CN112953865A - Channel estimation method for large-scale multi-input multi-output system - Google Patents

Abstract

The invention relates to the technical field of wireless communication, and provides a channel estimation method for a large-scale multiple-input multiple-output system, which comprises the following steps: constructing a large-scale multiple-input multiple-output system comprising: a transmitter, a receiver, and a first channel; constructing a mathematical model of the first channel; converting the channel estimation problem into a first problem; and solving the first problem according to the ALADIN method. The invention ensures the accuracy of channel estimation, has higher convergence speed and robustness compared with the prior art, and has stable performance under the conditions of different training lengths and signal-to-noise ratios.

Description

Channel estimation method for large-scale multi-input multi-output system

Technical Field

The present invention relates generally to the field of wireless communications. In particular, the present invention relates to a channel estimation method for a massive multiple-input multiple-output system.

Prior Art

A large-scale multiple-input multiple-output (Massive MIMO) system has the advantages of large capacity, high spectrum utilization rate, and the like, and is one of the keys for realizing 5G communication. Due to the low frequency and high directivity of the millimeter waves, the millimeter waves can accurately process large antenna arrays in the transmitting and receiving processes, so that the millimeter waves are widely applied to a Massive MIMO system. However, the advantages of the Massive MIMO system are based on the accurate acquisition of Channel State Information (Channel State Information CSI), the high frequency of the millimeter wave causes the coherence time of the Channel to be shortened, and the deployment of a large antenna array means a larger amount of calculation, so a Channel estimation method with high accuracy and fast convergence is required.

The partial channel estimation method utilizes the sparsity of the channel and converts the channel estimation into a Compressed Sensing (CS) problem. For example, Orthogonal Matching Pursuit (Orthogonal Matching Pursuit OMP) (Alexandrinopoulos G C, Choivardas S. Low Complex channel estimation for metric wave Systems with hybrid A/D anti-processing; proceedings of the 2016 IEEE Global work pages (GC Wkshps), F, 2016[ C ] IEEE ] and Vector messaging (Vector application messaging VAMP) (Schniter P, Ractan S, Fletcher A K. Vector application messaging for the Vector messaging, proceedings of the equation 50th application signaling, System F, 2016).

The partial channel estimation method utilizes the low rank property of the channel, such as Nguyen S L H et al (Compressive sensing-based channel estimation for massive multiple user MIMO systems; proceedings of the 2013 IEEE Wireless Communication and Networking Conference (WCNC), F, 2013[ C ] IEEE) to convert the channel estimation into a quadratic semi-definite programming problem (SDP) and solve it by a polynomial SDP method. However, the above-described channel estimation method using the sparsity or low rank property of the channel has a problem of depending on a large number of symbol trains.

In recent years, a channel estimation method combining sparsity and low rank property of a channel has been proposed. For example, Li X et al (Millimeter wave estimation video amplification joint and low-rank structures [ J ]. IEEE Transactions on Wireless Communications, 2017, 17 (2): 1123-33) propose a channel estimation method (TSSR) that separately utilizes sparsity and low rank of a channel in two steps, but this method has a problem of being computationally too complex. Vchannels E et al (Massive MIMO channel estimation for millimeter systems visual matrix completion [ J ]. IEEE Signal Processing Letters, 2018, 25 (11): 1675-9) propose a channel estimation Method based on an Alternating Direction multiplier Method (Alternating Direction Method of Multipliers ADMM), however, the convergence speed and robustness of the Method still need to be improved.

Disclosure of Invention

The problems that the channel estimation method in the prior art depends on a large amount of symbol training, the calculation is too complex, and the convergence speed and the robustness are to be improved are solved at least partially. The invention provides a channel estimation method for a large-scale multi-input multi-output system, which comprises the following steps:

constructing a large-scale multiple-input multiple-output system comprising:

transmitter having N_TA first antenna element;

receiver having N_RA second antenna element; and

a first channel, wherein the transmitter transmits signals to the receiver over the first channel;

constructing a mathematical model of the first channel, wherein the first channel is represented as a first channel matrix H', as shown in the following equation:

wherein the content of the first and second substances,

a first unitary matrix is represented that is,

a second unitary matrix is represented that is,

represents a sparse matrix and I_NRepresenting an N-order identity matrix;

converting the channel estimation problem into a first problem, wherein channel state information in a first channel matrix H' is solved through a sparse matrix Z; and

the first problem was solved according to the ALADIN method.

In the present invention, the term "ALADIN method" refers to a method based on the augmented Lagrangian alternating direction non-exact Newton method (Houska B, Frasch J, Diehlm. an augmented Lagrangian based Optimization for distributed non-orthogonal Optimization [ J ]. SIAM Journal on Optimization, 2016, 26 (2): 1101-27).

The meanings of the mathematical symbols in the present invention and its various embodiments are shown in table 1.

TABLE 1

In one embodiment of the invention, it is provided that the first problem comprises:

τ_Z，τ_H′＞0，

wherein, tau_H′Denotes a first weight factor, τ_ZA second weight factor is represented which is a function of,

denotes the overall active antenna matrix, H'_ΩA sub-sampling matrix representing the first channel matrix H'.

In one embodiment of the invention, it is provided that an auxiliary variable is introduced into the first question, which includes the following steps:

introducing a first auxiliary variable Y, wherein Y ═ H';

introducing a second auxiliary variable C, wherein

And

converting the first question into a second question according to the first auxiliary variable Y and the second auxiliary variable C, and the formula is represented as follows:

therein, sigma_kA first weight matrix is represented, which is second order semi-positive.

In one embodiment of the invention, it is provided that solving the first problem according to the ALADIN method comprises the following steps:

introducing a first couple operator according to the ALADIN method

And a second dual operator

Wherein T represents the number of signals transmitted by the transmitter to the receiver through the first channel;

according to the first even operator lambda₁And a second dual operator λ₂Converting the second question to a third question, represented by the following formula:

where ρ represents a first step size; and

solving the third problem according to the ALADIN method comprising the following steps:

inputting an initial value H 'of an iterative loop'⁽⁰⁾、Z⁽⁰⁾、C⁽⁰⁾、λ₁ ⁽⁰⁾And λ₂ ⁽⁰⁾；

To carry out I_maxA minor iteration loop with I as the number of iterations, where I is 0, 1_maxSolving for H 'in the ith iteration'⁽ⁱ⁺¹⁾、Y⁽ⁱ⁺¹⁾、Z⁽ⁱ⁺¹⁾、C⁽ⁱ⁺¹⁾、λ¹⁽ⁱ⁺¹⁾And λ₂ ⁽ⁱ⁺¹⁾(ii) a And

completion of I_maxIterate the loop again, and output H'^(max)。

In one embodiment of the invention it is provided that H 'is solved in the ith iteration'⁽ⁱ⁺¹⁾Comprises the following steps:

solving H 'according to the third problem'⁽ⁱ⁺¹⁾Is expressed as solution H'⁽ⁱ⁺¹⁾A first equation, shown as:

solving H 'according to singular value threshold method'⁽ⁱ⁺¹⁾First equation is converted into solution H'⁽ⁱ⁺¹⁾A second equation, shown below:

wherein the content of the first and second substances,

and

representation matrix

R represents the number of singular values, σ_jRepresenting the jth of the r singular values; and

according to the solution H'⁽ⁱ⁺¹⁾Solving a second equation of H'⁽ⁱ⁺¹⁾。

In one embodiment of the invention, it is provided that Y is solved in the ith iteration⁽ⁱ⁺¹⁾Comprises the following steps:

partial differentiation of Y according to the third problem, expressed as solving Y⁽ⁱ⁺¹⁾A first equation, shown as:

let the solution Y⁽ⁱ⁺¹⁾The first equation is equal to zero, and the solution Y is⁽ⁱ⁺¹⁾The first equation is expressed as solving for Y⁽ⁱ⁺¹⁾A second equation, shown below:

wherein I represents a unit momentArray, y represents vec (Y), H 'represents vec (H'), c represents vec (C), z represents vec (Z) and E_jjRepresents a jj matrix, wherein the jj matrix E_jjThe middle position (j, j) is 1, and the rest positions are zero;

according to the solution Y⁽ⁱ⁺¹⁾The second equation is solving for y⁽ⁱ⁺¹⁾(ii) a And

according to Y⁽ⁱ⁺¹⁾＝unvec(y⁽ⁱ⁺¹⁾) Solving for Y⁽ⁱ⁺¹⁾。

In one embodiment of the invention, it is provided that Z is solved in the ith iteration⁽ⁱ⁺¹⁾Comprises the following steps:

solving Z according to said third problem⁽ⁱ⁺¹⁾Expressed as solving for Z⁽ⁱ⁺¹⁾A first equation, shown as:

by vectorization, the solution Z⁽ⁱ⁺¹⁾The first equation translates to a sparse optimization problem, denoted as solving Z⁽ⁱ⁺¹⁾A second equation, shown below:

wherein z represents vec (Z);

solving the sparse optimization problem by minimum absolute shrinkage and selection method, denoted as solving Z⁽ⁱ⁺¹⁾A third equation, shown below:

wherein β represents a first intermediate quantity;

processing the solution Z through soft threshold decisions⁽ⁱ⁺¹⁾Third equation to solve for z⁽ⁱ⁺¹⁾Expressed as the following formula:

z⁽ⁱ⁺¹⁾＝sign(Re(β⁽ⁱ⁾))οmax(|Re(β⁽ⁱ⁾)|-τ′_Z，0)+sign(Im(β⁽ⁱ⁾))οmax(|Im(β⁽ⁱ⁾)|-τ′_Z，0)，

and

according to Z⁽ⁱ⁺¹⁾＝unvec(z⁽ⁱ⁺¹⁾) Solving for Z⁽ⁱ⁺¹⁾。

In one embodiment of the invention, it is provided that the solution of β is carried out by the ALADIN method based on the gradient descent method⁽ⁱ⁾The method comprises the following steps:

construction of solution beta⁽ⁱ⁾A first equation, shown as:

Φβ⁽ⁱ⁾＝b⁽¹⁾，

according to the ALADIN method with a second intermediate variable

Substituted for beta⁽ⁱ⁾Performing an iterative loop, wherein the solution of the ith iteration is represented by the following formula:

wherein r is⁽ⁱ⁾Residual error, alpha, representing the gradient decrease during each iteration⁽ⁱ⁾Represents a second step size; and

the second step size alpha⁽ⁱ⁾For settable fixed values or solved in an iterative loop by

In one embodiment of the invention, it is provided that C is solved in the ith iteration⁽ⁱ⁺¹⁾Comprises the following steps:

partial differentiation of C according to the third problem, denoted as solving C⁽ⁱ⁺¹⁾A first equation, shown as:

let the solution C⁽ⁱ⁺¹⁾The first equation is equal to zero, and the solution C is solved⁽ⁱ⁺¹⁾The first equation is represented as solving for C⁽ⁱ⁺¹⁾A second equation, shown below:

and

according to the solution C⁽ⁱ⁺¹⁾Solving of the second equation C⁽ⁱ⁺¹⁾。

In one embodiment of the invention, it is provided that λ is solved in the ith iteration₁ ⁽ⁱ⁺¹⁾And λ₂ ⁽ⁱ⁺¹⁾Comprises the following steps:

solving λ from the third problem₁ ⁽ⁱ⁺¹⁾Expressed as the following formula:

λ₁ ⁽ⁱ⁺¹⁾＝λ₁ ⁽ⁱ⁾+ρ(Y⁽ⁱ⁺¹⁾-H′⁽ⁱ⁺¹⁾) And an

According to the aboveSolving of the third problem₂ ⁽ⁱ⁺¹⁾Expressed as the following formula:

the invention has the advantages that the channel estimation of the large-scale multi-input multi-output system is carried out according to the ALADIN method, the accuracy of the channel estimation is ensured, compared with the prior art, the invention has higher convergence speed and robustness, and stable performance is shown under the conditions of different training lengths and signal-to-noise ratios.

Drawings

To further clarify the advantages and features that may be present in various embodiments of the present invention, a more particular description of various embodiments of the invention will be rendered by reference to the appended drawings. It is appreciated that these drawings depict only typical embodiments of the invention and are therefore not to be considered limiting of its scope. In the drawings, the same or corresponding parts will be denoted by the same or similar reference numerals for clarity.

Fig. 1 shows a comparison of NMSE for various channel estimation methods under different training lengths and signal-to-noise ratios in an embodiment of the present invention.

FIG. 2 shows the ASE comparison of the channel estimation methods under different training lengths and signal-to-noise ratios in one embodiment of the present invention.

Fig. 3 shows a comparison of NMSE at different path numbers for each channel estimation method in one embodiment of the invention.

Fig. 4 shows a comparison of the required time durations of each iteration of the channel estimation methods under different training lengths in one embodiment of the present invention.

Fig. 5 shows the convergence of the method of the present invention in one embodiment of the present invention.

Detailed Description

It should be noted that the components in the figures may be exaggerated and not necessarily to scale for illustrative purposes. In the figures, identical or functionally identical components are provided with the same reference symbols.

In the present invention, "disposed on …", "disposed over …" and "disposed over …" do not exclude the presence of an intermediate therebetween, unless otherwise specified. Further, "disposed on or above …" merely indicates the relative positional relationship between two components, and may also be converted to "disposed below or below …" and vice versa in certain cases, such as after reversing the product direction.

In the present invention, the embodiments are only intended to illustrate the aspects of the present invention, and should not be construed as limiting.

In the present invention, the terms "a" and "an" do not exclude the presence of a plurality of elements, unless otherwise specified.

It is further noted herein that in embodiments of the present invention, only a portion of the components or assemblies may be shown for clarity and simplicity, but those of ordinary skill in the art will appreciate that, given the teachings of the present invention, required components or assemblies may be added as needed in a particular scenario. Furthermore, features from different embodiments of the invention may be combined with each other, unless otherwise indicated. For example, a feature of the second embodiment may be substituted for a corresponding or functionally equivalent or similar feature of the first embodiment, and the resulting embodiments are likewise within the scope of the disclosure or recitation of the present application.

It is also noted herein that, within the scope of the present invention, the terms "same", "equal", and the like do not mean that the two values are absolutely equal, but allow some reasonable error, that is, the terms also encompass "substantially the same", "substantially equal". By analogy, in the present invention, the terms "perpendicular", "parallel" and the like in the directions of the tables also cover the meanings of "substantially perpendicular", "substantially parallel".

The numbering of the steps of the methods of the present invention does not limit the order of execution of the steps of the methods. Unless specifically stated, the method steps may be performed in a different order.

The invention is further elucidated with reference to the drawings in conjunction with the detailed description.

Constructing a large-scale multiple-input multiple-output system comprising:

transmitter having N_TA first antenna element;

receiver having N_RA second antenna element; and

a first channel, wherein the transmitter transmits signals to the receiver over the first channel;

the mathematical model of the first channel is constructed based on the study of Sayed A M (Sayed A M. deconstructing multiple influencing channels [ J ]. IEEE Transactions on Signal processing, 2002, 50 (10): 2563-79) and Brady J (Brady J, Behdad N, Sayed A M. Beamspace MIMO for mile-wave communications: System architecture, modeling, analysis, and measurement [ J ]. IEEE Transactions on extensions and processing, 2013, 61 (7): 3814-27.) et al, the mathematical model of the first channel is constructed from the perspective of the beam domain model, from the perspective of the matrix Completion theory (Cai J-F, cancer holes E J, Shell Z.A simulation), the simulation of the first channel, the study of simulation [ I-195J ] (Journal of simulation, I, simulation, 2, simulation, I, 195I-20. Journal J, simulation, M. 195I, 195I-82, and similar, f, 2015[ C ])) represents the first channel as a first channel matrix H', as shown in the following equation:

wherein the content of the first and second substances,

a first unitary matrix is represented that is,

representing a second unitary matrix, which is a unitary matrix based on a normalized discrete Fourier transform,

the elements of the representation matrix being complex numbers, N_R×N_RRepresenting the horizontal and vertical of the matrix.

The sparse matrix is shown to only contain a small amount of channel gain with high amplitude, almost all characteristics of a real channel can be reflected, and the sparse characteristic of the channel is represented. I is_NRepresenting an N-order identity matrix; the rank r of the first channel matrix H' satisfies r ═ min { N ═ N_T，N_R，N_pAnd H' is a low rank matrix.

The channel estimation problem is transformed into a first problem, wherein the channel state information in the first channel matrix H' is solved by the sparse matrix Z.

The first problem is a joint optimization problem, including:

τ_Z，τ_H′＞0，

the above formula is a problem of complete matrix with auxiliary information, i.e. Z non-calculation₁As the auxiliary information, the solution H' is assisted.

Wherein | H' | purple light_*Has low rank characteristic, and simultaneously | | | Z | | non-woven phosphor₁Has sparseness. Tau is_H′Denotes a first weight factor, τ_ZRepresenting a second weight factor, τ_Z，τ_H＞0。

Representing an overall active antenna matrix, where 0, 1 represents that the element in Ω takes 0 or 1, the non-zero entries in Ω are randomly distributed with the same probability since a switch-based Hybrid Beamforming (HBF) architecture is employed, and the transceiving antennas are randomly active at each time. H'_ΩA sub-sampling matrix representing the first channel matrix H'.

||H′||_*Has low rank characteristic, and simultaneously | | | Z | | non-woven phosphor₁Has sparseness and sparseness.

The overall active antenna matrix is represented, and due to the adoption of a switch-based HBF (hybrid base station) architecture, the transceiving antennas are randomly activated at each moment, so that non-zero items in omega are randomly distributed with the same probability, and M | | omega | | survival rate₀，(0≤M≤N_RN_T) Indicating the number of antennas that are activated simultaneously. Matrix H_ΩA sub-sampling matrix representing a channel matrix.

Introducing an auxiliary variable in the first question, comprising:

introducing a first auxiliary variable Y, wherein Y ═ H';

introducing a second auxiliary variable C, wherein

And

converting the first problem into a second problem according to the first auxiliary variable Y and a second auxiliary variable C, wherein the second problem is a dual-target optimization problem and is expressed as the following formula:

wherein, sigma_kRepresents the firstA weight matrix, which is second order semi-positive. The first weight matrix Σ_kAnd performing autonomous iteration, wherein k represents the iteration number. Sigma_kIn the case of a unit matrix, the equivalence is to solve for the F-norm.

As shown in the third and fourth terms of the above equation, the two introduced auxiliary variables separate the discrete error from the noise of an Additive White Gaussian Noise (AWGN) channel.

Introducing a first couple operator in the second problem according to the ALADIN method

And a second dual operator

Wherein T represents the number of signals transmitted by the transmitter to the receiver via the first channel, and the second problem is transformed into a third problem, which is expressed by the following equation:

wherein ρ represents a first step size, which is the convergence step size of the ALADIN method; and

solving the third problem according to an ALADIN method, which calls different low-level solvers internally as the case may be to solve the convex optimization and non-convex optimization problems, and there are different solving processes according to different problems, and this embodiment includes the following steps:

inputting an initial value H 'of an iterative loop'⁽⁰⁾、Z⁽⁰⁾、C⁽⁰⁾、λ₁ ⁽⁰⁾And λ₂ ⁽⁰⁾；

To carry out I_maxA minor iteration loop with I as the number of iterations, where I is 0, 1_maxSolving for H 'in the ith iteration'⁽ⁱ⁺¹⁾、Y⁽ⁱ⁺¹⁾、Z⁽ⁱ⁺¹⁾、C⁽ⁱ⁺¹⁾、λ₁ ⁽ⁱ⁺¹⁾And λ₂ ⁽ⁱ⁺¹⁾(ii) a And

completion of I_maxA sub-iteration loop, and outputting

Solving for H 'in the ith iteration'⁽ⁱ⁺¹⁾Comprises the following steps:

solving H from the third problem^’(i+1)Expressed as solving for H^’(i+1)A first equation, shown as:

according to the singular value threshold method (SVT) (Cai J-F, Cande E J, Shen Z.A single value threshold algorithm for matrix compression [ J]SIAM Journal on optimization, 2010, 20 (4): 1956-82.) will solve for H'⁽ⁱ⁺¹⁾The first equation is converted into solving H^’(i+1)A second equation, shown below:

wherein the content of the first and second substances,

and

representation matrix

R represents the number of singular values, σ_jRepresenting the jth of the r singular values; and

according to the solution H^’(i+1)Solving the second equation H^’(i+1)。

Solving for Y in the ith iteration⁽ⁱ⁺¹⁾Comprises the following steps:

partial differentiation of Y according to the third problem, expressed as solving Y⁽ⁱ⁺¹⁾A first equation, shown as:

let the solution Y⁽ⁱ⁺¹⁾The first equation is equal to zero, and the solution Y is⁽ⁱ⁺¹⁾The first equation is expressed as solving for Y⁽ⁱ⁺¹⁾A second equation, shown below:

wherein I represents an identity matrix, y represents vec (Y), H 'represents vec (H'), c represents vec (C), z represents vec (Z), and E_jjRepresents a jj matrix, wherein the jj matrix E_jjThe middle position (j, j) is 1, and the rest positions are zero;

according to the solution Y⁽ⁱ⁺¹⁾The second equation is solving for y⁽ⁱ⁺¹⁾(ii) a And

according to Y⁽ⁱ⁺¹⁾＝unvec(y⁽ⁱ⁺¹⁾) Solving for Y⁽ⁱ⁺¹⁾。

Solving for Z in the ith iteration⁽ⁱ⁺¹⁾Comprises the following steps:

solving Z according to said third problem⁽ⁱ⁺¹⁾Expressed as solving for Z⁽ⁱ⁺¹⁾A first equation, shown as:

by vectorization, the solution Z⁽ⁱ⁺¹⁾The first equation translates to a sparse optimization problem, denoted as solving Z⁽ⁱ⁺¹⁾A second equation, shown below:

wherein z represents vec (Z);

by the minimum absolute shrinkage and selection method (Tibshirani R. regression shrinkage and selection via the lasso [ J ]]Journal of the Royal Statistical Society: series B (Methodological), 1996, 58 (1): 267-88) solving the sparse optimization problem, denoted as solving Z⁽ⁱ⁺¹⁾A third equation, shown below:

wherein β represents a first intermediate quantity;

processing the solution Z through soft threshold decisions⁽ⁱ⁺¹⁾Third equation to solve for z⁽ⁱ⁺¹⁾Expressed as the following formula:

z⁽ⁱ⁺¹⁾＝sign(Re(β⁽ⁱ⁾))οmax(|Re(β⁽ⁱ⁾)|-τ′_Z，0)+sign(Im(β⁽ⁱ⁾))οmax(|Im(β⁽ⁱ⁾)|-τ′_z，0)，

and

according to Z⁽ⁱ⁺¹⁾＝unvec(z⁽ⁱ⁺¹⁾) Solving for Z⁽ⁱ⁺¹⁾。

Solving beta by the ALADIN method based on the gradient descent method⁽ⁱ⁾The method comprises the following steps:

construction of solution beta⁽ⁱ⁾A first equation, shown as:

Φβ⁽ⁱ⁾＝b⁽ⁱ⁾，

in the prior art, when beta is solved based on ADMM algorithm, matrix K needs to be solved₂Solving the Graham matrix is a process requiring a large amount of computation

Becomes the most time consuming part of the whole algorithm. The inventor finds the gram matrix in the research

Is a diagonal dominance matrix, the sum of the modulus of the non-diagonal elements of each row is less than the modulus of the diagonal elements of the row, so the complexity is reduced to O (LN) by adopting the Gradient Descent method (Gradient decision)_TN_R)。

According to the ALADIN method with a second intermediate variable

As beta⁽ⁱ⁾Approximation of, in place of beta⁽ⁱ⁾Performing an iterative loop, wherein the solution of the ith iteration is represented by the following formula:

wherein r is⁽ⁱ⁾Residual error, alpha, representing the gradient decrease during each iteration⁽ⁱ⁾Represents a second step size; and

the second step size alpha⁽ⁱ⁾For settable fixed values or solved in an iterative loop by

Solving for C in the ith iteration⁽ⁱ⁺¹⁾Comprises the following steps:

partial differentiation of C according to the third problem, denoted as solving C⁽ⁱ⁺¹⁾A first equation, shown as:

let the solution C⁽ⁱ⁺¹⁾The first equation is equal to zero, and the solution C is solved⁽ⁱ⁺¹⁾The first equation is represented as solving for C⁽ⁱ⁺¹⁾A second equation, shown below:

and

according to the solution C⁽ⁱ⁺¹⁾Solving of the second equation C⁽ⁱ⁺¹⁾。

Solving for λ in the ith iteration₁ ⁽ⁱ⁺¹⁾And λ₂ ⁽ⁱ⁺¹⁾Comprises the following steps:

solving λ from the third problem₁ ⁽ⁱ⁺¹⁾Expressed as the following formula:

λ₁ ⁽ⁱ⁺¹⁾＝λ₁ ⁽ⁱ⁾+ρ(Y⁽ⁱ⁺¹⁾-H′⁽ⁱ⁺¹⁾) And an

Solving λ from the third problem₂ ⁽ⁱ⁺¹⁾Expressed as the following formula:

the flow of channel estimation in this embodiment is shown in table 2:

TABLE 2

In one embodiment of the present invention, a system of 64 x 64 antenna arrays was set up and simulated using MATLAB. The channel estimation is carried out by selecting and comparing the Orthogonal Matching Pursuit (OMP), the vector message passing (VAMP), the two-step estimation (TSSR) and the alternating direction multiplier (ADMM) with the method of the invention. The hardware platform adopted by simulation is the hardware configuration of Intel Core I7-10710U CPU and 16GB memory, and the iteration number I of each time is set for ADMM, ALADIN and SVT stages of VAMP adopting the iterative algorithm through 100 Monte Carlo experiments on MATLAB_maxBoth are 100, comparing the performance gap of each method under different scenes.

To be provided with

Expressing the estimate of H', the performance is compared in this example using the Achievable Spectral Efficiency (ASE) and the Normalized Mean Square Error (NMSE) as shown in the following equation:

the performance boundaries of ASE are shown below:

in the embodiment, NMSE and ASE of each method under the conditions of different training lengths T and signal-to-noise ratios SNR are tested, and different path numbers N of each method are used_PThe following NMSE comparisons.

Figure 1 shows a comparison of NMSE for each method at different training lengths and signal-to-noise ratios. The scheme based on the OMP method is not obviously improved along with the increase of the training length and the signal-to-noise ratio, because the OMP algorithm does not consider the discrete error of the arrival angle, the channel model adopted by the embodiment is poor in adaptation. The VAMP method is very dependent on statistical information of sparse signals, when the training length is short, the VAMP cannot work normally, and the average iteration time consumption of the method is 1 to 2 orders of magnitude lower than that of the VAMP. The TSSR method is based on SVT and VAMP, but does not improve the disadvantage of VAMP through the low rank property that SVT utilizes, and performs poorly under different training lengths and signal-to-noise ratios. The ADMM method performs better, and compared with the ADMM method, the method based on ALADIN provided by the invention has higher accuracy and stronger robustness.

Figure 2 shows the ASE comparison for each method under different training lengths and signal-to-noise ratios. The calculation of the ASE is related to the NMSE from the calculation formula of the ASE, so that the channel estimation when the NMSE is zero is set as perfect channel estimation (perfect CSI), and the comparison shows that the method can be well close to the perfect channel estimation under the conditions of different training lengths and signal-to-noise ratios, and is obviously superior to other methods when the signal-to-noise ratio is more than 15 dB.

Fig. 3 shows a comparison of the NMSE for each method at different path numbers, with the parameter set to T1200 and SNR 30 dB. Because the influence of the path number on the millimeter wave channel is great, the performance of each method is obviously reduced along with the increase of the path number, but the performance of the method is always superior to that of other methods.

FIG. 4 shows the time duration required for each iteration of each method under different training lengths, when the parameter is set to SNR of 30dB, I_max100. The average iteration time of the TSSR method is stabilized at about 12s, which is not shown because it is inconvenient to put into the figure for comparison. As can be seen, the consumption of the OMP methodThe time is shortest, however, the scheme cannot be used under different training lengths and signal-to-noise ratios, and the VAMP method depends on the training length, and the time consumption is increased rapidly as the training length is increased. While the ADMM method and the method of the invention performed best and performed very stably at different training lengths, the method of the invention took about half the time as ADMM.

Fig. 5 separately shows the convergence of the method of the present invention, where the parameters are set to T1200 and SNR 30dB, and it can be seen that when T > 300, the algorithm converges to a steady value after 20 iterations, and when T > 600, more satisfactory performance can be achieved after 10 iterations (10)^-2)。

While various embodiments of the present invention have been described above, it should be understood that they have been presented by way of example only, and not limitation. It will be apparent to persons skilled in the relevant art that various combinations, modifications, and changes can be made thereto without departing from the spirit and scope of the invention. Thus, the breadth and scope of the present invention disclosed herein should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.

Claims (10)

1. A channel estimation method for a massive multiple-input multiple-output system, comprising the steps of:

constructing a large-scale multiple-input multiple-output system comprising:

transmitter having N_TA first antenna element;

receiver having N_RA second antenna element; and

a first channel, wherein the transmitter transmits signals to the receiver over the first channel;

constructing a mathematical model of the first channel, wherein the first channel is represented as a first channel matrix H', as shown in the following equation:

wherein the content of the first and second substances,

a first unitary matrix is represented that is,

a second unitary matrix is represented that is,

represents a sparse matrix and I_NRepresenting an N-order identity matrix;

converting the channel estimation problem into a first problem, wherein channel state information in a first channel matrix H' is solved through a sparse matrix Z; and

the first problem was solved according to the ALADIN method.

2. The method of claim 1, wherein the first problem comprises:

τ_Z，τ_H′＞0，

wherein, tau_H′Represents the firstWeight factor, τ_ZA second weight factor is represented which is a function of,

denotes the overall active antenna matrix, H'_ΩA sub-sampling matrix representing the first channel matrix H'.

3. The channel estimation method for massive multiple-input multiple-output system according to claim 2, further comprising introducing an auxiliary variable in the first problem, comprising the steps of:

introducing a first auxiliary variable Y, wherein Y ═ H';

introducing a second auxiliary variable C, wherein

And

converting the first question into a second question according to the first auxiliary variable Y and the second auxiliary variable C, and the formula is represented as follows:

therein, sigma_kA first weight matrix is represented, which is second order semi-positive.

4. The method of channel estimation for massive multiple-input multiple-output system according to claim 3, wherein solving the first problem according to the ALADIN method comprises the following steps:

introducing a first couple operator according to the ALADIN method

And a second dual operator

Wherein T represents the number of signals transmitted by the transmitter to the receiver through the first channel;

according to the first even operator lambda₁And a second dual operator λ₂Converting the second question to a third question, represented by the following formula:

where ρ represents a first step size; and

solving the third problem according to the ALADIN method comprising the following steps:

inputting an initial value H of an iterative loop^′(0)、Z⁽⁰⁾、C⁽⁰⁾、λ₁ ⁽⁰⁾And λ₂ ⁽⁰⁾；

To carry out I_maxA minor iteration loop with I as the number of iterations, where I is 0, 1_maxSolving for H 'in the ith iteration'⁽ⁱ⁺¹⁾、Y⁽ⁱ⁺¹⁾、Z⁽ⁱ⁺¹⁾、C⁽ⁱ⁺¹⁾、λ₁ ⁽ⁱ⁺¹⁾And λ₂ ⁽ⁱ⁺¹⁾(ii) a And

completion of I_maxA sub-iteration loop, and outputting

5. The channel estimation method for massive multiple-input multiple-output (MIMO) system according to claim 4, wherein H 'is solved in the ith iteration'⁽ⁱ⁺¹⁾Comprises the following steps:

solving H 'according to the third problem'⁽ⁱ⁺¹⁾Is expressed as solution H'⁽ⁱ⁺¹⁾A first equation, shown as:

solving H 'according to singular value threshold method'⁽ⁱ⁺¹⁾First equation is converted into solution H'⁽ⁱ⁺¹⁾A second equation, shown below:

wherein the content of the first and second substances,

and

representation matrix

R represents the number of singular values, σ_jRepresenting the jth of the r singular values; and

according to the solution H'⁽ⁱ⁺¹⁾Solving a second equation of H'⁽ⁱ⁺¹⁾。

6. The channel estimation method for massive multiple-input multiple-output system according to claim 4, wherein solving for Y in the ith iteration⁽ⁱ⁺¹⁾Comprises the following steps:

partial differentiation of Y according to the third problem, expressed as solving Y⁽ⁱ⁺¹⁾A first equation, shown as:

let the solution Y⁽ⁱ⁺¹⁾The first equation is equal to zero, and the solution Y is⁽ⁱ⁺¹⁾The first equation is expressed as solving for Y⁽ⁱ⁺¹⁾A second equation, shown below:

wherein I represents an identity matrix, y represents vec (Y), H 'represents vec (H'), c represents vec (C), z represents vec (Z), and E_jjRepresents a jj matrix, wherein the jj matrix E_jjThe middle position (j, j) is 1, and the rest positions are zero;

according to the solution Y⁽ⁱ⁺¹⁾The second equation is solving for y⁽ⁱ⁺¹⁾(ii) a And

according to Y⁽ⁱ⁺¹⁾＝unvec(y⁽ⁱ⁺¹⁾) Solving for Y⁽ⁱ⁺¹⁾。

7. The method of claim 4, wherein the solution of Z in the ith iteration is based on⁽ⁱ⁺¹⁾Comprises the following steps:

solving Z according to said third problem⁽ⁱ⁺¹⁾Expressed as solving for Z⁽ⁱ⁺¹⁾A first equation, shown as:

by vectorization, the solution Z⁽ⁱ⁺¹⁾The first equation translates to a sparse optimization problem, denoted as solving Z⁽ⁱ⁺¹⁾A second equation, shown below:

wherein z represents vec (Z);

solving the sparse optimization problem by a sparse regression method, denoted as solving Z⁽ⁱ⁺¹⁾A third equation, shown below:

wherein β represents a first intermediate quantity;

processing the solution Z through soft threshold decisions⁽ⁱ⁺¹⁾Third equation to solve for z⁽ⁱ⁺¹⁾Expressed as the following formula:

and

according to Z⁽ⁱ⁺¹⁾＝unvec(z⁽ⁱ⁺¹⁾) Solving for Z⁽ⁱ⁺¹⁾。

8. The channel estimation method for massive multiple-input multiple-output system as claimed in claim 7, wherein solving β by the ALADIN method based on gradient descent method⁽ⁱ⁾The method comprises the following steps:

construction of solution beta⁽ⁱ⁾A first equation, shown as:

Φβ⁽ⁱ⁾＝b⁽ⁱ⁾，

according to the ALADIN method with a second intermediate variable

Substituted for beta⁽ⁱ⁾Performing an iterative loop, wherein the solution of the ith iteration is represented by the following formula:

wherein r is⁽ⁱ⁾Residual error, alpha, representing the gradient decrease during each iteration⁽ⁱ⁾Represents a second step size; and

the second step size alpha⁽ⁱ⁾For settable fixed values or solved in an iterative loop by

9. The channel estimation method for massive multiple-input multiple-output system according to claim 4, wherein in the ith iterationMiddle solution C⁽ⁱ⁺¹⁾Comprises the following steps:

partial differentiation of C according to the third problem, denoted as solving C⁽ⁱ⁺¹⁾A first equation, shown as:

let the solution C⁽ⁱ⁺¹⁾The first equation is equal to zero, and the solution C is solved⁽ⁱ⁺¹⁾The first equation is represented as solving for C⁽ⁱ⁺¹⁾A second equation, shown below:

and

according to the solution C⁽ⁱ⁺¹⁾Solving of the second equation C⁽ⁱ⁺¹⁾。

10. The method of claim 4, wherein λ is solved in the ith iteration₁ ⁽ⁱ⁺¹⁾And λ₂ ⁽ⁱ⁺¹⁾Comprises the following steps:

solving λ from the third problem₁ ⁽ⁱ⁺¹⁾Expressed as the following formula:

λ₁ ⁽ⁱ⁺¹⁾＝λ₁ ⁽ⁱ⁾+ρ(Y⁽ⁱ⁺¹⁾-H′⁽ⁱ⁺¹⁾) And an

Solving λ from the third problem₂ ⁽ⁱ⁺¹⁾Expressed as the following formula:

Images