CN110941980A - Multipath time delay estimation method and device based on compressed sensing in dense environment - Google Patents

Abstract

The invention relates to a multipath time delay estimation method and a multipath time delay estimation device based on compressed sensing in a dense environment, wherein the method comprises the following steps: step S1: setting a reference signal, and preprocessing a received signal and the reference signal to a set length; step S2: performing cyclic correlation processing on the received signal and the reference signal to obtain a cyclic correlation function; step S3: expressing the obtained cyclic correlation function as an inverse Fourier transform form of the cyclic correlation function as a parameter signal; step S4: generating a parameter matrix according to the parameter signal; step S5: adopting a measurement matrix, constructing a sparse basis dictionary, and carrying out compression sampling on the time delay parameters by using a compression sensing algorithm; step S6: and matching and tracking the observation signal by adopting an orthogonal matching algorithm to obtain a multipath time delay parameter. Compared with the prior art, the method has the advantages of improving the resolution capability of time delay signal estimation in a dense environment and the like.

Description

Multipath time delay estimation method and device based on compressed sensing in dense environment

Technical Field

The invention relates to the technical field of signal processing, in particular to a multipath time delay estimation method and device based on compressed sensing in a dense environment.

Background

Wireless location systems use the principle of wireless signal propagation between a transmitter and a receiver, and the location process uses various characteristics of wireless propagation, most commonly, location is performed by signal strength, signal arrival angle, and signal arrival delay. Estimation of multipath delay parameters is a popular research subject in the signal processing field at present, and is widely applied to the fields of communication, radar, sonar, geological exploration and the like. Classical algorithms are only effective when multipath components are well separated in time of arrival or only one component is present in the received signal, they cannot separate signals closer than the resolution limit. Therefore, a cost function-based estimation method is proposed, and a minimum mean square error method (MMSE), a maximum likelihood Method (ML), and a nonlinear minimum multiplication (NLS) are typical cost function-based estimation methods. However, these estimation algorithms based on cost functions involve many parameter optimization problems, are large in calculation amount and difficult to implement, and cannot meet the requirement of real-time performance. With the gradual and deep research on multipath delay estimation, the idea of array signals is applied to delay estimation, a multiple signal classification algorithm based on eigenvalue decomposition is established, a cross-correlation and feature subspace decomposition method is combined on the basis of the multiple signal classification algorithm and introduced into the field of frequency domain delay estimation, so that the delay estimation of the MUSIC algorithm based on the frequency domain is researched, but the performance of the delay estimation method is usually good only for signals with approximate flat broadband and frequency spectrum, the estimation performance of the delay estimation method for narrowband signals is poor, and under the condition of short observation time (few fast beats), the obtained signal energy is less, the delay information of dense signals cannot be accurately estimated, and the application range of the delay estimation method is limited.

Compressed sensing is an information science which has been developed in recent years, and has a great influence on the fields of modern signal processing and the like, discrete samples of a signal are acquired by random sampling under the condition that the sampling rate is far less than the Nyquist sampling rate through the sparsity of a received signal, and then the signal is reconstructed with high accuracy through a corresponding algorithm. The method of compressed sensing is to substantially reduce the complexity in the signal sampling process by increasing the complexity of the reconstruction process, and its core idea mainly includes the sparse structure and uncorrelated characteristics of the signal.

Disclosure of Invention

The present invention aims to overcome the defects of the prior art and provide a multipath delay estimation method and device based on compressed sensing in a dense environment.

The purpose of the invention can be realized by the following technical scheme:

a multipath time delay estimation method based on compressed sensing in a dense environment comprises the following steps:

step S1: setting a reference signal, and preprocessing a received signal and the reference signal to a set length;

step S2: performing cyclic correlation processing on the received signal and the reference signal to obtain a cyclic correlation function;

step S3: expressing the obtained cyclic correlation function as an inverse Fourier transform form of the cyclic correlation function as a parameter signal;

step S4: generating a parameter matrix according to the parameter signal;

step S5: adopting a measurement matrix, constructing a sparse basis dictionary, and performing compression sampling on the time delay parameter by using a compression sensing algorithm;

step S6: and matching and tracking the observation signal by adopting an orthogonal matching algorithm to obtain a multipath time delay parameter.

The step S1 specifically includes:

step S11: acquiring a received signal, and sampling and observing the received signal to obtain a sampling signal;

step S12: uniformly performing time shift operation on the transmission signals subjected to the set sub-sampling to obtain reference signals;

step S13: and performing zero filling processing on the reference signal and the received signal to a set length.

The set length is specifically as follows:

K_A＝2K_r-1

wherein: k_ATo length after zero padding, K_rThe number of sampling points.

The step S2 specifically includes:

step S21: converting the zero-padded reference signal into an inverse Fourier transform form:

wherein: s (n-tau) is a preprocessed nth reference signal, tau is time delay, S (k) is a DFT conversion result of a signal s (n), j is an imaginary symbol, and k is a signal summation serial number;

step S22: performing cyclic correlation processing on the received signal and the reference signal to obtain a cyclic correlation function:

wherein: r_s,r(τ) is a function of the cyclic correlation,

for amplitude information of the signal on the ith path, N_A(k) Is the product of the fourier transform result of the signal and the fourier transform result of the noise, s is the identity of the reference signal, and r is the identity of the received signal.

The parameter matrix is specifically:

X_A＝Φ_Aλ_A+N_A

wherein: x_AAs a parameter matrix, phi_AFor a sparsely represented delay matrix, λ_AIs the magnitude vector, N, of the multipath signal_AIs a noise correlation function.

The step S5 specifically includes:

step S51: a Gaussian random matrix is used as a measurement matrix, and an observation matrix is obtained by carrying out compression sampling on a parameter matrix;

step S52: constructing sparse basis according to the matrix form of the parameter matrix:

wherein: Ψ is a sparse basis for the signal,

for all the possible searched delay values,

to construct a steering vector of potential search delays, L_NIs the number of possible values.

The step S6 specifically includes the steps of:

step S61: initializing residuals, vectors with reconstruction coefficients, index sets for storing atoms of the best linear combination:

r_n＝y＝Θα＝ΦΨx

pos _ array as empty set

Wherein r _ n is a residual error, y is an observation matrix, theta is a sensing matrix, α is a sparse vector to be solved, phi is a measurement matrix, and pos _ array is an index set;

step S62: finding out the maximum absolute value in the product of the residual error and the atoms in the sensing matrix to obtain the position of the corresponding atom in the sensing matrix, namely:

wherein ξ_tIs the atom number corresponding to the maximum delay value, r _ n is the residual error, j is the number of the guide vector,

is the steering vector of the jth delay.

Step S63: update index set pos _ array_t＝pos_array_t-1∪{ξ_tRecording the columns of the atoms of the optimal linear combination of the current iteration in the sensing matrix, merging the atoms into the empty matrix,

clearing the selected column;

step S64: obtaining an estimated value of the first iteration by a least square method, and if the estimated value meets Aug _ y | | y-Aug _ t | |, executing step S65;

step S65: updating residual error r _ n-y-Aug _ t-Aug _ y;

step S66: and judging whether the iteration time t reaches the upper limit, if so, stopping iteration, executing the step S67, otherwise, executing the next iteration, and returning to the step S62.

Step S67: multipath delay information is output based on the index set.

An apparatus for multipath delay estimation based on compressed sensing in dense environments, comprising a memory, a processor, and a program stored in the memory and executed by the processor, the processor implementing the following steps when executing the program:

step S1: setting a reference signal, and preprocessing a received signal and the reference signal to a set length;

step S2: performing cyclic correlation processing on the received signal and the reference signal to obtain a cyclic correlation function;

step S3: expressing the obtained cyclic correlation function as an inverse Fourier transform form of the cyclic correlation function as a parameter signal;

step S4: generating a parameter matrix according to the parameter signal;

step S5: adopting a measurement matrix, constructing a sparse basis dictionary, and performing compression sampling on the time delay parameter by using a compression sensing algorithm;

step S6: and matching and tracking the observation signal by adopting an orthogonal matching algorithm to obtain a multipath time delay parameter.

Compared with the prior art, the invention has the following beneficial effects: because the time delay information is separated from the frequency amplitude value through the inverse Fourier transform of the correlation function, the parameter signal is compressed and sampled under the condition of being lower than the Nyquist sampling frequency, the calculation complexity is reduced while the time delay information is saved, the multipath time delay in the dense environment is accurately estimated through the data obtained by low sampling, and the resolution capability of the time delay signal estimation in the dense environment is improved.

Drawings

FIG. 1 is a schematic flow chart of the main steps of the method of the present invention;

fig. 2 is a graph comparing the delay estimation of the conventional algorithm and the present method in high and low SNR, where (a) is SNR-15 dB, and (b) is SNR-2 dB;

FIG. 3 is a graph comparing errors of different snapshots in the conventional algorithm and the method;

FIG. 4 is a graph comparing the error of the conventional algorithm and the method under different SNR;

fig. 5 is a graph comparing the error of the conventional algorithm and the method under different multipath numbers, wherein (a) is a non-dense environment and (b) is a dense environment.

Detailed Description

The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.

Multipath delay estimation is always a hotspot problem in the field of delay estimation, and for the delay estimation problem applied to practice at present, accurate estimation of multipath delay in a dense environment is still a difficulty. And the multi-path time delay can be quickly and accurately estimated under the condition of short observation time, and the time delay signal can be optimally estimated by using a compressed sensing technology by utilizing the sparse characteristic of the time delay signal in the propagation process.

The compressed sensing theory breaks through the limitation of the traditional Nyquist sampling theorem, only needs few signal samples to accurately reconstruct the signals, and solves the defect of large calculation amount of a classical algorithm. The method comprises the steps of establishing a multi-path time delay estimation model based on compressed sensing by considering that time delay information in a time delay signal satisfies sparse and irrelevant characteristics in the transmission of the multi-path signal, estimating time delay parameters in the multi-path time delay signal by a compressed sensing method, considering that the estimation difficulty of the time delay parameters in a time domain is high, carrying out correlation processing on the time domain signal and a reference signal to inhibit noise influence, storing the time delay information in a diagonal matrix by inverse Fourier transform, obtaining a nonzero position of a sparse vector by constructing a sparse basis and an iterative algorithm, and reflecting the relative multi-path time delay of the signal, so that the compressed sensing method has super-resolution capability for the multi-path time delay estimation.

The present application is first described below: a method for multipath delay estimation based on compressed sensing in dense environment, the method is implemented by a computer system in the form of a computer program, and a corresponding apparatus includes a memory, a processor, and a program stored in the memory and executed by the processor, as shown in fig. 1, when the processor executes the program, the following steps are implemented:

step S1: setting a reference signal, and preprocessing a received signal and the reference signal to a set length, specifically comprising:

firstly, a multipath time delay signal model is constructed

In the above equation L represents the total number of paths between transceiving signals,

where lambda_iL (i-1 … L) is expressed as the amplitude information of the signal on the ith path, phi_nExpressed as the phase difference, τ, of the signal on the ith path relative to the signal on the shortest path_iExpressed as the time delay of the arrival of the ith path, s (T) is of duration T_rω (t) is additive white gaussian noise, which is used to simulate random noise generated during the transmission and reception of the signal.

Step S11: acquiring a received signal, sampling and observing the received signal to obtain a sampling signal:

here T_spIs the sampling period, K_rNumber of sample points is expressed, where for convenience we generally let T be_spThus, the sampled signal obtained by the nth sampling is denoted as s (n- τ), and the sampled signal received by the receiver is denoted as:

step S12: uniformly performing time shift operation on the transmission signals subjected to the set times of sampling to obtain reference signals, specifically, step 3) uniformly performing time shift operation on the transmission signals subjected to the n times of sampling to obtain reference signals s (n-tau),

step S13: because cyclic correlation processing is performed on the reference signal and the received signal, zero padding processing is performed on the reference signal and the received signal in advance, and zero padding is performed to K_ALength of, wherein K_A＝2K_r-1, where K needs to be guaranteed_A＞L。

Step S2: the method for obtaining the cyclic correlation function by performing cyclic correlation processing on the received signal and the reference signal specifically comprises the following steps:

step S21: converting the zero-padded reference signal into an inverse Fourier transform form:

wherein: s (n-tau) is a preprocessed nth reference signal, tau is time delay, S (k) is a DFT conversion result of a signal s (n), j is an imaginary symbol, and k is a signal summation serial number;

step S22: performing cyclic correlation processing on the received signal and the reference signal to obtain a cyclic correlation function:

wherein: r_s,r(τ) is the cyclic correlation function, N_A(k) Is the product of the Fourier transform of the signal and the Fourier transform of the noise, s is the identity of the reference signal, r is the identity of the received signal,

is λ_iThe conjugate of (a) to (b),

further:

wherein N is_A(k)＝S(k)·N(k)^*And N (k) is a cyclic correlation function R obtained by correlation of the received signal with a reference signal in the form of a Fourier transform of ω (n)_s,rThe delay information of the multipath appears at the peak of its linear envelope, but the correlation algorithm cannot distinguish different delay information in the dense signal. Considering the correlation process after the reference signal is represented as its inverse fourier transform, the purpose is to store the delay information in the index, and the next step is to extract the multipath delay information from the index.

Step S3: expressing the obtained cyclic correlation function as an inverse Fourier transform form of the cyclic correlation function as a parameter signal, and performing inverse Fourier transform on the correlation function through observation and deformation of the cyclic correlation function to obtain:

wherein x (k) is an inverse Fourier transform form of a time domain cyclic correlation function, and the time delay parameter signal is marked as x _ p;

step S4: a parameter matrix is generated from the parameter signals, specifically,

wherein: x_AFunction matrix expressed as sparse delay parameter, phi_AFor a time delay matrix which is a sparse representation, λ_AIs an amplitude vector of a multipath signal, N_AIs a noise correlation function.

X_A＝[x_A(0) x_A(1) … x_A(K_A-1)](9)

λ_A＝[λ₁λ₂···· λ_L]^T(10)

N_A＝[ω(0) ω(1) ···· ω(M-1)]^T

S＝[|S(0)|²|S(1)|²… |S(K_A-1)|²](12)

Φ_A＝[Λ_A(τ_l)S Λ_A(τ_l)S … Λ_A(τ_l)S](13)

Wherein Λ_AThe diagonal matrix contains the time delay information of all paths, the time delay parameters are stored in the exponential form of the diagonal matrix, and the time delay signals are considered to be sparse in the actual propagation path, so that the time delay signals can be compressed and sampled by using a compressed sensing technology under the condition of being far less than the signal sampling frequency.

Step S5: adopting a measurement matrix, constructing a sparse basis dictionary, carrying out compression sampling on the time delay parameter by using a compressed sensing algorithm, and estimating a parameter signal x _ p containing the time delay parameter by using the compressed sensing algorithm, wherein x _ p is [ x (0) x (1) … x (K)_A-1)]^TThe original signal is in a vector form of inverse Fourier transform after cyclic correlation processing, a matrix form of the original signal is observed, the original signal is represented as a linear combination of a set of uncorrelated vector bases psi by a compressed sensing technology, and corresponding coefficients are α_i(i＝0,1,2,…K_A-1) that is

Wherein

Requires to construct a proper sparse matrix Psi, and can enable the sparse vector α to satisfy | | α | survival₀L, i.e. α ═ 0 α ₁0 0 α ₂0 … 0 α_L0]^TThe parameter signal x _ p is a sparse signal having a sparsity L at the sparsity base Psi.

Since x _ p is a sparse signal related to time delay, the measurement matrix Phi is adopted to carry out compression sampling on the sparse signal, and an observation vector y is obtained after projection measurement, namely

y＝Phi*x_p＝Phi*Psi*α＝Θ*α (15)

In the formula of M is multiplied by K_AThe theory proves that when the sensing matrix meets the RIP condition, namely, any two matrix dictionaries are not related, the information vector α can be accurately reconstructed by solving the optimal norm problem through the observation vector y, and the obtained L maximum vector subscripts are time delay information of the multipath signals.

min||α||₁s.t.y＝Θ*α (16)

When the signal also has additive white Gaussian noise n, the above formula is rewritten as

y＝Θ*α+n (17)

In which n is K_AA noise vector of x 1, subject to a normal distribution, the estimated optimization model of vector α is

min||α||₁s.t.||y-Θα||₂＜ε (18)

In the embodiment, a Gaussian random matrix Phi is selected as a measurement matrix, and the parameter signal x _ p obtained after processing is subjected to compression dimensionality reduction, namely K_AAnd (3) compressing x _ p of x 1 into an observation matrix y of M x 1, replacing a traditional orthogonal matrix with a complete dictionary matrix as a sparse matrix Psi, and solving L optimal linear combination atoms from the complete dictionary through an orthogonal matching algorithm so as to estimate L time delay information in the source signal.

That is, includes:

step S51: a Gaussian random matrix is used as a measurement matrix, and an observation matrix is obtained by carrying out compression sampling on a parameter matrix;

step S52: constructing a complete sparse matrix according to the matrix form of the parameter matrix, dividing the time range into time vectors tim with small sampling intervals, obtaining the length of the divided time vectors, recording the length as Nt, and taking the sparse matrix Psi as K_AThe less the interval is, the higher the resolution is, and the dense multipath time delay signals can be distinguished:

wherein: Ψ is a sparse basis for the signal,

for all the possible searched delay values,

to construct a steering vector of potential search delays, L_NIs the number of possible values.

Wherein:

step S6: the orthogonal matching algorithm is adopted to match and track the observation signal to obtain the multipath time delay parameter, the orthogonal matching algorithm is widely applied, and the input of the orthogonal matching algorithm in the embodiment is as follows: the parameter signal x _ p obtained by the correlation transformation and the inverse Fourier transformation is output as follows: l multipath time delay estimated values of dense signal

The method specifically comprises the following steps:

step S61: initializing residual errors, vectors with reconstruction coefficients, and index sets for storing atoms of the best linear combination, and further iterating for a number of iterations t equal to 1:

r_n＝y＝Θα＝ΦΨx

pos _ array as empty set

Wherein r _ n is a residual error, y is an observation matrix, theta is a sensing matrix, α is a sparse vector to be solved, phi is a measurement matrix, and pos _ array is an index set;

step S62: finding out the maximum absolute value in the product of the residual error and the atoms in the sensing matrix to obtain the position of the corresponding atom in the sensing matrix, namely:

wherein ξ_tIs the atom number corresponding to the maximum delay value, r _ n is the residual error, j is the number of the guide vector,

is the steering vector of the jth delay.

Step S63: update index set pos _ array_t＝pos_array_t-1∪{ξ_tRecording the columns of the atoms of the optimal linear combination of the current iteration in the sensing matrix, merging the atoms into the empty matrix,

resetting the selected column to zero to avoid the influence on the subsequent iteration;

step S64: obtaining an estimated value of the first iteration through a least square method:

aug_y＝(Aug_t^T*Aug_t)^-1*Aug_t^T*y

if Aug _ y ═ argmin | | y-Aug _ t | |, then step S65 is executed;

step S65: updating residual error r _ n-y-Aug _ t-Aug _ y;

step S66: and judging whether the iteration time t reaches the upper limit, if so, stopping iteration, executing the step S67, otherwise, executing the next iteration, and returning to the step S62.

Step S67: multipath delay information is output based on the index set.

Step S7: and carrying out communication control by using the estimated time delay.

The method of the present application was experimentally verified as follows.

In order to verify the performance of the algorithm in a dense multipath environment, under different influence factors, the multipath delay estimation algorithm under the traditional algorithm and a time domain model is subjected to experimental simulation, the root mean square error of each algorithm result is compared by adopting a Monte Carlo experiment, the quality of each delay estimation algorithm under different conditions is visually evaluated, and the root mean square error definition formula is (21), namely:

wherein K is the multipath number of the time delay signal, CNT is the Monte Carlo cycle number, tau'_k,cntFor the k path in the proposed algorithm, the time delay estimation value, tau, at the cnt time_kThe k-th real delay value is the root mean square error obtained from simulation experiment RMSE _ TD.

Simulation conditions are as follows: the number of multipaths of the multipath delay signal is 4, wherein the delay value is set to [ 24.534.53554 ]]T_sWherein T is_sFor the sampling interval of the receiving system, the additive noise is white Gaussian noise, and the time delay search range is assumed to be (0-100) T_sAnd the Monte Carlo experiment frequency CNT is 200, and an OMP algorithm is adopted as a sparse estimation algorithm for solving.

Experiment one:

by comparing the estimation effects of the traditional algorithm and the proposed algorithm, the anti-noise performance of the algorithm in a dense multipath environment is observed more clearly, wherein XCOR is a correlation estimation method, MUSIC is a subspace decomposition method, CS-TD is a time delay estimation algorithm based on compressed sensing, CS-IDFT is the proposed algorithm, parameters in the lower graph are set to be respectively SNR (signal-to-noise ratio) 15dB and SNR-2 dB, and SnapShot number Snapshot is 100.

The correlation algorithm in (a) and (b) of fig. 2 cannot accurately estimate that the delay difference is smaller than the sampling interval T_sUnder the condition of higher signal-to-noise ratio in (a), the MUSIC and the algorithm can accurately estimate the multipath time delay value; observing a delay value of 24.5T in (b)_sAlready less than 12.5T_sTherefore, the delay value of the path cannot be accurately estimated, compared with the CS-TD algorithm which keeps four obvious peaks, but is denseThe time delay estimated value at the signal position deviates from the true value, and the algorithm can still accurately estimate the dense multipath signals under the low signal-to-noise ratio environment.

Experiment two:

in order to compare the accuracy and stability of each algorithm under different signal-to-noise ratios and different snapshots, a Monte Carlo experiment is adopted to analyze the performance difference of the algorithms in a dense environment, the time delay parameter setting in the dense environment is the same as that in the experiment I, and the graphs in FIG. 3 and FIG. 4 are respectively the influence of the snapshot number and the signal-to-noise ratio on the time delay estimation precision in the dense multipath environment.

The algorithm provided in fig. 3 can keep a lower estimation error under a low snapshot condition, has a faster convergence speed, and basically tends to be stable after the number of snapshots reaches 100, and the overall performance is better than that of MUSIC and CS-TD algorithms; the fast beat number set in fig. 4 is 150, the estimation performance of the other two algorithms in a dense environment is greatly limited, and the root mean square error of the proposed algorithm always tends to 0.2T along with the increase of the signal-to-noise ratio_sAnd high estimation accuracy is kept.

Experiment three:

in order to further highlight the estimation performance of the algorithm on the multipath time delay signals, the relation between the measurement number M and the estimation error of the CS-TD and the algorithm under different multipath numbers is tested under the dense environment and the non-dense environment respectively, and the error change generated by the result is observed. Setting simulation parameters: assume that the sparsity of signal 1 and signal 2 is K ₁2 and K₂Setting the delay values in the non-dense environment to [ 2268 ] respectively for 5]T_sAnd [ 2436548193]T_sThe delay values in the dense environment are set to [ 22.322.7 ]]T_sAnd [ 24.524.659.760.461.2]T_sThe fast beat number is 200, the signal-to-noise ratio is 0dB, the measurement number M is (20-300), and fig. 5(a) and (b) are experimental results in non-dense and dense environments respectively.

As can be seen from (a) and (b) of fig. 5, the delay estimation errors of the two CS theory-based algorithms decrease with the increase of the number of measurements, and the change of the number of multipaths has less influence on the delay estimation errors, and it can be seen by comparison that, in a non-dense environment, the CS-TD algorithm converges faster than the proposed algorithm, because the zero padding operation of the proposed algorithm lengthens the length of the parameter signal, and the number of measurements required is relatively large, so the convergence speed is slower, and the estimation effect in the non-dense condition is equivalent to that of the CS-TD algorithm; and (b) observing that the time delay search is carried out by reducing the time delay search step length, the algorithm still can keep a certain convergence speed, when the measured number reaches 220, the time delay estimation error is basically stabilized at a small value, the estimation effect of the CS-TD algorithm is reduced to some extent, and in conclusion, the IDFT compressed sensing algorithm based on the cross correlation has better overall performance in a low-snapshot dense environment.

Claims (8)

1. A multipath time delay estimation method based on compressed sensing in a dense environment is characterized by comprising the following steps:

step S1: setting a reference signal, and preprocessing a received signal and the reference signal to a set length;

step S2: performing cyclic correlation processing on the received signal and the reference signal to obtain a cyclic correlation function;

step S3: expressing the obtained cyclic correlation function as an inverse Fourier transform form of the cyclic correlation function as a parameter signal;

step S4: generating a parameter matrix according to the parameter signal;

step S5: adopting a measurement matrix, constructing a sparse basis dictionary, and carrying out compression sampling on the time delay parameters by using a compression sensing algorithm;

step S6: and matching and tracking the observation signal by adopting an orthogonal matching algorithm to obtain a multipath time delay parameter.

2. The method according to claim 1, wherein the step S1 specifically includes:

step S11: acquiring a received signal, and sampling and observing the received signal to obtain a sampling signal;

step S12: uniformly performing time shift operation on the transmission signals subjected to the set sub-sampling to obtain reference signals;

step S13: and performing zero filling processing on the reference signal and the received signal to a set length.

3. The method according to claim 2, wherein the set length specifically comprises:

K_A＝2K_r-1

wherein: k_ATo length after zero padding, K_rThe number of sampling points.

4. The method according to claim 3, wherein the step S2 specifically includes:

step S21: converting the zero-padded reference signal into an inverse Fourier transform form:

wherein: s (n-tau) is a preprocessed nth reference signal, tau is time delay, S (k) is a DFT conversion result of a signal s (n), j is an imaginary symbol, and k is a signal summation serial number;

step S22: performing cyclic correlation processing on the received signal and the reference signal to obtain a cyclic correlation function:

wherein: r_s,r(τ) is a function of the cyclic correlation,

for amplitude information of the signal on the ith path, N_A(k) Is the product of the fourier transform result of the signal and the fourier transform result of the noise, s is the identity of the reference signal, and r is the identity of the received signal.

5. The method according to claim 1, wherein the parameter matrix specifically comprises:

X_A＝Φ_Aλ_A+N_A

wherein: x_AAs a parameter matrix, phi_AFor a sparsely represented delay matrix, λ_AIs an amplitude vector of a multipath signal, N_AIs a noise correlation function.

6. The method according to claim 5, wherein the step S5 specifically includes:

step S51: a Gaussian random matrix is used as a measurement matrix, and an observation matrix is obtained by carrying out compression sampling on a parameter matrix;

step S52: constructing sparse basis according to the matrix form of the parameter matrix:

wherein:

in the form of a sparse basis,

for all the possible searched delay values,

to construct a steering vector of potential search delays, L_NThe number of possible delay values.

7. The method according to claim 6, wherein the step S6 specifically includes the steps of:

step S61: initializing residuals, vectors with reconstructed coefficients, index set for storing atoms of the best linear combination:

r_n＝y＝Θα＝ΦΨx

pos _ array as empty set

Wherein r _ n is a residual error, y is an observation matrix, theta is a sensing matrix, α is a sparse vector to be solved, phi is a measurement matrix, and pos _ array is an index set;

step S62: finding out the maximum absolute value in the product of the residual error and the atom in the sensing matrix to obtain the position of the corresponding atom in the sensing matrix, namely:

wherein ξ_tIs the atom number corresponding to the maximum delay value, r _ n is the residual error, j is the number of the guide vector,

is the steering vector of the jth delay.

Step S63: update index set pos _ array_t＝pos_array_t-1∪{ξ_tRecording the columns of the atoms of the optimal linear combination of the iteration in the sensing matrix, merging the atoms into the empty matrix,

clearing the selected column;

step S64: obtaining an estimated value of the first iteration by a least square method, and if Aug _ y | | | y-Aug _ t | |, executing step S65;

step S65: updating residual error r _ n-y-Aug _ t-Aug _ y;

step S66: and judging whether the iteration time t reaches the upper limit, if so, stopping iteration, executing the step S67, otherwise, executing the next iteration, and returning to the step S62.

Step S67: multipath delay information is output based on the index set.

8. An apparatus for multipath delay estimation based on compressed sensing in dense environment, comprising a memory, a processor, and a program stored in the memory and executed by the processor, wherein the processor executes the program to implement the following steps:

step S1: setting a reference signal, and preprocessing a received signal and the reference signal to a set length;

step S2: performing cyclic correlation processing on the received signal and the reference signal to obtain a cyclic correlation function;

step S3: expressing the obtained cyclic correlation function as an inverse Fourier transform form of the cyclic correlation function as a parameter signal;

step S4: generating a parameter matrix according to the parameter signal;

step S5: adopting a measurement matrix, constructing a sparse basis dictionary, and carrying out compression sampling on the time delay parameters by using a compression sensing algorithm;

step S6: and matching and tracking the observation signal by adopting an orthogonal matching algorithm to obtain a multipath time delay parameter.

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