Joint estimation method of multipath signal parameters in wireless channels based on variational Bayesian inference

Abstract

The present application relates to a method for joint estimation of multipath signal parameters in wireless channels based on variational Bayesian inference. Within the framework of VBI spatial generalized alternating iterative solution, the amplitude gain is first modeled using a Bernoulli-Gaussian hierarchical prior to obtain a pruning condition expression, and a delay parameter pre-estimate expression is obtained based on the autocorrelation characteristics of the observed transmitted signal. During each iteration, the delay parameter under the current number of mirror components is first estimated based on the delay parameter pre-estimate expression, and then the component estimate and dispersion parameter estimate of one mirror component are calculated. The method then determines whether the pruning condition expression is satisfied. If so, the amplitude gain parameter estimate is calculated. If not, the mirror component is pruned, and the parameter estimate of the next mirror component is alternately solved until convergence, resulting in the number of mirror components and parameter estimates for each mirror component. This method can effectively improve solution efficiency while ensuring the accuracy of the results.

Description

Technical Field

[0001] The present application relates to the technical field of wireless channel parameter extraction, and in particular to a method for joint estimation of wireless channel multipath signal parameters based on variational Bayesian inference. Background Art

[0002] With the emergence of beyond-5G and 6G technologies, wireless communications are evolving towards greater bandwidth, lower latency, and higher transmission rates. Multiple-input, multiple-output (MIMO) technology improves system capacity, spatial diversity gain, and spectrum efficiency by increasing spatial dimensions, but it also presents challenges for channel parameter estimation (CPE) for complex signal models.

[0003] Accurately estimating dispersion parameters such as delay, angle of arrival (AoA), angle of departure (AoD), and Doppler frequency from the received signal vector and establishing an appropriate channel model are of practical significance for optimizing wireless communication system design and improving wireless system communication capacity. While CPE algorithms have been extensively studied, their accuracy and complexity remain significant challenges. In CPE algorithms, the received signal vector is typically modeled as a superposition of multiple specular components (SCs). Each specular component can be viewed as the product of its dispersion parameter and amplitude gain. In this process, the component due to diffuse reflection (also known as the densely scattered component) is generally not considered. Its parameters can be estimated by subtracting the estimated specular component from the received signal vector, resulting in a residual signal. However, since the majority of the energy in the received signal vector is concentrated in the specular component, accurately estimating the diffusely scattered component requires first estimating the specular component.

[0004] However, the number of specular components determines the model order of the received signal vector. Given a fixed model order, spectral estimation algorithms and subspace-based algorithms can effectively estimate some dispersion parameters, while algorithms based on the maximum likelihood (ML) criterion offer relatively high accuracy. However, these algorithms rely on prior information about the model order, and an incorrect model order can severely degrade their accuracy. Specifically, an excessively high model order can lead to the estimation of spurious components (non-existent specular components and their dispersion parameters), while a low model order can lead to the omission of specular components. Therefore, in practical applications, it is necessary to augment the parameter estimation algorithm with algorithms that estimate the model order, such as the Akaike or Bayesian information criterion (AIC), BIC, or the minimum description length (MDL) criterion. However, these methods not only increase the computational complexity of the algorithm but also tend to be positively biased when the signal-to-noise ratio and observation sample are non-asymptotic. Summary of the Invention

[0005] Based on this, it is necessary to provide a joint estimation method for multipath signal parameters of wireless channels based on variational Bayesian inference, which can improve the solution efficiency while ensuring accuracy in response to the above technical problems.

[0006] A method for jointly estimating multipath signal parameters, the method comprising:

[0007] The amplitude gain is modeled using Bernoulli-Gaussian hierarchical priors to obtain the pruning condition expression, and the delay parameter estimation expression is obtained based on the autocorrelation characteristics of the observed transmitted signal.

[0008] Acquiring an observation reception signal, where the observation reception signal is obtained based on a single-transmit-multiple-receive detection system;

[0009] Under the framework of sparse variational Bayesian inference theory and spatial generalized alternating iterative solution, the number of mirror components and the amplitude gain and dispersion parameters of each mirror component are pre-estimated based on the observed received signal;

[0010] During each iteration, the delay parameter under the current number of mirror components is first estimated based on the delay parameter pre-estimate expression, and then a component estimate and a dispersion parameter estimate of one mirror component are calculated. It is then determined whether the pruning condition expression is satisfied based on the component estimate and the dispersion parameter estimate. If so, an amplitude gain parameter estimate is calculated, wherein the dispersion parameter estimate includes a delay parameter and an angle parameter estimate, and the angle parameter estimate introduces an estimated expression for the amplitude gain.

[0011] If not, the mirror component is cut off and the parameter estimation of the next mirror component is solved alternately until convergence, thereby obtaining the number of mirror components of the observed received signal and the parameter estimation of each mirror component.

[0012] In one embodiment, the pruning condition expression is expressed as:

[0013]

[0014] In the above formula, the left-hand term represents the signal-to-noise ratio on the l-th mirror component, and the right-hand term represents the threshold value of the change, where: represents the amplitude gain on the lth mirror component, represents the variance, ρ and ε represent hyperparameters.

[0015] In one embodiment, the delay parameter pre-estimation expression is expressed as:

[0016]

[0017] In the above formula, δ(n) represents the impulse function, g(0) is the sampling value of g(t) at t=0, and α l The estimated expression of the introduced amplitude gain, a(φ l ) represents the incident angle φ l The steering vector formed, belongs to [b0,b1,…,b K-1 ] represents a known K-period detection sequence, represents the conjugate complex number of .

[0018] In one embodiment, before estimating the number and parameters of mirror components under the framework of sparse variational Bayesian inference theory and spatial generalized alternating iterative solution, the number of mirror components is initialized according to a preset number, and at the same time, the component estimation of the mirror components and the dispersion parameter estimation are randomly initialized.

[0019] In one embodiment, an estimation expression of the amplitude gain is introduced in the angle parameter estimation, and the angle parameter estimation expression is expressed as:

[0020]

[0021] In the above formula, Represents the component estimate obtained in the current iteration, represents the delay estimate obtained in the current iteration, α l The estimated expression for the introduced amplitude gain is expressed as Represents the incident angle estimate obtained in the current iteration, φ l Indicates the incident angle estimate of the lth mirror component obtained in the last iteration, Σl represents the second-order moment of the noise vector of the lth mirror component, (·) H represents the conjugate transpose of the matrix, and s(·) represents the detection signal vector.

[0022] The present application also provides a device for jointly estimating multipath signal parameters of a wireless channel based on variational Bayesian inference, the device comprising:

[0023] An estimation expression obtaining module is used to model the amplitude gain using a Bernoulli-Gaussian hierarchical prior to obtain a pruning condition expression, and obtain a delay parameter pre-estimation expression based on the autocorrelation characteristics of the observed transmitted signal;

[0024] An observation signal receiving module is used to obtain an observation reception signal, where the observation reception signal is obtained based on a single-transmit-multiple-receive detection system;

[0025] A joint parameter solution module is used to pre-estimate the number of mirror components and the amplitude gain and dispersion parameters of each mirror component based on the observed received signal under the framework of sparse variational Bayesian inference theory and spatial generalized alternating iterative solution;

[0026] an iterative parameter updating module, configured to, during each iteration, first estimate the delay parameter for the current number of mirror components based on a pre-estimated delay parameter expression, then calculate a component estimate and a dispersion parameter estimate for one mirror component, and determine whether the pruning condition expression is satisfied based on the component estimate and the dispersion parameter estimate; if so, calculate an amplitude gain parameter estimate, wherein the dispersion parameter estimate includes a delay parameter and an angle parameter estimate, and the angle parameter estimate introduces an estimated expression for the amplitude gain;

[0027] The pruning and multipath signal parameter acquisition module is used to prune the mirror component if it is not satisfied, and alternately solve the parameter estimation of the next mirror component until convergence, thereby obtaining the number of mirror components of the observed received signal and the parameter estimation of each mirror component.

[0028] A computer device includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented:

[0029] The amplitude gain is modeled using Bernoulli-Gaussian hierarchical priors to obtain the pruning condition expression, and the delay parameter estimation expression is obtained based on the autocorrelation characteristics of the observed transmitted signal.

[0030] Acquiring an observation reception signal, where the observation reception signal is obtained based on a single-transmit-multiple-receive detection system;

[0031] Under the framework of sparse variational Bayesian inference theory and spatial generalized alternating iterative solution, the number of mirror components and the amplitude gain and dispersion parameters of each mirror component are pre-estimated based on the observed received signal;

[0032] During each iteration, the delay parameter under the current number of mirror components is first estimated based on the delay parameter pre-estimate expression, and then a component estimate and a dispersion parameter estimate of one mirror component are calculated. It is then determined whether the pruning condition expression is satisfied based on the component estimate and the dispersion parameter estimate. If so, an amplitude gain parameter estimate is calculated, wherein the dispersion parameter estimate includes a delay parameter and an angle parameter estimate, and the angle parameter estimate introduces an estimated expression for the amplitude gain.

[0033] If not, the mirror component is cut off and the parameter estimation of the next mirror component is solved alternately until convergence, thereby obtaining the number of mirror components of the observed received signal and the parameter estimation of each mirror component.

[0034] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the following steps:

[0035] The amplitude gain is modeled using Bernoulli-Gaussian hierarchical priors to obtain the pruning condition expression, and the delay parameter estimation expression is obtained based on the autocorrelation characteristics of the observed transmitted signal.

[0036] Acquiring an observation reception signal, where the observation reception signal is obtained based on a single-transmit-multiple-receive detection system;

[0037] Under the framework of sparse variational Bayesian inference theory and spatial generalized alternating iterative solution, the number of mirror components and the amplitude gain and dispersion parameters of each mirror component are pre-estimated based on the observed received signal;

[0038] During each iteration, the delay parameter under the current number of mirror components is first estimated based on the delay parameter pre-estimate expression, and then a component estimate and a dispersion parameter estimate of one mirror component are calculated. It is then determined whether the pruning condition expression is satisfied based on the component estimate and the dispersion parameter estimate. If so, an amplitude gain parameter estimate is calculated, wherein the dispersion parameter estimate includes a delay parameter and an angle parameter estimate, and the angle parameter estimate introduces an estimated expression for the amplitude gain.

[0039] If not, the mirror component is cut off and the parameter estimation of the next mirror component is solved alternately until convergence, thereby obtaining the number of mirror components of the observed received signal and the parameter estimation of each mirror component.

[0040] The above-mentioned method for joint estimation of multipath signal parameters of wireless channels based on variational Bayesian inference first adopts Bernoulli Gaussian hierarchical prior to model the amplitude gain to obtain the pruning condition expression, and obtains the delay parameter pre-estimation expression based on the autocorrelation characteristics of the observed transmitted signal. In addition, under the framework of sparse variational Bayesian inference theory and spatial generalized alternating iterative solution, the number of mirror components, as well as the amplitude gain and dispersion parameter of each mirror component are pre-estimated according to the observed received signal. In each iteration process, the delay parameter under the current number of mirror components is first estimated according to the delay parameter pre-estimation expression. The method estimates the number of mirror components, then calculates the component estimate and dispersion parameter estimate of one mirror component. Based on the component and dispersion parameter estimates, it determines whether the pruning condition expression is satisfied. If so, the amplitude gain parameter estimate is calculated. The dispersion parameter estimate includes the delay parameter and the angle parameter estimate. To avoid falling into a local optimum during the solution, the angle parameter estimate introduces an estimated expression for the amplitude gain. If not satisfied, the mirror component is pruned, and the parameter estimate of the next mirror component is solved alternately until convergence. The number of mirror components in the observed received signal and the parameter estimate of each mirror component are obtained. This method can effectively improve the solution speed and reduce the convergence time of the iterative solution, while ensuring the accuracy of the results. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 1 is a flow chart of a method for joint estimation of multipath signal parameters in wireless channels based on variational Bayesian inference in one embodiment;

[0042] Figure 2 A schematic diagram showing a comparison of the average convergence time of the method of the present invention and two other existing joint parameter estimation methods under different model orders in one embodiment;

[0043] Figure 3 1 is a structural block diagram of a device for jointly estimating multipath signal parameters of a wireless channel based on variational Bayesian inference in one embodiment;

[0044] Figure 4 FIG. 1 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0046] Aiming at the problem that the multipath signal parameter estimation in the prior art requires a lot of calculations, consumes a lot of time, and cannot obtain a more accurate estimation result, in this application, as Figure 1As shown, a method for joint estimation of multipath signal parameters in wireless channels based on variational Bayesian inference is provided, which specifically includes the following steps:

[0047] Step S100 , using Bernoulli-Gaussian hierarchical prior to model the amplitude gain, obtain a pruning condition expression, and obtain a delay parameter pre-estimation expression based on the autocorrelation characteristics of the observed transmitted signal.

[0048] Step S110: Acquire an observation reception signal, where the observation reception signal is obtained based on a single-transmit multiple-receive detection system.

[0049] Step S120 , under the framework of sparse variational Bayesian inference theory and spatial generalized alternating iterative solution, the number of mirror components, as well as the amplitude gain and dispersion parameters of each mirror component are pre-estimated based on the observed received signal.

[0050] In step S130, during each iteration, the delay parameter under the current number of mirror components is first estimated based on the delay parameter pre-estimate expression, and then the component estimate and dispersion parameter estimate of one mirror component are calculated. It is determined whether the pruning condition expression is satisfied based on the component estimate and the dispersion parameter estimate. If so, the amplitude gain parameter estimate is calculated, where the dispersion parameter estimate includes the delay parameter and the angle parameter estimate, and the angle parameter estimate introduces an estimated expression for the amplitude gain.

[0051] Step S140: If not, the mirror component is cut off and the parameter estimation of the next mirror component is solved alternately until convergence, thereby obtaining the number of mirror components of the observed received signal and the parameter estimation of each mirror component.

[0052] In this embodiment, within the framework of sparse variational Bayesian inference theory, a Bernoulli-Gaussian hierarchical prior is used to obtain an optimized pruning condition expression, and the delay parameters are pre-estimated based on the autocorrelation characteristics of the observed transmitted signal. This makes the method more accurate in estimating the number of mirror components of the signal and the parameters of each mirror component, and its solution process is simpler and faster.

[0053] First, before explaining step S100 in detail, the observed received signal received in step S110 , that is, the object processed in this method, is modeled.

[0054] In a single-input–multiple-output (SIMO) detection system, when the distance between the transmitter and receiver is sufficiently far, the effect of the antenna elevation difference on the incident angle of the received signal can be ignored. In a two-dimensional plane, the received signal is composed of multipath signals generated by specular reflection and noise in space. The DMC energy caused by diffuse reflection is relatively small and is also considered noise. Therefore, the received signal of an M-element linear uniform antenna array is specifically expressed as:

[0055]

[0056] In formula (1), α l It represents the complex gain of the signal on the lth path, that is, the amplitude gain, α=[α1,...,α L ] w(t) represents complex Gaussian noise, w(t)=[w1(t),w2(t),…,w M (t)] T Assume that w(t) is a zero-mean spatially white and temporally wide-sense stationary Gaussian process, that is and s(t;θ l ) represents the specular reflection component on the lth path, which can be further expressed as:

[0057]

[0058] In formula (2), θ l =[τ l ,φ l ]. S(t) represents the detection signal, τ l It represents the time delay caused by the mirror reflection of the lth path. It is a pulse signal train sent repeatedly. is [b0,b1,…,b K-1 ] is generated after the shaped pulse g(t), [b0,b1,…,b K-1 ] represents a known K-period detection sequence. T b =KT g , T g represents the period of g(t). a(φ l ) is the incident angle φ l The steering vector formed can be further expressed as:

[0059]

[0060] In formula (3), λ represents the signal wavelength, u(φ l ) represents the unit direction vector on the lth path, r m Represents the position vector of the mth array element.

[0061] In the actual process, y(t) is T s Sampling is performed periodically, and each antenna array element is sampled N times. By superimposing the sampling output on a vector y, formula (1) can be further expressed as:

[0062]

[0063] In formula (4), s(θ l )=[s0(θ l ) T ,…,s M-1 (θ l ) T ] T ,w=[w0 T ,…,w M-1 T ] T , and s m (θ l )=[s m (0; θ l ),…,s m ((N-1)T s θ l )] T , w m =[w m (0),w m (T s ),…,w m ((N-1)T s )] T ,m=0,...,M-1. To simplify the expression, define Ω={α1,θ1,...,α L ,θ L} is the set of parameters on each mirror component, where α L and θ L They represent the amplitude gain and dispersion parameter on the Lth mirror component respectively. At the same time, the noise vector satisfies ∑=E[ww H ].

[0064] In the framework of Sparse Bayesian Learning (SBL), it is usually assumed that α satisfies a two-layer hierarchical prior. In this method, it is modeled as a Bernoulli-Gaussian distribution. L ] T The posterior distribution of is given by the independent Bernoulli variables c=[c1,...,c L ] T It is decided, therefore, p(α l |c l) represents the sparse prior of the lth mirror component, which is specifically expressed as:

[0065] p(α l |c l ;ε)=(1-c l )δ(α l )+c l f CN (α l ;0,ε) (5)

[0066] In formula (5), Therefore, when c l =0 when α l =0, when c l =1 when p(α l |c l =1;ε)=f CN (α l ; 0,ε). The hyperparameter ρ controls the possibility of the existence of the lth mirror component, and the hyperparameter ε controls the α l The degree of discreteness. CN (·; μ, ∑) represents the complex Gaussian probability density function with mean μ and covariance ∑. In order to facilitate the calculation of the variational approximate probability distribution, expression (5) is redefined as follows:

[0067]

[0068] In formula (6), p(α l |c l ;ε) still satisfies when c l =0 when α l =0, when c l =1 when p(α l |c l =1;ε)=f CN (α l ; 0,ε), so it is equivalent to Eq.

[0069] Secondly, it is important to explain that it is usually extremely difficult to directly calculate the posterior probability p(Ω,c|y) associated with the unknown parameters {Ω,c} based on the observation y.

[0070] Therefore, in the VBI framework (variational Bayesian Inference), a variational approximate probability distribution q(Ω,c) is generally used to approximate the posterior probability p(Ω,c|y). The similarity metric between the two is the KL divergence, so this process can be expressed as KL(q(Ω,c)||p(Ω,c|y)). In the SAGE algorithm (space generalized alternating iterative solution), there is an additional hidden variable x l, so when solving, the goal is to minimize KL(q(Ω,c,x l )||p(Ω,c,y,x l )). where Ω={α1,θ1,...,α L ,θ L} represents the amplitude gain and dispersion parameters (delay and AoA, i.e., angle of arrival) of each mirror component, y represents the received signal vector, c=[c1,...,c L ] T represents mutually independent Bernoulli variables.

[0071] For KL(q(Ω,c,x l )||p(Ω,c,y,x l )) is still difficult to solve directly, so we further assume that q(Ω,c,x l ) satisfies the mean field approximation, that is:

[0072]

[0073] By minimizing the KL divergence between the variational approximate probability distribution of the hidden variables contained in each mirror component in formula (7) and the true distribution, it is equivalent to minimizing KL(q(Ω,c,x l )||p(Ω,c,y,x l )). Therefore, for {Ω,c,x l By minimizing the KL divergence of each variable in} alternately, we can get:

[0074] ln(q(Φ i ))=<lnp(y,Φ)> k≠i +c i (8)

[0075] In formula (8), Φ={Ω,c,x l}, Φ i represents each variable of Φ. Here <·> k≠i Indicates that Φ is removed from Φ i The variational approximate probability distribution q(·) of each variable is used to find the expected operator. According to formula (8), q(x l ),q(θ l ),q(α l ),q(c l ) requires calculating the joint distribution of parameters lnp(y,Φ) using the following formula:

[0076]

[0077] Since in the solution process, we are more concerned with {x l ,θ l,α l ,c l} related variational approximate probability distribution function, so the joint probability distribution p(y,Φ) can be expressed as:

[0078]

[0079] In formula (10), In the alternating update q(x l ),q(θ l ),q(α l ),q(c l ), assuming are determined, so we have:

[0080]

[0081] The SAGE algorithm assumes that spatial noise can be decomposed into L groups of mutually uncorrelated noise vectors, that is,

[0082] According to the above basic signal model, in order to estimate the model order from the observation y and the corresponding parameter set In this embodiment, an improved VBI-based space alternating generalized expectation maximization (SAGE) joint parameter estimation method is proposed.

[0083] In step S100, the Bernoulli-Gaussian hierarchical prior is used to construct the variational estimates of each parameter (i.e., q(x l ),q(θ l ),q(α l ),q(c l ), where x l and c l represent latent variables and Bernoulli variables respectively) and pruning condition expressions.

[0084] It should be noted that in this method, the Bernoulli-Gaussian hierarchical prior is specially introduced to construct the pruning condition expression, and in the alternating iteration process, the parameter q(x l ),q(θ l ),q(α l ) actually needs to be updated based on the corresponding update formula given by the Bernoulli-Gaussian hierarchical prior as the parameter update scheme of this method.

[0085] Specifically, when updating q(x l ), we rely on formula (8) to calculate the expectation of lnp(y,Φ) with respect to {q(θ),q(c),q(α)}, so Observe that q(x l ) About x l is quadratic, we can convert lnq(x l ) is expressed as a high probability density function of the following form:

[0086]

[0087] therefore in:

[0088]

[0089]

[0090] The SAGE algorithm assumes that β l →1, then ∑ l =β l ∑,q(x l ) is approximately a Dirac distribution. represents the latent variable x l The estimated value of the latent variable x is calculated using formula (14). l Solve it.

[0091] Specifically, when updating q(θ l ). Also relying on formula (8), calculate lnp(y,Φ) about expectations, so

[0092]

[0093] In formula (15), θ l represents the set of dispersion parameters corresponding to the lth mirror component, which can be regarded as a parameter set of discrete distribution.

[0094] Therefore, q(θ l ) is similar to the Dirac distribution, that is, Under this assumption, The estimated value of is expressed as:

[0095]

[0096] In estimating q(θ l ) in the process, it is necessary to target the dispersion parameter τ l ,φ lComplete the update. Considering s(θ l ) and θ l The nonlinear relationship between the two makes the optimization process based on the gradient formula (16) difficult, so the optimal solution is generally found through continuous search. At the same time, in order to reduce the complexity of the calculation, the dispersion parameter τ is updated alternately. l ,φ l , other parameters are fixed unchanged during the update. Under this condition, formula (16) is decomposed into the following process:

[0097]

[0098] Then use formula (21) to complete the l-th mirror component amplitude gain α l Updates.

[0099] Compared with joint search τ l ,φ l ,α l The optimal value of τ is updated alternately l ,φ l ,α l The process narrows the scope of the solution space, but it is also easier to fall into the local optimal solution, which reduces the estimation accuracy of the dispersion parameters.

[0100] However, low-precision dispersion parameter estimation will increase the probability of detecting pseudo components, leading to incorrect estimation of the model order. Therefore, without increasing the computational complexity, this method adopts a partial joint optimization of φ l ,α l The specific process is as follows:

[0101]

[0102] In the joint optimization φ l ,α l In the process, only the α l This process does not increase the amount of calculation and avoids falling into the local optimal solution. This is also the case in step S130. In each iterative solution process, when calculating φ l When α is introduced l The solution formula of .

[0103] Furthermore, in the update α l When , we also rely on formula (8) to calculate lnp(y,Φ) about expectations, so

[0104]

[0105] Similar to q(x l ),q(αl )About α l is quadratic. l ) is regarded as a Gaussian probability distribution function, that is, in

[0106]

[0107] In formula (20), The dispersion parameter and amplitude gain representing the mirror component have physical meanings. In this case, formula (20) can be further simplified as follows:

[0108]

[0109] on the contrary, Indicates that the mirror component should be "sparse". At this time, it can be inferred that

[0110] Furthermore, when updating q(c l ), we also rely on formula (8) to calculate lnp(y,Φ) about The expectation is:

[0111]

[0112] In formula (22), <δ(α l )> and Indicates the relationship between q(α l ) to find the expectation. Modeled as a Dirac distribution, parameter Takes discrete values ​​0 or 1, so when q(c l )satisfy hour, Keep the specular component, otherwise, "sparse" the specular component. Therefore, the specular component will be retained if it meets the following expression, that is, the pruning condition:

[0113]

[0114] Formula (23) can be further simplified as follows:

[0115]

[0116] In formula (24), the left-hand term represents the signal-to-noise ratio on the l-th mirror component, and the right-hand term represents the threshold of change. The left-hand term can be simplified to In the right-hand side, represents the amplitude gain on the lth mirror component, represents variance, ρ and ε represent hyperparameters, and the threshold on the right is the threshold value of the change affected by q(α l ) and constraints on hyperparameters ρ and ε.

[0117] The update of the hyperparameter ρ is determined by the current model order. At the same time, ε represents the distribution of the amplitude gain, so it can be estimated by the second-order moment of the amplitude gain.

[0118] Next, in this method, in each iteration process, the delay parameter is pre-estimated based on the good autocorrelation characteristics of the transmitted sounding sequence, in step S130.

[0119] Specifically, according to the above formula (2), the transmission signal model is a repeated detection sequence, and the received signal model is the superposition of the detection sequence in the time domain. The detection sequence has a strong autocorrelation characteristic, so the delay parameter can be estimated by correlation detection. In this process, it is assumed that the estimated value of the model order is Sure.

[0120] Furthermore, the autocorrelation function of the detection sequence is defined as:

[0121]

[0122] For detection sequences, such as m sequence, ZC sequence, Gold sequence, etc., they have good autocorrelation characteristics, namely |R b (0)|>>|R b (τ>0)|.

[0123] The process of generating b(t) requires the detection sequence [b0,b1,…,b K-1 ] shaping, the shaping pulse g(t) duration is T g In order to reconstruct y(t) without distortion, the sampling interval T s Meet T s ≤T g To simplify the derivation process, assume that T s =T g , and the minimum delay interval satisfies Δτ min ≥T s .

[0124] Then define the sampled signal y d (n) is:

[0125]

[0126] In formula (26), s(nT s θ l )=[s1(nT s θ l),…,s M (nT s θ l )] T ,w(nT s )=[w1(nT s ),…,w M (nT s )] T Obviously, y d (n) can be obtained by receiving the signal vector y.

[0127] Then y d After correlation operation of (n) and the detection sequence, we can get:

[0128]

[0129] In formula (27), b(n) is the period T s The detection sequence after sampling:

[0130]

[0131] In formula (29), δ(n) is the impulse function, and g(0) is the sample value of g(t) at t = 0. Therefore, according to the autocorrelation characteristics of b(n), R yb (τ) can be further expressed as:

[0132]

[0133] Because, |R b (0)|>>|R b (τ>0)|, so we select The delay corresponding to the maximum value is taken as the delay. Therefore, according to R yb (τ) to obtain the estimated value of the delay It should be noted that when T s <T g , the received signal needs to be downsampled first.

[0134] In the actual calculation process, the delay parameter pre-estimation expression is expressed as:

[0135]

[0136] In the above formula, α l represents the complex gain of the signal on the lth path, i.e., the amplitude gain, a(φ l ) represents the incident angle φ l The steering vector formed,

[0137] After obtaining the aforementioned pruning condition expression, delay parameter pre-estimation formula, and other parameter solution formulas, the number of mirror components and the parameters of each mirror component can be estimated based on the received signal detected in step S110 using sparse variational Bayesian inference theory and a spatial generalized alternating iterative solution framework. This includes performing multiple iterations of the solution process (steps S130 and S140).

[0138] In this embodiment, before performing the alternating iterative solution, the number of mirror components is initialized according to a preset number, and at the same time, the component estimation of the mirror components and the dispersion parameter estimation are randomly initialized. That is, the model order is randomly initialized. (number of specular components) and the corresponding parameter set And hyperparameters ρ, ε. According to formula (31), the delay of each mirror component is estimated Then, in each iteration, According to formula (14) and formula (18), the variational approximate probability distribution q(x l ),q(θ), and then judge whether the mirror component should be "sparse" according to the pruning condition expression, that is, formula (24). If it is satisfied, update the corresponding hyperparameters and use formula (20) to update q(α l ). Otherwise, remove the mirror component.

[0139] Through multiple iterations, that is, repeating the above steps until the algorithm converges, the final estimation result is obtained, including the model order and the corresponding parameter set

[0140] In this embodiment, the update of the hyperparameter is determined by the current model order and also represents the distribution of the amplitude gain, so it can be estimated by the second-order moment of the amplitude gain.

[0141] In this embodiment, an algorithm flow that can implement this method is provided.

[0142]

[0143] like Figure 2 As shown in the figure, the average convergence time of the method and two existing joint estimation algorithms, VB-SAGE-G and VB-SAGE-F, under different model orders are also given.

[0144] To ensure fairness in comparison, all parameters are set when initializing. Ω is randomly initialized. The compared algorithms include the variational Bayesian iterative estimation algorithm using Gamma-Gaussian hierarchical prior (VB-SAGE-G) and the variational Bayesian iterative estimation algorithm using Gamma-Flat hierarchical prior (VB-SAGE-F). The average convergence time of the algorithms is compared under the conditions of model order L = 10, 20, 30, and 40, and the number of Monte Carlo runs is 100. Figure 3 As shown in the figure, the results show that using the autocorrelation characteristics of the detection sequence to pre-estimate the delay parameters can reduce the convergence time of the algorithm, and the average convergence time of the proposed algorithm is shorter than that of the existing algorithm.

[0145] In the above-mentioned joint estimation method of wireless channel multipath signal parameters based on variational Bayesian inference, the amplitude gain is first modeled by using Bernoulli Gaussian hierarchical prior to obtain the pruning condition expression, and the delay parameter pre-estimation expression is obtained based on the autocorrelation characteristics of the observed transmitted signal. In addition, under the framework of sparse variational Bayesian inference theory and spatial generalized alternating iterative solution, the number of mirror components, as well as the amplitude gain and dispersion parameter of each mirror component are pre-estimated according to the observed received signal. In each iteration process, the delay under the current number of mirror components is first estimated according to the delay parameter pre-estimation expression. The parameters are estimated, and then the component estimate and dispersion parameter estimate of one mirror component are calculated. Based on the component and dispersion parameter estimates, it is determined whether the pruning condition expression is satisfied. If so, the amplitude gain parameter estimate is calculated. The dispersion parameter estimate includes the delay parameter and the angle parameter estimate. To avoid falling into a local optimum during the solution, the angle parameter estimate introduces an estimated expression for the amplitude gain. If it is not satisfied, the mirror component is pruned, and the parameter estimate of the next mirror component is solved alternately until convergence. The number of mirror components of the observed received signal and the parameter estimate of each mirror component are obtained. Experimental comparison with two existing joint parameter estimation methods demonstrates that this method can effectively improve the solution speed, reduce the convergence time of the iterative solution, and ensure the accuracy of the results.

[0146] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. In addition, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0147] In one embodiment, Figure 3 As shown, a device for joint estimation of multipath signal parameters in wireless channels based on variational Bayesian inference is provided, comprising: an estimation expression obtaining module 200, an observation signal receiving module 210, a joint parameter solving module 220, an iterative parameter updating module 230, and a pruning and multipath signal parameter obtaining module 240, wherein:

[0148] An estimated expression obtaining module 200 is used to model the amplitude gain using a Bernoulli-Gaussian hierarchical prior to obtain a pruning condition expression, and obtain a delay parameter pre-estimate expression based on the autocorrelation characteristics of the observed transmitted signal;

[0149] The observation signal receiving module 210 is used to obtain the observation reception signal, which is obtained based on a single-transmit multiple-receive detection system.

[0150] A joint parameter solving module 220 is configured to pre-estimate the number of mirror components, and the amplitude gain and dispersion parameters of each mirror component based on the observed received signal within the framework of sparse variational Bayesian inference theory and spatial generalized alternating iterative solution;

[0151] An iterative parameter updating module 230 is configured to, during each iteration, first estimate the delay parameter for the current number of mirror components based on a pre-estimated delay parameter expression, then calculate a component estimate and a dispersion parameter estimate for one mirror component, and determine whether the pruning condition expression is satisfied based on the component estimate and the dispersion parameter estimate. If so, calculate an amplitude gain parameter estimate, wherein the dispersion parameter estimate includes a delay parameter and an angle parameter estimate, and the angle parameter estimate incorporates an estimated expression for the amplitude gain.

[0152] The pruning and multipath signal parameter obtaining module 240 is used to prune the mirror component if the condition is not met, and alternately solve the parameter estimation of the next mirror component until convergence, thereby obtaining the number of mirror components of the observed received signal and the parameter estimation of each mirror component.

[0153] Regarding the specific limitations of the device for jointly estimating multipath signal parameters of wireless channels based on variational Bayesian inference, please refer to the limitations of the method for jointly estimating multipath signal parameters of wireless channels based on variational Bayesian inference above, which will not be repeated here. The various modules in the above-mentioned device for jointly estimating multipath signal parameters of wireless channels based on variational Bayesian inference can be implemented in whole or in part by software, hardware, and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above-mentioned modules.

[0154] In one embodiment, a computer device is provided. The computer device may be a terminal, and its internal structure diagram may be as follows: Figure 4 As shown. The computer device includes a processor, a memory, a network interface, a display screen and an input device connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, a method for joint estimation of multipath signal parameters of a wireless channel based on variational Bayesian inference is implemented. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covering the display screen, or a key, trackball or touchpad provided on the computer device housing, or an external keyboard, touchpad or mouse.

[0155] Those skilled in the art will understand that Figure 4 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0156] In one embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the computer program, the following steps are implemented:

[0157] The amplitude gain is modeled using Bernoulli-Gaussian hierarchical priors to obtain the pruning condition expression, and the delay parameter estimation expression is obtained based on the autocorrelation characteristics of the observed transmitted signal.

[0158] Acquire an observation reception signal, where the observation reception signal is obtained based on a single-transmit-multiple-receive detection system.

[0159] Under the framework of sparse variational Bayesian inference theory and spatial generalized alternating iterative solution, the number of mirror components and the amplitude gain and dispersion parameters of each mirror component are pre-estimated based on the observed received signal;

[0160] During each iteration, the delay parameter under the current number of mirror components is first estimated based on the delay parameter pre-estimate expression, and then a component estimate and a dispersion parameter estimate of one mirror component are calculated. It is then determined whether the pruning condition expression is satisfied based on the component estimate and the dispersion parameter estimate. If so, an amplitude gain parameter estimate is calculated, wherein the dispersion parameter estimate includes a delay parameter and an angle parameter estimate, and the angle parameter estimate introduces an estimated expression for the amplitude gain.

[0161] If not, the mirror component is cut off and the parameter estimation of the next mirror component is solved alternately until convergence, thereby obtaining the number of mirror components of the observed received signal and the parameter estimation of each mirror component.

[0162] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the following steps are implemented:

[0163] The amplitude gain is modeled using Bernoulli-Gaussian hierarchical priors to obtain the pruning condition expression, and the delay parameter estimation expression is obtained based on the autocorrelation characteristics of the observed transmitted signal.

[0164] Acquire an observation reception signal, where the observation reception signal is obtained based on a single-transmit-multiple-receive detection system.

[0165] Under the framework of sparse variational Bayesian inference theory and spatial generalized alternating iterative solution, the number of mirror components and the amplitude gain and dispersion parameters of each mirror component are pre-estimated based on the observed received signal;

[0166] During each iteration, the delay parameter under the current number of mirror components is first estimated based on the delay parameter pre-estimate expression, and then a component estimate and a dispersion parameter estimate of one mirror component are calculated. It is then determined whether the pruning condition expression is satisfied based on the component estimate and the dispersion parameter estimate. If so, an amplitude gain parameter estimate is calculated, wherein the dispersion parameter estimate includes a delay parameter and an angle parameter estimate, and the angle parameter estimate introduces an estimated expression for the amplitude gain.

[0167] If not, the mirror component is cut off and the parameter estimation of the next mirror component is solved alternately until convergence, thereby obtaining the number of mirror components of the observed received signal and the parameter estimation of each mirror component.

[0168] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0169] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0170] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art could make various modifications and improvements without departing from the spirit of the present application, all of which fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

Claims

1. A method for joint estimation of multipath signal parameters in wireless channels based on variational Bayesian inference, characterized in that: The method comprises: The amplitude gain is modeled using Bernoulli-Gaussian hierarchical priors to obtain the pruning condition expression, and the delay parameter estimation expression is obtained based on the autocorrelation characteristics of the observed transmitted signal. Acquiring an observation reception signal, where the observation reception signal is obtained based on a single-transmit-multiple-receive detection system; Under the framework of sparse variational Bayesian inference theory and spatial generalized alternating iterative solution, the number of mirror components and the amplitude gain and dispersion parameters of each mirror component are pre-estimated based on the observed received signal; During each iteration, the delay parameter under the current number of mirror components is first estimated based on the delay parameter pre-estimate expression, and then a component estimate and a dispersion parameter estimate of one mirror component are calculated. It is then determined whether the pruning condition expression is satisfied based on the component estimate and the dispersion parameter estimate. If so, an amplitude gain parameter estimate is calculated, wherein the dispersion parameter estimate includes a delay parameter and an angle parameter estimate, and the angle parameter estimate introduces an estimated expression for the amplitude gain. If not, the mirror component is cut off and the parameter estimation of the next mirror component is solved alternately until convergence, thereby obtaining the number of mirror components of the observed received signal and the parameter estimation of each mirror component.

2. The method for joint estimation of multipath signal parameters of wireless channels according to claim 1, characterized in that: The pruning condition expression is expressed as: ； In the above formula, the left side term represents the The signal-to-noise ratio on the mirror component, the right-hand side term represents the threshold of the change, where Indicates the The amplitude gain on the mirror component, represents the variance, and represents a hyperparameter.

3. The method for joint estimation of multipath signal parameters of wireless channels according to claim 1, wherein: The delay parameter pre-estimation expression is expressed as: ； In the above formula, represents the impulse function, for exist The sampling value at represents the estimated expression of the introduced amplitude gain, Indicates the angle of incidence The steering vector formed, belong Indicates known Periodic detection sequence, represents the conjugate complex number of .

4. The method for joint estimation of multipath signal parameters of wireless channels according to any one of claims 1 or 2, characterized in that: Before estimating the number and parameters of mirror components under the framework of sparse variational Bayesian inference theory and spatial generalized alternating iterative solution, the number of mirror components is initialized according to a preset number. At the same time, the component estimation of the mirror components and the dispersion parameter estimation are randomly initialized.

5. The method for joint estimation of multipath signal parameters of wireless channels according to claim 2, characterized in that: The estimation expression of the amplitude gain is introduced in the angle parameter estimation, and the angle parameter estimation expression is expressed as: ； In the above formula, Represents the component estimate obtained in the current iteration, represents the delay estimate obtained in the current iteration, The estimated expression for the introduced amplitude gain is expressed as represents the incident angle estimate obtained in the current iteration, Indicates that the last iteration obtained The incidence angle estimation of the specular component, Indicates the The second moment of the noise vector of the specular component, represents the conjugate transpose of the matrix, Represents the detection signal vector.

6. A device for joint estimation of multipath signal parameters in wireless channels based on variational Bayesian inference, characterized in that: The device comprises: An estimation expression obtaining module is used to model the amplitude gain using a Bernoulli-Gaussian hierarchical prior to obtain a pruning condition expression, and obtain a delay parameter pre-estimation expression based on the autocorrelation characteristics of the observed transmitted signal; An observation signal receiving module is used to obtain an observation reception signal, where the observation reception signal is obtained based on a single-transmit-multiple-receive detection system; A joint parameter solution module is used to pre-estimate the number of mirror components and the amplitude gain and dispersion parameters of each mirror component based on the observed received signal under the framework of sparse variational Bayesian inference theory and spatial generalized alternating iterative solution; an iterative parameter updating module, configured to, during each iteration, first estimate the delay parameter for the current number of mirror components based on a pre-estimated delay parameter expression, then calculate a component estimate and a dispersion parameter estimate for one mirror component, and determine whether the pruning condition expression is satisfied based on the component estimate and the dispersion parameter estimate; if so, calculate an amplitude gain parameter estimate, wherein the dispersion parameter estimate includes a delay parameter and an angle parameter estimate, and the angle parameter estimate introduces an estimated expression for the amplitude gain; The pruning and multipath signal parameter acquisition module is used to prune the mirror component if it is not satisfied, and alternately solve the parameter estimation of the next mirror component until convergence, thereby obtaining the number of mirror components of the observed received signal and the parameter estimation of each mirror component.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 5 are implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

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