Bayesian wireless channel estimation method and system suitable for same-frequency interference

Abstract

The invention provides a Bayesian wireless channel estimation method and a Bayesian wireless channel estimation system suitable for same-frequency interference, and the method uses variational inference based on LSI to capture frequency points with large interference power in a considered frequency band, and can more effectively extract frequency points with real interference from an actual frequency selective fading channel. The method comprises the following steps: carrying out GI and LSI-based alternate variational inference for optimizing an algorithm model and reducing overfitting of the algorithm, introducing a hyper-parameter adaptive updating method of an interference level so as to introduce more prior information entropy during iteration, and completing position estimation through channel parameter estimation in a pilot frequency band of OFDM in combination with ToA / TDoA / AoA and other algorithms, so that the estimation accuracy is improved. Kalman / Particle Filter can also be combined to complete navigation prediction, and the communication quality of signal subcarriers can also be improved by using a related equalization algorithm.

Description

Technical Field

[0001] The present invention belongs to the technical fields of digital signal processing and wireless communication, and relates to a Bayesian wireless channel estimation method and system applicable to co-channel interference. Background Art

[0002] Currently, channel estimation algorithms based on tensor decomposition generally include two steps: the first step is rank estimation, corresponding to the number of multipath components; the second step is to use the obtained rank to estimate the channel parameters of the multipath components. As is well known, determining the rank of a tensor is an NP-hard problem. However, the current main rank estimation methods are information-theory-based methods, and the most commonly used methods include the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). However, these methods have the disadvantages of over-simplification and overfitting. Based on the obtained rank, the current mainstream Tensor decomposition models are Tucker and CANDECOMP / PARAFAC (abbreviated as CP). However, when there is co-channel interference in the channel, not only the statistical characteristics (such as correlation, variance, etc.) of the target signal are masked by the characteristics of the interfering signal, but also the co-channel interference (CCI) will reduce the effective signal-to-noise ratio (SNR) of the system, thereby causing a significant decline in the rank estimation performance, and thus directly affecting the serious degradation of the rank estimation performance of traditional tensor methods.

[0003] For the above reasons, the robust variational Bayesian method came into being. Since Qibin Zhao in the field of machine learning derived a robust variational Bayesian method for image denoising (article [Q. Zhao, G. Zhou, L. Zhang, A. Cichocki and S.-I. Amari, "Bayesian Robust Tensor Factorization for Incomplete Multiway Data," in IEEE Transactions on Neural Networks and Learning Systems, vol. 27, no. 4, pp. 736-748, April 2016, doi: 10.1109 / TNNLS.2015.2423694.]). This method formulates the CP decomposition of the signal using the Bayesian probability hierarchical model respectively by assuming that the interference, noise and signal are additive models, and makes assumptions about the interference terms lattice by lattice, thus completing the automatic rank determination, as well as accurate signal recovery and interference estimation. However, in the actual communication channel, the above method cannot be directly compatible, lacking the mapping relationship between mathematics and physics. Therefore, the author proposed an invention patent based on the idea of alternating prior assumptions (patent [Wang Wei, Sun Yuzhe, Wang Yufan. A Robust Variational Tensor Channel Estimation and Interference Location Method and System [P]. Shaanxi Province: CN202410287207.5, 2024-07-02.]) for fault device location detection according to the tensor data structure at the receiving end. It should be noted that the above device interference modeling classifies hardware faults, mainly divided into front-end interference (FEI) and co-frequency interference (CFI). However, the co-frequency interference mentioned here is caused by the shared electromagnetic path or internal circuit leakage in the device, rather than the co-channel interference (CCI) caused by spectrum overlap in the channel. The physical modeling of these two kinds of interference is completely different. At the same time, due to the complex wavefront structure of CCI, the structured wavefront and unstructured wavefront interference pose stronger requirements for the algorithm robustness of the algorithm to be developed. And under the background of information confrontation today, the co-frequency sparse frequency domain interference estimation is also of great significance for information reconstruction and decryption. Summary of the Invention

[0004] To solve the problems existing in the prior art, the present invention provides a Bayesian wireless channel estimation method (URCP) applicable to co-channel interference, aiming to perform fast-converging synchronous estimation of channel parameters and interference information by using the spatial structure of frequency-domain data. Based on the physical wavefront structure characteristics of CCI, the present invention first classifies CCI into structured wavefront and unstructured wavefront. Then, a reasonable and unified additive variational model is established based on global interference (GlobleInterference, GI) plus sub-channel link-level interference (Link-Specific Interference, LSI).

[0005] To achieve the above object, in a first aspect, the present invention provides a Bayesian wireless channel estimation method applicable to co-channel interference, including the following steps:

[0006] a. According to the co-channel interference wavefront characteristics, perform tensor modeling on the received data to obtain the tensor composition for describing the frequency-domain representation of the received data;

[0007] b. Initialize the co-channel interference frequency position; specifically, set the variational iteration of the number of iterations by selecting the interference prior type as link-level interference, so as to initially determine the frequency position in the frequency domain, and update the initialization parameters according to the results obtained in steps c to e;

[0008] c. Perform alternating posterior inference on global interference and link-level interference; the variational inference based on LSI always searches for link-level interference in the entire tensor space, and for global interference inference, GI inference is only performed in the co-channel interference frequency interval inferred by LSI;

[0009] d. Sequentially and alternately iterate to calculate the inferred variables in the variational inference, that is, infer the posterior distributions of the parameter sets such as LSI, GI, factor matrix, and noise precision; in the alternating iteration, each time GI inference is performed, according to the newly obtained frequency-domain position of the third-dimensional co-channel interference, compare the index changes in the previous and subsequent iterations, update the frequency index, initialize the interference terms corresponding to the new frequency index using non-informative priors, and remove the interference terms corresponding to the non-existent indices;

[0010] e. Perform maximization calculation according to the evidence lower bound calculated according to the interference type, and adaptively update the hyperparameters of LSI and GI;

[0011] f. Perform redundant multipath cancellation based on principal component extraction. Specifically: set a threshold for measuring the path weight, and determine the redundant multipaths to be eliminated in combination with the relationship between the multiple of the maximum and minimum values of the measured path weight and the threshold;

[0012] ​g. When the iterative step iterates to the set termination condition, the factor matrix obtained by using the estimated hyperparameters of LSI and GI and the interference parameters, and the harmonic parameters [θ, φ, τ] values are obtained using the maximum likelihood method, and then the complex amplitude α of each path is obtained according to the least squares operation.

[0013] Further, in step a, according to the characteristics of the co-frequency interference wavefront, the received data is modeled with a tensor structure to obtain the received tensor in the frequency domain:

[0014] The signals transmitted by the transmitting end are reflected by multiple targets in the environment and reach the receiving end, forming a two-path signal. The receiving end uses a planar array antenna of size N 1 ×N 2 to capture the elevation angle θ, azimuth angle φ, delay τ and complex amplitude α of the multipath. A symbol sequence of K subcarrier transmission periods with a transmission bandwidth of B and a modulation method of OFDM is considered. Considering the SIMO scenario, the channel matrices of the sampled K frequency points are stacked in the third dimension to obtain the channel tensor in the form of CP decomposition.

[0015] In the structured interference tensor, from the perspective of the tensor, the spherical wave interference is modeled with an additive model (naturally, it can be known that the plane wave interference is just a special case of the spherical wave interference). The structured spherical wave interference tensor is modeled as the sum of the global interference tensor and the link-level interference tensor;

[0016] Model the random wavefront interference tensor with unstructured characteristics. Considering the differences in the normalized antenna gains of the receiving array, the receiving array gains of the random wavefront interference exhibit random characteristics. To fully describe the characteristics of the additive model, the global interference is defined as the average power value of the array at a certain frequency point. The LSI power is divided into two types: positive LSI and negative LSI, so as to obtain the composition of the receiving tensor based on the random wavefront;

[0017] The frequency domain composition of the receiving tensor is expressed as channel tensor, interference tensor and noise tensor, completing the unified modeling of the structured and unstructured co-frequency interference in the channel, including global interference and link-level interference. The co-frequency interference tensor model is

[0018] Further, the global interference is composed of a matrix of size N 1 ×N 2 indicating that the global interference is the interference acting on all sub-channels, with the same power and phase; the link-level interference is composed of a single element in the interference tensor indicating that the LSI is the interference acting on a specific sub-channel.

[0019] Further, in step b, a certain type of interference is indexed by superscript Tp for the category, Tp ∈ {GI, LSI}, and a single interference in this type of interference is denoted as Its specific position in the time-frequency domain is determined by subscript Ind(Tp), and there are mappings Ind(GI) = {i 3} and Ind(LSI) = {i 1 , i 2 , i 3}. The complete set of interference terms for a certain category is A single interference term is denoted as Among them, the relationship between interferences of different types Tp and the interference terms is expressed as and The inference variable is where λ is the factor matrix hyperparameter, is the interference term, γ Ξ is the interference term hyperparameter, and v is the environmental noise precision;

[0020] Next, the frequencies with co-channel interference are initialized. Specifically, the variational iteration with a set number of iterations is initialized by selecting the interference prior type as T p = LSI; in the variational iteration of LSI, considering all interference tensor units Ω, the high-power frequency positions of each link are captured, which are the positions most likely to have co-channel interference. The selected threshold T LSI and the estimated LSI indices are as follows:

[0021]

[0022] Among them, represents the estimated LSI interference value during initialization, P LSI represents the maximum power of the estimated LSI, T LSI represents the interference power threshold, represents the set of LSI third-dimensional frequency domain indices that meet the interference threshold condition.

[0023] Further, in step c, the posterior distribution of the inference variable in the inference, where A (n) is the factor matrix, λ is the factor matrix hyperparameter, is the interference term, γ Ξ is the interference term hyperparameter, and v is the environmental noise precision, is specifically as follows:

[0024] The posterior distribution of the factor matrix A (n) Based on different prior assumptions of interference categories, the posterior mean of the n-mode factor matrix A (n) uses the observed values after removing other interferences where the subscript Ω indicates the operation of the interference term, and the posterior distribution of the factor matrix has the following variance and mean:

[0025]

[0026] where, denotes the expectation operation, the multiple Khatri-Rao product the superscript "*" represents the conjugate, the superscript "H" represents the conjugate transpose, and "\" represents the elimination operation;

[0027] For the posterior distribution of the hyperparameter λ, according to the generalized stationary uncorrelated scattering assumption, λ among different paths l , l = 1, 2, …, L are uncorrelated, and the posterior distribution of the hyperparameter in vector form is expressed as:

[0028]

[0029] where, and the posterior expectation of λ is c 0 and d 0 come from the prior assumption

[0030] The interference has the following posterior distribution. In the actual channel scenario, different interferences at the same frequency are uncorrelated, and different interferences at different frequencies are uncorrelated. For the posterior distribution of different types of interference we have:

[0031]

[0032] In the formula, "<·>" represents the inner product operator. When Tp is equal to GI, the remaining term operation \Ind(GI) = {i 1 , i 2}, Cst[·] is the operator of the maximum index product, and Cst[i 1 , i 2 = I 1 I 2 = N 1 N 2 . In the posterior estimation of each type of interference, the global information of the channel tensor is used

[0033] For the posterior distribution of the hyperparameter γ, in the alternative prior assumption, the hyperparameter of the posterior distribution of the interference term precision is expressed as follows:

[0034]

[0035] In the formula and come from a prior assumption and

[0036] The posterior distribution of the noise precision V. In the alternating prior assumption, the noise precision follows a Gamma distribution q(ν) = Ga(ν|e M , f M ) is as follows:

[0037] e M = M + e 0

[0038]

[0039] where, e 0 and f 0 come from the prior assumption p(v) = Ga(v|e 0 , f 0 ), and the expectation operation is as follows:

[0040]

[0041] where the i (n) -th row of F n is expressed as

[0042] Furthermore, in step d, the evidence lower bound calculated based on the interference type is used to adaptively update the initialized interference hyperparameters There is the following optimization process:

[0043]

[0044] where "argmax(·)" represents solving for the parameter that maximizes the given function, and the initialized parameter set is assumed to be equal and infinitesimal, satisfying the condition of the non-informative prior assumption, and the updated parameter set is and the index set of the global interference is The adaptive update of the hyperparameters is default in all posterior inferences and the operations of the evidence lower bound after each iteration in step c as the updated

[0045] Furthermore, in the iteration, a fixed number of variational iterations is used as the termination condition, and the complex amplitude α of each path is obtained by using the least squares method according to the values of the harmonic parameters [θ, φ, τ].

[0046] Second aspect, the present invention provides a Bayesian wireless channel estimation system applicable to co-channel interference, including a modeling module, an initialization and alternating iteration module, and an estimation module;

[0047] The modeling module is used to perform tensor modeling on the received data according to the characteristics of the co-channel interference wavefront, and obtain the tensor composition for describing the frequency-domain representation of the received data;

[0048] The initialization and alternating iteration module is used for cyclic iteration: by selecting the interference prior type as link-level interference to perform variational iteration for a set number of iterations, thereby initially determining the frequency-domain position, and updating the initialization parameters according to the results obtained in the following steps;

[0049] Perform alternating posterior inference on global interference and link-level interference; the variational inference based on LSI always searches for link-level interference in the entire tensor space. For global interference inference, GI inference is only performed in the co-channel interference frequency interval inferred by LSI;

[0050] Sequentially perform alternating iteration to calculate the inferred variables in the variational inference, that is, infer the posterior distributions of parameter sets such as LSI, GI, factor matrix, and noise precision; in the alternating iteration, each time GI inference is performed, according to the newly obtained frequency-domain position of the third-dimensional co-channel interference, compare the index changes in the previous and current iterations, update the frequency index, initialize the interference terms corresponding to the new frequency index using non-informative priors, and remove the interference terms corresponding to the non-existent indices; Maximize the evidence lower bound calculated according to the interference type, and adaptively update the hyperparameters of LSI and GI;;

[0051] Perform redundant multipath cancellation based on principal component extraction. Specifically: set a threshold for measuring the path weight, and determine the redundant multipaths to be eliminated in combination with the relationship between the multiple of the maximum and minimum values of the measured path weight and the threshold;

[0052] The estimation module is used to, when the iteration step iterates to the set termination condition, use the factor matrix obtained by using the estimated hyperparameters of LSI and GI and the interference parameters, obtain the values of the harmonic parameters [θ, φ, τ] using the maximum likelihood method, and then obtain the complex amplitude α of each path according to the least squares operation.

[0053]

[0054] Third aspect, the present invention can also provide a computer device, including a processor and a memory. The memory is used to store computer-executable programs. The processor reads the computer-executable programs from the memory and executes them. When the processor executes the computer-executable programs, it can implement the Bayesian wireless channel estimation method applicable to co-channel interference described in the present invention.

[0055] ​Meanwhile, a computer-readable storage medium is provided, in which a computer program is stored. When the computer program is executed by a processor, the Bayesian wireless channel estimation method applicable to co-channel interference described in the present invention can be realized.

[0056] Compared with the prior art, the present invention has at least the following beneficial effects: First, the present invention constructs a high-dimensional channel Tensor based on the spatial structure of the transceiver arrays, where the first and second dimensions correspond to the angular domain space and the third dimension corresponds to the delay domain space; Second, the present invention rigorously divides the types of interference into structured interference and unstructured interference, and then performs additive modeling of the interference tensor according to the frequency domain spatial structure of the real CCI (divided into global interference GI and link-level interference LSI); Compared with the traditional Robust variational algorithm (RCP) of Tensor, there are the following major differences: 1. The present invention also performs a very crucial LSI inference before the alternating iteration to find the frequency points where interference may occur; 2. The GI inference and LSI inference of the present invention have different inference spaces in the alternating variational; 3. The present invention provides more information entropy in the same dimension, so the interference hyperparameters are adaptively updated in different types of inferences; In summary, the present invention will further improve the channel rank estimation, parameter estimation, and interference estimation performance in the complex co-channel interference situation, laying a foundation for subsequent online spectrum allocation, channel feature mapping under interference, and communication sensing under interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a SIMO channel scenario under co-channel interference.

[0058] Figure 2 It is the interference tensor modeling of the structured spherical wavefront.

[0059] Figure 3 It is the receiver tensor decomposition of the structured interference.

[0060] Figure 4 It is the interference tensor composition of the unstructured random wavefront.

[0061] Figure 5 It is the receiver tensor composition of the unstructured interference.

[0062] Figure 6 It is a flowchart of an implementable method based on the concept of the present invention.

[0063] Figure 7 It is the necessity of the adaptive update of the interference hyperparameters.

[0064] Figure 8 It is to verify the effectiveness of the proposed URCP algorithm under spherical wavefront interference and compare the performance with the traditional RCP.

[0065] Figure 9 The comparison results of the proposed URCP algorithm and the traditional RCP algorithm under plane-wave interference and spherical-wave interference with the change of interference bandwidth (IB).

[0066] Figure 10 With the change of the interference power factor The comparison results of the proposed URCP algorithm and the traditional RCP algorithm under plane-wave interference and spherical-wave interference. Detailed implementation manners

[0067] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0068] The present invention uses the spatial structure of frequency-domain data to perform fast-converging synchronous estimation of channel parameters and interference information. Based on the physical wavefront structure characteristics of CCI, the present invention first classifies CCI into structured wavefronts and unstructured wavefronts. Then, a reasonable and unified additive variational model is established, based on global interference (GI) plus sub-channel link-level interference (LSI).

[0069] Based on the above accurate physical modeling, first, variational inference based on LSI is used to capture the frequency points with large interference power in the considered frequency band, and it can more effectively extract the frequency points where real interference exists from the actual frequency-selective fading channel. Then, alternating variational inference based on GI and LSI is performed to optimize the algorithm model and reduce the overfitting effect of the algorithm. Finally, in order to complete convergence more quickly and make up for the overfitting phenomenon in small data scenarios, the present invention introduces a hyperparameter adaptive update method at the interference level to introduce more prior information entropy during iteration. The present invention can complete position estimation by combining algorithms such as ToA / TDoA / AoA with channel parameter estimation in the pilot frequency band of OFDM, can also complete navigation prediction by combining Kalman / Particle Filter, and can also improve the communication quality of signal subcarriers using relevant equalization algorithms. In addition, the position estimation of interference is beneficial to subsequent dynamic spectrum allocation, and the size estimation of interference is beneficial to subsequent signal capture and cracking.

[0070] Example 1, refer to Figure 2, the present invention provides a Bayesian wireless channel estimation method applicable to co-channel interference, comprising the following steps:

[0071] Step 1, according to the co-channel interference wavefront characteristics, perform tensor modeling on the received data to obtain the tensor composition for describing the frequency-domain representation of the received data;

[0072] As Figure 1 shown, in the scenario where co-channel interference appears as shown by the red circle, since the angles and distances presented by the arrival at the receiving end array are different as shown by the green circle and the white wedge, two types of structured interference will be formed, namely plane wave interference and spherical wave interference. At the same time, due to the beam patterns of the antennas at the receiving end and the interfering end and the influence of the complex environment in the interference channel, the interfering signals arriving at the receiving end have random amplitudes and phases, thus constituting unstructured interference with a random wavefront. Based on Figure 1 it can still be seen that the signals transmitted by the transmitter will be reflected by multiple targets (Target-1 / 2) in the environment and arrive at the receiver, which constitutes a two-path signal. The receiver uses a planar array antenna of size N 1 ×N 2 to capture the elevation angle θ, azimuth angle φ, delay τ, and complex amplitude α of the multipath. During simulation, it is assumed that the transmission bandwidth is B and the modulation method is an OFDM (Orthogonal Frequency Division Multiplexing) symbol sequence for K subcarrier transmission periods, and then at the receiving end, the orthogonality of the transmission symbols is used to eliminate the influence of the transmission symbols on the channel characteristics. Considering Figure 1 the actual SIMO (Single-Input Multiple-Output) scenario in the channel matrix of the sampled K frequency points is stacked in the third dimension, so that the channel tensor in the form of CP decomposition (Canonical Polyadic Decomposition) can be obtained

[0073]

[0074] where L represents the number of multipaths; represents the outer product; is the Kruskal operator, which is a simplified expression. All column vectors of the factor matrix {A (n)} n＝1,2,3 are composed of antenna array responses, as Figure 1 there is in ω k= π - 2kπ / (K - 1), k = 0, 1, 2,.., K - 1, whose phase information is μ(θl l ) = (2π / λ c )dcosθ l and κ(θ l , φ l ) = (2π / λ c )dsinθ l sinφ l . At the same time, let i 1 , i 2 , i 3 represent the indices of dimensions N 1 , N 2 , K (also called I 1 , I 2 , I 3 ), λ c is the signal bandwidth, and d is the antenna spacing.

[0075] In the structured interference tensor, plane wave interference signals are often assumed to come from infinity. Therefore, when arriving at the receiving array, the only difference in the reception of plane wave interference signals by the array antenna elements is the regular phase change. However, a plane wave is just a special form of a spherical wave. As shown in Figure (1) of Figure 2 , the regular power variation of the array antenna elements can be seen from the color gradient. Figure 2 The physical composition of Figure (1) in Figure 1 is formed by the outer product of Figure (2) and Figure (3). Among them, Figure (2) shows that the interference only appears in the middle section of the frequency band of the effective bandwidth, and Figure (3) shows the normalized power gain of the 6 * 6 receiving array for the interference signal. Based on the above physical explanations, here we model the spherical wave interference from the perspective of tensors, such as the additive model in Figures (4) and (5). Figure (4) is the Global Interference, representing a complex value with a specific power and phase shared by all sub-channels, while Figure (5) is the Link-specific Inference of a specific sub-channel, representing a complex value with a specific change on the GI for a certain sub-channel. To sum up, considering both Figure 3 the two-path channel for effective signal transmission, the composition of the received tensor is drawn as shown in ( Figure 3 denoted as Original Signal in Figure 2As shown, it is the sum of the global interference tensor and the link-level interference tensor. Since the signal-to-noise ratio ρ = 20 dB, the noise power has the darkest color.

[0076] Similarly, the present invention also models the random wavefront interference tensor with unstructured characteristics, such as Figure 4 As shown, it can be seen that Figure 4 the difference between the (3) figure in Figure 2 and the (3) figure in Figure 4 and Figure 3 lies in the different normalized antenna gains of the receiving array. The receiving array gain of the random wavefront interference shows random characteristics and is unpredictable. At the same time, regarding the additive modeling of the interference tensor, Figure 4 both Figure 2 and Figure 5 show the superposition of power, which essentially reflects the superposition of complex numbers. To express the additive model more clearly, the global interference (GI) is defined as the average power value of the array at a certain frequency point, and then the LSI power is divided into two types: positive LSI and negative LSI. Essentially, it is to describe that GI is not limited to the lowest power value shown in the (4) figure in ). Therefore, GI is composed of a matrix of size N 1 ×N 2 2 2 , which means that this GI is the interference acting on all sub-channels and has the same power and phase. Similarly, LSI is composed of a single element in the channel tensor , which means that this LSI is the interference acting on a specific sub-channel. So far, the modeling of the co-frequency interference tensor in the channel has been elaborated

[0077] Step 2, initialization of the co-frequency interference frequency position; specifically, by selecting the interference prior type as link-level interference to set the variational iteration of the number of iterations, so as to initially determine the frequency domain position, refer to Figure 2

[0078] The present invention first declares the use of symbols. For a certain type of interference Denoted by the superscript Tp as the class index, Tp ∈ Ξ = {GI, LSI}. A single interference in this class is denoted as Its specific position in the time-frequency domain is determined by the subscript Ind(Tp), and there are mappings Ind(GI) = {i 3} and Ind(LSI) = {i 1 , i 2 , i 3}. The complete set of interference terms of a certain class is denoted as A single interference term is denoted as Among them, the relationship between the interferences of different types Tp and the interference terms is expressed as and The inference variable is where λ is the factor matrix hyperparameter, is the interference term, γ Ξ is the interference term hyperparameter, and v is the environmental noise precision.

[0079] The URCP method proposed by the present invention first needs to initialize the frequency positions with co-channel interference, and it is completed through variational iteration with a set number of iterations by selecting the interference prior type as T p = LSI. Due to reasons such as frequency-selective fading and random interference in the channel, the power received on different antenna elements of the antenna array usually changes drastically at the same frequency point. At this time, in the variational iteration of LSI (see Equations 2 to 6), all interference tensor units Ω are considered, aiming to capture the high-power frequency positions of each link, and these high-power frequency positions are also the positions where co-channel interference is most likely to occur. The selected threshold T LSI and the estimated LSI index are as follows:

[0080]

[0081] Among them, represents the estimated LSI interference value during initialization, P LSI represents the maximum power of the estimated LSI, T LSI represents the interference power threshold, represents the set of third-dimensional frequency domain indices of LSI that meet the interference threshold condition. In the present invention, the threshold is set to the maximum interference power value minus 20 dB, denoted as T LSI = P LSI / 100.

[0082] Step 3, alternately perform posterior inference on GI and LSI;

[0083] It should be noted that the present invention performs alternating posterior inference for different interference parameter spaces. For LSI inference, Ind(LSI) = {i 1 , i2 , i 3} ∈ Ω, which indicates that the variational inference based on LSI always conducts link-level interference search in the entire tensor space. For GI inference, it is first necessary to obtain the index terms of the index set of the third dimension which will enable GI inference to be performed only in the co-channel interference frequency range inferred by LSI. Next, calculate the posterior distribution of the inferred variables in the variational inference in sequence, where A (n) is the factor matrix, n = 1, 2, 3, λ is the factor matrix hyperparameter, is the interference term, γ Ξ is the interference term hyperparameter, and v is the environmental noise precision.

[0084] Posterior distribution of the factor matrix A (n) : Based on different prior assumptions of interference categories, the posterior mean of the n-mode factor matrix A (n) uses the observed values after removing other interferences where the subscript Ω indicates the operation of the interference term. Therefore, the posterior distribution (n) of the factor matrix A has the following variance and mean:

[0085]

[0086] where, represents the expectation operation, multiple Khatri-Rao products The superscript "*" represents conjugation, the superscript "H" represents conjugate transpose, and "\" represents the elimination operation.

[0087] Posterior distribution of the hyperparameter λ: According to the Wide-Sense Stationary Uncorrelated Scattering (WSSUS) assumption, λ l , l = 1, 2, …, L among different paths is also uncorrelated. Therefore, the vector form of the hyperparameter in the posterior distribution is expressed as:

[0088]

[0089] where, and The posterior expectation of λ is c 0 and d 0 come from the prior assumption

[0090] Interference Posterior distribution: In the actual channel scenario, different interferences at the same frequency are uncorrelated, and different interferences at different frequencies are also uncorrelated. For the posterior of different types of interference is:

[0091]

[0092] where the "<·>" in the formula is the inner product operator. When Tp is equal to GI, the remaining term operation \Ind(GI) = {i 1 , i 2}. Cst[·] is the operator of the maximum index product. For example, Cst[i 1 , i 2 = I 1 I 2 = N 1 N 2 . Obviously, in the posterior estimation of each interference type, the global information of the channel tensor must be utilized This enables consistent estimation among multiple prior assumptions.

[0093] Posterior distribution of the hyperparameter γ: In the alternating prior assumptions, the posterior distribution of the hyperparameter is expressed as follows:

[0094]

[0095] where and come from the prior assumptions and

[0096] Posterior distribution of the noise precision ν: In the alternating prior assumptions, the noise precision follows a Gamma distribution q(ν) = Ga(ν|e M , f M ) and is:

[0097]

[0098] where e 0 and f 0 come from the prior assumption p(v) = Ga(v|e 0 , f 0 ), and the expectation operation is shown as follows:

[0099]

[0100] where the i (n) -th row of F n is expressed as

[0101] Note that for LSI inference, the mapping relationship of the maximum index product operator under conditions is such that Cst[Ind(LSI)] = Π n＝1,2,3 I n = M and Cst[\Ind(LSI)] = Cst[{·}] = 1. The mapping relationship of the maximum index product operator under conditions is as follows and Cst[\Ind(GI)] = Cst[{i 1 ,i 2 [[ID=10}}] = I 1 I 2 , where represents the number of elements in the determined set. At the same time, in the alternating iteration, the interference position is re-obtained each time GI inference is performed At this time, the index changes in the previous and subsequent iterations are compared to timely capture the new frequency index. For the new frequency index, the corresponding interference term is initialized using the non-informative prior. For the index that no longer exists, the relevant interference term will be removed. Therefore, the present invention increases the information entropy of the subsequent iteration by appropriately selecting the interference position and the LSI inference performed on the entire set Ω also ensures the continuity of the global search.

[0102] Step 4, Adaptive update of interference hyperparameters;

[0103] The present invention adds a new operation in each alternating iteration, that is, updating the hyperparameter information of LSI and GI, to reduce the uncertainty of the next iteration and improve the convergence and stability of the model. Based on the interference type The ELBO calculated is used to adaptively update the initialized interference hyperparameters through the following optimization process:

[0104]

[0105] where "argmax(·)" represents solving for the parameter that maximizes the given function, and the initialized parameter set is (assuming equal and infinitesimal, satisfying the condition of the non-informative prior assumption), and the updated parameter set is and the index set of the above GI is still Note that the above adaptive update of hyperparameters is after each iteration, so in all posterior inferences and operations of the Evidence Lower Bound (ELBO) proposed by the present invention, it is default is the updated

[0106] Step 5, Redundant multipath elimination based on principal component extraction

[0107] Set a threshold for measuring the path weight, and determine the redundant multipaths to be eliminated by combining the relationship between the multiple of the maximum and minimum values of the measured path weight and the threshold; specific examples are as follows: The reciprocal used to measure the path weight The larger the value, the smaller the contribution of the corresponding path to the main path. Therefore, the present invention observes The multiple relationship between the maximum and minimum values, and determines the estimated value of the hyperparameter through the following conditions Eliminate the corresponding redundant multipaths, and call MTH the "multiple threshold".

[0108] Step six, reach the variational iteration termination condition;

[0109] In actual iteration, use the fixed number of variational iterations MaxIters as the termination condition. Through the finally estimated factor matrix, obtain the values of the harmonic parameters [θ, φ, τ] using the maximum likelihood method, and then obtain the complex amplitude α of each path using the least squares method.

[0110] The present invention will be described in detail below with reference to the accompanying drawings and specific examples.

[0111] Based on Figure 1 the SIMO experimental environment, the present invention classifies the wavefront characteristics of the real co-channel interference reaching the receiving array through the interference signal, as shown in Figure 2 and Figure 4 . And, the URCP algorithm of the present invention uniformly models different interference types, highlighting the robustness of the proposed URCP algorithm to interference, as shown in Figure 3 and Figure 5 . Figure 6 This is the implementation process of an embodiment of the present invention. The difference from the traditional alternating prior hypothesis is that the size of the parameter space inferred by the URCP algorithm is different. So far, referring to Figure 3 , the process of the embodiment includes:

[0112] (1) Simulation hypothesis: The true number of multipaths L = 2, the SNR at the receiving end = 20 dB, the threshold MTH = 20, and the relevant parameters of the channel are set as: default settings of relevant parameters: α = [0.8i, 0.6], θ = [80°, 85°], φ = [15°, 10°], Bτ = [4, 5]. The structure of the receiving planar array is N 1 = N 2 = 6, and the maximum number of iterations is M I= 300. Among them, assumptions are made for the interference bandwidth (IB) and the interference factor (IF). IB determines the number of consecutive points in the frequency band occupied by the interference; IF is related to the interference variance That is, the magnitude of the interference variance is determined. In the feasibility verification of this embodiment, it is default that IF = 1 and IB = 20.

[0113] (2) Composition of the channel tensor: Using the orthogonality of the Pilot symbols of the OFDM transmitted signal for the received data, the influence of the transmitted signal is eliminated, and then the channel matrices at each sampling frequency point are stacked in the third-dimensional space to form the channel tensor

[0114] (3) Parameter settings for variational initialization: The initial iteration path L = 30, and the hyperparameters c 0 , d 0 , e 0 , f 0 , are assumed to be a sufficiently small 1×10 -6 so as to achieve a uniform distribution (constituting an uninformative prior condition). Iter = 1, Way = 1 are used to indicate the interference prior assumption currently used by the variational method. In addition, random initialization is used for both the initial interference and the signal tensor, but with the true variance magnitude.

[0115] (4) Initialization of the co-channel interference frequency position: Select the interference prior type as T p = LSI, perform a certain number of iterations using formulas (3) to (7), and then use formula (2) to find the initial frequency position of the interference so as to wait for GI inference.

[0116] (5) The nth iteration of the alternating variational method:

[0117] (a) Tp = Ξ[Way], indicating the type of interference currently being inferred;

[0118] (b) Iter + 1, indicating the current iteration number;

[0119] (c) Way method + 1, used to alternately point to different posteriors in GI and LSI inferences;

[0120] (d) Calculate the posterior distribution of the factor matrix

[0121] (e) Calculate the posterior distribution of the hyperparameter λ

[0122] (f) Select the appropriate tensor interval for interference inference according to the interference type. For inference based on LSI, the entire interval Ω is used; for inference based on GI, a partial interval is used.

[0123] (g) Perform the corresponding interference type in the appropriate inference interval. The posterior distribution

[0124] (h) Similarly, calculate the posterior distribution of the interference hyperparameter γ in the appropriate inference interval. Tp The posterior distribution

[0125] (i) Calculate the posterior distribution of the environmental noise precision q(ν) = Ga(v|e M , f M );

[0126] (j) Way = (Way == 3)? 1 : Way, to ensure alternation between the two interference types of LSI and GI.

[0127] (6) Redundant multipath rejection operation:

[0128] Check and satisfy The condition Then delete the corresponding 1 column of all factor matrices A (n) To complete the principal component extraction operation.

[0129] (7) Iteration termination condition detection:

[0130] According to the finite duration condition, use a fixed number of variational iterations as the termination condition. When the number of iterations Iter > MaxIters, the iteration ends; otherwise, continue to execute the operation in (5).

[0131] (8) Perform channel parameter estimation: Through the factor matrix obtained by the final estimation, use the maximum likelihood method and the least squares method to obtain all the channel parameter [α, θ, φ, τ] values.

[0132] To verify the effectiveness of the method proposed by the present invention, the algorithm is verified according to the simulation conditions of the embodiment, and the analysis is carried out under different interference factors IF and different interference bandwidths IB. The application effect of the present invention is described in detail below in combination with the simulation results.

[0133] Figure 7To verify the necessity of adaptive update of interference hyperparameters. The amount of data is controlled by changing the number of subcarriers K used, and simulation verification is carried out when K is 32, 64, and 128 respectively. First, in the variational Bayesian method, the larger the ELBO value, the better the model usually fits the observed data. As shown in the figure, under APH (alternating prior hypothesis), the ELBO (ELBO for LSI and ELBO for GI) of URCP with hyperparameter update is always numerically better than that of URCP without hyperparameter update (URCP without Updating) algorithm, which indicates that the proposed algorithm has better observed fitting characteristics. Then, when the amount of data is small (K = 32), the increase in ELBO can more significantly improve the stability of parameter estimation, because in this case, a larger ELBO usually means better suppression of the influence of noise. At the same time, as the amount of data increases, the above difference gradually decreases, and when K = 128, the update with or without hyperparameters has no effect on the estimation performance. In summary, the proposed URCP method effectively responds to the situation of less data volume through adaptive update of hyperparameters after each iteration to improve the estimation accuracy.

[0134] Figure 8 Figure (a) in [reference] shows that as the number of iterations increases, redundant paths are removed until the true number of paths is reached. It should be noted that there is no black dotted line in the first 20 iterations because in the first 20 iterations, the URCP algorithm only performs LSI inference to initialize and determine the frequencies where co-channel interference exists in the channel. However, after 20 iterations, alternating iterations of GI and LSI are carried out, and the non-decreasing property of ELBO in both inferences also proves the feasibility of the algorithm. In Figure 8 In Figure (b) in [reference], compared with the RCP algorithm that is always in an overfitting situation, the proposed URCP reaches the true rank after 13 iterations and gradually achieves a lower mean square error (MSE) through iterations, which also shows the superior convergence characteristics of the proposed method. It should be noted that Figure 8 Figure (b) in [reference] shows that the MSE of the URCP algorithm for estimating the parameter Bτ shows large fluctuations because the MSE in the present invention is the estimation error calculation for the maximum power single path, while the variational algorithm optimizes 30 initialized paths simultaneously. Therefore, single-path fluctuations will occur under the overall optimal situation.

[0135] Figure 8Figure (c) shows the estimated interference frequency-domain power magnitudes at 128 frequency points on the antenna at position (2, 2) in the receiving array. It can be seen that the true interference (shown in blue) only exists in the middle part of the frequency band. The traditional RCP method searches globally, so it exists in all frequency points generally. The proposed URCP method determines the frequency initialization for co-channel interference, thus significantly reducing the interference power values outside the interference band, and showing an estimated value closer to the true interference value. In addition, we choose the interference threshold as 4 times the noise power will filter out 95% of the noise magnitude. It should be noted that the selection of this threshold is related to the SNR ρ and the magnitude of the interference variance. The threshold estimated by the traditional method cannot accurately screen out the interference frequency positions. The interference frequency-domain estimation under the above threshold is as Figure 8 shown in Figure (d). It can be clearly seen that the URCP method has better estimation characteristics, manifested as more green areas and fewer red areas (the color markings in the figure use a binary classification method).

[0136] Figure 9 Shows the performance comparison between the proposed URCP algorithm and the traditional RCP algorithm under plane-wave interference and spherical-wave interference with the change of the interference bandwidth (IB). Figure 9 The channel estimation results in Figures (a) to (d) show that for the interference environment with structural wavefront characteristics, the proposed URCP method has consistent robustness. From Figure 9 Figures (e) to (f) for the interference position and interference MSE estimation, it can be seen that the accuracy of the proposed algorithm model enables the separation and estimation of different interference bandwidths to be robust under a limited number of iterations.

[0137] Figure 10 Shows that with the change of the interference power factor the proposed URCP algorithm has better performance than the traditional RCP algorithm under plane-wave interference and spherical-wave interference.

[0138] For the evaluation metrics in Table 1, the present invention uses the mean square error (MSE) as the evaluation metric and decomposes the MSE into two parts: the variance term and the offset term where represents the estimated parameter in the i-th OFDM symbol period, and the estimated mean is Table 1 shows the random wave parameter estimation of the proposed algorithm under different IB conditions. It can be seen that the proposed URCP algorithm has lower estimation error and more accurate interference position estimation.

[0139] Table 2 shows the random wave parameter estimation of the proposed algorithm under different IF conditions. It can be seen that the proposed URCP algorithm has lower estimation error and more accurate interference position estimation.

[0140] Table 1 Random wave parameter estimation under different IB conditions

[0141]

[0142]

[0143] Table 2 Random wave parameter estimation under different IF conditions

[0144]

[0145]

[0146] Example 2. Based on the concept of the above method, the present invention can provide a Bayesian wireless channel estimation system applicable to co-channel interference, including a modeling module, an initialization and alternating iteration module, and an estimation module;

[0147] The modeling module is used to perform tensor modeling on the received data according to the characteristics of the co-channel interference wavefront, and obtain the tensor composition for describing the frequency-domain representation of the received data;

[0148] The initialization and alternating iteration module is used for iterative loop: by selecting the interference prior type as link-level interference to perform variational iteration for a set number of iterations, so as to initially determine the frequency-domain position, and update the initialization parameters according to the results obtained in the following steps;

[0149] Perform alternating posterior inference on global interference and link-level interference; the variational inference based on LSI always searches for link-level interference in the entire tensor space. For global interference inference, GI inference is only performed in the co-channel interference frequency interval inferred by LSI;

[0150] Sequentially perform alternating iterative calculation of the inferred variables in variational inference, that is, infer the posterior distributions of parameter sets such as LSI, GI, factor matrix, and noise precision; In the alternating iteration, each time GI inference is performed, according to the newly obtained frequency-domain position of the third-dimensional co-channel interference, compare the index changes in the previous and subsequent iterations, update the frequency index, initialize the interference terms corresponding to the new frequency index using non-informative priors, and remove the interference terms corresponding to non-existent indexes;

[0151] Perform maximization calculation according to the evidence lower bound calculated based on the interference type, and adaptively update the hyperparameters of LSI and GI;;

[0152] Perform redundant multipath cancellation based on principal component extraction. Specifically: set a threshold for measuring the path weight, and determine the redundant multipaths to be eliminated in combination with the relationship between the multiple of the maximum and minimum values of the measured path weight and the threshold;

[0153] The estimation module is used to obtain the harmonic parameter [θ, φ, τ] values by using the maximum likelihood method with the factor matrix obtained from the estimated hyperparameters of LSI and GI and the interference parameters when the iterative step iterates to the set termination condition, and then obtain the complex amplitude α of each path according to the least squares operation.

[0154] On the other hand, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, can implement the Bayesian wireless channel estimation method applicable to co-channel interference of the present invention.

[0155] The present invention can also provide a computer device including a processor and a memory. The memory is used to store computer-executable programs. The processor reads and executes the computer-executable programs from the memory, and when the processor executes the computer-executable programs, it can implement the Bayesian wireless channel estimation method applicable to co-channel interference of the present invention.

[0156] The computer device can be a laptop computer, a desktop computer or a workstation.

[0157] The processor can be a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), an application specific integrated circuit (ASIC) or a field programmable gate array (FPGA).

[0158] For the memory of the present invention, it can be an internal storage unit of a laptop computer, a desktop computer or a workstation, such as a memory or a hard disk; it can also use an external storage unit, such as a mobile hard disk or a flash card.

[0159] The computer-readable storage medium can include a computer storage medium and a communication medium. The computer storage medium includes volatile and non-volatile, removable and non-removable media implemented by any method or technology for storing information such as computer-readable instructions, data structures, program modules or other data. The computer-readable storage medium can include: read-only memory

[0160] (ROM, Read Only Memory), random access memory (RAM, Random Access Memory), solid state drives (SSD) or optical discs, etc. Among them, the random access memory can include resistive random access memory (ReRAM, Resistance Random Access Memory) and dynamic random access memory (DRAM, Dynamic Random Access Memory).

[0161] The above content is only for explaining the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. Any modification made on the basis of the technical solution according to the technical idea proposed by the present invention falls within the protection scope of the claims of the present invention.

Claims

1. A Bayesian wireless channel estimation method suitable for co-channel interference, characterized in that: The following steps are involved: a. Based on the co-frequency interference wavefront characteristics, tensor modeling is performed on the received data to obtain the tensor structure used to describe the frequency domain representation of the received data; b. Initialization of the frequency position of the co-channel interference; specifically, by selecting the interference prior type as link-level interference and performing a variational iteration with a set number of iterations, the frequency domain position is initially determined, and the initialization parameters are updated according to the results obtained in steps c to e; c. Alternate a posteriori inference of global interference and link-level interference. LSI-based variational inference always searches for link-level interference in the entire tensor space. For global interference inference, GI inference is only performed in the co-frequency interference frequency interval inferred by LSI. d. Iterate and calculate the inferred variables in the variational inference in sequence, that is, infer the full set of parameters such as LSI, GI, factor matrix and noise accuracy posterior distribution; in alternating iterations, each time GI inference is performed, the frequency domain position of the third-dimensional co-frequency interference is re-obtained, the index changes in the two iterations are compared, the frequency index is updated, the interference item corresponding to the new frequency index is initialized using a non-informationized prior, and the interference item corresponding to the non-existent index is removed; e. Maximize the lower bound of evidence calculated based on the interference type and adaptively update the hyperparameters of LSI and GI; f. Eliminate redundant multipaths based on principal component extraction. Specifically, set a threshold for measuring path weights, and determine the redundant multipaths that need to be eliminated by combining the relationship between the multiples of the maximum and minimum values ​​of the path weights and the threshold; g, the iteration step is iterated until the set termination condition is reached. The factor matrix obtained by estimating the hyperparameters of LSI and GI and the interference parameters is used to obtain the harmonic parameters [θ, φ, τ] using the maximum likelihood method, and then the complex amplitude α of each path is obtained based on the least squares operation.

2. The Bayesian wireless channel estimation method suitable for co-channel interference according to claim 1, characterized in that: In step a, according to the co-frequency interference wavefront characteristics, the received data is modeled as a tensor structure to obtain the frequency domain receiving tensor: The signal emitted by the transmitter is reflected by multiple targets in the environment and reaches the receiver, forming a dual-path signal. The receiver uses a planar array antenna of size N1×N2 to capture the elevation angle θ, azimuth angle φ, delay τ and complex amplitude α of the multipath. The transmission bandwidth is B, and the modulation mode is the symbol sequence of the K subcarrier transmission period of OFDM. Considering the SIMO scenario, the channel matrix of the sampled K frequency points is stacked in the third dimension to obtain the channel tensor in the form of CP decomposition. In the structured interference tensor, the spherical wave interference is modeled with an additive model from the perspective of the tensor (of course, it can be seen that plane wave interference is just a special case of spherical wave interference). The structured spherical wave interference tensor is modeled as the sum of the global interference tensor and the link-level interference tensor. The random wavefront interference tensor with unstructured characteristics is modeled. Considering the different normalized antenna gains of the receiving array, the receiving array gain of random wavefront interference presents random characteristics. In order to fully describe the characteristics of the additive model, the global interference is defined as the average power value of the array at a certain frequency point, and the LSI power is divided into positive LSI and negative LSI, thereby obtaining the receiving tensor composition based on random wavefront. The frequency domain composition of the received tensor is expressed as Channel tensor, Perturb tensor and Noise tensor, completes the unified modeling of structured and unstructured co-channel interference in the channel, including global interference and link-level interference. The co-channel interference tensor model is 3. The Bayesian wireless channel estimation method suitable for co-channel interference according to claim 2, characterized in that: The global interference is composed of a matrix of size N1×N2, which means that the global interference is the interference acting on all sub-channels with the same power and phase; the link-level interference is the interference tensor It is composed of a single element in , indicating that the LSI is the interference acting on a specific sub-channel.

4. The Bayesian wireless channel estimation method suitable for co-channel interference according to claim 1, characterized in that: In step b, a certain type of interference The superscript Tp is used as the category index, Tp∈{GI,LSI}, and a single interference in this category is represented as Its specific position in the time-frequency domain is determined by the subscript Ind(Tp), with mappings Ind(GI) = {i3} and Ind(LSI) = {i1, i2, i3}. The complete set of interference items of a certain category is A single distractor is denoted by Among them, the relationship between interference and interference terms of different types of Tp is expressed as and The inferred variable is Where λ is the factor matrix hyperparameter, is the interference term, γ Ξ is the interference hyperparameter, v is the environmental noise accuracy; Next, the frequency with co-frequency interference is initialized. Specifically, by selecting the interference prior type as T p =LSI performs a variational iteration with a set number of iterations to initialize; in the variational iteration of LSI, all interference tensor units Ω are considered to capture the high-power frequency position of each link, which is the position where the same-frequency interference is most likely to occur, and the threshold T is selected LSI And the estimated LSI index is as follows: in, represents the estimated LSI interference value during initialization, P LSI represents the estimated maximum power of LSI, T LSI represents the interference power threshold, Indicates the LSI third-dimensional frequency domain index set that meets the interference threshold condition.

5. The Bayesian wireless channel estimation method suitable for co-channel interference according to claim 4, characterized in that: In step c, infer variables in the inference The posterior distribution of (n) is the factor matrix, λ is the factor matrix hyperparameter, is the interference term, γ Ξ is the interference hyperparameter, and v is the environmental noise accuracy, as follows: Factor Matrix A (n) The posterior distribution of, based on the prior assumptions of different types of interference, n-module factor matrix A (n) The posterior mean of The subscript Ω indicates the operation of interference term, and the posterior distribution of factor matrix The variance and mean of are as follows: in, represents the expectation operation, Multiple Khatri-Rao products The superscript "*" indicates conjugation, the superscript "H" indicates conjugate transposition, and "\" indicates a elimination operation; The posterior distribution of the hyperparameter λ, based on the assumption of wide-sense stationary uncorrelated scattering, is l ,l=1,2,…,L is irrelevant, the posterior distribution The vector form of the hyperparameters is expressed as: in, and The posterior expectation of λ is c0 and d0 come from the prior assumption interference The posterior distribution of, in the actual channel scenario, different interferences at the same frequency are unrelated to each other, and different interferences at different frequencies are unrelated. For the posterior distribution of different types of interference have: Where "<·>" represents the inner product operator. When Tp is equal to GI, the remaining term operation \Ind(GI) = {i1, i2}, Cst[·] is the maximum index multiplication operator, Cst[i1, i2] = I1I2 = N1N2, and the global information of the channel tensor is used in the posterior estimation of each interference type. The posterior distribution of the hyperparameter γ and the posterior distribution of the accuracy of the distractor under the alternating prior hypothesis The hyperparameters are expressed as follows: In the formula and From the prior assumption and The posterior distribution of the noise accuracy V. Under the alternating prior hypothesis, the noise accuracy follows the Gamma distribution q(v) = Ga(ν|e M ,f M )for: Among them, e0 and f0 come from the prior assumption p(v) = Ga(v|e0,f0), and the expectation operation is as follows: where F (n) The i n The row is represented as 6. The Bayesian wireless channel estimation method suitable for co-channel interference according to claim 1, characterized in that: In step d, based on the interference type The computed evidence lower bound is used to adaptively update the initial perturbation hyperparameters There are the following optimization processes: Where "argmax(·)" means solving the parameters that maximize the given function, and the initialization parameter set is Assuming they are equal and infinitesimal, satisfying the condition of the uninformative prior assumption, the updated parameter set is And the index set of global interference is The adaptive update of the hyperparameters is performed after each iteration of step c, and is used by default in all posterior inferences and evidence lower bound operations. For the updated 7. The Bayesian wireless channel estimation method suitable for co-channel interference according to claim 1, characterized in that: In the iteration, a fixed number of variational iterations is used as the termination condition, and the complex amplitude α of each path is obtained using the least squares method according to the values ​​of the harmonic parameters [θ, φ, τ].

8. A Bayesian wireless channel estimation system suitable for co-channel interference, characterized in that: It includes a modeling module, an initialization and alternating iteration module, and an estimation module; The modeling module is used to perform tensor modeling on the received data according to the co-frequency interference wavefront characteristics, and obtain the tensor structure used to describe the frequency domain representation of the received data; The initialization and alternating iteration module is used for cyclic iteration: by selecting the interference prior type as link-level interference and performing variational iteration for a set number of iterations, the frequency domain position is initially determined, and the initialization parameters are updated according to the results obtained in the following steps; Alternate a posteriori inferences are performed on global interference and link-level interference. LSI-based variational inference always searches for link-level interference in the entire tensor space. For global interference inference, GI inference is performed only in the co-frequency interference frequency interval inferred by LSI. Calculate the inferred variables in variational inference in an iterative order, that is, infer the full set of parameters such as LSI, GI, factor matrix, and noise accuracy posterior distribution; in alternating iterations, each time GI inference is performed, the frequency domain position of the third-dimensional co-frequency interference is re-obtained, the index changes in the two iterations are compared, the frequency index is updated, the interference item corresponding to the new frequency index is initialized using a non-informationized prior, and the interference item corresponding to the non-existent index is removed; Based on the evidence lower bound calculated based on the interference type, the hyperparameters of LSI and GI are updated adaptively; Eliminate redundant multipaths based on principal component extraction, specifically: set a threshold for measuring path weights, and determine the redundant multipaths that need to be eliminated by combining the relationship between the multiples of the maximum and minimum values ​​of the path weights and the threshold; The estimation module is used to obtain the harmonic parameters [θ, φ, τ] values ​​using the maximum likelihood method by using the estimated hyperparameters of LSI and GI and the factor matrix obtained by the interference parameters when the iteration step reaches the set termination condition, and then obtain the complex amplitude α of each path based on the least squares operation.

9. A computer device, characterized in that: It includes a processor and a memory, the memory is used to store a computer executable program, the processor reads part or all of the computer executable program from the memory and executes it, and when the processor executes part or all of the computer executable program, it can implement the Bayesian wireless channel estimation method suitable for co-channel interference described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that: A computer program is stored in a computer-readable storage medium. When the computer program is executed by a processor, the Bayesian wireless channel estimation method applicable to co-channel interference according to any one of claims 1 to 7 can be implemented.

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