DOA estimation method for wideband signals based on message passing algorithm

Abstract

The present invention discloses a DOA estimation method for broadband signals based on a message passing algorithm, and the steps are as follows: S1: construct a statistical model according to a signal model; then express the joint distribution of the statistical model in the form of multiplication of polynomials according to the Bayesian chain rule; S2: record the polynomials as factor nodes, and the variables in each polynomial as variable nodes, and connect the factor nodes and the variable nodes in turn according to the distribution form of each polynomial, that is, express the statistical model in the form of a factor graph; S3: derive the update formula of the variable through multiple rules; S4: start from the observation node again, update and iterate different messages in turn according to the order of message passing, and calculate the confidence of each variable node, so as to obtain the estimated value of the variable, and then determine the position of the non-zero element according to the sparsity of the estimated value, so as to determine the corresponding grid angle, and improve the DOA estimation accuracy. The method improves the estimation accuracy of the algorithm while ensuring the convergence of the algorithm.

Description

Technical Field

[0001] The invention belongs to the technical field of wireless communications, and in particular relates to a DOA estimation method for broadband signals based on a message passing algorithm. Background Art

[0002] Since the second generation of mobile networks (2G), wireless positioning has been an important feature of mobile communication systems, and the positioning accuracy of each generation has been continuously improved. In the fifth generation (5G) mobile network, positioning is considered to be one of its key features because it is the basic premise of various location-based services. Although 5G mobile networks are being gradually deployed, the International Telecommunication Union has proposed the key features of the sixth generation (6G) mobile communication in "Network 2030". At the same time, "Key Drivers and Research Challenges of 6G Wireless Intelligence Everywhere" points out that integrated sensing (ISAC) is a key function of the next generation of wireless communication (6G) and a key enabling technology to promote the integration of the future physical, biological and digital worlds. Angle of arrival estimation (DOA) can not only realize the azimuth perception of the incident signal, but also is an important part of the channel estimation of the wireless communication system. Therefore, a high-precision DOA estimation algorithm can improve the communication quality and perceive users more accurately. In the 6G system, higher frequency bands (from millimeter waves to terahertz), wider bandwidths and larger antenna arrays will be used to closely integrate RF sensing and communication, enhance each other, and thus reduce the overall cost.

[0003] Therefore, high-precision broadband DOA algorithms have always attracted extensive attention from scholars and industry at home and abroad. The existing broadband DOA estimation algorithms are all the extension of narrowband DOA estimation algorithms to broadband. They all assume that the frequency band occupancy is the same, but this assumption does not conform to the actual situation. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a DOA estimation method for broadband signals based on a message passing algorithm. The present invention provides a DOA estimation method for broadband signals based on a message passing algorithm, which can be applied to broadband, large-scale MIMO mobile communication systems to achieve high-precision direction perception and channel estimation.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is: the DOA estimation method of the broadband signal based on the message passing algorithm specifically comprises the following steps:

[0006] S1: constructing a statistical model according to the signal model; and then expressing the joint distribution of the statistical model in the form of multiplication of polynomials according to the Bayesian chain rule;

[0007] S2: Record the polynomials as factor nodes, record the variables in each polynomial as variable nodes, and connect the factor nodes and the variable nodes in turn according to the distribution form of each polynomial, so as to express the statistical model in the form of a factor graph;

[0008] S3: Derivation of variable update formulas through multiple rules;

[0009] S4: Starting from the observation node again, different messages are updated and iterated in turn according to the order of message transmission, and the confidence of each variable node is calculated to obtain the estimated value of the variable until the algorithm converges or the iteration termination condition is met, and the optimal estimated value with estimated variables is obtained. Then, according to the sparsity of the estimated value, the position of the non-zero element is determined to determine the corresponding grid angle, thereby improving the DOA estimation accuracy.

[0010] Adopting the above technical scheme, firstly, a sparse signal statistical model is established according to the characteristics of the incident signal, and then the variables in the statistical model are represented by a factor graph, and then the update formula of the position variable is obtained by multiple rules of BP, EP, and MF; wherein the statistical model is represented as a factor graph, and the specific relationship between each factor node and the variable node and the distribution form of the probability density function can be known from the graph subgraph, so as to divide different message nodes, and calculate the message of each node by using different message transmission rules, and finally, starting from the observation, according to the direction of message transmission, iterative update is carried out in sequence according to the iterative update order of each message, so as to design a high-precision DOA estimation algorithm. The present invention gives full play to the advantages of each rule, improves the estimation accuracy of the algorithm and ensures the convergence of the algorithm.

[0011] Preferably, the signal model in step S1 is a broadband signal model, which is expressed as:

[0012]

[0013] Where N is the number of grid divisions of the overcomplete dictionary, M is the number of sensors in the ULA array, F is the number of subbands after the received signal is converted into a frequency domain signal by DFT, and y f ∈C M×1 is the observed data, is a first-order approximation to an overcomplete dictionary A f is the grid dictionary, B f A f The derivative of f =diag(β f ) is the deviation of the true angle from the grid β f The diagonal matrix formed by f ∈C N×1 is the amplitude vector of the source, C is a set of complex numbers, w nis complex Gaussian noise.

[0014] Preferably, the step S1 of constructing a statistical model according to the signal model is specifically: f ∈C M×1 Subject to complex Gaussian noise with precision α0, C is a set of complex numbers, and the likelihood function is expressed as α0 follows the Gamma distribution with parameters a and b, denoted as x f The precision matrix is ​​Λ f =diag(α f ), α f The Gamma distribution with parameters c and d is denoted as {α f} f＝1：F It follows the G distribution, where G is a random measure of the Dirichlet process DP(G|γ, G0) with parameters γ and G0, and is obtained by the intercept method. Among them, π k The Beta distribution is recorded as γ follows the Gamma distribution with parameters e and h, denoted as The allocation vector zf follows a multinomial distribution When the conditional probability distribution of xf is where 1{z f =k} ​​represents x f When the kth type f The kth position value of is 1 and the rest are 0.

[0015] Preferably, in step S1, the joint distribution p({y f} f＝1：F ,θ) is expressed as a polynomial multiplication, the formula is:

[0016]

[0017] in, It is the implicit variable of the statistical model, in which the hyperparameter set {a, b, c, d, e, h} are all smaller than zero.

[0018] Preferably, the factor graph representation of the statistical model in step S2 is specifically as follows: the variables and distribution in the polynomial distribution of the statistical model are represented by variable nodes and factor nodes respectively, and the factor nodes and the variable nodes are connected to form a factor graph.

[0019] Preferably, in step S3, the variable formula is derived based on the MF rule, the BP rule and the EP rule respectively and by integrating the MF rule, the BP rule and the EP rule.

[0020] Preferably, in step S3, each variable based on the message passing algorithm is updated in a cyclic iteration, and this iteration assumes that the result of the previous iteration is known, and the current variable is more detailed, and other variables are assumed to remain unchanged; the specific steps are:

[0021] S31: Obtain sparse signal x through MF rule f The update formula is expressed as:

[0022]

[0023]

[0024]

[0025] Among them, φ f，k is the matching vector z f The expected value of Γ f is x f The precision value, u f is x f Expected value;

[0026] S32: Obtaining intermediate variable parameters through MF rules The update formula is expressed as:

[0027]

[0028] Among them, δ f，i is Γ f The i-th element of the diagonal, u f，i is the vector u f The i-th element of ;

[0029] S33: Derivation of allocation variables through BP-MF rules The update formula is expressed as:

[0030]

[0031]

[0032]

[0033] in, Δ k =diag(β k );

[0034] S34: The update formula of the discrete degree parameter γ is obtained by the MF rule, which is expressed as:

[0035]

[0036] S35: Obtain the stick theorem variable π through the EP-BP-MF rule k The update formula is expressed as:

[0037]

[0038] in,

[0039]

[0040]

[0041] The normalization constant is expressed as:

[0042]

[0043]

[0044]

[0045] S36: The update formula of the noise accuracy α0 is obtained by the MF rule, which is expressed as:

[0046]

[0047] S37: Obtaining the off-grid deviation β through the EM rule k The update formula is expressed as:

[0048]

[0049]

[0050] The above formula is a loop iteration update. The default for this iteration is given in the previous iteration. For example, φ in step S31 f，k In step S33, π is given. k′ The update is given in step S35; the only known variables are {y f , A f , B f} f＝1：F , and the rest are intermediate variables, i.e. hidden variables.

[0051] Preferably, the step S4 is specifically as follows: the step S4 is specifically as follows: inputting the observation value y f , A f , B f, set the algorithm's iteration termination condition Thr and maximum number of iterations Itmax, initialize implicit variables θ and hyperparameters {a, b, c, d, e, h}; starting from the observation node, update different messages in turn according to the order of message transmission, and calculate the confidence of each variable node, that is, get x in turn f Update value, Update value, Update value, π k Update value, γ update value, α0 update value and β k Update the value until the algorithm converges or meets the iteration termination condition, so as to find {x f} f＝1：F The estimated value of the variable; that is, x f The optimal estimate, then according to {x f} f＝1：F The sparsity of , determines the position of non-zero elements to determine the corresponding grid angle, and completes β k Off-grid angle, improves DOA estimation accuracy.

[0052] Compared with the prior art, the present invention has the following beneficial effects: firstly, a sparse signal statistical model is established according to the characteristics of the incident signal, and secondly, the variables in the statistical model are represented by a factor graph, and then the update formula of the position variable is obtained by multiple rules such as BP, EP, and MF; wherein the statistical model is represented as a factor graph, and the specific relationship between each factor node and the variable node and the distribution form of the probability density function can be known from the graph subgraph, so as to divide different message nodes, calculate the message of each node by using different message transmission rules, and finally, starting from the observation, according to the direction of message transmission, iteratively update in the iterative update order of each message in turn, so as to design a high-precision DOA estimation algorithm. The present invention gives full play to the advantages of each rule, improves the estimation accuracy of the algorithm and ensures the convergence of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 The present invention is a flow chart of a method for estimating DOA of a broadband signal based on a message passing algorithm.

[0054] Figure 2 It is a factor graph of the statistical model of the DOA estimation method for broadband signals based on the message passing algorithm of the present invention. DETAILED DESCRIPTION

[0055] The embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the protection scope of the present invention.

[0056] Example: Figure 1As shown, the DOA estimation method of the broadband signal based on the message passing algorithm specifically includes the following steps:

[0057] S1: constructing a statistical model according to the signal model; and then expressing the joint distribution of the statistical model in the form of multiplication of polynomials according to the Bayesian chain rule;

[0058] The signal model in step S1 is a broadband signal model, which is expressed as:

[0059]

[0060] Where N is the number of grid divisions of the overcomplete dictionary, M is the number of sensors in the ULA array, F is the number of subbands after the received signal is converted into a frequency domain signal by DFT, and y f ∈C M×1 is the observed data, is a first-order approximation to an overcomplete dictionary A f is the grid dictionary, B f A f The derivative of f =diag(β f ) is the deviation of the true angle from the grid β f The diagonal matrix formed by f ∈C N×1 is the amplitude vector of the source, C is a set of complex numbers, w n is complex Gaussian noise;

[0061] The statistical model constructed according to the signal model in step S1 is specifically: f ∈C M×1 Subject to complex Gaussian noise with precision α0, C is a set of complex numbers; the likelihood function is expressed as α0 follows the Gamma distribution with parameters a and b, denoted as x f The precision matrix is ​​Λ f =diag(α f ), α f The Gamma distribution with parameters c and d is denoted as {α f} f＝1：F It follows the G distribution, where G is a random measure of the Dirichlet process DP(G|γ, G0) with parameters γ and G0, and is obtained by the intercept method. Among them, π k The Beta distribution is recorded as γ follows the Gamma distribution with parameters e and h, denoted as Assign vector z fFollows multinomial distribution When the conditional probability distribution of xf is where 1{z f =k} ​​means that when xf is of the kth category, the kth position value of zf is 1 and the rest are 0.

[0062] In step S1, the joint distribution p({y f} f＝1：F ,θ) is expressed as a polynomial multiplication, the formula is:

[0063]

[0064] in, It is the implicit variable of the statistical model, in which the hyperparameter set {a, b, c, d, e, h} are all smaller than zero;

[0065] S2: Record the polynomials as factor nodes, record the variables in each polynomial as variable nodes, and connect the factor nodes and the variable nodes in turn according to the distribution form of each polynomial, so as to express the statistical model in the form of a factor graph;

[0066] The factor graph representation of the statistical model in step S2 is specifically as follows: the variables and distribution in the polynomial distribution of the statistical model are represented by variable nodes and factor nodes respectively, and the factor nodes and the variable nodes are connected to form a factor graph, such as Figure 2 As shown;

[0067] S3: Derivation of variable update formulas through multiple rules;

[0068] In step S3, variable formulas are derived based on the MF rule, the BP rule and the EP rule respectively and by integrating the MF rule, the BP rule and the EP rule;

[0069] The step S3 is specifically as follows:

[0070] S31: Obtain sparse signal x through MF rule f The update formula is expressed as:

[0071]

[0072]

[0073]

[0074] Among them, φ f，k is the matching vector z f The expected value of Γ f is x f The precision value, uf is x f Expected value;

[0075] S32: Obtaining intermediate variable parameters through MF rules The update formula is expressed as:

[0076]

[0077] Among them, δ f，i is Γ f The i-th element of the diagonal, u f，i is the vector u f The i-th element of ;

[0078] S33: Derivation of allocation variables through BP-MF rules The update formula is expressed as:

[0079]

[0080]

[0081]

[0082] in, Δ k =diag(β k );

[0083] S34: The update formula of the discrete degree parameter γ is obtained by the MF rule, which is expressed as:

[0084]

[0085] S35: Obtain the stick theorem variable π through the EP-BP-MF rule k The update formula is expressed as:

[0086]

[0087] in,

[0088]

[0089]

[0090] The normalization constant is expressed as:

[0091]

[0092]

[0093]

[0094] S36: The update formula of the noise accuracy α0 is obtained by the MF rule, which is expressed as:

[0095]

[0096] S37: Obtaining the off-grid deviation β through the EM rule k The update formula is expressed as:

[0097]

[0098]

[0099] The above formula is a loop iteration update. The default for this iteration is given in the previous iteration. For example, φ in step S31 f，k In step S33, π is given. k′ The update is given in step S35; the only known variables are {y f , A f , B f} f＝1：F , the rest are intermediate variables, i.e. hidden variables;

[0100] S4: Starting from the observation node again, different messages are updated and iterated in turn according to the order of message transmission, and the confidence of each variable node is calculated to obtain the estimated value of the variable until the algorithm converges or the iteration termination condition is met, and the optimal estimated value with estimated variable is obtained. Then, according to the sparsity of the estimated value, the position of the non-zero element is determined to determine the corresponding grid angle, thereby improving the DOA estimation accuracy;

[0101] The step S4 is specifically as follows: inputting the observed value y f , A f , B f , set the algorithm's iteration termination condition Thr and maximum number of iterations Itmax, initialize implicit variables θ and hyperparameters {a, b, c, d, e, h}; starting from the observation node, update different messages in turn according to the order of message transmission, and calculate the confidence of each variable node, that is, get x in turn f Update value, Update value, Update value, π k Update value, γ update value, α0 update value and β k Update the value until the algorithm converges or meets the iteration termination condition, so as to find {x f} f＝1：F The estimated value of the variable; that is, x f The optimal estimate, then according to {x f} f＝1：FThe sparsity of , determines the position of non-zero elements to determine the corresponding grid angle, and completes β k Off-grid angle, improves DOA estimation accuracy.

[0102] For ordinary technicians in this field, the specific embodiments are only illustrative descriptions of the present invention. It is obvious that the specific implementation of the present invention is not limited to the above-mentioned methods. As long as various non-substantial improvements are made using the method concepts and technical solutions of the present invention, or the concepts and technical solutions of the present invention are directly applied to other occasions without improvement, they are all within the protection scope of the present invention.

Claims

1. A DOA estimation method for broadband signals based on a message passing algorithm, characterized in that: The specific steps include: S1: constructing a statistical model according to the signal model; and then expressing the joint distribution of the statistical model in the form of multiplication of polynomials according to the Bayesian chain rule; S2: Record the polynomials as factor nodes, record the variables in each polynomial as variable nodes, and connect the factor nodes and the variable nodes in turn according to the distribution form of each polynomial, so as to express the statistical model in the form of a factor graph; S3: Derivation of variable update formulas through multiple rules; S4: Starting from the observation node, different messages are updated and iterated in turn according to the order of message transmission, and the confidence of each variable node is calculated to obtain the estimated value of the variable. Then, according to the sparsity of the estimated value, the position of the non-zero element is determined to determine the corresponding grid angle, thereby improving the DOA estimation accuracy. The signal model in step S1 is a broadband signal model, which is expressed as: Where N is the number of grid divisions of the overcomplete dictionary, M is the number of sensors in the ULA array, F is the number of subbands after the received signal is converted into a frequency domain signal by DFT, and y f ∈C M×1 is the observed data, is a first-order approximation to an overcomplete dictionary A f is the grid dictionary, B f A f The derivative of f =diag(β f ) is the deviation of the true angle from the grid β f The diagonal matrix formed by f ∈C N×1 is the amplitude vector of the source, C is a set of complex numbers, w n is complex Gaussian noise; The step S1 of constructing a statistical model according to the signal model is specifically as follows: w f ∈C M×1 Subject to complex Gaussian noise with precision α0, C is a set of complex numbers; the likelihood function is expressed as α0 follows the Gamma distribution with parameters a and b, denoted as x f The precision matrix is ​​Λ f =diag(α f )’s Gaussian distribution, α f The Gamma distribution with parameters c and d is denoted as {α f } f＝1:F It follows the G distribution, where G is a random measure of the Dirichlet process DP(G|γ,G0) with parameters γ,G0, and is obtained by the intercept method. Among them, π k The Beta distribution is recorded as γ follows the Gamma distribution with parameters e and h, denoted as Assign vector z f Follows multinomial distribution When x f The conditional probability distribution of where 1{z f =k} ​​represents x f When the kth type f The kth position value of is 1 and the rest are 0. In step S1, the joint distribution p({y f } f＝1:F ,θ) is expressed as a polynomial multiplication, the formula is: in, It is the implicit variable of the statistical model, in which the hyperparameter set {a, b, c, d, e, h} are all smaller than zero; In step S3, variable formulas are derived based on the MF rule, the BP rule and the EP rule respectively and by integrating the MF rule, the BP rule and the EP rule; In step S3, each variable based on the message passing algorithm is updated in a cyclic iteration. In this iteration, the result of the previous iteration is assumed to be known, and the current variable is more detailed. Other variables are assumed to remain unchanged. The specific steps are: S31: Obtain sparse signal x through MF rule f The update formula is expressed as: Among them, φ f,k is the matching vector z f The expected value of Γ f is x f The precision value, u f is x f Expected value; S32: Obtaining intermediate variable parameters through MF rules The update formula is expressed as: Among them, δ f,i is Γ f The i-th element of the diagonal, u f,i is the vector u f The i-th element of ; S33: Derivation of allocation variable update formula through BP-MF rule It is expressed as: Among them, D k =diag(β k ); S34: The update formula of the discrete degree parameter γ is obtained by the MF rule, which is expressed as: S35: Obtain the stick theorem variable π through the EP-BP-MF rule k The update formula is expressed as: in, The normalization constant is expressed as: S36: The update formula of the noise accuracy α0 is obtained by the MF rule, which is expressed as: S37: Obtaining the off-grid deviation β through the EM rule k The update formula is expressed as:

2. The DOA estimation method for broadband signals based on the message passing algorithm according to claim 1, characterized in that: The factor graph representation of the statistical model in step S2 is specifically as follows: the variables and distribution in the polynomial distribution of the statistical model are represented by variable nodes and factor nodes respectively, and the factor nodes and the variable nodes are connected to form a factor graph.

3. The DOA estimation method for broadband signals based on the message passing algorithm according to claim 1, characterized in that: The step S4 is specifically as follows: inputting the observed value y f , A f , B f , set the algorithm's iteration termination condition Thr and maximum number of iterations Itmax, initialize implicit variables θ and hyperparameters {a, b, c, d, e, h}; starting from the observation node, update different messages in turn according to the order of message transmission, and calculate the confidence of each variable node, that is, get x in turn f Update value, Update value, Update value, π k Update value, γ update value, α0 update value and β k Update the value until the algorithm converges or the iteration termination condition is met, so as to find {xf} f＝1：F The estimated value of the variable; that is, x f The optimal estimate, then according to {x f } f＝1：F The sparsity of , determines the position of non-zero elements to determine the corresponding grid angle, and completes β k Off-grid angle, improves DOA estimation accuracy.

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