-zero only if discrete grid points match real physical paths). Indicates the first The channel impulse response corresponds to each discrete grid point. First, the full-band space is mapped to construct a structure containing... Fourier dictionary matrix of virtual subcarriers Its matrix elements are ; Indicates the first The time delay corresponds to each discrete grid point. For the discrete spectrum, a row selection matrix is ​​introduced. Used for precise extraction One practically usable subcarrier. Therefore, the compensated global coherent multi-band channel frequency response column vector can be... This can be represented as a linear sparse reconstruction model as follows:

[0119] (twenty one)

[0120] in, This represents the sum of the residual comprehensive estimation error and background noise after coarse estimation of time delay and compensation for incoherent deviations between systems.

[0121] Step S42: Local search interval establishment: Based on the coarse delay estimation vector of the reference subsystem, the local search interval is determined with the delay resolution corresponding to the shortest sub-band in the subsystem as the interval, so as to include the true delay with the highest probability.

[0122] Coarsely estimate the time delay vector using the reference subsystem (typically the system with the widest bandwidth). Based on this, a local search interval is dynamically divided around the coarsely estimated time delay. To maximize the probability that the search interval contains the coarse estimate of the subsystem, the search neighborhood boundary... , For the first Subsystem Each unit has bandwidth.

[0123] (twenty three)

[0124] Step S43: OMP Joint Fine Estimation: Based on the full-band incoherent compensation of formula (19), the multi-band joint fine estimation is transformed into multi-band joint fine estimation within a given reconstruction error tolerance. Solve the following OMP sparse optimization problem to obtain accurate complex amplitude and high-precision time delay estimation results.

[0125] (twenty two)

[0126] in, Represents a sparse coefficient vector; This indicates the number of non-zero elements in a vector. Error tolerance set according to noise level.

[0127] In this local search range Inside, with Accuracy reconstruction of local networks ; Indicates the first Local grid delay; This represents the total number of local grid cells. A local Fourier dictionary matrix is ​​constructed under this fine-grained grid. Its matrix elements are .in This is used to index local grid points. Subsequently, OMP is strictly limited to the local search interval. Execution within the specified timeframe. When the reconstruction error is less than the reconstruction error tolerance. The iteration stops when the maximum number of multipaths is reached, and the final output is a sparse coefficient vector. The non-zero value is the accurate complex amplitude, and the corresponding grid position is the high-precision time delay estimation result.

[0128] Invention Point 2: A Coarse Estimation-Guided Restricted Domain Search Strategy Effectively Avoiding False Peak Interference: Faced with highly fragmented spectra, the column vectors of the traditional compressed sensing dictionary matrix exhibit extremely high cross-correlation. Global search inevitably falls into a strong trap of false sidelobes (pseudo-peaks), and the high-precision grid across the entire domain leads to an exponential increase in computational overhead. This invention utilizes coarse estimation priors as physical boundaries, rigidly isolating most phase ambiguity regions and invalid blank areas. Furthermore, by reasonably setting the boundary size, it maximizes the probability of including the coarse estimation results of the subsystem. This strategy fully leverages the significant resolution gain brought by multi-band aggregation while completely avoiding the inherent sidelobe interference of sparse frequency bands, achieving a perfect trade-off between extremely low computational complexity and extremely high sensing accuracy.

[0129] Step S5: Simulation Verification: To verify the effectiveness of the proposed algorithm, the simulation scenario, system parameter settings, and evaluation criteria are described in detail. Finally, simulation results are presented to evaluate the performance advantages of the proposed algorithm.

[0130] (1) Simulation scenario: In a reflection and reception scenario, three targets are set at a signal-to-noise ratio of 20dB. The first target is relatively close (the distance to the first target is...). The amplitude of the first target complex amplitude (Random phase) is used as a reference path instead of the Loss path to estimate the error between systems; the other two targets are measured signals (the distance to the second target). The distance to the third target ,in This indicates the target spacing, which is 1.5cm. The amplitudes of the complex amplitudes of the second and third targets are both 0.3. Each group underwent 500 Monte Carlo experiments. The target channel frequency response model is as follows:

[0131] (twenty four)

[0132] in, Indicates the first Subcarrier channel frequency response model; It represents the speed of light.

[0133] (2) System parameters: Four different system parameters were set for comparison, with each system having a full-bandwidth starting frequency. Both are 60 GHz, with an 8 ns time shift added to the second subsystem. The phase shift.

[0134] Table 1 System Parameters

[0135]

[0136] (3) Evaluation criteria: In order to comprehensively measure the performance of the algorithm, an evaluation framework including two dimensions of accuracy and completeness was constructed.

[0137] (a) Ranging accuracy index: The deviation of the estimated value is quantified by the root mean square error (RMSE), and it is only included in the calculation when the target is successfully detected.

[0138] (25)

[0139] in, Number of successful tests Indicates the first Second estimate, The actual distance to the target.

[0140] (b) Detection capability index: The analytical target ratio (FRT) is introduced. When the output deviation is less than half of the minimum spacing, it is considered a correct detection.

[0141] (26)

[0142] (4) Algorithm comparison: In order to demonstrate the effectiveness of the algorithm of the present invention, it is compared with the following four algorithms.

[0143] (a) Full Bandwidth OMP: Assuming the entire bandwidth is available, the full bandwidth CFR estimate is used to solve the problem using the OMP algorithm.

[0144] (b) Actual Continuous Bandwidth OMP(Cont): All available frequency bands are spliced ​​into a continuous subband and solved by the OMP algorithm.

[0145] (c) HiSAC algorithm: The coarse estimation uses OMP to obtain the estimate and compensate for the relative error, and finally uses multiple frequency bands for joint estimation.

[0146] (d) Multi-band weighted delay estimation algorithm (MB): requires consistent sub-band subcarrier numbers and does not consider relative errors. For comparison, MB is used for coarse estimation, and relative errors are compensated by a reference path. Finally, OMP is used for global estimation, and it is only applied to systems 3 and 4.

[0147] Figure 1 This diagram illustrates the spectrum allocation characteristics and distributed hardware architecture of a multi-subband OFDM communication system. The upper part of the diagram shows the "full-band system," indicating the total bandwidth of the entire frequency band and showing that it consists of multiple frequency-discrete subsystems. The diagram clearly indicates that, due to the independent hardware of each subsystem, the signal frequency bands of different subsystems are in a phase-incoherent state. The lower part of the diagram zooms in to show the internal architecture of a single subsystem, which contains multiple sparsely allocated available subbands. The diagram emphasizes that, because these local subbands share the same RF front-end, the signals within them are phase-coherent. This diagram visually reveals the physical layer challenges of local coherence and global incoherence faced in cross-band fusion.

[0148] Figure 2 This diagram illustrates the physical scenario and signal transmission link of a co-located Sensor-Integrated Communication (ISAC) base station performing high-precision detection of surrounding targets. The diagram clearly shows the ISAC multi-subsystem signals transmitted by the base station, multiple reflected path signals formed by reflections from targets such as vehicles and buildings, and a line-of-sight (LoS) path signal directly reaching the target. This diagram not only illustrates the physical model of signal propagation including multipath interference but also provides application scenario support for subsequent steps using the LoS direct path as a common reference anchor point to estimate and compensate for relative timing and phase offsets between different subsystems.

[0149] Figure 3 This demonstrates the working principle of using the DBSCAN density clustering algorithm to fuse multi-band estimates in the parameter domain (delay domain). The horizontal axis in the figure represents the delay estimation domain, marking the target true delay, the independent estimated delay of each sub-band, and the high-density estimated clusters divided by the adaptive cluster radius R. The figure clearly shows that the clustering algorithm can successfully divide high-density estimated points near the true "target delay" into effective clusters (thus extracting statistical consensus); simultaneously, scattered, deviating "estimated delays not included in clusters" (i.e., local erroneous estimates and spurious peaks caused by narrow bandwidth or noise) are effectively identified and removed as isolated points.

[0150] Figure 4This paper presents a comparison of the RMSE and FRT of the proposed estimation algorithm with the benchmark algorithm under four different subband configurations (System 1-4). For irregular spectra (System 1 & 2): these two systems have inconsistent subband bandwidths. Simulation results show that the proposed algorithm significantly outperforms the HiSAC algorithm in both RMSE and FRT. Specifically, in System 1, the average RMSE is reduced by approximately 42.75%, and the FRT is improved by 52.05%. This demonstrates that fusion in the parameter domain through DBSCAN density clustering can effectively overcome the signal-level splicing problem caused by spectrum fragmentation and avoid the severe spurious peak interference that traditional OMP easily generates when processing irregular subbands. For regular narrowband spectra (System 3 & 4): even with consistent subband structures but extremely sparse available bandwidth, the proposed algorithm still maintains superior accuracy compared to the MB algorithm.

[0151] To verify the stability of the algorithm under different signal-to-noise ratios, 400 Monte Carlo experiments were conducted in the range of 0–15 dB (1 dB intervals). Figure 5 and Figure 6 The performance and stability of each algorithm were verified under conditions ranging from poor to ideal signal-to-noise ratios, based on two core dimensions: RMSE and FRT. Figure 5 and Figure 6 The results show that the algorithm proposed in this invention exhibits significant advantages in both noise resistance accuracy and multi-target resolution. Regarding error convergence ( Figure 5 As the signal-to-noise ratio (SNR) increases, the errors of all algorithms decrease, but the algorithm of this invention (blue circle) decreases the fastest and is closest to the lower bound of the performance of the ideal full-bandwidth OMP in the high SNR region. Especially in low SNR environments (0~10 dB), the HiSAC algorithm is highly susceptible to noise and gets trapped in local optima during the coarse estimation stage; while the algorithm of this invention, thanks to the natural noise suppression capability of the local in-band ESPRIT algorithm combined with the adaptive elimination mechanism of DBSCAN for isolated points, ensures that the defined search interval can stably enclose the real target delay, thus maintaining extremely low estimation error even under harsh channel conditions. When the SNR exceeds 10 dB, the FRT performance of the algorithm of this invention remains stable and significantly outperforms the directly spliced ​​actual continuous bandwidth OMP algorithm (Cont).

[0152] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A high-resolution time delay estimation method based on multi-subband OFDM signals and density clustering, characterized in that, The method includes the following steps: Step S1: Construct a multi-band channel frequency response model and combine it with the discrete received signal in the frequency domain to construct a global optimization problem; Step S2: Combine multiple coherent subbands within the subsystem to estimate the coarse time delay vector and equivalent complex amplitude of the subsystem; Step S3: Perform incoherent offset compensation between subsystems based on the reference path mechanism to obtain the compensated global coherent multi-band channel frequency response column vector; Step S4: Based on the compensated global coherent multi-band channel frequency response column vector, perform coarse estimation of the prior-constrained search domain and joint sparse fine estimation of the multi-band channels within the system to obtain accurate complex amplitude and high-precision time delay estimation results.

2. The high-resolution time delay estimation method based on multi-subband OFDM signals and density clustering according to claim 1, characterized in that, Step S2 includes the following steps: Step S21: Construct a joint optimization problem for each subsystem to solve the coarse time delay set and the equivalent complex amplitude set of the target multipath; Step S22: Solve the time delay independently using the local equal-interval characteristics of a single subband: Solve on a single continuous subband, split the joint optimization problem into each subband, and obtain a coarse estimate set of time delay for each subband; Step S23: Joint fusion in the parameter domain by density clustering: After obtaining the coarse time delay estimate set of all single subbands, density clustering is used to fuse the time delay estimate results of multiple coherent subbands, and the fused time delay is used as the coarse time delay estimate vector of the subsystem. After obtaining the coarse time delay estimate vector, the equivalent complex amplitude is calculated.

3. The high-resolution time delay estimation method based on multi-subband OFDM signals and density clustering according to claim 1, characterized in that, Step S3 includes the following steps: Step S31: Construct an optimization problem for relative phase offset and relative timing offset estimation; Step S32: Based on the coarse estimation vector of the time delay of each subsystem, calculate the initial estimate of the relative timing offset of each subsystem based on the reference path; Step S33: Use the interior point method to solve the optimization problem of relative phase offset and relative timing offset estimation, and obtain the relative timing offset estimate and relative phase offset estimate of each subsystem; Step S34: Full-band incoherent compensation: After obtaining the relative timing offset estimate and relative phase offset estimate of each subsystem, the channel frequency response of each sub-band is compensated to obtain the compensated global coherent multi-band channel frequency response column vector.

4. The high-resolution time delay estimation method based on multi-subband OFDM signals and density clustering according to claim 3, characterized in that, Step S4 includes the following steps: Step S41: Construct a discrete reconstruction model in the sparse frequency domain: reconstruct the compensated global coherent multi-band channel frequency response column vector into a linear sparse reconstruction model; Step S42: Local search interval establishment: Based on the coarse time delay estimation vector of the reference subsystem, the local search interval is determined with the time delay resolution corresponding to the shortest sub-band in the subsystem as the interval. Step S43: Use OMP joint fine estimation within the given range: Based on full-band incoherent compensation, the multi-band joint fine estimation of the linear sparse reconstruction model is transformed into solving the OMP sparse optimization problem within the given reconstruction error tolerance to obtain accurate complex amplitude and high-precision time delay estimation results.

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