A method for blind estimation of opportunity signal beacon based on tensor decomposition

Abstract

The present disclosure provides a tensor decomposition based blind estimation method of opportunity signal beacon. Step 1: the received beacon samples in the coherent integration period are rearranged by using a tensor to obtain a tensor representation of the received beacon samples; Step 2: the rank of the tensor is determined as the number of SOP signals of the opportunity signal source in the received beacon samples; Step 3: the arrival angle, Doppler and beacon sequence of each SOP signal are determined through tensor regular decomposition. The method utilizes the diversity of the received samples in the antenna spatial domain, the Doppler frequency domain and the beacon symbol domain, and realizes the estimation of the arrival angle, Doppler and beacon sequence of each SOP signal through tensor characterization, rank calculation and tensor decomposition, and can realize the blind estimation of the beacon sequence under any modulation system.

Description

Technical Field

[0001] This invention relates to the fields of signal processing and navigation positioning technology, and specifically to a blind estimation method for opportunistic signal beacons based on tensor decomposition. Background Technology

[0002] Opportunity signal navigation can utilize all potential opportunity signal sources (SOPs) in the environment and is considered an effective supplement to or alternative to GNSS navigation in complex environments. One of the key technologies of opportunity signal navigation is to distinguish different SOP signal sources and acquire pseudorange, Doppler, and other observations from the receiver for each SOP.

[0003] Unlike GNSS or network-based cellular positioning, SOP signals mostly come from private networks, and their signal system, modulation method and other parameters are unknown. Therefore, it is necessary to perform blind estimation of the beacon sequence in the SOP signal, so as to use the local loop to track it and obtain the observations.

[0004] Existing blind beacon estimation methods are based on the generalized likelihood ratio test (GLRT). While effective in detecting and estimating blind beacons, they require maximum likelihood searches in the frequency domain or frequency variation domain. Therefore, the estimation accuracy of GLRT-based methods directly depends on the fineness of the search grid. When the search range is large, GLRT methods introduce high computational complexity. Furthermore, when the coherent integration time is short or the Doppler differences between different SOP signals are small, GLRT struggles to separate multiple SOP signals, thus degrading the performance of beacon sequence estimation. Summary of the Invention

[0005] In view of this, the present invention provides a blind estimation method for SOP signals based on tensor decomposition. This method utilizes the diversity of received samples in the antenna spatial domain, Doppler frequency domain, and beacon symbol domain to rearrange the received samples using tensors. Through translation-invariant subspace matching, the number of SOP signals in the received samples is determined, and through tensor regularization, the angle of arrival, Doppler frequency, and beacon sequence of each SOP signal are determined. The method of the present invention can achieve blind estimation of beacon sequences under arbitrary modulation schemes.

[0006] To solve the above-mentioned technical problems, the present invention is implemented as follows.

[0007] A blind estimation method for chance signal beacons based on tensor decomposition includes:

[0008] Step 1: Rearrange the received beacon samples within the coherent integration period using tensors to obtain the tensor representation of the received beacon samples.

[0009] Step 2: Determine the tensor The rank of the signal is the number of SOP signals from the opportunity signal source in the received beacon sample.

[0010] Step 3: Determine the angle of arrival, Doppler, and beacon sequence of each SOP signal through tensor regularization.

[0011] Preferably, in step 1, tensors are used to rearrange the received beacon samples.

[0012] Suppose the receiver can receive I SOP signals from different directions with the same downlink signal parameters, and the center frequency of the SOP signal is f. c The wavelength is λ, and the downlink signal has a duration of T. f The signal consists of consecutive frames; for the i-th SOP signal, its frame signal contains periodically broadcast signals for a duration of T. b beacon signal c i (t); The receiver is equipped with a uniform linear array ULA with M elements, the spacing between the elements satisfying d≤λ / 2; the relative velocity between the i-th SOP signal source and the receiver is v. i The clock frequency synchronization deviation is δf i The angle of arrival is θ i Then, after the beacon sequence propagates through the channel, the baseband received signal vector of the receiver array elements is represented as:

[0013]

[0014] Among them, g i For the complex channel gain, β i =f c v i / c+δf i It is the carrier frequency offset, where c represents the speed of light; τ i The signal delay is unknown, w(t) is noise; α i The arrival angle steering vector representing the ULA is denoted as:

[0015]

[0016] The receiver uses f s The received signal is sampled at a sampling rate of T; each frame contains P sampling points, i.e., T f =PT s T s =1 / f s For the i-th SOP, a complete beacon sequence contains L sampling points, i.e., s i =[s i,1 ,…,s i,l ,…,s i,L ] T T b =LT s ;

[0017] The receiver rearranges the SOP signal within a coherent integration period, which contains K frames of signal. During this period, the relative velocity and clock frequency synchronization deviation between the receiver and the signal source remain constant. Therefore, a received beacon sample sampled within a radar coherent processing index (CPI) is written as:

[0018]

[0019] Where 1≤m≤M, 1≤k≤K, 1≤l≤L; y m,k,l This represents the sampling result of the l-th beacon in the k-th frame received by the m-th array element; w k,l This represents the sampling noise of the l-th beacon in the k-th frame; by symbol combining the above equation, we obtain the rearranged received signal:

[0020]

[0021] By rearranging the received beacon samples within a coherent integration period, a typical element y is obtained. m,k,l The three-dimensional tensor of M×K×L 3D tensor Each element in the equation is α. i,m f i,k , The product of three terms; where α i,m Characterizes the channel response of the m-th array element to the SOP signal i. Characterize the effect of carrier Doppler on the beacon in the k-th frame within the coherent integration period of frequency domain signal i. A beacon sample, g, represents the superposition of carrier Doppler effects and channel gain within a sequence. i The channel gain characterizes the SOP signal i.

[0022] Preferably, in step 2, the tensor is determined. The rank is: the tensor is estimated by matching translation-invariant subspaces. Rank.

[0023] Preferably, the tensor is estimated by matching translation-invariant subspaces. The steps for determining the rank include:

[0024] right Perform mode-1 matrix conversion to obtain

[0025]

[0026] in, It is the Hadamard product, ⊙ is the Khatri-Rao product, A, F, Let G be the factor matrix of angle of arrival, Doppler, and beacon sequence, where G = diag{g1,...,g I} is represented as the complex channel gain matrix, where E is the Vandermonde matrix, representing the carrier Doppler effect in the beacon sequence, where,

[0027]

[0028] Considering the differences in the angle of arrival, Doppler effect, and beacon sequence of different SOP signals, it can be known that

[0029]

[0030] get therefore The column vector space, i.e. The column vector space is I-dimensional; The eigenvalue decomposition of the covariance matrix is ​​written as

[0031]

[0032] Where the V column vectors correspond to the right feature vectors. It is an eigenvalue matrix; since rank(A) = I, then there exists a matrix Make

[0033]

[0034] Where V I Let A be a matrix consisting of the largest I eigenvectors; (1) and A (2) This represents the matrix obtained by deleting the first and last rows of matrix A.

[0035] A (1) =A (2) D

[0036] in If the matrix is ​​diagonal, then we have Right now and They have the same translation-invariant signal subspace; the projection onto this subspace is represented by a projection matrix, which is... and and

[0037] The number I of SOP signal sources is obtained by minimizing the following objective.

[0038]

[0039] in, tr() represents the 2-norm of a matrix, and tr() represents the trace of a matrix.

[0040] Preferably, in step 3, the angle of arrival for each SOP signal is determined as follows:

[0041] Step a1: For tensor signals Perform mode-(1,2) matrix transformation to obtain

[0042]

[0043] For Y (1,2) Perform singular value decomposition to obtain Y (1,2) =UΣV H ;because Therefore, a non-singular matrix exists. satisfy

[0044] U I Q = A⊙F

[0045] Let U I,1 and U I,2 To delete U separately I The matrix obtained by taking the top K rows and the bottom K rows is then:

[0046] U I,1 Q = A (1) ⊙F,U I,2 Q = A (2) ⊙F

[0047] Where A (1) and A (2) The matrix obtained by deleting the first and last rows of A can be obtained as follows:

[0048]

[0049] calculate Then, eigenvalue decomposition is performed to estimate Q and D, resulting in... and

[0050] Step a2: According to Estimate the angle of arrival for each SOP signal:

[0051]

[0052] Step a3: According to Reconstruct the arrival angle factor matrix

[0053] Preferably, in step 3, the Doppler determination method for each SOP signal is to use the estimated SOP signal angle of arrival. and the corresponding factor matrix For the factor matrix F and the SOP signal Doppler β i Make an estimate:

[0054] Step b1: Construct the generating factors z of the factor matrix F i :

[0055] byU I Q = A⊙F, construct It is the Kronecker product;

[0056] Then f i It has the following characteristics:

[0057]

[0058] Then utilize U I , Estimate f i :

[0059]

[0060] Since F is a Vandermonde matrix, therefore The generating factor z in column i i Estimate using the following methods:

[0061]

[0062] in,

[0063] Step b2: Utilize Estimate the Doppler β of each SOP signal i :

[0064]

[0065] Step b3: According to Reconstruct the Doppler factor matrix

[0066] Preferably, in step 3, the beacon sequence for each SOP signal is determined as follows:

[0067] Using the obtained angle of arrival factor matrix Doppler factor matrix And the representation of the beacon sequence factor matrix, constructing the beacon sequence factor matrix after removing the Doppler effect. Then, the estimation result of the SOP beacon sequence is obtained by power normalization.

[0068] Beneficial effects:

[0069] This invention enables blind estimation of beacon sequences under arbitrary modulation schemes. It leverages the diversity of received samples in the antenna spatial domain, Doppler frequency domain, and beacon symbol domain, rearranging the received samples using tensors. Through translation-invariant subspace matching, the number of SOP signals in the received samples is determined, and through tensor regularization, the angle of arrival, Doppler frequency, and beacon sequence of each SOP signal are determined. Compared to existing algorithms, this invention eliminates the need for maximum likelihood search, offering advantages such as low computational complexity and high estimation accuracy. Attached Figure Description

[0070] Figure 1 This is a flowchart of a blind estimation method for opportunistic signal beacons based on tensor decomposition.

[0071] Figure 2 This is a schematic diagram of sample rearrangement and tensor decomposition. Detailed Implementation

[0072] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0073] This invention provides a blind estimation method for opportunistic signal beacons based on tensor decomposition. The basic idea is to utilize the diversity of received samples in the antenna spatial domain, Doppler frequency domain, and beacon symbol domain to rearrange the received samples using tensors; then, through translation-invariant subspace matching, the number of SOP signals in the received samples is determined; finally, through tensor regularization decomposition, the angle of arrival, Doppler frequency, and beacon sequence of each SOP signal are determined. This invention can achieve blind estimation of beacon sequences under arbitrary modulation schemes.

[0074] The structural block diagram of this invention is as follows: Figure 1 As shown, it includes five steps: received sample rearrangement, estimation of the number of opportunity signal sources, estimation of the angle of arrival of opportunity signals, estimation of Doppler probability of opportunity signals, and estimation of the beacon sequence of opportunity signals.

[0075] The specific steps of this invention are as follows:

[0076] Without loss of generality, the receiver can receive I SOP signals from different directions, each with the same downlink signal parameters. The center frequency of the SOP signal is f. c The wavelength is λ, and the downlink signal has a duration of T. f The signal is composed of consecutive frames. For the i-th SOP signal, its frame signal contains periodically broadcast signals for a duration of T. b beacon signal c i (t). The receiver is equipped with a uniform linear array (ULA) with M elements. The spacing between the elements satisfies d ≤ λ / 2. Assume the relative velocity between the i-th SOP signal source and the receiver is v. i The clock frequency synchronization deviation is δf iThe angle of arrival is θ i Then, after the beacon sequence propagates through the channel, the baseband received signal vector of the receiver array elements can be expressed as:

[0077]

[0078] Among them, g i For the complex channel gain, β i =f c v i / c+δf i This is the carrier frequency offset, where c represents the speed of light. τ i The delay is an unknown signal, and w(t) represents noise. α i The arrival angle steering vector representing the ULA is denoted as:

[0079]

[0080] The receiver uses f s The received signal is sampled at a sampling rate of T. In this case, each frame contains P sampling points, i.e., T f =PT s T s =1 / f s For the i-th SOP, a complete beacon sequence contains L sampling points, i.e., s i =[s i,1 ,...,s i,l ,...,s i,L ] T ,T b =LT s The receiver uses a coherent integration period to perform beacon blind estimation of the SOP. It is assumed that the coherent integration period contains K frames of signal, during which the relative motion speed and clock frequency synchronization deviation between the receiver and the signal source remain constant.

[0081] The objective of this invention is to estimate the angle of arrival with respect to each signal source using the received signal. Carrier Doppler and beacon sequences Subsequently, the receiver generates a replica beacon signal locally and uses conventional PLL and DLL loops to track the beacon in the actual received signal, thereby obtaining pseudorange and pseudo-Doppler observations similar to those of a GNSS receiver, enabling the receiver to perform opportunistic navigation.

[0082] The specific implementation of each step of the present invention is as follows:

[0083] Step 1: Rearrange received samples

[0084] The receiver rearranges the SOP signal within a coherent integration period, which contains K frames of signal. During this period, the relative velocity and clock frequency synchronization deviation between the receiver and the signal source remain constant. Therefore, a received beacon sample sampled within a radar coherent processing index (CPI) is written as...

[0085]

[0086] Where 1≤m≤M, 1≤k≤K, 1≤l≤L. m,k,l This represents the sampling result of the l-th beacon in the k-th frame received by the m-th array element. k,l This represents the sampling noise of the l-th beacon in the k-th frame. By symbol combining equation (3), the received beacon sample can be obtained:

[0087]

[0088] in,

[0089]

[0090] In the above formula, α i,m Characterizes the channel response of spatial array element m to signal i. Characterize the effect of carrier Doppler on the beacon in the k-th frame within the coherent integral. A beacon sample that represents the superposition of carrier Doppler effects and channel gain within a sequence.

[0091] This step, by rearranging the received beacon samples within a coherent integration period, yields a sample with typical elements y. m,k,l The three-dimensional tensor of M×K×L This reflects the diversity of received beacon signals in the spatial, frequency, and symbol domains; this process... Figure 2 It was showcased in [the document / platform].

[0092] 3D tensor Each element in the equation is α. i,m f i,k , The product of three terms, through the three-dimensional tensor By decomposing, α can be achieved i,m f i,k , The estimation is used to estimate the angle of arrival, Doppler, and beacon sequence of each SOP signal.

[0093] Step 2: Estimation of the number of opportunity signal sources

[0094] The three-dimensional tensor obtained by rearranging received beacon samples The rank is equal to the number of SOP signal sources in the received sample. For the tensor... To perform the decomposition, it is first necessary to estimate the number of SOP signal sources in the received samples, i.e., the tensor. Rank.

[0095] This embodiment utilizes translation-invariant subspace matching to estimate... Rank.

[0096] First of all By performing mode-1 matrix conversion, we can obtain

[0097]

[0098] in It is the Hadamard product, ⊙ is the Khatri-Rao product, A, F, G = diag{g1,...,g} is the factor matrix for angle of arrival, Doppler, and beacon symbol. I} is represented as the complex channel gain matrix, where E is the Vandermonde matrix, representing the carrier Doppler effect in the beacon sequence, where,

[0099]

[0100]

[0101]

[0102]

[0103] Considering the differences in the angle of arrival, Doppler effect, and beacon sequence of different SOP signals, it can be known that

[0104]

[0105] Therefore, we can obtain therefore The column vector space, i.e. The column vector space is I-dimensional. The eigenvalue decomposition of the covariance matrix can be written as

[0106]

[0107] in The column vectors correspond to the right eigenvectors. It is an eigenvalue matrix. Since rank(A) = I, then there exists a matrix... Make

[0108]

[0109] Where VI It is a matrix composed of the first I eigenvectors (corresponding to the largest I eigenvalues). Let A (1) and A (2) This represents the matrix obtained by deleting the first and last rows of matrix A.

[0110] A (1) =A (2) D (13)

[0111] in It is a diagonal matrix. Using the above formula (13), we can obtain... Right now and They have the same translation-invariant signal subspace. Therefore, projection onto this subspace can be done through the projection matrix. and To characterize. Because and Having the same translation-invariant signal subspace, we can obtain Therefore, the number I of SOP signal sources can be obtained by minimizing the following objective.

[0112]

[0113] in, tr() represents the 2-norm of a matrix, and tr() represents the trace of the matrix.

[0114] Step 3: Opportunity Signal Angle of Arrival Estimation

[0115] After estimating the number of signal sources I, the tensor is known. The rank of, and given A, F, The number of columns in the factor matrix. Next, tensor decomposition is used to estimate the factor matrix, and then the angle of arrival of the SOP signal is estimated.

[0116] For tensor signals By performing mode-(1,2) matrix transformation, we can obtain

[0117]

[0118] For Y (1,2) Singular value decomposition can be performed to obtain Y. (1,2) =UΣV H .because Therefore, a non-singular matrix exists. satisfy

[0119]

[0120] Let U I,1 and U I,2Deleting U respectively I The matrix obtained by the top K rows and the bottom K rows then has

[0121]

[0122] Where A( 1 ) and A (2) This is the matrix obtained by deleting the first and last rows of A. According to (16), we can obtain...

[0123]

[0124] Therefore, by calculation By performing eigenvalue decomposition, we can estimate Q and D, and obtain... and

[0125] according to The angle of arrival (Angle of Arrival) of each SOP signal can be estimated:

[0126]

[0127] Furthermore, it can be based on Reconstruct the arrival angle factor matrix

[0128] Step 4: Opportunity Signal Doppler Estimation

[0129] Estimate the angle of arrival of the SOP signal and the corresponding factor matrix Next, the factor matrix F and the SOP signal Doppler β were analyzed. i Make an estimate.

[0130] According to (16), we can obtain

[0131]

[0132] in It is the Kronecker product. and f i The definition is given in formulas (5) and (6). i It has the following characteristics:

[0133]

[0134] Therefore, f can be estimated in the following way. i

[0135]

[0136] Since F is a Vandermonde matrix, therefore The generating factor z in column i i It can be estimated in the following ways

[0137]

[0138] in Depend on The factor matrix F and the SOP signal Doppler β can be estimated. i :

[0139]

[0140] Furthermore, it can be based on The estimation results of the Doppler factor matrix are obtained.

[0141] (3) Opportunity signal beacon sequence estimation

[0142] get Subsequently, the final target is the factor matrix. and each SOP signal beacon sequence An estimate is made. According to formula (8), the following can be obtained:

[0143]

[0144] Furthermore, we can obtain Factor matrix after removing Doppler effects

[0145]

[0146] According to (26), the SOP beacon sequence after power normalization can be obtained.

[0147]

[0148] in, for The elements in the array, where ρ is the scaling factor.

[0149] This achieves the control of the SOP signal arrival angle. Doppler beacon sequence The estimation results.

[0150] The specific embodiments described above only illustrate the design principles of the present invention. The shapes and names of the components in this description may differ and are not limited. Therefore, those skilled in the art can modify or make equivalent substitutions to the technical solutions described in the foregoing embodiments; and these modifications and substitutions do not depart from the inventive spirit and technical solutions of the present invention, and should all fall within the protection scope of the present invention.

Claims

1. A blind estimation method for opportunistic signal beacons based on tensor decomposition, characterized in that, include: Step 1: Rearrange the received beacon samples within the coherent integration period using tensors to obtain the tensor representation Y of the received beacon samples; Step 2: Determine the rank of tensor Y, as the number of SOP signals from the received beacon samples; Step 3: Determine the angle of arrival, Doppler, and beacon sequence of each SOP signal through tensor regularization. In step 1, the received beacon samples are rearranged using tensors as follows: Suppose the receiver can receive I SOP signals from different directions with the same downlink signal parameters, and the center frequency of the SOP signal is f. c The wavelength is λ, and the downlink signal has a duration of T. f The signal consists of consecutive frames; for the i-th SOP signal, its frame signal contains periodically broadcast signals for a duration of T. b beacon signal c i (t); The receiver is equipped with a uniform linear array ULA with M elements, the spacing between the elements satisfying d≤λ / 2; the relative velocity between the i-th SOP signal source and the receiver is v. i The clock frequency synchronization deviation is δf i The angle of arrival is θ i Then, after the beacon sequence propagates through the channel, the baseband received signal vector of the receiver array elements is represented as: Among them, g i For the complex channel gain, β i =f c v i / c+δf i It is the carrier frequency offset, where c represents the speed of light; τ i The signal delay is unknown, w(t) is noise; α i The arrival angle steering vector representing the ULA is denoted as: The receiver uses f s The received signal is sampled at a sampling rate of T; each frame contains P sampling points, i.e., T f =PT s T s =1 / f s For the i-th SOP, a complete beacon sequence contains L sampling points, i.e., s i =[s i,1 ,…,s i,l ,…,s i,L ] T T b =LT s ; The receiver rearranges the SOP signal within a coherent integration period, which contains K frames of signal. During this period, the relative velocity and clock frequency synchronization deviation between the receiver and the signal source remain constant. Therefore, a received beacon sample sampled within a radar coherent processing index (CPI) is written as: Where 1≤m≤M, 1≤k≤K, 1≤l≤L; y m,k,l This represents the sampling result of the l-th beacon in the k-th frame received by the m-th array element; w k,l This represents the sampling noise of the l-th beacon in the k-th frame; by symbol combining the above equation, we obtain the rearranged received signal: By rearranging the received beacon samples within a coherent integration period, a typical element y is obtained. m,k,l A three-dimensional tensor Y of size M×K×L, where each element of the three-dimensional tensor Y is α. i,m f i,k , The product of three terms; where α i,m Characterizes the channel response of the m-th array element to the SOP signal i. Characterize the effect of carrier Doppler on the beacon in the k-th frame within the coherent integration period of frequency domain signal i. A beacon sample, g, represents the superposition of carrier Doppler effects and channel gain within a sequence. i The channel gain characterizes the SOP signal i.

2. The method as described in claim 1, characterized in that, In step 2, the rank of tensor Y is determined by estimating the rank of tensor Y through translation-invariant subspace matching.

3. The method as described in claim 2, characterized in that, The step of estimating the rank of tensor Y through translation-invariant subspace matching includes: Perform mode-1 matrix transformation on Y to obtain in, It is the Hadamard product, ⊙ is the Khatri-Rao product, A, F, Let G be the factor matrix of angle of arrival, Doppler, and beacon sequence, where G = diag{g1,…,g I } is represented as the complex channel gain matrix, where E is the Vandermonde matrix, representing the carrier Doppler effect in the beacon sequence, where, Considering the differences in the angle of arrival, Doppler effect, and beacon sequence of different SOP signals, it can be known that get therefore The column vector space, i.e. The column vector space is I-dimensional; The eigenvalues ​​of the covariance matrix are written as in The column vectors correspond to the right eigenvectors. It is an eigenvalue matrix; since rank(A) = I, then there exists a matrix... Make in Let A be a matrix consisting of the largest I eigenvectors; (1) and A (2) This represents the matrix obtained by deleting the first and last rows of matrix A. A (1) =A (2) D in If the matrix is ​​diagonal, then we have Right now and They have the same translation-invariant signal subspace; the projection onto this subspace is represented by a projection matrix, which is... and and The number I of SOP signal sources is obtained by minimizing the following objective. in, tr() represents the 2-norm of a matrix, and tr() represents the trace of the matrix.

4. The method as described in claim 3, characterized in that, In step 3, the angle of arrival for each SOP signal is determined as follows: Step a1: Perform mode-(1,2) matrix transformation on the tensor signal Y to obtain For Y (1,2) Perform singular value decomposition to obtain Y (1,2) =UΣV H ;because Therefore, a non-singular matrix exists. satisfy U I Q=A⊙F Let U I,1 and U I,2 To delete U separately I The matrix obtained by taking the top K rows and the bottom K rows is then: U I,1 Q=A (1) ⊙F,U I,2 Q=A (2) ⊙F Where A (1) and A (2) The matrix obtained by deleting the first and last rows of A can be obtained as follows: calculate Then, eigenvalue decomposition is performed to estimate Q and D, resulting in... and Step a2: According to Estimate the angle of arrival for each SOP signal: Step a3: According to Reconstruct the arrival angle factor matrix 5. The method as described in claim 4, characterized in that, In step 3, the Doppler determination method for each SOP signal is to use the estimated SOP signal angle of arrival. and the corresponding factor matrix For the factor matrix F and the SOP signal Doppler β i Make an estimate: Step b1: Construct the generating factors z of the factor matrix F i : byU I Q = A⊙F, construct It is the Kronecker product; Then f i It has the following characteristics: Then utilize U I , Estimate f i : Since F is a Vandermonde matrix, therefore The generating factor z in column i i Estimate using the following methods: in, Step b2: Utilize Estimate the Doppler β of each SOP signal i : Step b3: According to Reconstruct the Doppler factor matrix 6. The method as described in claim 5, characterized in that, In step 3, the beacon sequence for each SOP signal is determined as follows: Using the obtained angle of arrival factor matrix Doppler factor matrix And the representation of the beacon sequence factor matrix, constructing the beacon sequence factor matrix after removing the Doppler effect. Then, the estimation result of the SOP beacon sequence is obtained by power normalization.

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