CN112887233A - Sparse Bayesian learning channel estimation method based on 2-dimensional cluster structure - Google Patents

Sparse Bayesian learning channel estimation method based on 2-dimensional cluster structure Download PDF

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CN112887233A
CN112887233A CN202110081476.2A CN202110081476A CN112887233A CN 112887233 A CN112887233 A CN 112887233A CN 202110081476 A CN202110081476 A CN 202110081476A CN 112887233 A CN112887233 A CN 112887233A
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channel
sparse
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channel estimation
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CN112887233B (en
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张枫
邱玲
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University of Science and Technology of China USTC
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
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    • H04L25/0202—Channel estimation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/024—Channel estimation channel estimation algorithms

Abstract

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.

Description

Sparse Bayesian learning channel estimation method based on 2-dimensional cluster structure
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 NBSAn 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 taup(ii) a And exists in the pth main path
Figure BDA0002909475450000011
A sub-path; s of the p main pathpOf the sub-paths,
Figure BDA0002909475450000012
for the corresponding complex channel gain, the gain of the channel,
Figure BDA0002909475450000013
in order to be a doppler frequency offset,
Figure BDA0002909475450000014
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:
Figure BDA0002909475450000021
wherein d is the antenna spacing of the base station and λ is the carrier wavelength; the corresponding channel function is then expressed as:
Figure BDA0002909475450000022
where i is the delay domain tap index of the channel; t issIs the system sampling interval; tau ispIs the channel delay, wherep＝ITs，
Figure BDA0002909475450000023
In addition, the first and second substrates are,
Figure BDA0002909475450000024
is shown as
Figure BDA0002909475450000025
Wherein 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,
Figure BDA0002909475450000026
obeying a complex gaussian distribution; the cyclic prefix is denoted as NCPThe length of each training is (N)CP+Nl)Ts(ii) a The training signal becomes
Figure BDA0002909475450000027
Without loss of generality, the time is counted from zero at time Ts(NCP+n)(n＝0，1，...，Nl-1) receiving a signal
Figure BDA0002909475450000028
Is defined as:
Figure BDA0002909475450000029
wherein wnIs complex white Gaussian noise which is independently and equally distributed;
set a corner region with GAA sample grid represented as
Figure BDA00029094754500000210
Doppler domain has GDA sample grid represented as
Figure BDA00029094754500000211
Thereby forming a two-dimensional grid; the corresponding delay grid is
Figure BDA00029094754500000212
The sparse grid Q is a sparse matrix in which the sparse pattern is a 2-dimensional cluster; from PMs and their respective
Figure BDA00029094754500000213
The subpath is mapped to Q; the expression angle dictionary matrix T is
Figure BDA00029094754500000214
Inserting corresponding Doppler index matrix into Q to obtain new mapping matrix
Figure BDA00029094754500000215
Figure BDA00029094754500000216
Meanwhile, the variation of the pilot matrix C with time:
Figure BDA0002909475450000031
wherein the content of the first and second substances,
Figure BDA00029094754500000316
representing a Hadamard product; l islIs to reflect the corresponding
Figure BDA0002909475450000032
The l cyclic permutation matrix of influence; thereby experiencing the whole NlThe received signal of a slot is defined as:
Y＝TQC+W (6)
wherein the content of the first and second substances,
Figure BDA0002909475450000033
the noise matrix is formed bynIs formed by the following steps; the time delay tap of the equation (6) is obtained:
yn＝TQ[C]：，n+wn (7)
and is
Figure BDA0002909475450000034
Order to
Figure BDA0002909475450000035
q＝vec(Q)，
Figure BDA0002909475450000036
Obtaining a sparse expression:
y＝Φq+w (8)
at the above-mentioned bayful setting, the following distribution exists:
Figure BDA0002909475450000037
wherein the content of the first and second substances,
Figure BDA0002909475450000038
is the variance of the noise, order
Figure BDA0002909475450000039
α0Obeying a Gamma (c, d) distribution; using a local beta process, q is denoted as
Figure BDA00029094754500000310
Wherein
Figure BDA00029094754500000311
Is a weight element describing sparsity, z represents a non-zero matrix in q;
Figure BDA00029094754500000312
following a complex Gaussian distribution
Figure BDA00029094754500000313
Wherein 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 as
Figure BDA00029094754500000314
And 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)),
Figure BDA00029094754500000315
Figure BDA0002909475450000041
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＝2NBCGAGDNlMaximum number of iterations κmaxAnd a stop criterion th;
in the k +1 th iteration,
(1) updating theta:
Figure BDA0002909475450000042
(2) and updating z:
Figure BDA0002909475450000043
wherein the content of the first and second substances,
Figure BDA0002909475450000044
and is
Figure BDA0002909475450000045
(3) Updating the alpha:
Figure BDA0002909475450000046
wherein, a′(κ+1)＝a+1，
Figure BDA0002909475450000047
(4) Updating alpha0：
α0 (κ+1)＝c′(κ+1)/d′(κ+1) (14)
Wherein, c′(κ+1)＝c+NlGAGDNBSAnd
Figure BDA0002909475450000048
in addition, the
Figure BDA0002909475450000049
(5) And (3) updating zeta: zetasCompliance
Figure BDA00029094754500000410
Wherein
Figure BDA00029094754500000411
And
Figure BDA0002909475450000051
therefore, the temperature of the molten metal is controlled,
Figure BDA0002909475450000052
Figure BDA0002909475450000053
in an iterative process, if κ > κmaxOr
Figure BDA0002909475450000054
The iteration terminates, wherein the cost function of the algorithm is defined as:
Figure BDA0002909475450000055
wherein Ω ═ a-1I+ΦZA-1ZΦH；
Finally, the estimation result is output
Figure BDA0002909475450000056
The third step: acquiring parameter information for reconstruction;
is recovered
Figure BDA0002909475450000057
To pair
Figure BDA0002909475450000058
Rearranged to be recovered
Figure BDA0002909475450000059
Then according to
Figure BDA00029094754500000510
And 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 NBSAn 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 ofp(ii) a And exists in the pth main path
Figure BDA0002909475450000061
A sub-path; s of the p main pathpOf the sub-paths,
Figure BDA0002909475450000062
for the corresponding complex channel gain, the gain of the channel,
Figure BDA0002909475450000063
in order to be a doppler frequency offset,
Figure BDA0002909475450000064
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:
Figure BDA0002909475450000065
wherein d is the antenna spacing of the base station and λ is the carrier wavelength; the corresponding channel function is then expressed as:
Figure BDA0002909475450000066
where i is the delay domain tap index of the channel; t issIs the system sampling interval; tau ispIs the channel delay, wherep＝ITs，
Figure BDA0002909475450000067
In addition, the first and second substrates are,
Figure BDA0002909475450000068
is shown as
Figure BDA0002909475450000069
Wherein 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,
Figure BDA00029094754500000610
obeying a complex gaussian distribution; the cyclic prefix is denoted as NCPThe length of each training is (N)CP+Nl)Ts(ii) a The training signal becomes
Figure BDA00029094754500000611
Without loss of generality, the time is counted from zero at time Ts(NCP+n)(n＝0，1，...，Nl-1) receiving a signal
Figure BDA00029094754500000612
Is defined as:
Figure BDA0002909475450000071
wherein wnIs complex white Gaussian noise which is independently and equally distributed;
set a corner region with GAA sample grid represented as
Figure BDA0002909475450000072
Doppler domain has GDA sample grid represented as
Figure BDA0002909475450000073
Thereby forming a two-dimensional grid; the corresponding delay grid is
Figure BDA0002909475450000074
The sparse grid Q is a sparse matrix in which the sparse pattern is a 2-dimensional cluster; from PMs and their respective
Figure BDA0002909475450000075
The subpath is mapped to Q; the expression angle dictionary matrix T is
Figure BDA0002909475450000076
In QInserting corresponding Doppler index matrix to obtain new mapping matrix
Figure BDA0002909475450000077
Figure BDA0002909475450000078
Meanwhile, the variation of the pilot matrix C with time:
Figure BDA0002909475450000079
wherein the content of the first and second substances,
Figure BDA00029094754500000717
representing a Hadamard product; l islIs to reflect the corresponding
Figure BDA00029094754500000710
The l cyclic permutation matrix of influence; thereby experiencing the whole NlThe received signal of a slot is defined as:
Y＝TQC+W (6)
wherein the content of the first and second substances,
Figure BDA00029094754500000711
the noise matrix is formed bynIs formed by the following steps; the time delay tap of the equation (6) is obtained:
yn＝TQ[C]：，n+wn (7)
and is
Figure BDA00029094754500000712
Order to
Figure BDA00029094754500000713
q＝vec(Q)，
Figure BDA00029094754500000718
Obtaining a sparse expression:
y＝Φq+w (8)
at the above-mentioned bayful setting, the following distribution exists:
Figure BDA00029094754500000714
wherein the content of the first and second substances,
Figure BDA00029094754500000715
is the variance of the noise, order
Figure BDA00029094754500000716
α0Obeying a Gamma (c, d) distribution; using a local beta process, q is denoted as
Figure BDA0002909475450000081
Wherein
Figure BDA0002909475450000082
Is a weight element describing sparsity, z represents a non-zero matrix in q;
Figure BDA0002909475450000083
following a complex Gaussian distribution
Figure BDA0002909475450000084
Wherein 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 as
Figure BDA0002909475450000085
And 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,
Figure BDA0002909475450000086
Figure BDA0002909475450000087
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＝2NBCGAGDNlMaximum number of iterations κmaxAnd a stop criterion th;
in the k +1 th iteration,
(1) updating
Figure BDA0002909475450000088
Figure BDA0002909475450000089
(2) And updating z:
Figure BDA00029094754500000810
wherein the content of the first and second substances,
Figure BDA00029094754500000811
and is
Figure BDA00029094754500000812
(3) Updating the alpha:
Figure BDA0002909475450000091
wherein, a′(κ+1)＝a+1，
Figure BDA0002909475450000092
(4) Updating alpha0：
α0 (κ+1)＝c′(κ+1)/d′(κ+1) (14)
Wherein, c′(κ+1)＝c+NlGAGDNBSAnd
Figure BDA0002909475450000093
in addition, the
Figure BDA0002909475450000094
(5) And (3) updating zeta: zetasCompliance
Figure BDA0002909475450000095
Wherein
Figure BDA0002909475450000096
And
Figure BDA0002909475450000097
therefore, the temperature of the molten metal is controlled,
Figure BDA0002909475450000098
Figure BDA0002909475450000099
in an iterative process, if κ > κmaxOr
Figure BDA00029094754500000910
Iteration terminationWherein the cost function of the algorithm is defined as:
Figure BDA00029094754500000911
wherein Ω ═ a-1I+ΦZA-1ZΦH；
Finally, the estimation result is output
Figure BDA00029094754500000912
The third step: acquiring parameter information for reconstruction;
is recovered
Figure BDA00029094754500000913
To pair
Figure BDA00029094754500000914
Rearranged to be recovered
Figure BDA00029094754500000915
Then according to
Figure BDA00029094754500000916
And 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.

Claims (1)

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 NBSAn 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 taup(ii) a And exists in the pth main path
Figure FDA0002909475440000011
A sub-path; s of the p main pathpOf the sub-paths,
Figure FDA0002909475440000012
for the corresponding complex channel gain, the gain of the channel,
Figure FDA0002909475440000013
in order to be a doppler frequency offset,
Figure FDA0002909475440000014
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:
Figure FDA0002909475440000015
wherein d is the antenna spacing of the base station and λ is the carrier wavelength; the corresponding channel function is then expressed as:
Figure FDA0002909475440000016
where i is the delay domain tap index of the channel; t issIs the system sampling interval; tau ispIs the channel delay, wherep＝ITs，
Figure FDA0002909475440000017
In addition, the first and second substrates are,
Figure FDA0002909475440000018
is shown as
Figure FDA0002909475440000019
Wherein 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,
Figure FDA00029094754400000110
obeying a complex gaussian distribution; the cyclic prefix is denoted as NCPThe length of each training is (N)CP+Nl)Ts(ii) a The training signal becomes
Figure FDA00029094754400000111
Without loss of generality, the time is counted from zero at time Ts(NCP+n)(n＝0,1,...,Nl-1) receiving a signal
Figure FDA00029094754400000112
Is defined as:
Figure FDA00029094754400000113
wherein wnIs complex white Gaussian noise which is independently and equally distributed;
set a corner region with GAA sample grid represented as
Figure FDA00029094754400000114
Doppler domain has GDA sample grid represented as
Figure FDA00029094754400000115
Thereby forming a two-dimensional grid; the corresponding delay grid is
Figure FDA00029094754400000116
The sparse grid Q is a sparse matrix in which the sparse pattern is a 2-dimensional cluster; from PMs and their respective
Figure FDA00029094754400000117
The subpath is mapped to Q; the expression angle dictionary matrix T is
Figure FDA00029094754400000118
Inserting corresponding Doppler index matrix into Q to obtain new mapping matrix
Figure FDA00029094754400000119
Figure FDA0002909475440000021
Meanwhile, the variation of the pilot matrix C with time:
Figure FDA0002909475440000022
wherein the content of the first and second substances,
Figure FDA0002909475440000023
representing a Hadamard product; l isιIs to reflect the corresponding
Figure FDA0002909475440000024
The affected iota cyclic permutation matrix; thereby experiencing the whole NlThe received signal of a slot is defined as:
Y＝TQC+W (6)
wherein the content of the first and second substances,
Figure FDA0002909475440000025
the noise matrix is formed bynIs formed by the following steps; pair type (6)And performing time delay tapping to obtain:
yn＝TQ[C]:,n+wn (7)
and is
Figure FDA0002909475440000026
Order to
Figure FDA0002909475440000027
q＝vec(Q)，
Figure FDA0002909475440000028
Obtaining a sparse expression:
y＝Φq+w (8)
at the above-mentioned bayful setting, the following distribution exists:
Figure FDA0002909475440000029
wherein the content of the first and second substances,
Figure FDA00029094754400000210
is the variance of the noise, order
Figure FDA00029094754400000211
α0Obeying a Gamma (c, d) distribution; using a local beta process, q is denoted as
Figure FDA00029094754400000212
Wherein
Figure FDA00029094754400000213
Is a weight element describing sparsity, z represents a non-zero matrix in q;
Figure FDA00029094754400000214
following a complex Gaussian distribution
Figure FDA00029094754400000215
Wherein 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 as
Figure FDA00029094754400000216
And 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,
Figure FDA0002909475440000031
Figure FDA0002909475440000032
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＝2NBCGAGDNlMaximum number of iterations κmaxAnd a stop criterion th;
in the k +1 th iteration,
(1) updating
Figure FDA0002909475440000033
Figure FDA0002909475440000034
(2) And updating z:
Figure FDA0002909475440000035
wherein the content of the first and second substances,
Figure FDA0002909475440000036
and is
Figure FDA0002909475440000037
(3) Updating the alpha:
Figure FDA0002909475440000038
wherein, a'(κ+1)＝a+1，
Figure FDA0002909475440000039
(4) Updating alpha0：
α0 (κ+1)＝c′(κ+1)/d′(κ+1) (14)
Wherein, c'(κ+1)＝c+NlGAGDNBSAnd
Figure FDA0002909475440000041
in addition, the
Figure FDA0002909475440000042
(5) And (3) updating zeta: zetasCompliance
Figure FDA0002909475440000043
Wherein
Figure FDA0002909475440000044
And
Figure FDA0002909475440000045
therefore, the temperature of the molten metal is controlled,
Figure FDA0002909475440000046
Figure FDA0002909475440000047
in an iterative process, if κ > κmaxOr
Figure FDA00029094754400000414
The iteration terminates, wherein the cost function of the algorithm is defined as:
Figure FDA0002909475440000048
wherein Ω ═ a-1I+ΦZA-1ZΦH；
Finally, the estimation result is output
Figure FDA0002909475440000049
The third step: acquiring parameter information for reconstruction;
is recovered
Figure FDA00029094754400000410
To pair
Figure FDA00029094754400000411
Rearranged to be recovered
Figure FDA00029094754400000412
Then according to
Figure FDA00029094754400000413
And obtaining corresponding channel parameters according to the grid parameters, and recovering the channel data according to the formula (2).
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113542162A (en) * 2021-06-02 2021-10-22 杭州电子科技大学 Up-down link communication perception integrated method based on block sparse Bayesian algorithm
CN116094876A (en) * 2023-03-10 2023-05-09 南京邮电大学 Channel estimation method of orthogonal time-frequency-space system based on asymmetric architecture

Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102332957A (en) * 2011-09-23 2012-01-25 南昌大学 Radio wave propagation multidimensional characteristic cognitive method in dynamic heterogeneous network environment
CN104168228A (en) * 2014-08-06 2014-11-26 哈尔滨工业大学深圳研究生院 Compressed sensing ultra-wide band channel estimation method and system based on cluster position set
CN108365874A (en) * 2018-02-08 2018-08-03 电子科技大学 Based on the extensive MIMO Bayes compressed sensing channel estimation methods of FDD
US20180287822A1 (en) * 2017-03-31 2018-10-04 Mitsubishi Electric Research Laboratories, Inc. System and Method for Channel Estimation in mmWave Communications Exploiting Joint AoD-AoA Angular Spread
CN109768943A (en) * 2019-03-05 2019-05-17 北京邮电大学 Based on the channel estimation methods of Variational Bayesian Learning in broadband multiuser millimeter-wave systems
CN110071881A (en) * 2019-04-26 2019-07-30 北京理工大学 A kind of any active ues detection of adaptive expense and channel estimation methods
CN111131097A (en) * 2019-12-27 2020-05-08 浙江大学 Block diagonal sparse Bayesian channel estimation method under SC-MIMO underwater acoustic communication environment
CN111666688A (en) * 2020-06-09 2020-09-15 太原科技大学 Corrected channel estimation algorithm combining angle mismatch with sparse Bayesian learning

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102332957A (en) * 2011-09-23 2012-01-25 南昌大学 Radio wave propagation multidimensional characteristic cognitive method in dynamic heterogeneous network environment
CN104168228A (en) * 2014-08-06 2014-11-26 哈尔滨工业大学深圳研究生院 Compressed sensing ultra-wide band channel estimation method and system based on cluster position set
US20180287822A1 (en) * 2017-03-31 2018-10-04 Mitsubishi Electric Research Laboratories, Inc. System and Method for Channel Estimation in mmWave Communications Exploiting Joint AoD-AoA Angular Spread
CN108365874A (en) * 2018-02-08 2018-08-03 电子科技大学 Based on the extensive MIMO Bayes compressed sensing channel estimation methods of FDD
CN109768943A (en) * 2019-03-05 2019-05-17 北京邮电大学 Based on the channel estimation methods of Variational Bayesian Learning in broadband multiuser millimeter-wave systems
CN110071881A (en) * 2019-04-26 2019-07-30 北京理工大学 A kind of any active ues detection of adaptive expense and channel estimation methods
CN111131097A (en) * 2019-12-27 2020-05-08 浙江大学 Block diagonal sparse Bayesian channel estimation method under SC-MIMO underwater acoustic communication environment
CN111666688A (en) * 2020-06-09 2020-09-15 太原科技大学 Corrected channel estimation algorithm combining angle mismatch with sparse Bayesian learning

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
WEI JI，LING QIU: ""Common Sparsity based Channel Estimation for Massive MIMO-OFDM Systems via Multitask"", 《IEEE》 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113542162A (en) * 2021-06-02 2021-10-22 杭州电子科技大学 Up-down link communication perception integrated method based on block sparse Bayesian algorithm
CN113542162B (en) * 2021-06-02 2023-05-23 杭州电子科技大学 Uplink and downlink communication perception integrated method based on block sparse Bayesian algorithm
CN116094876A (en) * 2023-03-10 2023-05-09 南京邮电大学 Channel estimation method of orthogonal time-frequency-space system based on asymmetric architecture
CN116094876B (en) * 2023-03-10 2023-08-29 南京邮电大学 Channel estimation method of orthogonal time-frequency-space system based on asymmetric architecture

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