CN114629533A - Information geometry method and system for large-scale MIMO channel estimation - Google Patents

Information geometry method and system for large-scale MIMO channel estimation Download PDF

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CN114629533A
CN114629533A CN202210147310.0A CN202210147310A CN114629533A CN 114629533 A CN114629533 A CN 114629533A CN 202210147310 A CN202210147310 A CN 202210147310A CN 114629533 A CN114629533 A CN 114629533A
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CN114629533B (en
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高西奇
杨济源
卢安安
陈衍
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Southeast University
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Abstract

The invention discloses an information geometric method for large-scale MIMO channel estimation and a related system. The invention carries out channel estimation according to the information geometric theory, and obtains the posterior statistical information of each user terminal channel, including posterior mean and variance. The information geometry method defines a set of Gaussian distribution as an original manifold, constructs a target manifold and an auxiliary manifold according to the posterior distribution of a channel, iteratively calculates m-projections of the auxiliary manifold on the target manifold, updates the auxiliary manifold and parameters distributed in the target manifold according to the m-projections, and finally takes the mean value and the variance of the distribution on the target manifold as the posterior mean value and the posterior variance of channel estimation. The information geometry method provided by the invention can obviously reduce the calculation complexity and pilot frequency overhead of channel estimation on the premise of ensuring the accuracy of the channel estimation, and effectively solves the problem of channel information acquisition of a large-scale MIMO system.

Description

Information geometry method and system for large-scale MIMO channel estimation
Technical Field
The invention belongs to the technical field of communication, and relates to an information geometry method for large-scale MIMO channel estimation and a related system.
Background
The massive Multiple Input Multiple Output (MIMO) technology is a core enabling technology of a 5G cellular system and its continuous evolution system. In a massive MIMO system, a Base Station (BS) equipped with a large number of antennas can simultaneously serve tens of users on the same time and frequency resources, thereby potentially providing a huge capacity gain and significantly improving energy efficiency. Among all types of antenna arrays, Uniform Planar Arrays (UPA) have compact size and three-dimensional coverage capability, and are a good choice for practical applications. Orthogonal Frequency Division Multiplexing (OFDM) is a multi-carrier modulation technique that can mitigate the effects of Frequency selective fading in broadband wireless communication. Massive MIMO-OFDM plays an important role in 5G systems and receives widespread attention in future 6G systems.
In massive MIMO-OFDM systems, channel estimation plays a crucial role, since the system performance is highly dependent on the quality of the channel information acquired by the system. In an actual system, Channel estimation of auxiliary pilot, that is, a transmitter periodically transmits a pilot signal, and a receiver obtains Channel State Information (CSI) according to the received pilot signal, is a commonly used Channel estimation method. Given the received pilot signal, the task of channel estimation is to obtain a posteriori statistical information of the channel parameters. When the prior distribution of the channel parameters is Gaussian distribution, the posterior distribution is also Gaussian distribution, and posterior information is given by posterior mean and posterior covariance matrix. However, due to the large dimensionality of the channel in massive MIMO-OFDM systems, the computation of a posteriori information is challenging. The conventional channel estimation algorithm, such as Minimum Mean Square Error (MMSE) estimation, is difficult to be applied to a massive MIMO-OFDM system because of the inversion of a large-dimensional matrix in the calculation process. With the further and great increase of the number of antenna units at the base station side and the number of supportable user terminals, the computational complexity and pilot frequency overhead for conventional channel information acquisition are both greatly increased, which becomes a bottleneck problem to be cracked.
The space defined by the a posteriori probability density function can be viewed as a microfluidics with a riemann structure. Therefore, the definitions and tools in differential geometry can be applied here well, which is one of the subjects of information geometry. Therefore, it is reasonable to apply the information geometry to the channel estimation. The main idea of information geometry is to study the intrinsic geometry of a specific set of PDFs by considering the parameter space of the Probability Density Function (PDF) as a microtube. In recent years, information geometry has been successfully applied to aspects such as multi-sensor estimation fusion, false alarm rate detection and generalized Bayesian prediction. Using information geometry theory to analyze the estimation problem has several advantages: firstly, the information geometry can provide a uniform framework for the theoretical analysis of the existing algorithm; secondly, the method provides visual understanding of the statistical model from a geometric perspective, and can promote the internal research of the existing problems; furthermore, the information geometry may also improve the algorithm from a more general and intrinsic perspective.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the defects of the prior art, the invention discloses a large-scale MIMO channel estimation information geometric method and a related system, which can obtain posterior information of each user terminal channel, and can further reduce the calculation complexity compared with the prior similar technical means while ensuring the estimation performance.
The technical scheme is as follows: in order to achieve the purpose, the invention provides the following technical scheme:
the large-scale MIMO channel estimation method comprises the following steps:
base station side/user terminal obtains prior statistical information of channel through uplink/downlink detection;
the base station side/user terminal obtains the posterior statistical information of the channel by using an information geometry method through the received uplink/downlink pilot signals and the prior statistical information; the information geometry method defines a set of Gaussian distributions as an original manifold, constructs a target manifold and an auxiliary manifold according to the posterior distribution of a channel, the target manifold and the auxiliary manifold are sub-manifolds of the original manifold, iteratively calculates m-projections of the distribution in the auxiliary manifold on the target manifold, updates the target manifold and the distribution in the auxiliary manifold according to the m-projections, and finally takes the mean value and the variance of the distribution on the target manifold as the posterior mean value and the posterior variance of channel estimation.
Preferably, the target manifold is a set of gaussian distributions with mutually independent elements, and the auxiliary manifold is a set of gaussian distributions with a covariance matrix being an inverse matrix of the sum of a diagonal matrix and a matrix with a rank of 1; the m-projection is obtained by minimizing the KL divergence between the distribution in the auxiliary manifold and the target manifold.
Preferably, the mean and covariance matrices of the distribution in the target manifold and the auxiliary manifold are represented by respective auxiliary computed parameter vectors and parameter real diagonal matrices; wherein the covariance of the distribution in the target manifold is expressed as an inverse matrix of the difference between the inverse of the prior variance and the real diagonal matrix of the parameter, and the mean value is expressed by the product of the covariance matrix and the parameter vector; the covariance matrix of the distribution in the auxiliary manifold is represented as the difference between the inverse of the prior variance and the real diagonal matrix of the parameter and then is represented as the inverse matrix of the sum of the matrix with the rank of 1, wherein the matrix with the rank of 1 is represented by the variance of the corresponding row and the noise in the sensing matrix, and the mean value is represented by the product of the covariance and the parameter vector combined with the vector composed of the corresponding row in the sensing matrix, the corresponding element of the received pilot signal vector and the noise variance.
Preferably, the covariance matrix of the auxiliary manifold is developed using the Sherman-Morrison equation.
Preferably, the step of obtaining the posterior mean and posterior variance of the channel estimation by using the information geometry method comprises:
(1) establishing an original manifold, a target manifold and an auxiliary manifold of a massive MIMO channel;
(2) initializing parameters distributed on the auxiliary manifold and the target manifold;
(3) calculating m-projections distributed on a target manifold in the auxiliary manifolds according to the parameters distributed on the auxiliary manifolds, the received pilot signals and the prior channel statistical information;
(4) updating parameters distributed on the auxiliary manifold and the target manifold according to the m-projection; and (5) repeating the steps (3) to (4) until the preset iteration number or the parameters distributed on the target manifold are converged.
Preferably, the priori statistical information and the posterior statistical information of the Space-Frequency Beam domain channel are calculated Based on a Space-Frequency Beam-Based (Space-Frequency Beam Based) channel statistical characterization model, in the Space-Frequency Beam-Based channel statistical characterization model, a Space-Frequency domain channel matrix is obtained by multiplying a Space-Frequency Beam domain channel matrix by a sampling Space rudder vector matrix at left and multiplying a transpose matrix of the sampling Frequency rudder vector matrix at right, and each element of the Space-Frequency Beam domain channel is statistically independent; for the base station side, the posterior mean value and the posterior variance of the space-frequency beam domain channel are converted into the posterior mean value and the posterior variance of the space-frequency beam domain channel by utilizing a sampling space rudder vector matrix and a sampling frequency rudder vector matrix; and for the user terminal side, feeding back the posterior statistical information of the respective space-frequency beam domain channels to the base station, and converting the posterior mean and the posterior variance of the obtained space-frequency beam domain channels into the posterior mean and the posterior variance of the space-frequency domain channels by using the sampling space rudder vector matrix and the sampling frequency rudder vector matrix.
A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the computer program when loaded into the processor implementing the massive MIMO channel estimation method.
A massive MIMO communication system comprising a base station and a plurality of user terminals, the base station being configured to: acquiring prior statistical information of channels of each user terminal through uplink detection; acquiring posterior statistical information of each user terminal by using an information geometry method through the received uplink pilot signal and the prior statistical information; the information geometry method defines a set of Gaussian distributions as an original manifold, constructs a target manifold and an auxiliary manifold according to the posterior distribution of a channel, the target manifold and the auxiliary manifold are sub-manifolds of the original manifold, iteratively calculates m-projections of the distribution in the auxiliary manifold on the target manifold, updates the target manifold and the distribution in the auxiliary manifold according to the m-projections, and estimates posterior mean and posterior variance for the channel by using the mean and variance of the distribution on the target manifold.
A massive MIMO communication system comprising a base station and a plurality of user terminals, the user terminals being configured to: acquiring prior statistical information of respective channels through downlink channel detection; through the received downlink pilot frequency signal and the prior statistical information, the posterior statistical information of each channel is obtained by using an information geometry method and a channel prediction method and is fed back to the base station; the information geometry method defines a set of Gaussian distributions as an original manifold, constructs a target manifold and an auxiliary manifold according to the posterior distribution of a channel, the target manifold and the auxiliary manifold are sub-manifolds of the original manifold, iteratively calculates m-projections of the distribution in the auxiliary manifold on the target manifold, updates the target manifold and the distribution in the auxiliary manifold according to the m-projections, and estimates posterior mean and posterior variance for the channel by using the mean and variance of the distribution on the target manifold.
A massive MIMO communication system comprising a base station and a plurality of user terminals, the base station or user terminals comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the computer program, when loaded into the processor, implementing the massive MIMO channel estimation method.
Has the advantages that: compared with the prior art, the information geometry method for large-scale MIMO channel estimation provided by the invention can obtain the posterior mean value and posterior variance of the channel with lower computation complexity and pilot frequency overhead on the premise of ensuring the accuracy of channel estimation. The obtained posterior mean value and the posterior variance can be further applied to robust precoding and robust detection, and the system performance is improved, so that the overall transmission efficiency of the system is further improved.
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FIG. 1 is a flow chart of a channel estimation method according to an embodiment of the present invention;
FIG. 2 is a flow chart of a channel estimation method according to another embodiment of the present invention;
FIG. 3 is a flow chart of an information geometry method for channel estimation in an embodiment of the present invention;
FIG. 4 is a diagram illustrating a comparison of channel estimation performance between an information geometry method and a prior art method according to an embodiment of the present invention;
FIG. 5 is a diagram illustrating a comparison of the convergence curves of the information geometry method and the prior art method at a signal-to-noise ratio of 20dB according to an embodiment of the present invention.
Detailed Description
The technical solutions provided by the present invention will be described in detail below with reference to specific examples, and it should be understood that the following specific embodiments are only illustrative of the present invention and are not intended to limit the scope of the present invention.
As shown in fig. 1, the large-scale MIMO channel estimation method disclosed in the embodiment of the present invention is applicable to a base station side, and includes that the base station side obtains prior statistical information of channels of each user terminal through uplink detection; the base station side obtains posterior statistical information of the channel of each user terminal by using an information geometry method through the received uplink pilot signal and the prior statistical information, wherein the posterior statistical information comprises posterior mean and posterior variance; the information geometry method defines a set of Gaussian distributions as an original manifold, constructs a target manifold and an auxiliary manifold according to the posterior distribution of a channel, iteratively calculates m-projections of the distribution in the auxiliary manifold on the target manifold, updates the distribution in the target manifold and the auxiliary manifold according to the m-projections, and finally takes the mean value and the variance of the distribution on the target manifold as the posterior mean value and the posterior variance of channel estimation.
As shown in fig. 2, a large-scale MIMO channel estimation method disclosed in another embodiment of the present invention is applicable to a user terminal side, and includes that the user terminal obtains prior statistical information of respective channels through downlink channel detection; the user terminal obtains the posterior statistical information of each channel by an information geometry method through the received downlink pilot signal and the prior statistical information, wherein the posterior statistical information comprises posterior mean and posterior variance; the information geometric method is consistent with the base station side method, and only multiple users are degenerated into a single user. The user terminal can be a mobile terminal or a fixed terminal such as a mobile phone, vehicle-mounted equipment, intelligent equipment and the like.
Fig. 3 illustrates the specific steps of obtaining posterior statistical information by using an information geometry method, including: (1) establishing an original manifold, an auxiliary manifold and a target manifold of a massive MIMO channel; (2) initializing parameters distributed on the auxiliary manifold and the target manifold; (3) calculating m-projections distributed on a target manifold in the auxiliary manifolds according to the parameters distributed on the auxiliary manifolds, the received pilot signals and the prior channel statistical information; (4) updating parameters distributed on the auxiliary manifold and the target manifold according to the m-projection; and (5) repeating the steps (3) to (4) until the preset iteration times or the parameters distributed on the target manifold are converged, wherein the mean value and the variance distributed on the target manifold are the posterior mean value and the posterior variance of the channel respectively.
The method of the invention is mainly suitable for a large-scale MIMO system which is provided with a large-scale antenna array at the base station side to serve a plurality of users simultaneously. The following describes a detailed implementation process of the channel estimation information geometry method according to the present invention with reference to a specific communication system example, and it should be noted that the method of the present invention is not only applicable to the specific system model as illustrated in the following example, but also applicable to system models of other configurations.
First, system configuration
Consider a massive MIMO-OFDM system operating in Time Division Multiplexing (TDD) mode. The base station side is provided with a UPA antenna array, wherein the number of the antennas is Nr＝Nr,v×Nr,h，Nr,vAnd Nr,hThe number of antennas per column and per row, respectively, and the antenna spacing in the horizontal and vertical directions, respectively, are denoted as ΔvAnd Δh. The base station serves K users equipped with single antenna in the same cell at the same time. In OFDM modulation, the number of subcarriers is NcThe system sampling interval and cyclic prefix length are respectively noted as TsAnd Ng. Takes subcarrier sets as
Figure BDA0003508785260000051
Wherein the subcarrier set for the uplink training amount is recorded as
Figure BDA0003508785260000052
It has a size of
Figure BDA0003508785260000053
In the TDD mode, due to channel reciprocity, CSI obtained by uplink training may be used for uplink signal detection and downlink precoding transmission, so in the embodiment, uplink massive MIMO-OFDM channel estimation is considered.
Second, space-frequency beam base channel statistical characterization model and channel estimation problem statement
The system model, the space-frequency beam-based channel statistical characterization model, and the channel estimation problem are described in detail below.
1. System model
Note the book
Figure BDA0003508785260000054
The sequence is transmitted in the frequency domain within a single OFDM symbol for the kth user. In the uplink training, the frequency domain received signal vector on the nth subcarrier can be represented as
Figure BDA0003508785260000055
Wherein
Figure BDA0003508785260000056
The spatial channel on the nth subcarrier for the kth user,
Figure BDA0003508785260000057
is circularly symmetric Gaussian noise with noise power of
Figure BDA0003508785260000058
Further, defining the space-frequency domain channel matrix of the k user as
Figure BDA0003508785260000059
Order to
Figure BDA00035087852600000510
Wherein xk＝[xk[N1]…xk[N2]]TAnd order
Figure BDA00035087852600000511
Figure BDA00035087852600000512
The superscript T represents the transpose of a matrix or vector. Further, the spatial frequency domain received signal model can be written as
Figure BDA00035087852600000513
2. Statistical representation model for space-frequency beam-based channel
The direction cosine u-sin θ, v-cos θ sin Φ are defined, where θ, Φ ∈ [ -pi/2, pi/2 ] are the polar angle and the azimuth angle, respectively. Further, a spatial rudder vector v (u, v) is defined as
Figure BDA00035087852600000514
Figure BDA00035087852600000515
Figure BDA0003508785260000061
Wherein
Figure BDA0003508785260000062
Denotes the Kronecker product, lambdacIs the wavelength. Defining a frequency-steering vector u (τ) as
Figure BDA0003508785260000063
Where τ is the time delay, Δf＝1/NcTsIs the subcarrier spacing. Further, the direction cosine u, v ∈ [ -1,1]And the time delay tau epsilon [0, NgTs) Quantification of sampling
Figure BDA0003508785260000064
Wherein
Figure BDA0003508785260000065
And is provided with
Figure BDA0003508785260000066
Nv,Nh,NτIs a sampling multiple. The sampling space rudder vector matrix and the sampling frequency rudder vector matrix can be expressed as
Figure BDA0003508785260000067
Figure BDA0003508785260000068
Figure BDA0003508785260000069
Figure BDA00035087852600000610
Then the statistical characterization model of the space-frequency beam-based channel considered is: the space frequency domain channel matrix is obtained by multiplying the space frequency beam domain channel by a sampling space rudder vector matrix at the left side and multiplying the sampling frequency rudder vector matrix at the right side, wherein each element of the space frequency beam domain channel is statistically independent. The specific expression is
Gk＝VHkFT (12)
Wherein
Figure BDA00035087852600000611
Defined as a space-frequency beam domain channel matrix. Suppose a sampling multiple Nv≥Nr,v,Nh≥Nr,h,Nτ≥NfAnd defining refinement factors
Figure BDA00035087852600000612
When the refinement factor is an integer, the refinement factor,it can be verified that the sampled rudder vector matrix has a DFT structure.
It can be understood by those skilled in the art that the specific vector representation in the model is only a uniform planar array as an example, and for a system using different antenna arrays such as a uniform linear array, a uniform circular array, etc., the spatial frequency beam based channel statistical characterization model is still applicable, and only V needs to be changed into a corresponding spatial sampling rudder vector matrix.
3. Question statement
Combining a space frequency domain received signal model (3) and a space frequency beam base channel statistical characterization model (12), obtaining
Y＝VHaM+Z (13)
Wherein
Figure BDA00035087852600000613
Further, vectorizing and removing zero elements in the space-frequency beam domain on two sides of the peer-to-peer mode can obtain
y＝Ah+z (14)
Wherein
Figure BDA0003508785260000071
Is according to HaNon-zero element position from
Figure BDA0003508785260000072
Extracting the relevant columns to obtain a matrix, N ═ NrNpM is HaThe number of non-zero elements in (1); y and Z are vectors after vectorization of Y and Z respectively; h is HaVectorizing and extracting a vector obtained by non-zero elements. The channel estimation problem is to obtain the posterior statistical information of the space-frequency beam domain channel h of each user terminal by using the received pilot signal y. The posterior statistical channel information of the space-frequency wave beam domain channel is the posterior mean value and the posterior variance of the space-frequency wave beam domain channel; the channel posterior means and posterior variance include: and the base station side gives the conditional mean value and the conditional variance of the space-frequency beam domain channel under the condition of the received uplink pilot signal. Suppose that
Figure BDA0003508785260000073
Wherein DIs a positive definite real diagonal matrix, is the prior variance of each user, I is a unit matrix,
Figure BDA0003508785260000074
in order to be the variance of the noise,
Figure BDA0003508785260000075
a circularly symmetric gaussian distribution with mean μ and covariance matrix Σ is represented. Thus, the posterior distribution p (h | y) of the space-frequency beam domain channel also belongs to a Gaussian distribution, and the mean and covariance thereof are respectively
Figure BDA0003508785260000076
Figure BDA0003508785260000077
Where the superscript H is the conjugate transpose of the matrix or vector. It can be verified that the a posteriori mean (15) and Minimum Mean Square Error (MMSE) estimation results are equivalent. The posterior information of the space-frequency beam domain channel comprises the computation complexity of posterior mean (15) and posterior covariance (16) of
Figure BDA0003508785260000078
A low-complexity space-frequency beam domain channel estimation method is designed based on an information geometry method.
It will be understood by those skilled in the art that the sensing matrix a in the received signal model (14) may have different forms in other statistical characterization models of the channel, and any statistical inference problem that satisfies the received signal model (14) and the same gaussian prior can be solved by using the information geometry method, not only limited to the beam domain channel estimation problem. The elimination of zeros in the received signal model (14) is preferred but not necessary to reduce the amount of computation.
Information geometric method for space-frequency beam domain channel estimation
1. Creation of original, target and auxiliary manifolds
First, a set of Gaussian distributions is defined as an original manifold, specifically
Mor:p(h)＝pG(h；μ,Σ)＝exp{-(h-μ)Σ-1(h-μ)H} (17)
Where mu, sigma are the distribution p on the original manifold, respectivelyGMean and covariance of (h; mu, sigma). Further, under the Gaussian assumption
Figure BDA0003508785260000079
On the basis of (a), the posterior distribution p (h | y) can be expressed as
Figure BDA0003508785260000081
Wherein h isiIs the ith element of h, ynFor the nth element of y,
Figure BDA0003508785260000082
line n of A; dh＝f(0,-D-1)，th＝f(h,I⊙(hhT) Therein [ ] is Hadamard product, and the function f (a, A) [ a ]T,vec(A)T]T(ii) a Symbol
Figure BDA00035087852600000815
An operator symbol representing a vector of the same dimension,
Figure BDA0003508785260000083
C,ψqis a normalization factor; c. Cn(h) Is composed of
Figure BDA0003508785260000084
Further, the target manifold is defined as a set of Gaussian distributions with independent elements, specifically
Figure BDA0003508785260000085
Wherein
Figure BDA0003508785260000086
Respectively assisted by a calculated parameter vector and a parameter real diagonal matrix,
Figure BDA0003508785260000087
is a set of M-dimensional real diagonal matrices. The target manifold is a sub manifold of the original manifold, and the target manifold is distributed on
Figure BDA0003508785260000088
Mean value of (a)0And variance Σ0And theta0,Θ0In a relationship of
Figure BDA0003508785260000089
Σ0＝(D-1-Θ0)-1 (22)
Further, N auxiliary manifolds are defined, an auxiliary manifold is a set of Gaussian distribution of a type of inverse matrix with covariance matrix being the sum of a diagonal matrix and a matrix with rank 1, wherein the nth auxiliary manifold comprises cn(h) Is concretely provided with
Figure BDA00035087852600000810
Wherein
Figure BDA00035087852600000811
The auxiliary manifold is a sub-manifold of the original manifold and is distributed on the auxiliary manifold
Figure BDA00035087852600000812
Mean value of (a)nAnd covariance ∑nAnd thetan,ΘnIn a relationship of
Figure BDA00035087852600000813
Figure BDA00035087852600000814
Covariance matrix sigma distributed over auxiliary manifoldnAn inverse matrix, which is the sum of a diagonal matrix and a matrix of rank 1, can be expanded using the Sherman-Morrison equation, so ΣnCan be written as
Figure BDA0003508785260000091
2. Channel estimation method
The channel estimation information geometric method is divided into four steps, namely establishing an original manifold, an auxiliary manifold and a target manifold of a large-scale MIMO space-frequency beam domain channel, initializing parameters distributed on the auxiliary manifold and the target manifold, calculating m-projection distributed on the target manifold in the auxiliary manifold according to the parameters distributed on the auxiliary manifold, a received pilot signal and space-frequency beam domain prior channel information, and updating the parameters distributed on the auxiliary manifold and the target manifold according to the m-projection. The steps of establishing the original manifold, the auxiliary manifold and the target manifold of the massive MIMO space-frequency beam domain channel are described in the above section, and the following steps are described in detail below.
(1) Initializing parameters of an auxiliary manifold and distribution over a target manifold
Setting the initial value t of the iteration number to be 0, and initializing a target manifold parameter
Figure BDA0003508785260000092
And auxiliary manifold parameters
Figure BDA0003508785260000093
(2) Computing m-projections in an auxiliary manifold distributed over a target manifold
According to the parameters distributed on the auxiliary manifold, the received pilot signal and the space frequency waveThe beam domain prior channel information computes m-projections of the auxiliary manifold that are distributed over the target manifold. Will assist in the distribution over the manifold
Figure BDA0003508785260000094
M-projection to the target manifold, the resulting distribution is noted as
Figure BDA0003508785260000095
The m-projection is to find a distribution on the target manifold
Figure BDA0003508785260000096
Make it
Figure BDA0003508785260000097
And auxiliary manifold up-distribution
Figure BDA0003508785260000098
With a minimum KL divergence between, i.e.
Figure BDA0003508785260000099
Wherein KL divergence is defined as
Figure BDA00035087852600000910
Wherein
Figure BDA00035087852600000911
Representing the expectation with respect to the probability distribution p (x). Given auxiliary manifold parameters
Figure BDA00035087852600000912
KL divergence can be expressed as
Figure BDA00035087852600000913
Wherein c ispIs a constant.
Figure BDA00035087852600000914
Can be expressed as
Figure BDA0003508785260000101
Further are respectively paired
Figure BDA0003508785260000102
ΘonDerivation of the deviation
Figure BDA0003508785260000103
Figure BDA0003508785260000104
Wherein the upper and lower lines indicate the taking of the conjugate. Making the partial derivative equal to 0 can obtain
Figure BDA0003508785260000105
Figure BDA0003508785260000106
The original manifold is an e-flat sub manifold, the distribution on the auxiliary manifold belongs to the original manifold, and the target manifold is a sub manifold of the original manifold, so that the m-projection of the distribution on the auxiliary manifold to the target manifold is unique, and the parameter obtained by the first-order sufficient condition is the parameter of the m-projection point. In combination with the formulae (32) (33) and (24) (26), the m-projection results can be obtained by
Figure BDA0003508785260000107
Figure BDA0003508785260000108
(3) Updating parameters distributed over auxiliary manifold and target manifold
The goal of the information geometry method is to find a probability distribution that approximates the a posteriori distribution on the auxiliary manifold and the target manifold, respectively. So as to be distributed over the target manifold
Figure BDA0003508785260000109
Is to
Figure BDA00035087852600001010
Approximation of, auxiliary distribution over manifold
Figure BDA00035087852600001011
Is to
Figure BDA00035087852600001012
An approximation of.
Figure BDA00035087852600001013
The result of the projection on the target manifold is
Figure BDA0003508785260000111
Wherein
Figure BDA0003508785260000112
And can be obtained according to the definitions of the auxiliary manifold and the target manifold
Figure BDA0003508785260000113
Is to cn(h) An approximation of. Further, the updating mode of the parameters distributed on the auxiliary manifold and the target manifold can be obtained
Figure BDA0003508785260000114
Figure BDA0003508785260000115
To make the algorithm more stable, the above iteration is relaxed, and the updating of the parameters distributed over the auxiliary manifold and the target manifold can be further expressed as
Figure BDA0003508785260000116
Figure BDA0003508785260000117
Figure BDA0003508785260000118
Wherein alpha is more than or equal to 0 and less than or equal to 1.
Further, the iteration number t is t +1, and the iterations (34), (35), (39), (40) and (41) converge to a preset iteration number or a parameter distributed on the target manifold. In the iteration process, the multiplication operation only involves multiplication of an N-dimensional diagonal matrix and an N-dimensional vector, multiplication of the N-dimensional diagonal matrix and multiplication of a scalar quantity and the N-dimensional vector, and the multiplication numbers of the operation are all M, so the calculation complexity of each iteration is M
Figure BDA0003508785260000119
Far below MMSE estimation
Figure BDA00035087852600001110
Thereby supporting the simultaneous estimation of channels of a large number of users and effectively reducing the pilot frequency overhead. The mean and variance of the target manifold distribution are the posterior mean and posterior variance of the space-frequency beam domain channel, specifically
Figure BDA00035087852600001111
Figure BDA00035087852600001112
Further, obtaining posterior mean value of space-frequency wave beam domain channel of each user through non-zero element position of space-frequency wave beam domain channel of each user
Figure BDA00035087852600001113
And posterior variance
Figure BDA00035087852600001114
Further converting the posterior mean value and posterior variance of the space-frequency wave beam domain channel of each user into the posterior mean value of the space-frequency wave beam domain channel through the sampling space rudder vector matrix and the sampling frequency rudder vector matrix
Figure BDA00035087852600001115
And posterior variance
Figure BDA00035087852600001116
In particular to
Figure BDA00035087852600001117
Figure BDA00035087852600001118
It will be understood by those skilled in the art that when the information geometry method is applied to the downlink channel estimation, the calculation process is substantially consistent with the uplink estimation. At this time, the received signal model (3) is degenerated to include only a single user, i.e., the index k takes only 1. Then, the application of the channel standard model, the signal processing process and the information geometric method is completely consistent with the uplink channel estimation, after the posterior statistical information of the channel is obtained, the obtained posterior statistical information of the channel is sent to the base station by each user terminal by combining methods such as channel prediction and the like. And the base station side converts the obtained posterior mean and posterior variance of the space-frequency beam domain channel into the posterior mean and posterior variance of the space-frequency beam domain channel by using the sampling space rudder vector matrix and the sampling frequency rudder vector matrix.
Fourth, effect of implementation
In order to make those skilled in the art better understand the solution of the present invention, the following presents the channel estimation performance results of the information geometry method in this embodiment and the existing method under two specific system configurations.
First, a comparison of the estimated performance results of the information geometry method in the present embodiment with the existing method is given. The methods of comparison are the MMSE estimation, GAMP method proposed in the literature "Generalized adaptive message passing for estimation with random linear approximation, in IEEE IST, St.Petersburg, Russia, July 31-August 5,2011, pp.2168-2172" and Algorithm 2 of the literature "unification of algorithm of the framework of constrained beta free approximation, IEEE.Wireless Commun., vol.20, No.7, pp.4144-4158, Jul.2021" (hereinafter referred to as VEP for short). Consider a configuration of Nr128, K48 and NtLarge scale MIMO system of 1, where base station antennas are configured as Nr,v＝8，Nr,h16. Fig. 4 shows the channel estimation performance comparison of the information geometry method in this embodiment with the GAMP and VEP methods under different snr under the considered uplink of the massive MIMO system. The maximum number of iterations of the information geometry method, GAMP and VEP are all set to 100. From fig. 4, it can be seen that the Information Geometry Approach (IGA) can achieve almost the same channel estimation performance as MMSE estimation at all signal-to-noise ratios. The signal-to-noise ratio gain of the information geometry method compared to GAMP and VEP is about 5dB when the channel estimation performance is-29 dB. This shows that the information geometry method in this embodiment can obtain more accurate channel estimation performance than the GAMP and VEP methods.
Next, a schematic diagram comparing the convergence curves of the information geometry method in the present embodiment and the existing method is given. Keeping the parameters of the considered large scale unchanged, setting the signal-to-noise ratio to be 20dB, taking MMSE estimation as a performance baseline for reference, and making a convergence curve of an information geometric method, GAMP and VEP methods. From fig. 5, it can be seen that the Information Geometry Approach (IGA) requires about 200 iterations to converge, and its estimation performance after convergence almost completely coincides with the MMSE estimation. Whereas the GAMP and VEP methods require more than 550 iterative convergence. This indicates that the information geometry converges faster than existing algorithms.
Based on the same inventive concept, a computer device disclosed in the embodiments of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor, where the computer program is loaded into the processor to implement the massive MIMO channel estimation method suitable for a base station or a user terminal.
In a particular implementation, the device includes a processor, a communication bus, a memory, and a communication interface. The processor may be a general purpose Central Processing Unit (CPU), microprocessor, Application Specific Integrated Circuit (ASIC), or one or more integrated circuits for controlling the execution of programs in accordance with the inventive arrangements. The communication bus may include a path that transfers information between the aforementioned components. A communications interface, using any transceiver or the like, for communicating with other devices or communications networks. The memory may be, but is not limited to, a read-only memory (ROM) or other type of static storage device that may store static information and instructions, a random-access memory (RAM) or other type of dynamic storage device that may store information and instructions, an electrically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CD-ROM) or other optical disk storage, a disk storage medium or other magnetic storage device, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer. The memory may be self-contained and coupled to the processor via a bus. The memory may also be integral to the processor.
Wherein, the memory is used for storing application program codes for executing the scheme of the invention and is controlled by the processor to execute. The processor is configured to execute the application program codes stored in the memory, thereby implementing the channel estimation method provided by the above-mentioned embodiments. The processor may include one or more CPUs, or may include a plurality of processors, and each of the processors may be a single-core processor or a multi-core processor. A processor herein may refer to one or more devices, circuits, and/or processing cores for processing data (e.g., computer program instructions).
Based on the same inventive concept, the large-scale MIMO communication system disclosed by the embodiment of the invention comprises a base station and a plurality of user terminals, wherein the base station obtains the prior statistical information of the channel of each user terminal through uplink detection, and obtains the posterior statistical information of each user terminal through a received uplink pilot signal and the prior statistical information by using an information geometry method. For a specific channel estimation information geometry method, refer to the foregoing embodiments, and details are not repeated here.
Based on the same inventive concept, the large-scale MIMO communication system disclosed by the embodiment of the invention comprises a base station and a plurality of user terminals, wherein the user terminals acquire prior statistical information of respective channels through downlink channel detection, and acquire posterior statistical information of the respective channels by using an information geometry method and a channel prediction method through received downlink pilot signals and the prior statistical information and feed the posterior statistical information back to the base station. For a specific channel estimation information geometry method, refer to the foregoing embodiments, and details are not repeated here.
Based on the same inventive concept, a massive MIMO communication system disclosed in the embodiments of the present invention includes a base station and a plurality of user terminals, wherein the base station or the user terminals include a memory, a processor, and a computer program stored in the memory and executable on the processor, and when the computer program is loaded into the processor, the massive MIMO channel estimation method is implemented. In the examples provided herein, it is understood that the disclosed methods may be practiced in other ways without departing from the spirit and scope of the present application. The present embodiment is an exemplary example only, and should not be taken as limiting, and the specific disclosure should not be taken as limiting the purpose of the application. For example, some features may be omitted, or not performed.
The technical means disclosed in the invention scheme are not limited to the technical means disclosed in the above embodiments, but also include the technical scheme formed by any combination of the above technical features. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and such improvements and modifications are also considered to be within the scope of the present invention.

Claims (10)

1. The large-scale MIMO channel estimation method is characterized by comprising the following steps:
base station side/user terminal obtains prior statistical information of channel through uplink/downlink detection;
the base station side/user terminal obtains the posterior statistical information of the channel by using an information geometry method through the received uplink/downlink pilot signals and the prior statistical information; the information geometry method defines a set of Gaussian distributions as an original manifold, constructs a target manifold and an auxiliary manifold according to the posterior distribution of a channel, the target manifold and the auxiliary manifold are sub-manifolds of the original manifold, iteratively calculates m-projections of the distribution in the auxiliary manifold on the target manifold, updates the target manifold and the distribution in the auxiliary manifold according to the m-projections, and finally takes the mean value and the variance of the distribution on the target manifold as the posterior mean value and the posterior variance of channel estimation.
2. The massive MIMO channel estimation method according to claim 1, wherein the target manifold is a set of gaussian distributions whose respective elements are independent of each other, and the auxiliary manifold is a set of gaussian distributions whose covariance matrix is an inverse matrix of a sum of a diagonal matrix and a matrix with rank 1; the m-projection is obtained by minimizing the KL divergence between the distribution in the auxiliary manifold and the target manifold.
3. The massive MIMO channel estimation method of claim 1, wherein the mean and covariance matrices of the distribution in the target manifold and the auxiliary manifold are represented by respective auxiliary computed parameter vectors and parameter real diagonal matrices; wherein the covariance matrix of the distribution in the target manifold is expressed as an inverse matrix of the difference between the inverse of the prior variance and the real diagonal matrix of the parameter, and the mean value is expressed by the product of the covariance and the parameter vector; the covariance of the distribution in the auxiliary manifold is represented as the difference between the inverse of the prior variance and the real diagonal matrix of the parameter and then is represented as the inverse matrix of the sum of the matrix with the rank of 1, wherein the matrix with the rank of 1 is represented by the corresponding row and the noise variance in the sensing matrix, and the mean value is represented by the product of the covariance matrix and the parameter vector combined with the corresponding row in the sensing matrix, the corresponding element of the received pilot signal vector and the noise variance to form a vector.
4. The massive MIMO channel estimation method of claim 2, wherein the covariance matrix of the auxiliary manifold is developed using a Sherman-Morrison formula.
5. The massive MIMO channel estimation method according to claim 1, wherein the step of obtaining the posterior mean and posterior variance of the channel using the information geometry method comprises:
(1) establishing an original manifold, a target manifold and an auxiliary manifold of a massive MIMO channel;
(2) initializing parameters distributed on the auxiliary manifold and the target manifold;
(3) calculating m-projections distributed on a target manifold in the auxiliary manifolds according to the parameters distributed on the auxiliary manifolds, the received pilot signals and the prior statistical information of the channels;
(4) updating parameters distributed on the auxiliary manifold and the target manifold according to the m-projection; and (5) repeating the steps (3) to (4) until the preset iteration times or the parameters distributed on the target manifold are converged.
6. The massive MIMO channel estimation method according to claim 1, wherein the prior statistical information and the posterior statistical information of the space-frequency beam domain channel are calculated based on a space-frequency beam-based channel statistical characterization model, in the space-frequency beam-based channel statistical characterization model, the space-frequency domain channel matrix is obtained by multiplying the space-frequency beam domain channel matrix by the sampling space rudder vector matrix in the left direction and multiplying the space-frequency beam domain channel matrix by the transpose matrix of the sampling frequency rudder vector matrix in the right direction, and each element of the space-frequency beam domain channel is statistically independent; for the base station side, the posterior mean value and the posterior variance of the space-frequency beam domain channel are converted into the posterior mean value and the posterior variance of the space-frequency beam domain channel by utilizing a sampling space rudder vector matrix and a sampling frequency rudder vector matrix; and for the user terminal side, feeding back the posterior statistical information of the respective space-frequency wave beam domain channel to the base station, and converting the posterior mean value and the posterior variance of the obtained space-frequency wave beam domain channel into the posterior mean value and the posterior variance of the space-frequency wave beam domain channel by using the sampling space rudder vector matrix and the sampling frequency rudder vector matrix by the base station side.
7. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the computer program, when loaded into the processor, implements the massive MIMO channel estimation method according to any one of claims 1-6.
8. A massive MIMO communication system comprising a base station and a plurality of user terminals, wherein the base station is configured to: acquiring prior statistical information of channels of each user terminal through uplink detection; acquiring posterior statistical information of each user terminal by using an information geometry method through the received uplink pilot signal and the prior statistical information; the information geometry method defines a set of Gaussian distributions as an original manifold, constructs a target manifold and an auxiliary manifold according to posterior distribution of a channel, wherein the target manifold and the auxiliary manifold are both sub manifolds of the original manifold, iteratively calculates m-projections of the distributions in the auxiliary manifold on the target manifold, updates the target manifold and the distributions in the auxiliary manifold according to the m-projections, and finally takes the mean and the variance of the distributions on the target manifold as the posterior mean and the posterior variance of channel estimation.
9. A massive MIMO communication system comprising a base station and a plurality of user terminals, wherein the user terminals are configured to: acquiring prior statistical information of each channel through downlink channel detection; through the received downlink pilot frequency signal and the prior statistical information, the posterior statistical information of each channel is obtained by using an information geometry method and a channel prediction method and is fed back to the base station; the information geometry method defines a set of Gaussian distributions as an original manifold, constructs a target manifold and an auxiliary manifold according to the posterior distribution of a channel, the target manifold and the auxiliary manifold are sub-manifolds of the original manifold, iteratively calculates m-projections of the distribution in the auxiliary manifold on the target manifold, updates the target manifold and the distribution in the auxiliary manifold according to the m-projections, and finally takes the mean value and the variance of the distribution on the target manifold as the posterior mean value and the posterior variance of channel estimation.
10. A massive MIMO communication system comprising a base station and a plurality of user terminals, wherein the base station or user terminals comprise a memory, a processor and a computer program stored on the memory and executable on the processor, the computer program, when loaded into the processor, implementing the massive MIMO channel estimation method according to any one of claims 1 to 6.
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