A Joint Channel Estimation and Signal Detection Method Based on Angular Delay Sparsity

Abstract

The present invention belongs to the field of wireless communication technologies, and particularly relates to a joint channel estimation and signal detection method based on angular-delay sparsity. The present invention proposes a joint channel estimation and signal detection framework based on EM and approximate message passing. The framework includes two modules: Module A is an angular-delay ultra-precision parameter estimator based on EM; Module B is a channel and signal estimator based on approximate message passing. The framework uses an iterative update strategy, taking the output of the parameter estimator at the previous moment as the input of the channel and signal estimator to complete the update of the channel and signal estimation; then using the updated channel and signal estimation as the input of the parameter estimator to obtain the updated parameters. The two modules iterate alternately until the algorithm converges. By utilizing the sparsity of the channel in the angular-delay domain, the present invention can reduce the pilot overhead.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication, and particularly relates to a joint channel estimation and signal detection method based on angular-delay sparsity. Background Art

[0002] The large-scale MIMO technology has greatly improved the system capacity and transmission reliability. As a multi-carrier modulation technology, orthogonal frequency division multiplexing (OFDM) has advantages such as high spectral efficiency and anti-multipath fading. In the academic and industrial fields, the combination of large-scale MIMO and OFDM technologies - large-scale MIMO-OFDM technology has been widely studied and applied in various fields of wireless communication. For large-scale MIMO systems, it is noted that the scattering effect of electromagnetic waves will cause the electromagnetic waves received by the antenna array to have a spreading phenomenon in the angular domain. This makes the channel exhibit the so-called sparse correlation, that is, the non-zero elements in the angular domain appear clustering effect. At the same time, the commonly used model for OFDM communication channels is the delay tap model, which exhibits frequency-selective characteristics in the frequency domain. In the actual transmission environment of large-scale MIMO-OFDM, due to the existence of a large number of randomly located scatterers, the channel is sparse in both the angular domain and the delay domain. Accurately obtaining the channel state information (CSI) is essential to achieve various gains. However, as the antenna dimension increases and parameters such as the noise power in the system are unknown, the pilots required to obtain accurate CSI become increasingly challenging, and the required pilot overhead also increases. Therefore, it is particularly important to find a joint channel estimation and signal detection scheme that reduces the pilot overhead. We will use the sparse characteristics of the channel in the delay-angular domain to design an efficient channel estimation algorithm under the Bayesian framework. Summary of the Invention

[0003] The object of the present invention is to propose a MIMO-OFDM joint channel estimation and signal method. For a half-wavelength uniform linear antenna array (ULA), under the uniform sampling grid and DFT basis, a virtual channel representation model is used to characterize the large-scale MIMO-OFDM channel. Since the lattice representation will cause problems such as energy leakage, and at the same time, in order to reduce the pilot overhead, a method is needed to accurately estimate the representation of the channel in the angular-delay domain so as to achieve a lower bit error rate. In view of this, the present invention models the sampling grid in the angular domain as non-uniform and takes the positions of each lattice point as system parameters to be estimated. And the estimation of the system parameters is updated by the EM algorithm to reduce the error between the model and the actual channel.

[0004] The solution of the present invention is based on the EM algorithm and the Bayesian framework, and includes two modules: a system parameter estimator A and a channel and signal estimator B. In module A, the system parameters are updated, and the updated system parameters are input into module B. Then, module B updates the channel and signal estimation values with the updated system parameters. The two modules iterate alternately to optimize the estimation values until convergence.

[0005] The technical solution adopted by the present invention is: a joint channel estimation and signal detection method for MIMO-OFDM based on approximate message passing, which is used for an MIMO-OFDM system. It is defined that the base station in the system is configured with M antennas, and the arrangement is a uniform linear array, serving 1 single-antenna user, and using N c sub-carriers for OFDM modulation. The wavelength corresponding to the center frequency of the OFDM carrier is ε, and the system sampling interval is T s , and the cyclic prefix length is N g , and it includes the following steps:

[0006] S1. Construct a channel model in the angular-delay domain: First, set the discretized angle-of-arrival grid as the discretized delay grid as Then the channel in the angular-delay domain can be expressed as the form of the product of a steering vector matrix, an angular-delay channel impulse response, and a delay response matrix. It is represented by the following formula:

[0007]

[0008] Among them, is a matrix composed of steering vectors, is a sparse channel matrix in the angular-delay domain, is a matrix composed of delay response vectors. Among them, the steering vector and the delay response vector are respectively represented by the following formulas:

[0009]

[0010]

[0011] S2. Model the received signal, and represent the received signal in the form of the product of a channel matrix and a transmitted signal matrix plus superimposed noise, as shown in the following formula:

[0012] Y = HX + N

[0013] = V(θ)AW(τ) T X + N

[0014] Among them is the transmitted signal matrix, which is a diagonal matrix, and the elements on the diagonal represent the data transmitted on each subcarrier within one OFDM symbol. The transmitted data includes pilot symbols and user data, and the comb-shaped pilot pattern is adopted with a pilot interval of △N. Let the pilot position be N t , and the data position be N d . N represents the external additive white Gaussian noise, and its statistical characteristics are modeled as a complex Gaussian distribution with zero mean and variance .

[0015] S3. Construct a probability model, specifically: Define Assume the noise is AWGN, then

[0016]

[0017] Assume the signals are independently generated, that is:

[0018]

[0019] The channel matrix in the angular-delay domain is modeled as the following distribution:

[0020]

[0021] where the element in the l-th row and k-th column of C is a binary state variable indicating whether the corresponding element in A is 0, and it is independently and identically distributed according to the Bernoulli distribution where λ represents the Bernoulli parameter. Then the marginal distribution of the element in the l-th row and k-th column of A is

[0022]

[0023] S4. Obtain and solve the problem for joint channel estimation and signal detection, specifically: Given the prior distribution, the maximum a posteriori estimator is given by the following formula:

[0024]

[0025] For the unknown parameter being Then according to the EM algorithm, the posterior probability is given by the following formula:

[0026]

[0027] where H(·) is the entropy function, and q is any probability distribution q(A,X|Y) of A and X.

[0028] For computational convenience, assume that the probability density q(A,X|Y) can be written as the product of the following probability densities:

[0029]

[0030] At this time, q(A, X|Y) can be regarded as an approximation of the accurate posterior probability p(A, X|Y). Among them, the probability densities p(x n |Y; Ψ) and (s lk |Y; Ψ) can be approximately obtained through the output of module B.

[0031] First, according to the initialization parameter Ψ (0) , the posterior mean and variance are solved through module B. The posterior mean and variance output from module B are input into module A, and the parameters are updated through the EM algorithm. The specific steps are as follows:

[0032] S41. Implement parameter update in module A, specifically:

[0033] E-step: If it is the 0th iteration, directly output the initial parameter Ψ (0) ; For the jth (j≠0) iteration, let

[0034]

[0035] M-step: Update Ψ through the following formula (j+1)

[0036]

[0037] S42. Module B calculates the estimated values of the channel and the transmitted signal. First, the system parameter Ψ is obtained from S41, and then and The system model is updated as shown in the following formula:

[0038]

[0039] Define The system joint distribution is given by the following formula:

[0040]

[0041] Construct a factor graph through the joint distribution and calculate the messages transmitted on each edge of the factor graph. Through the bilinear generalized approximate message passing algorithm (BiGAMP), the posterior probabilities of the angular delay domain channel and the transmitted signal can be calculated, and the posterior mean and variance of the channel, as well as the posterior mean and variance of the signal can be calculated. Among them, The matrix formed by is The estimated value of The matrix formed by is the estimated value of A.

[0042] Next, through an estimate of X is obtained, and the formula is as follows

[0043]

[0044] where w kn is the element in the k-th row and n-th column of W(τ) T .

[0045] S43. If the algorithm converges, it ends and obtains and Otherwise, substitute the posterior probability density obtained in S42 back into S41 for continued iteration.

[0046] The beneficial effects of the present invention are as follows: It can be used in a large-scale MIMO-OFDM communication system. By configuring a large-scale antenna array on the base station side, the channel is transformed into the angular-delay domain, and the sparsity of the channel in the angular-delay domain is fully utilized, which can reduce the pilot overhead for joint channel estimation and signal detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is the application environment diagram in the embodiment.

[0048] Figure 2 is the structural schematic diagram of joint channel estimation and signal detection based on message passing in the embodiment.

[0049] Figure 3 is the schematic diagram of the factor graph based on message passing in the embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0050] In order to make the objectives, technical solutions, and advantages of the present application clearer, the following further describes the specific embodiments of the present invention in detail with reference to the drawings. The receiver flowchart of the present invention is as Figure 2 shown, including two modules, module A and module B. Among them, module A is used to estimate the parameters of the system, and module B jointly estimates the channel and the signal.

[0051] S1. Channel modeling in the angular-delay domain, specifically: As Figure 1 shown, assume that the base station is configured with M antennas to serve 1 single-antenna user. Use N c subcarriers for OFDM modulation. The cyclic prefix length is N g , then the durations of the OFDM symbols with and without the cyclic prefix are respectively expressed as T sym =(N c +N g ) and T c =N c T s , where Ts Denote the system sampling interval. Assume that the channel remains unchanged within one OFDM symbol period and varies for different OFDM symbol periods. In any OFDM symbol period, there are only P paths from the user side to the base station side, and the path attenuation of the p-th path is α p , and the angle of arrival (AoA) is θ p , and the propagation delay is τ p , using the physical channel model method, the uplink channel frequency response vector on the n-th subcarrier can be expressed as the following formula:

[0052]

[0053] where v(θ) is the steering vector of the channel. Assume that the receiving end is a ULA, and the channel steering vector can be expressed as:

[0054]

[0055] where ε is the wavelength of the center frequency of the OFDM carrier, d is the spacing between adjacent array elements, j represents the imaginary part, and [·] T is the transpose operation.

[0056] Let denote the set composed of L discrete angle sampling grid points, and the covered angle range is denote the set composed of K discrete angle sampling grid points, and the covered time range is [0, T s ). In the present invention, τ takes equally spaced sampling, that is, W(τ) is a matrix composed of some columns in the discrete Fourier transform (DFT) matrix.

[0057] is the set composed of the true AoAs. When L is large enough such that , the system channel matrix for all subcarriers can be expressed as:

[0058]

[0059] where is the matrix composed of the steering vectors, is the sparse channel matrix in the angle-delay domain. is the matrix composed of the delay response vectors, where the delay response vector is expressed as the following formula:

[0060]

[0061] S2. Modeling of the received signal, specifically: Denote the signal sent by the user as where the comb-shaped pilot pattern is adopted, and the pilot interval is △N. Define N tis a vector composed of pilot positions, N d is a vector composed of data positions. The transmitted signal is represented as a diagonal matrix Then the received signal at the base station can be expressed as

[0062] Y = HX + N

[0063] = V(θ)AW(τ) T X + N

[0064] where represents noise, modeled as Gaussian white noise with zero mean and variance .

[0065] S3. Construct a probability model, specifically: Define Assume the noise is AWGN, then

[0066]

[0067] Assume the signals are independently generated, that is:

[0068]

[0069] The channel matrix in the angle-delay domain is modeled as the following distribution:

[0070]

[0071] where the element in the l-th row and k-th column of C is a binary state variable indicating whether the corresponding element in A is 0, and it is independently and identically distributed according to the Bernoulli distribution where λ represents the Bernoulli parameter. Then the marginal distribution of the element in the l-th row and k-th column of A is

[0072]

[0073] S4. Obtain and solve the problem for joint channel estimation and signal detection, specifically: Given the prior distribution, the maximum a posteriori estimator is given by the following formula:

[0074]

[0075] The unknown parameters are Then according to the EM algorithm, the posterior probability is given by the following formula:

[0076]

[0077] where H(·) is the entropy function, and q is any probability distribution about A and X.

[0078] For the convenience of calculation, assume that q(A, X|Y) can be decomposed into the following form of multiplying probabilities:

[0079]

[0080] At this time, q(A, X|Y) can be regarded as an approximation of the accurate posterior probability p(A, X|Y). Among them, p(x n |Y; Ψ), p(s lk |Y; Ψ) can be approximately obtained through the output of module B.

[0081] As Figure 2 shown, first, according to the initialization parameter Ψ (0) , the posterior mean and variance are solved through module B. The posterior mean and variance output from module B are input into module A, and the parameters are updated through the EM algorithm. The specific steps are as follows:

[0082] S41. Implement parameter update in module A, specifically:

[0083] Use the EM algorithm to estimate the system parameters. The specific steps are:

[0084] If it is the 0th iteration, output the initial parameter Ψ (0) , and the initial parameter Ψ (0) is defined by the following formula:

[0085] λ (0) = 0.1, consisting of equally spaced sampled grid points from above}{

[0086] If it is the (j + 1)th iteration, then update the parameters through the following steps: Specifically:

[0087] First, obtain q (j) (A, X|Y) through the following formula:

[0088]

[0089] where q (j) (A, X|Y) is an approximation of the posterior probability p(A, X|Y; Ψ (j) ). p(x n |Y; Ψ (j) ), p(s lk |Y; Ψ (j) ) is obtained from the output of module B.

[0090] Then update Ψ through the following formula,

[0091]

[0092] The specific steps are:

[0093] Update θ using the gradient descent algorithm l ,

[0094]

[0095] where ξ is the step size, which is given by the following formula:

[0096]

[0097] where v l represents the l-th column of V(θ), and y n represents the n-th column of Y, is the element in the l-th row and n-th column of, where

[0098] is updated by the following formula

[0099]

[0100] λ is updated by the following formula:

[0101]

[0102] is updated by the following formula

[0103]

[0104] S42. Module B calculates the estimated values of the channel and the transmitted signal. Specifically: First, the system parameter Ψ is obtained from S4. Then, based on the observed values, the bilinear generalized approximate message passing algorithm BiGAMP is used to calculate that the messages from the factor nodes to the variable nodes are approximately Gaussian distributed to obtain the mean and variance. The specific steps are as follows:

[0105] Define and Then the system model is updated as shown in the following formula:

[0106]

[0107] Define Then the system joint distribution is given by the following formula:

[0108]

[0109] Construct a factor graph according to the joint distribution, as Figure 3 shown for an L = 3, K = 2, N cSchematic diagram of a factor graph with = 2, where the first sub - carrier transmits a pilot signal and the second sub - carrier transmits user data. Then, this application proposes to calculate the messages on the factor graph through the bilinear approximation message passing algorithm. Based on the observations Calculate the message passed to the variable node is approximately Gaussian distributed with mean {p ln}, and variance Specifically, it can be shown by the following formula in sequence:

[0110] For n ∈ N t :

[0111]

[0112]

[0113] For n ∈ N d :

[0114]

[0115]

[0116]

[0117]

[0118] According to the observations and Calculate the mean and variance of the intermediate variable which are

[0119]

[0120]

[0121] where

[0122] Next, calculate the normalized residual and its inverse to obtain the mean and variance Specifically, it is shown by the following formula:

[0123]

[0124]

[0125] Then, calculate the mean and variance of the messages passed to the variable node and {α lk} which are and and

[0126]

[0127]

[0128]

[0129]

[0130] Finally, based on the calculated mean and residuals, combined with the prior probability densities of the channel and the transmitted signal, the posterior probabilities of the channel and the transmitted signal can be calculated, and the formula is as follows:

[0131]

[0132]

[0133] The posterior mean and variance are calculated through the posterior probability, as shown in the following formula:

[0134]

[0135]

[0136]

[0137] where the matrix formed is the estimated value of the matrix formed is the estimated value of A.

[0138] Next, an estimate of X is obtained through as shown in the following formula

[0139]

[0140] where w kn is the element in the k-th row and n-th column of W(τ) T in.

[0141] S43. If the algorithm converges, end and obtain and Otherwise, substitute the posterior probability density obtained in S42 back into S41 and continue the iteration.

Claims

1. A joint channel estimation and signal detection method based on angular-delay sparsity, which is used for MIMO-OFDM systems. It is defined that in the system, the base station is configured with M antennas, and the arrangement is a uniform linear array. It serves 1 single-antenna user and uses N c sub-carriers for OFDM modulation. The wavelength corresponding to the center frequency of the OFDM carrier is ε, and the system sampling interval is T s , and the cyclic prefix length is N g ; It is characterized in that including the following steps: S1. Define the discretized incident angle grid as the discretized time delay grid as where L refers to L discrete angle sampling grid points, and K refers to K discrete angle sampling grid points. The channel model in the angle-time delay domain is constructed as follows: Among them, is a matrix composed of steering vectors, is a sparse channel matrix in the angular delay domain, is a matrix composed of delay response vectors; the steering vector and the delay response vector are respectively expressed as: where λ is the carrier wavelength, d is the spacing between adjacent array elements, j represents the imaginary part, and [·] T is the transpose operation; S2. Express the received signal as the form of multiplying the channel matrix and the transmitted signal matrix and adding noise, then model the received signal as: Among them, is the transmission signal matrix, N represents the external additive white Gaussian noise, and its statistical characteristics are modeled as a complex Gaussian distribution with zero mean and variance ; S3. Define There is If the signals are independently generated, that is: Model the channel matrix in the angular-delay domain as the following distribution: The element in the \(l\)-th row and \(k\)-th column of \(C\) is a binary state variable indicating whether the corresponding element in \(A\) is \(0\), and it is independently and identically distributed according to the Bernoulli distribution \(\lambda\) represents the Bernoulli parameter; then for the element in the \(l\)-th row and \(k\)-th column of \(A\) the marginal distribution is as follows: S4. Given the prior distribution, the maximum a posteriori estimator is given by the following formula: Convert the estimation of channels and signals into the solution of an optimization problem, where the unknown parameters are Then, according to the EM algorithm, the posterior probability is given by the following formula: where H(·) is the entropy function, and q is any probability distribution q(A, X|Y) about A and X; Write the probability density q(A, X|Y) as the form of multiplying the following probability densities: At this time, q(A, X|Y) is an approximation of the accurate posterior probability p(A, X|Y), where the probability densities p(x n |Y; Ψ) and (s lk |Y; Ψ) are approximately obtained from the outputs of the channel and the signal estimator. The solution process is as follows: First, according to the initial parameter Ψ (0) , the posterior mean and variance are obtained by solving through the channel and the signal estimator. Then, the posterior mean and variance output from the channel and the signal estimator are input into the system parameter estimator, and the parameters are updated by the EM algorithm. The specific steps are as follows: S41. Implement the update of the angular and delay ultra-precision parameters in the system parameter estimator, and use the EM algorithm to estimate the system parameters; S42. Calculate the posterior estimation values of the channel and the transmitted signal by using the approximate message passing method in the channel and signal estimator S43. If the algorithm converges, end the process, and respectively output the posterior mean values in S42 to obtain channel and signal estimations, which are respectively denoted as and Otherwise, return to S41 to continue the iteration.

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