A millimeter-wave massive MIMO channel estimation method based on one-bit quantization reception

Abstract

The present invention provides a millimeter wave large-scale MIMO channel estimation method based on one-bit quantized reception. First, the sparsity of the millimeter wave channel in the virtual angle domain is utilized to convert the channel estimation problem of a large-scale MIMO system with a one-bit analog-to-digital converter into a framework of sparse signal recovery. A one-bit analog-to-digital converter is adopted at the base station end, which reduces the cost and energy consumption of the large-scale MIMO system. Then, a sparse Bayesian learning (SBL) method is used to achieve the estimation of the sparse channel in the angle domain by solving the second-class maximum likelihood problem. Compared with the existing one-bit channel estimation method that does not consider the sparsity of the angle domain channel, the channel estimation accuracy is greatly improved. The SBL method can realize the automatic selection of a sparse promotion prior model, and compared with the existing expectation maximization basis pursuit denoising method of manually selecting the hyperparameters of the prior model, the sensitivity problem of the estimation performance to the hyperparameter selection is avoided, thereby achieving the improvement of the estimation performance.

Description

Technical Field

[0001] The present invention relates to radio frequency signal estimation technology, and in particular to millimeter wave large-scale MIMO channel estimation technology. Background Art

[0002] Millimeter wave communication has become one of the key technologies for future outdoor cellular systems due to its huge bandwidth. Since the wavelength of millimeter wave frequencies is much smaller than that of microwaves, base stations can be equipped with large-scale antenna arrays to obtain higher spectral efficiency. However, due to the use of a large number of antennas, large-scale MIMO systems usually have high complexity and high power consumption problems. The analog-to-digital converter (ADC) is one of the most power-consuming devices, but its power consumption can be reduced exponentially by reducing the resolution. Therefore, the use of low-resolution analog-to-digital converters, especially one-bit analog-to-digital converters, can greatly reduce the power consumption and cost of the system. To study the communication problems and signal processing techniques in large-scale MIMO millimeter wave systems with one-bit analog-to-digital converters, it is necessary to know the channel state information of the system. Traditional channel estimation methods, such as the least squares LS estimator, have very unsatisfactory estimation performance when applied to one-bit quantized MIMO millimeter wave systems because they completely ignore the one-bit quantization characteristics of the signal.

[0003] In order to utilize the one-bit quantized signal, a low-complexity near maximum likelihood (nML) channel estimator is proposed for uplink massive MIMO systems with one-bit DACs. In addition, due to the lack of scattering, the channels in mmWave communication systems are usually sparse in both time and angle domains.

[0004] Although the channel estimator based on the approximate maximum likelihood (nML) algorithm takes into account the one-bit quantization characteristic of the received signal, it does not utilize the sparse characteristics of the millimeter wave channel. Therefore, the estimation accuracy is very low and the training overhead is high.

[0005] Therefore, by taking advantage of the a priori characteristic of the millimeter wave channel being sparse, some people have transformed the one-bit channel estimation problem of the MIMO millimeter wave system into a sparse signal recovery problem, and combined the expectation-maximization algorithm EM (expectation-maximization) with the basis pursuit denoising BPDN (basis pursuit denoise) method to obtain the maximum a posteriori estimate of the channel, further reducing the training overhead. However, the basis pursuit denoising method relies heavily on the selection of a prior distribution that promotes sparsity, and may have structural errors. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a channel estimation method for an uplink massive MIMO millimeter wave communication system applicable to a one-bit analog-to-digital converter.

[0007] The technical solution adopted by the present invention to solve the above technical problems is a millimeter wave massive MIMO channel estimation method based on one-bit quantized reception, comprising the following steps:

[0008] Step 1: Determine the number of base station antennas N BS 、Number of mobile user antennas MS , the number of paths between the user and the base station, the path loss, the arrival azimuth of the base station and the departure azimuth of the user to generate the millimeter wave system channel H, and the pilot symbols sent by the user within the training duration Q constitute a dimension N MS ×Q pilot symbol matrix X, generate complex Gaussian noise W, and obtain a one-bit received signal R = sgn (HX + W) output by a one-bit analog-to-digital converter at the base station after the uplink signal arrives at the base station, where sgn is a step function;

[0009] Step 2: The base station quantizes the one-bit received signal R to obtain a one-bit quantized signal r, and then converts the one-bit quantized signal r into a real number to obtain r R ;

[0010] Among them, r = sgn (Φh + w), r R =sgn(Φ R h R +w R ), where the median Median Noise w = vec(W), vec is the matrix column vectorization operator, is the angular domain sparse channel matrix of the millimeter wave system channel H, U R and U T The angular resolutions in the virtual angle domain of the millimeter wave system channel H are G r and G t Transform dictionary matrix, · H represents conjugate transpose; Φ R ,h R and w R They are the real field results of Φ, h and w respectively;

[0011] Step 3: Initialize the number of iterations p = 0; (p) Indicates the pth iteration, the estimated value of the initial hyperparameter α in The length is 2G r G t A vector of all 1s; initialize hR The mean vector of the posterior distribution of Where pinv(Φ R ) represents the matrix Φ R of pseudo-rebellion;

[0012] Step 4: In the pth iteration, calculate Φ R h R +w R The mean vector of the posterior distribution of vector The i-th element in for:

[0013]

[0014] σ R is the real-domain noise w R The standard deviation of R,i Yes R The i-th element of Indicates the intermediate value Φ R The i-th row vector of T Indicates transposition, middle value Median exp is the exponential with the natural constant e as the base;

[0015] Step 5: Calculate h R The mean vector of the posterior distribution of and the covariance matrix

[0016]

[0017] Diag is a function for constructing a diagonal matrix, (·) -1 is the matrix inversion operator;

[0018] Step 6: Update the estimate of the hyperparameter α for the next iteration The nth element for:

[0019]

[0020] [·] n Represents the nth element of the vector; [·] n,n It means taking the element of the nth row and nth column of the matrix;

[0021] Step 7: Determine whether the convergence condition is met. If yes, proceed to step 8. If not, update the number of iterations p=p+1 and repeat steps 4-6.

[0022] Step 8: Obtain the real domain channel vector h REstimated value of Then we get the sparse channel vector estimate in the complex domain [·] a:b It represents the column vector formed by taking the a-th element to the b-th element of the vector, and j is the imaginary number symbol; then the result is obtained by matrix operation. The final estimated value of the millimeter wave system channel H is Millimeter-wave MIMO signal estimation is complete.

[0023] The present invention first utilizes the sparsity of millimeter wave channels in the virtual angle domain to convert the channel estimation problem of a large-scale MIMO system with a one-bit analog-to-digital converter into the framework of sparse signal recovery. A one-bit analog-to-digital converter is used at the base station end to reduce the cost and energy consumption of large-scale MIMO systems. Then, the sparse Bayesian learning (SBL) method is used to solve the second type of maximum likelihood problem (type-II ML) to achieve the estimation of sparse channels in the angle domain. The SBL method can not only realize the automatic selection of sparse promotion prior models, but also avoid any structural errors, thereby improving the channel estimation performance.

[0024] The beneficial effects of the present invention are:

[0025] 1. The present invention utilizes the sparsity of the millimeter wave communication system channel in the virtual angle domain to convert the channel estimation problem into a sparse signal recovery problem. Compared with the existing one-bit channel estimation method that does not consider the sparsity of the angle domain channel, the channel estimation accuracy is greatly improved.

[0026] 2. The present invention is based on the sparse Bayesian learning method. Compared with the existing expectation-maximization basis pursuit denoising (EM BPDN) method of manually selecting hyperparameters of the prior model, it can realize the automatic selection of the prior model, avoid the sensitivity of the estimation performance to the hyperparameter selection, and thus achieve the improvement of the estimation performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 The normalized mean square error (NMSE) performance of the example method SBL is compared with the existing expectation-maximization basis pursuit denoising (EM BPDN) method and the approximate maximum likelihood (nML) method over the training duration Q. DETAILED DESCRIPTION

[0028] Assume that in a MIMO mmWave system there is a BS A base station with N antennas and a MSThe user end continuously sends a pilot signal to the base station through the uplink channel for a period of time. When the pilot signal arrives at the base station, it first passes through a one-bit analog-to-digital converter to output a one-bit quantized signal. Then, the base station estimates the uplink channel using the received one-bit quantized signal.

[0029] The channel estimation method of the present invention is as follows:

[0030] S1: Let dimension be N MS The matrix X of ×Q represents the matrix composed of pilot symbols sent by the user during the training duration Q. Therefore, the signal received at the base station, that is, before one-bit quantization, can be expressed as follows:

[0031] Y=HX+W(1)

[0032] Where H is the dimension N BS ×N MS The channel matrix; W is the receiving end noise, each element of which is independently and identically distributed with zero mean and variance σ 2 The received signal R after a one-bit analog-to-digital converter is recorded as:

[0033] R = sgn(Y) = sgn(HX+W)(2)

[0034] where sgn(·) represents the element-by-element sign function, which operates on the real and imaginary parts of the complex number separately. For example, for N BS = Q matrix Y row i column q element in Represents the complex number y i,q The real part of Represents the complex number y i,q The imaginary part of j represents the imaginary number sign; when when The same can be said Thus, the element r in the ith row and qth column of the received signal matrix R after one-bit quantization is i,q ,i=1,...,N BS ,q=1,...,the value set of Q can be expressed as {1+j,-1+j,-1-j,1-j}.

[0035] In the millimeter wave system, assuming that both the base station and the user end use uniform linear arrays, the channel H from the user to the base station can be given by the following formula:

[0036]

[0037] Where L represents the number of multipaths; represents the path loss of the lth path; d and λ represent the antenna spacing and the carrier wavelength respectively, and the relationship between the two is set to d / λ = 1 / 2; and They represent the arrival azimuth of the base station end and the departure azimuth of the user end of the lth path respectively;

[0038]

[0039] Representation vector The conjugate transpose of .

[0040] The virtual angle domain representation of the channel matrix H is as follows:

[0041]

[0042] Among them, N BS ×G r The matrix U of dimension R and N MS ×G t The matrix U of dimension T The resolution is G r (G r ≥N BS ) and G t (G t ≥N MS )’s angle domain dictionary matrix, matrix U R The g-th column (g=1,…,G r ) It can be expressed as Similarly, the matrix U T The gth column It can be expressed as is the virtual angle domain G r =G t Dimensional channel matrix, which is a matrix with only L (L<<G r G t ) non-zero elements.

[0043] The virtual angle domain of H is expressed as Substituting into the one-bit received signal expression (2) and performing matrix vectorization operations, we can obtain:

[0044]

[0045] Among them, vec(R) means to vectorize the matrix R by column to obtain a matrix with dimension QN BS ×1 vector r; sgn is the step function, represents the Kronecker product; The angular domain dimension is G r G t ×1 sparse channel vector; w = vec(W) is the dimension QN BS ×1 noise vector. Convert the above complex-valued one-bit received signal vector r to the real number domain, and we have:

[0046] r R =sgn(y R )=sgn(Φ R h R +w R )

[0047] in, and and They represent the operations of taking the real part and imaginary part element by element respectively; the symbol R represents the set of real numbers.

[0048] S2: Given a one-bit received vector r R Under this condition, the sparse Bayesian learning (SBL) method is used to estimate the sparse channel vector h R The sparse Bayesian learning framework assigns a parameterized zero-mean Gaussian distribution to the sparse channel vector h R :

[0049]

[0050] in It is composed of 2N BS N MS A column vector of hyperparameters, each element of which controls the channel vector h R The sparse Bayesian learning method maximizes the marginal probability density function (also known as the second-type maximum likelihood optimization) p(r R ; α) = ∫∫p(r R ,y R ,h R ; α)dy R dh R To obtain the estimated value of the hyperparameter α, so as to realize the automatic selection of the model.

[0051] S3: Maximize the marginal probability density function p(r R ; α) to obtain the estimated value of the hyperparameter α, and then infer the sparse channel vector h R The expectation maximization algorithm converts the received signal y before one bit quantization intoR and sparse channel h R As a hidden variable, the expectation step (E-step) and the maximization step (M-step) are iteratively performed to maximize the expectation of the log-likelihood of the complete data To obtain an estimate of the hyperparameter α, is about the latent variable y R and h R The posterior distribution p(y R ,h R |r R ; α) expectation: lnp(r R ,y R ,h R ; α) is the complete data {r R ,y R ,h R The specific steps of the variational expectation maximization algorithm are as follows:

[0052] S31: Approximating y via variational inference R and h R The mean and covariance matrix of the posterior distribution of .

[0053] The mean-field variational inference method uses a decomposable simple distribution q(y R ,h R )=q(y R )q(h R ) to approximate the posterior distribution p(y R ,h R |r R ; α), that is, p(y R ,h R |r R ; α)≈q(y R ,h R )=q(y R )q(h R ). Using the general results of variational inference, we can obtain in It's about h R The approximate posterior q(h R ) takes the expectation; const represents an additional constant, which can be obtained by normalization if necessary. Similarly, we can get in It's about R The approximate posterior q(y R ) to take expectations.

[0054] In the pth iteration (p = 0, 1, 2, ...), yR The mean vector of the variational posterior distribution of The i-th element of can be calculated by the following formula:

[0055]

[0056] i=1,…2QN BS .in, Represents y R The variational posterior mean vector μ y The i-th element in the p-th iteration; It's about R The approximate posterior q(y R ) takes the expectation; σ R is the real-domain noise w R Standard Deviation r R,i is a one-bit observation vector r R The i-th element of ;

[0057]

[0058] Represents Φ R The i-th row vector of . Represents the sparse channel vector h calculated in the previous round of iterations R The variational posterior mean vector of

[0059] The pth iteration h R The variational posterior distribution mean vector μ h and the covariance matrix Σ h The calculation formula is as follows:

[0060]

[0061] in, represents the y calculated in the pth round of iterations R The variational posterior mean vector of ; represents the current estimate of the hyperparameter α; Indicates the use of Construct a diagonal matrix where each diagonal element is a vector The corresponding element in ; (·) -1 is the matrix inversion operator.

[0062] S32: Update the estimated value of the hyperparameter α

[0063] By maximizing the expectation of the variational posterior with respect to the full data log-likelihood To update the hyperparameter α. In the pth iteration, the update formula of the hyperparameter α is:

[0064]

[0065] in is about the approximate posterior distribution q(y R ,h R ). The terms in the summation symbol in the above formula are To α n Take the derivative and set its first-order derivative to 0 to get the nth element α of the hyperparameter α n The update formula in the pth round of iteration is:

[0066]

[0067] n=1,…,2G r G t .in Indicates h R The mean vector of the posterior distribution of The square of the nth element; Indicates h R The posterior distribution covariance matrix of The nth diagonal element of .

[0068] S33: Iterate and calculate formulas (4) and (5) in step S31 and formula (6) in step S32 until the loop termination condition is met: the number of iterations is greater than or equal to a predetermined integer p max or

[0069] S4: Acquisition of channel estimation value

[0070] After the above loop iterations converge, the real domain sparse channel vector estimation value is assigned as:

[0071]

[0072] in is the h calculated by formula (4) after the loop in step S3 converges R The variational posterior distribution mean vector μ h . Then we get the sparse channel vector estimate in the complex domain:

[0073]

[0074] in Representation vector The first element to the Gth element r G t A column vector of bit elements; Representation vector G r G t+1 element to 2G r G t Column vector consisting of bit elements; j is the imaginary sign.

[0075] Will Matrixing to recover the virtual angle domain sparse channel matrix Estimated value of Then we can get the estimated value of the channel matrix H from the user to the base station

[0076]

[0077] Among them, the symbol vec -1 (·) represents the matrix operation of the vector, which is the inverse relationship of the matrix column vector operation operator vec(·).

[0078] 3. Comparison of experimental results: In the following scenario, the number of antennas at the base station and the user end is N respectively. BS =64 and N MS =4; the angular resolution of the virtual angle domain is set to G r =64 and G t =8; the number of paths between the user and the base station L = 6; path loss Obeying the complex Gaussian distribution of unit power; the arrival azimuth of the base station and the departure azimuth of the user end and Randomly selected in the interval [-π / 2,π / 2]; the elements in the pilot symbol matrix X are independently and randomly selected from zero mean and variance Select from the QPSK constellation diagram; the signal-to-noise ratio is set to The maximum number of allowed iterations p max =150.

[0079] Figure 1 The relationship between the normalized mean square error (NMSE) and the training duration Q is shown, and two existing one-bit channel estimation methods are compared, namely the expectation maximization basis pursuit denoising (EM BPDN) method and the approximate maximum likelihood (nML) method. It can be seen from the figure that compared with the existing EM BPDN method and the nML method, the method based on sparse Bayesian learning (SBL) provided by the present invention greatly improves the estimation performance (the normalized mean square error of channel estimation is minimized).

[0080] Example

[0081] In the example, there is a BS = A base station with 64 antennas, a MS= 4 antennas mobile user, where the mobile user sends a pilot symbol X to the base station in Q = 88 time slots. After the uplink signal reaches the base station, it first outputs a one-bit received signal R through a one-bit analog-to-digital converter, and then the base station uses the one-bit received signal R to estimate the millimeter wave system channel H. Considering the sparse characteristics of the millimeter wave channel in the angle domain, the system channel is expressed as in is the angle domain sparse channel matrix; U R and U T is the known virtual angle domain conversion dictionary matrix, and the angle resolutions are G r =64 and G t = 8. Therefore, we can use sparse Bayesian learning to estimate the sparse channel Finally, restore channel H.

[0082] Assume that the number of paths between the user and the base station is L = 6, and each pilot symbol is transmitted from unit power The signal-to-noise ratio is randomly selected from the QPSK constellation diagram. Path loss Obeying the complex Gaussian distribution of unit power; the arrival azimuth of the base station and the departure azimuth of the user end and Randomly selected in the interval [-π / 2,π / 2]. The ratio of antenna spacing to carrier wavelength is set to d / λ = 1 / 2.

[0083] Next, perform the following operations in sequence to estimate the channel H. The specific steps are as follows:

[0084] Step 1: Generate mmWave system channels Generate the pilot symbol matrix X and complex Gaussian noise W, so the base station receiving signal after a one-bit analog-to-digital converter can be obtained as R = sgn (Y) = sgn (HX + W)

[0085] Step 2: Vectorize the one-bit received signal R to r = vec(R) = sgn(Φh+w), and then realize r R =sgn(y R )=sgn(Φ R h R +w R ),in, The intermediate value w = vec(W), vec is the matrix column vectorization operator r R , Φ R ,h R and w R are real vectors or real matrices after the realization of r, Φ, h and w respectively.

[0086] Step 3: Initialize hyperparameters in The length is 2G r G t Initialize h R The mean vector of the posterior distribution of Where pinv(Φ R ) represents the matrix Φ R The pseudo-inverse.

[0087] Step 4: In the pth iteration, calculate y R The mean of the posterior distribution of

[0088]

[0089] Step 5: Calculate h R The mean vector of the posterior distribution of and the covariance matrix

[0090]

[0091] Step 6: Update the estimate of the hyperparameter α

[0092]

[0093] Step 7: Repeat steps 4 to 6 until the convergence condition is met: the number of iterations is greater than p max =150 or

[0094] Step 8: Obtain the real domain channel vector h R Estimated value of Then we get the sparse channel vector estimate in the complex domain Then perform matrix operations on it Finally, the estimated value of the channel matrix H is recovered as

Claims

1. A millimeter wave massive MIMO channel estimation method based on one-bit quantization reception, characterized in that: The following steps are involved: Step 1: Determine the number of base station antennas N BS 、Number of mobile user antennas MS , the number of paths between the user and the base station, the path loss, the arrival azimuth of the base station and the departure azimuth of the user to generate the millimeter wave system channel H, and the pilot symbols sent by the user within the training duration Q constitute a dimension N MS ×Q pilot symbol matrix X, generate complex Gaussian noise W, and obtain a one-bit received signal R = sgn (HX + W) output by a one-bit analog-to-digital converter at the base station after the uplink signal arrives at the base station, where sgn is a step function; Step 2: The base station quantizes the one-bit received signal R to obtain a one-bit quantized signal r, and then converts the one-bit quantized signal r into a real number to obtain r R ; Among them, r = sgn (Φh + w), r R =sgn(Φ R h R +w R ), where the median Median Noise w = vec(W), vec is the matrix column vectorization operator, is the angular domain sparse channel matrix of the millimeter wave system channel H, U R and U T The angular resolutions in the virtual angle domain of the millimeter wave system channel H are G r and G t Transform dictionary matrix, · H represents conjugate transpose; Φ R ,h R and w R They are the real field results of Φ, h and w respectively; Step 3: Initialize the number of iterations p = 0; (p) Indicates the pth iteration, the estimated value of the initial hyperparameter α in The length is 2G r G t A vector of all 1s; initialize h R The mean vector of the posterior distribution of Where pinv(Φ R ) represents the matrix Φ R of pseudo-rebellion; Step 4: In the pth iteration, calculate Φ R h R +w R The mean vector of the posterior distribution of vector The i-th element in for: σ R is the real-domain noise w R The standard deviation of R,i Yes R The i-th element of Indicates the intermediate value Φ R The i-th row vector of T Indicates transposition, middle value Median exp is the exponential with the natural constant e as the base; Represents the sparse channel vector h calculated in the previous round of iterations R The variational posterior mean vector of ; Step 5: Calculate h R The mean vector of the posterior distribution of and the covariance matrix Diag is a function for constructing a diagonal matrix, (·) -1 is the matrix inversion operator; Step 6: Update the estimate of the hyperparameter α for the next iteration The nth element for: [·] n Represents the nth element of the vector; [·] n,n It means taking the element of the nth row and nth column of the matrix; Step 7: Determine whether the convergence condition is met. If yes, proceed to step 8. If not, update the number of iterations p=p+1 and repeat steps 4-6. Step 8: Obtain the real domain channel vector h R Estimated value of Then we get the sparse channel vector estimate in the complex domain [·] a:b It represents taking the a-th element to the b-th element of the vector to form a column vector, j is the imaginary number symbol; then the result is obtained by matrix operation The final estimated value of the millimeter wave system channel H is Millimeter-wave MIMO signal estimation is complete.

2. The method according to claim 1, characterized in that: In step 1, the specific method of generating the millimeter wave system channel H is: By determining the number of base station antennas N BS 、Number of mobile user antennas MS , the number of paths between the user and the base station L, and the path loss Antenna spacing d and carrier wavelength λ, as well as the arrival azimuth of the lth path at the base station and the departure azimuth at the user end and To generate the mmWave system channel H: Among them, l represents the path number, the intermediate vector With the middle vector Respectively expressed as: W represents the intermediate vector With the middle vector variables.

3. The method according to claim 1, characterized in that: Convergence condition in step 7: The number of iterations is greater than the maximum number of iterations or Less than the set value.

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