阅读说明：本技术 一种基于2维簇结构的稀疏贝叶斯学习信道估计方法 (Sparse Bayesian learning channel estimation method based on 2-dimensional cluster structure ) 是由 张枫 邱玲 于 2021-01-21 设计创作，主要内容包括：本发明公开了一种大规模多输入多输出系统下基于2维簇结构的稀疏贝叶斯学习信道估计方法,特征是利用信道在多普勒和角域上的联合稀疏性,在多普勒域和角域上布置网格,形成簇结构；利用2维簇的性质,采用局部贝塔过程来描述稀疏信号的内在结构；再稀疏贝叶斯学习来解决估计问题,并且提出了一种基于局部贝塔过程的层次贝叶斯信道信息估计方法。采用本发明方法信道估计的结果和现有的大规模多输入多输出正交时频空系统的信道估计结果相比准确性有很理想的提升。(The invention discloses a sparse Bayesian learning channel estimation method based on a 2-dimensional cluster structure under a large-scale multi-input multi-output system, which is characterized in that a cluster structure is formed by arranging grids on a Doppler domain and an angular domain by utilizing the joint sparsity of a channel on the Doppler domain and the angular domain; describing the internal structure of the sparse signal by using the property of a 2-dimensional cluster and adopting a local beta process; and then sparse Bayesian learning is carried out to solve the estimation problem, and a hierarchical Bayesian channel information estimation method based on a local beta process is provided. Compared with the channel estimation result of the existing large-scale multi-input multi-output orthogonal time-frequency space system, the channel estimation result of the method has ideal improvement on the accuracy.)

1. A sparse Bayesian learning channel estimation method based on a 2-dimensional cluster structure is characterized in that:

for a massive MIMO orthogonal time-frequency-space system, in which a single base station is equipped with N_BSAn antenna; the base station serving a plurality of single antenna users; for a certain user, P main paths exist in the channel, and each main path has a corresponding delay tau_p(ii) a And exists in the pth main pathA sub-path; s of the p main path_pOf the sub-paths,for the corresponding complex channel gain, the gain of the channel,in order to be a doppler frequency offset,is the angle of departure; setting the channel parameters of each path to be kept quasi-static within a certain time period; the array direction vector for a typical uniform linear array channel is expressed as:

wherein d is the antenna spacing of the base station and λ is the carrier wavelength; the corresponding channel function is then expressed as:

where i is the delay domain tap index of the channel; t is_sIs the system sampling interval; tau is_pIs the channel delay, where_p＝IT_s，In addition, the first and second substrates are,is shown asWherein v is₀Is the speed of the user;

users in the system send pilot frequency to a base station; the training signal is set to be x,obeying a complex gaussian distribution; the cyclic prefix is denoted as N_CPThe length of each training is (N)_CP+N_l)T_s(ii) a The training signal becomesWithout loss of generality, the time is counted from zero at time T_s(N_CP+n)(n＝0,1,...,N_l-1) receiving a signalIs defined as:

wherein w_nIs complex white Gaussian noise which is independently and equally distributed;

set a corner region with G_AA sample grid represented asDoppler domain has G_DA sample grid represented asThereby forming a two-dimensional grid; the corresponding delay grid isThe sparse grid Q is a sparse matrix in which the sparse pattern is a 2-dimensional cluster; from PMs and their respectiveThe subpath is mapped to Q; the expression angle dictionary matrix T isInserting corresponding Doppler index matrix into Q to obtain new mapping matrix

Meanwhile, the variation of the pilot matrix C with time:

wherein the content of the first and second substances,representing a Hadamard product; l is_ιIs to reflect the correspondingThe affected iota cyclic permutation matrix; thereby experiencing the whole N_lThe received signal of a slot is defined as:

Y＝TQC+W (6)

wherein the content of the first and second substances,the noise matrix is formed by_nIs formed by the following steps; pair type (6)And performing time delay tapping to obtain:

y_n＝TQ[C]_:,n+w_n (7)

and isOrder toq＝vec(Q)，Obtaining a sparse expression:

y＝Φq+w (8)

at the above-mentioned bayful setting, the following distribution exists:

wherein the content of the first and second substances,is the variance of the noise, orderα₀Obeying a Gamma (c, d) distribution; using a local beta process, q is denoted asWhereinIs a weight element describing sparsity, z represents a non-zero matrix in q;following a complex Gaussian distributionWherein α is designated as α ═ Gamma (a, b); the beta process is described in terms of ζ, which satisfies ζ ═ beta (e, f);

the recovery process of the channel is as follows:

the first step is as follows: converting the signal recovery problem into a function maximization problem;

(1) let Y be { Y } as observation data, and hidden variables and hyper-parameters are respectively expressed asAnd xi ═ α, α₀ζ, prior parameter Λ ═ a, c, d, b, e, f };

according to the variational expectation maximization method, the following decomposition is performed:

ln p(Y|Λ)＝F(q(X),q(Ξ))+KL(q(X)q(Ξ)||p) (10)

wherein the content of the first and second substances,

q (x) and q (xi) are probability density functions, KL (q (x) q (xi) | p) is information divergence;

(3) KL (q (x) q (xi) | p) > 0, F (q (x), q (xi)) is the lower bound of the function lnp (Y | Λ); optimizing the X and xi problems translates into maximizing the F (q (X), q (xi)) problem;

the second step is that: performing iterative solution by using the algorithm steps shown as follows;

input y, a, b, d, 10^-6，c＝2N_BCG_AG_DN_lMaximum number of iterations κ_maxAnd a stop criterion th;

in the k +1 th iteration,

(1) updating

(2) And updating z:

wherein the content of the first and second substances,and is

(3) Updating the alpha:

wherein, a'^(κ+1)＝a+1，

(4) Updating alpha₀：

α₀ ^(κ+1)＝c′^(κ+1)/d′^(κ+1) (14)

Wherein, c'^(κ+1)＝c+N_lG_AG_DN_BSAndin addition, the

(5) And (3) updating zeta: zeta_sComplianceWhereinAnd

therefore, the temperature of the molten metal is controlled,

in an iterative process, if κ > κ_maxOrThe iteration terminates, wherein the cost function of the algorithm is defined as:

wherein Ω ═ a^-1I+ΦZA^-1ZΦ^H；

Finally, the estimation result is output

The third step: acquiring parameter information for reconstruction;

is recoveredTo pairRearranged to be recoveredThen according toAnd obtaining corresponding channel parameters according to the grid parameters, and recovering the channel data according to the formula (2).

Technical Field

The invention belongs to the technical field of wireless communication, and particularly relates to an uplink channel estimation method based on sparse Bayesian learning of a 2-dimensional cluster structure, which is suitable for a large-scale multi-input multi-output orthogonal time-frequency space system.

Background

The International institute of Electrical and electronics Engineers (International institute of Electrical and electronics Engineers) communication research and guidance ("Next Generation 5G Wireless Networks: A Comprehensive Surveiy," in IEEE Communications Surveiys & Tutorials, vol.18, No.3, pp.1617-1655, and thirdquater 2016 ") states that large-scale MIMO systems can greatly increase Wireless communication capacity, and are suitable for meeting the high throughput requirements of fifth Generation mobile communication technologies, even the 6 th Generation. The application of the orthogonal frequency division multiplexing modulation to a large-scale multi-input multi-output system can meet the large-scale data transmission requirement; however, the international society of electrical and electronics engineers (ieeem) Conference on Wireless communication and network ("Orthogonal Time Frequency Space modulation") "2017 IEEE Wireless Communications and Network Conference (WCNC) IEEE, 2017) indicates that in a high-speed scenario, the performance of the existing ofdm modulation is no longer ideal due to inter-carrier interference caused by doppler Frequency offset, and therefore an alternative scheme for modulation is proposed. Under the background of orthogonal time-frequency-space modulation, it is very important to complete channel estimation and acquire channel information. Journal of the Selected field of Communications of the institute of electrical and electronics engineers ("Uplink-aid High Mobility Downlink Channel Estimation Over Massive MIMO-OTFS system," in IEEE Journal on Selected Areas in Communications, vol.38, No.9, pp.1994-2009, sept.2020) proposes a variational bayesian method based on expectation maximization for extracting required Channel parameters from a trellis forming an angle domain and a delay domain, thereby recovering Channel information using the Channel parameters. But this method does not take into account the inherent structure of angular and delay domain sparsity. The problem that multi-dimensional sparsity is ignored exists in a current large-scale multi-input multi-output orthogonal time-frequency space system, and therefore the estimation result is inaccurate.

Disclosure of Invention

The invention provides a sparse Bayesian learning channel estimation method based on a 2-dimensional cluster structure under a large-scale multi-input multi-output orthogonal time-frequency space system, which aims to reduce the influence of Doppler frequency offset on the accuracy of channel estimation under the condition of high Doppler transmission and further improve the accuracy of an estimation result by utilizing the inherent joint sparsity of a Doppler domain and an angular domain.

The invention discloses a sparse Bayesian learning channel estimation method based on a 2-dimensional cluster structure, which is characterized by comprising the following steps of:

for a massive MIMO orthogonal time-frequency-space system, in which a single base station is equipped with N_BSAn antenna; the base station serving a plurality of single antenna users; for a certain user, P main paths exist in the channel, and each main path has a corresponding delay tau_p(ii) a And exists in the pth main pathA sub-path; s of the p main path_pOf the sub-paths,for the corresponding complex channel gain, the gain of the channel,in order to be a doppler frequency offset,is the angle of departure; setting the channel parameters of each path to be kept quasi-static within a certain time period; the array direction vector for a typical uniform linear array channel is expressed as:

wherein d is the antenna spacing of the base station and λ is the carrier wavelength; the corresponding channel function is then expressed as:

where i is the delay domain tap index of the channel; t is_sIs the system sampling interval; tau is_pIs the channel delay, where_p＝IT_s，In addition, the first and second substrates are,is shown asWherein v is₀Is the speed of the user;

users in the system send pilot frequency to a base station; the training signal is set to be x,obeying a complex gaussian distribution; the cyclic prefix is denoted as N_CPThe length of each training is (N)_CP+N_l)T_s(ii) a The training signal becomesWithout loss of generality, the time is counted from zero at time T_s(N_CP+n)(n＝0，1，...，N_l-1) receiving a signalIs defined as:

wherein w_nIs complex white Gaussian noise which is independently and equally distributed;

set a corner region with G_AA sample grid represented asDoppler domain has G_DA sample grid represented asThereby forming a two-dimensional grid; the corresponding delay grid isThe sparse grid Q is a sparse matrix in which the sparse pattern is a 2-dimensional cluster; from PMs and their respectiveThe subpath is mapped to Q; the expression angle dictionary matrix T isInserting corresponding Doppler index matrix into Q to obtain new mapping matrix

Meanwhile, the variation of the pilot matrix C with time:

wherein the content of the first and second substances,representing a Hadamard product; l is_lIs to reflect the correspondingThe l cyclic permutation matrix of influence; thereby experiencing the whole N_lThe received signal of a slot is defined as:

Y＝TQC+W (6)

wherein the content of the first and second substances,the noise matrix is formed by_nIs formed by the following steps; the time delay tap of the equation (6) is obtained:

y_n＝TQ[C]_：，n+w_n (7)

and isOrder toq＝vec(Q)，Obtaining a sparse expression:

y＝Φq+w (8)

at the above-mentioned bayful setting, the following distribution exists:

wherein the content of the first and second substances,is the variance of the noise, orderα₀Obeying a Gamma (c, d) distribution; using a local beta process, q is denoted asWhereinIs a weight element describing sparsity, z represents a non-zero matrix in q;following a complex Gaussian distributionWherein α is designated as α ═ Gamma (a, b); the beta process is described in terms of ζ, which satisfies ζ ═ beta (e, f);

the recovery process of the channel is as follows:

the first step is as follows: converting the signal recovery problem into a function maximization problem;

(1) let Y be { Y } as observation data, and hidden variables and hyper-parameters are respectively expressed asAnd xi ═ α, α₀ζ, prior parameter Λ ═ a, c, d, b, e, f };

(2) according to the variational expectation maximization method, the following decomposition is performed:

ln p(Y|A)＝F(q(X)，q(Ξ))+KL(q(X)q(Ξ)||p) (10)

wherein, F (q (X)),

q (x) and q (xi) are probability density functions, KL (q (x) q (xi) | p) is information divergence;

(3) KL (q (x) q (xi) | p) > 0, F (q (x), q (xi)) is the lower bound of the function ln p (Y | Λ); optimizing the X and xi problems translates into maximizing the F (q (X), q (xi)) problem;

the second step is that: performing iterative solution by using the algorithm steps shown as follows;

input y, a, b, d, 10^-6，c＝2N_BCG_AG_DN_lMaximum number of iterations κ_maxAnd a stop criterion th;

in the k +1 th iteration,

(1) updating theta:

(2) and updating z:

wherein the content of the first and second substances,and is

(3) Updating the alpha:

wherein, a^′(κ+1)＝a+1，

(4) Updating alpha₀：

α₀ ^(κ+1)＝c^′(κ+1)/d^′(κ+1) (14)

Wherein, c^′(κ+1)＝c+N_lG_AG_DN_BSAndin addition, the

(5) And (3) updating zeta: zeta_sComplianceWhereinAnd

therefore, the temperature of the molten metal is controlled,

in an iterative process, if κ > κ_maxOrThe iteration terminates, wherein the cost function of the algorithm is defined as:

wherein Ω ═ a^-1I+ΦZA^-1ZΦ^H；

Finally, the estimation result is output

The third step: acquiring parameter information for reconstruction;

is recoveredTo pairRearranged to be recoveredThen according toAnd obtaining corresponding channel parameters according to the grid parameters, and recovering the channel data according to the formula (2).

The invention discloses sparse Bayesian learning channel estimation of a 2-dimensional cluster structure under a large-scale multi-input multi-output orthogonal time-frequency space system. The channel estimation method considers a 2-dimensional cluster structure in the doppler angular domain, which is not considered in the existing channel estimation work. The method comprises the steps that grids are deployed in Doppler and angular domains to extract channel parameters in a channel, and the channel estimation problem in a large-scale multi-input multi-output orthogonal time-frequency space system is described as a 2-dimensional cluster sparse problem; due to the property of the 2-dimensional cluster, the internal structure of the sparse signal is described by adopting a local beta process; and then sparse Bayesian learning is carried out to solve the estimation problem, and a hierarchical Bayesian channel information acquisition method based on a local beta process is provided. The super-parameters in the model have traceability by adopting a hierarchical structure; and finally, channel estimation is completed by utilizing the parameters. Compared with the channel estimation result of the existing large-scale multi-input multi-output orthogonal time-frequency space system, the channel estimation result has the advantage that the accuracy is improved reasonably.

Description of the drawings:

FIG. 1 is a graph comparing Mean Square Error (MSE) performance of the channel estimation of the method of the present invention with that of the existing large-scale MIMO orthogonal time-frequency-space system under different signal-to-noise ratio (SNR) settings;

fig. 2 is a comparison graph of Mean Square Error (MSE) performance of the channel estimation of the method of the present invention and the existing large-scale multiuser multiple-input multiple-output orthogonal time-frequency-space system under different speed settings.

Detailed Description

The following describes and explains the sparse bayesian learning channel estimation method of the 2-dimensional cluster structure in the large-scale multiple-input multiple-output orthogonal time-frequency space system in further detail by embodiments in combination with the accompanying drawings.

Example 1:

in order to facilitate understanding of the specific implementation of the method, the reason why the channel in the method exhibits 2-dimensional joint sparsity is briefly described. In the actual propagation scatterer environment, due to the existence of large angular spread, sparse cluster-like distribution occurs in an angular domain, Doppler spread is caused by the existence of the angular spread, and a cluster structure in the Doppler domain is generated along with a constantly changing departure angle; thus, the channel exhibits a 2-dimensional joint sparse cluster structure in the doppler angular domain over a period of time. The local beta process is generally used to solve the problem of binary clustering of the bernoulli process, and describes the overall coefficients of the sparse matrix; in the method, a local beta process is utilized to grasp 2-dimensional joint sparsity. In addition, the 2-dimensional joint sparsity mapping into the grid forms a cluster structure grid. This type of sparseness problem is suitable for solving with sparse bayesian, i.e. using probabilistic statistical knowledge, introducing parameterized priors for sparse representation.

The following describes how the invention constructs a grid structure with a 2-dimensional cluster structure and uses sparse bayesian learning to perform channel estimation.

For a massive MIMO orthogonal time-frequency-space system, in which a single base station is equipped with N_BSAn antenna; the base station serving a plurality of single antenna users; for a certain user, P main paths exist in the channel, and each main path corresponds to the same main pathIs delayed by a delay of_p(ii) a And exists in the pth main pathA sub-path; s of the p main path_pOf the sub-paths,for the corresponding complex channel gain, the gain of the channel,in order to be a doppler frequency offset,is the angle of departure; setting the channel parameters of each path to be kept quasi-static within a certain time period; the array direction vector for a typical uniform linear array channel is expressed as:

wherein d is the antenna spacing of the base station and λ is the carrier wavelength; the corresponding channel function is then expressed as:

where i is the delay domain tap index of the channel; t is_sIs the system sampling interval; tau is_pIs the channel delay, where_p＝IT_s，In addition, the first and second substrates are,is shown asWherein v is₀Is the speed of the user;

the system isA user in the system sends pilot frequency to a base station; the training signal is set to be x,obeying a complex gaussian distribution; the cyclic prefix is denoted as N_CPThe length of each training is (N)_CP+N_l)T_s(ii) a The training signal becomesWithout loss of generality, the time is counted from zero at time T_s(N_CP+n)(n＝0，1，...，N_l-1) receiving a signalIs defined as:

wherein w_nIs complex white Gaussian noise which is independently and equally distributed;

set a corner region with G_AA sample grid represented asDoppler domain has G_DA sample grid represented asThereby forming a two-dimensional grid; the corresponding delay grid isThe sparse grid Q is a sparse matrix in which the sparse pattern is a 2-dimensional cluster; from PMs and their respectiveThe subpath is mapped to Q; the expression angle dictionary matrix T isIn QInserting corresponding Doppler index matrix to obtain new mapping matrix

Meanwhile, the variation of the pilot matrix C with time:

wherein the content of the first and second substances,representing a Hadamard product; l is_lIs to reflect the correspondingThe l cyclic permutation matrix of influence; thereby experiencing the whole N_lThe received signal of a slot is defined as:

Y＝TQC+W (6)

wherein the content of the first and second substances,the noise matrix is formed by_nIs formed by the following steps; the time delay tap of the equation (6) is obtained:

y_n＝TQ[C]_：，n+w_n (7)

and isOrder toq＝vec(Q)，Obtaining a sparse expression:

y＝Φq+w (8)

at the above-mentioned bayful setting, the following distribution exists:

wherein the content of the first and second substances,is the variance of the noise, orderα₀Obeying a Gamma (c, d) distribution; using a local beta process, q is denoted asWhereinIs a weight element describing sparsity, z represents a non-zero matrix in q;following a complex Gaussian distributionWherein α is designated as α ═ Gamma (a, b); the beta process is described in terms of ζ, which satisfies ζ ═ beta (e, f);

the recovery process of the channel is as follows:

the first step is as follows: converting the signal recovery problem into a function maximization problem;

(1) let Y be { Y } as observation data, and hidden variables and hyper-parameters are respectively expressed asAnd xi ═ α, α₀ζ, prior parameter Λ ═ a, c, d, b, e, f };

according to the variational expectation maximization method, the following decomposition is performed:

ln p(Y|Λ)＝F(q(X)，q(Ξ))+KL(q(X)q(Ξ)||p) (10)

wherein the content of the first and second substances,

q (x) and q (xi) are probability density functions, KL (q (x) q (xi) | p) is information divergence;

(3) KL (q (x) q (xi) | p) > 0, F (q (x), q (xi)) is the lower bound of the function ln p (Y | Λ); optimizing the X and xi problems translates into maximizing the F (q (X), q (xi)) problem;

the second step is that: performing iterative solution by using the algorithm steps shown as follows;

input y, a, b, d, 10^-6，c＝2N_BCG_AG_DN_lMaximum number of iterations κ_maxAnd a stop criterion th;

in the k +1 th iteration,

(1) updating

(2) And updating z:

wherein the content of the first and second substances,and is

(3) Updating the alpha:

wherein, a^′(κ+1)＝a+1，

(4) Updating alpha₀：

α₀ ^(κ+1)＝c^′(κ+1)/d^′(κ+1) (14)

Wherein, c^′(κ+1)＝c+N_lG_AG_DN_BSAndin addition, the

(5) And (3) updating zeta: zeta_sComplianceWhereinAnd

therefore, the temperature of the molten metal is controlled,

in an iterative process, if κ > κ_maxOrIteration terminationWherein the cost function of the algorithm is defined as:

wherein Ω ═ a^-1I+ΦZA^-1ZΦ^H；

Finally, the estimation result is output

The third step: acquiring parameter information for reconstruction;

is recoveredTo pairRearranged to be recoveredThen according toAnd obtaining corresponding channel parameters according to the grid parameters, and recovering the channel data according to the formula (2).

The sparse Bayesian learning channel estimation method based on 2-dimensional cluster sparsity in the large-scale multi-input multi-output orthogonal time-frequency space system is compared with the existing channel estimation method in the system by simulation. The compared indicator is the mean square error.

The simulation of the sparse Bayesian learning channel estimation method based on 2-dimensional cluster sparsity in the large-scale multiple-input multiple-output orthogonal time-frequency space system is specifically set as follows:

for simulation of different signal-to-noise ratios, the number of base station antennas is 64, the sampling time period is set to be 0.5 mu s, the number of main paths in a channel is 3, each main path comprises 2 sub-paths, the user speed is 100km/h, the length of a training signal is 8, the transmitting power is subjected to normalization processing, and the signal-to-noise ratio is expressed in a form of a logarithmic function.

For simulations at different speeds, the signal-to-noise ratio was 20dB, the simulations were performed at speeds of 50, 100, 200, 300, 400km/h, and the remaining parameters were unchanged from the previous settings.

FIG. 1 shows the comparison of the mean square error of the present invention with the existing estimation method at different SNR, wherein the solid line A1 marked by the top diamond indicates the Bayesian method of variation based on expectation maximization in the existing estimation method, and the solid line A2 marked by the bottom circle indicates the present invention method. As can be seen from the attached figure 1, the mean square error of the large-scale multi-input multi-output orthogonal time-frequency space system adopting the method is smaller than that of a variational Bayes method based on expectation maximization. And under the condition of low signal-to-noise ratio, the curve of figure 1 shows that the method has stronger self-adaptive capacity.

Figure 2 compares the mean square error of the method of the invention with the existing method for different speeds. Wherein the uppermost dotted line B1 represents the variational bayesian method based on expectation maximization and the lowermost dotted line B2 represents the method. As can be seen from the attached figure 2, under the same speed, the mean square error of the large-scale multi-input multi-output orthogonal time-frequency space system detection adopting the method of the invention is smaller, and the Doppler frequency shift is increased along with the increase of the speed, so that the channel support is expanded along the Doppler domain direction. Therefore, more observations are needed to keep the mean square error constant, which results in a slight rise of the mean square error curve with increasing speed, but the method is more adaptive to high mobility scenarios than previous solutions do not change significantly.

Through the embodiment, the Bayesian learning channel estimation based on the 2-dimensional cluster is proved to have more accurate channel estimation results and ideal performance when the channel is at low signal-to-noise ratio and high speed because the channel is recovered by using the joint sparsity of the Doppler domain and the angular domain of the channel compared with the existing channel estimation method.