CN112565122B - Super-large-scale MIMO channel estimation method based on Newton-orthogonal matching pursuit - Google Patents

Super-large-scale MIMO channel estimation method based on Newton-orthogonal matching pursuit Download PDF

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CN112565122B
CN112565122B CN202011423176.XA CN202011423176A CN112565122B CN 112565122 B CN112565122 B CN 112565122B CN 202011423176 A CN202011423176 A CN 202011423176A CN 112565122 B CN112565122 B CN 112565122B
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刘洋
朱璇
戴蓉
谷稳
李钢
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Jiangnan University
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    • H04L25/0202—Channel estimation
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Abstract

The invention discloses a super-large scale MIMO channel estimation method based on Newton-orthogonal matching pursuit, which comprises the following steps: establishing a signal model according to the space non-stationary characteristic and the near field effect; obtaining a maximum likelihood estimate of the gain and position of the scatterers by minimizing the residual power according to the signal model; dividing an initial grid, searching a grid point by using an orthogonal matching pursuit algorithm, and roughly estimating the position of a scatterer and path gain; and carrying out accurate estimation by using a Newton iterative optimization method according to the initial value obtained by the rough estimation. The ultra-large-scale MIMO channel estimation method based on Newton-orthogonal matching pursuit considers the near field effect and the spatial non-stationary characteristic, increases the scattering body extinction process, simulates the appearance and disappearance of scattering bodies on an array and a time axis, increases Newton iteration on the basis of the orthogonal matching pursuit algorithm to improve the channel estimation precision and reduce the calculation complexity, and can accurately position the scattering bodies and determine the non-stationary channel.

Description

Super-large-scale MIMO channel estimation method based on Newton-orthogonal matching pursuit
Technical Field
The invention relates to the technical field of wireless communication, in particular to a super-large scale MIMO channel estimation method based on Newton-orthogonal matching pursuit.
Background
With the rapid development of mobile communication technology, the ultra-large-scale mimo is one of the key technologies of communication networks of more than the fifth generation. Accurate estimation of channel state information is very important to improve the performance of very large scale multiple input multiple output systems.
The traditional massive mimo channel estimation method is to directly estimate the channel matrix. Due to the small number of array elements, the distance between the transmitter and receiver is much greater than the rayleigh range, which is generally considered to be plane wave incidence. With the increase of the number of array elements in a super-large-scale multi-input multi-output system, the conditions of Rayleigh distance are no longer met by transmitting and receiving. The above-described assumption based on plane waves may result in a mismatch of the channel model. The introduction of spherical wavefront can more accurately describe the propagation mechanism of the super-large-scale multiple-input multiple-output channel.
In recent years, many scholars have focused their research on channel estimation with spherical wavefront. Unlike the traditional plane wave model, the channel impulse response phase of the spherical wave model is nonlinear, and this nonlinear relationship increases the difficulty of channel estimation. The current channel estimation methods based on spherical wave models are mainly divided into two categories. A method aims to reconstruct a channel matrix by estimating multipath components, and estimates time delay, arrival angle, departure angle and the like of a super-large-scale multi-input multi-output channel mainly by a space alternation generalized expectation-maximization algorithm, an expectation-maximization algorithm, a maximum likelihood algorithm and the like. However, the complexity of these algorithms is too high when searching for high-dimensional joint parameters. As is well known, the multipath components are determined by the spatial location of scatterers, and therefore, another approach focuses on estimating the spatial location of a very large scale mimo channel scatterer. A subarray channel estimation method based on an orthogonal matching pursuit algorithm has been proposed. Although the method considers the spatial non-stationary characteristic, the visible relation between each antenna and the scatterer is predefined, and the life-time and death process of the scatterer among different antennas cannot be accurately described. In addition, the orthogonal matching pursuit algorithm based on grid search has the problems of high computational complexity, large off-grid error and the like.
Disclosure of Invention
The invention aims to provide a super-large-scale MIMO channel estimation method based on Newton-orthogonal matching pursuit, which is simple and feasible and has high precision. The technical scheme is as follows:
in order to solve the above problems, the present invention provides a method for estimating a super-large MIMO channel based on newton-orthogonal matching pursuit, comprising:
establishing a signal model according to the space non-stationary characteristic and the near field effect;
obtaining a maximum likelihood estimate of the gain and position of the scatterers by minimizing the residual power according to the signal model;
dividing an initial grid, searching a grid point by using an orthogonal matching pursuit algorithm, and roughly estimating the position of a scatterer and path gain;
and carrying out accurate estimation by using a Newton iterative optimization method according to the initial value obtained by the rough estimation.
As a further improvement of the present invention, the establishing a signal model based on the spatial non-stationary characteristic and the near-field effect includes:
establishing a visible relation between a scatterer and an antenna according to the spatial non-stationary characteristic;
a signal model is established based on the near field effect and based on the visible relationship between the scatterers and the antenna.
As a further improvement of the present invention, the establishing a visible relationship between the scatterer and the antenna according to the spatially non-stationary characteristic includes:
the base station end adopts a uniform linear array and is provided with M antennas, the user end adopts a single antenna, only a downlink is considered, a plurality of scattering points exist in a link, in a super-large-scale multi-input multi-output channel, scattering assumptions are Poisson distribution, and the survival probability of scatterers among different antennas can be expressed as follows:
Figure BDA0002823463570000021
wherein λrIs the survival rate of the scatterers, D is an environment-dependent coherence factor, δ represents the spacing between different antenna elements;
the average number of newly generated scatterers may be expressed as:
is composed of
Figure BDA0002823463570000022
Wherein λ isgRepresenting the regeneration rate of the scatterers;
by psinArray psi indicating that scatterers are visiblen＝{sn,1,...,sn,m},m∈{1,2,...,M}，sn,mRepresenting the mth visible antenna relative to the scatterer n, the visible relationship between the scatterer and all antennas can be expressed as
Figure BDA0002823463570000031
If s isn,mIn the set psinIn (1),
Figure BDA0002823463570000032
as a further improvement of the present invention, the establishing a signal model according to the near-field effect and according to the visible relationship between the scatterer and the antenna includes:
the channel impulse response is characterized using a spherical wave model considering the near field effect, the response between the scatterers and the antenna is as follows:
Figure BDA0002823463570000033
wherein the content of the first and second substances,
Figure BDA0002823463570000034
representing the distance between the scatterer and the center of the array,
Figure BDA0002823463570000035
representing the distance between the scatterer and the array element m;
in the spherical wave model, the phase change and path loss change on the array are nonlinear, and the channel matrix of the downlink is
Figure BDA0002823463570000036
Wherein (x)n,yn) Coordinates representing the nth scatterer, N being the number of scatterers; gnRepresents the complex path gain; an indication of a hadamard product;
representing the signal model as a matrix representation
Figure BDA0002823463570000037
Wherein
Figure BDA0002823463570000038
w is additive white Gaussian noise satisfying
Figure BDA0002823463570000039
And (4) distribution.
As a further improvement of the invention, a maximum likelihood estimate of the gain and position of the scatterers is obtained by minimizing the residual power according to the signal model, wherein the maximum likelihood estimate is:
Figure BDA00028234635700000310
to obtain the optimal solution of the objective function, the objective problem is further transformed as follows:
Figure BDA00028234635700000311
wherein the content of the first and second substances,
Figure BDA00028234635700000312
are the scatterer coordinates obtained after the estimation,
Figure BDA0002823463570000041
the path gain is expressed as:
Figure BDA0002823463570000042
as a further improvement of the present invention, the dividing the initial grid, searching grid points by using an orthogonal matching pursuit algorithm, and roughly estimating the scatterer position and the path gain includes:
assuming that the position information of the target scatterer satisfies Xmin＜xn＜Xmax，Ymin＜yn＜Ymax，Xmin、Xmax、YminAnd YmaxThe minimum and maximum values of the scatterer position within the visible range of the array are represented separately, and the grid is divided as follows:
Z＝{(x,y)|x＝Xmin,Xmin+Δx,...,Xmax；y＝Ymin,Ymin+Δy,...,Ymax}
wherein ΔxAnd Δ y are the step sizes on the x-axis and y-axis, respectively;
the roughly estimated scatterer position and path gain are obtained by searching grid points in detail, only one path is extracted in each iteration, and the residual error obtained after the (s-1) th iteration is as follows:
Figure BDA0002823463570000043
coarse estimation of scatterer position
Figure BDA0002823463570000044
As a further improvement of the present invention, the performing the accurate estimation by using a newton iterative optimization method according to the initial value obtained by the rough estimation includes:
handle gnAs a redundancy parameter, assume
Figure BDA0002823463570000045
Is the current estimated value, the iteration step is:
Figure BDA0002823463570000046
wherein the content of the first and second substances,
Figure BDA0002823463570000047
is a first order partial derivative vector, the second order partial derivative matrix is:
Figure BDA0002823463570000051
according to
Figure BDA0002823463570000052
Handle
Figure BDA0002823463570000053
The first partial derivative of (d) is written as:
Figure BDA0002823463570000054
Figure BDA0002823463570000055
the second partial derivative of (c) is calculated as follows:
Figure BDA0002823463570000056
Figure BDA0002823463570000057
obtained by the same method
Figure BDA0002823463570000058
When the remaining power is less than the total noise power, the iterative process terminates and the threshold is set to:
Figure BDA0002823463570000059
where F { a } is a discrete Fourier transform of a, and PfaIs the false alarm rate and can obtain (x)n,yn) The generalized likelihood ratio test estimate of (1), the path gain is expressed as:
Figure BDA00028234635700000510
the invention has the beneficial effects that:
the ultra-large-scale MIMO channel estimation method based on Newton-orthogonal matching pursuit considers the near field effect and the spatial non-stationary characteristic, increases the scattering body extinction process, simulates the appearance and disappearance of scattering bodies on an array and a time axis, increases Newton iteration on the basis of the orthogonal matching pursuit algorithm to improve the channel estimation precision and reduce the calculation complexity, and can accurately position the scattering bodies and determine the non-stationary channel.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical means of the present invention more clearly understood, the present invention may be implemented in accordance with the content of the description, and in order to make the above and other objects, features, and advantages of the present invention more clearly understood, the following preferred embodiments are described in detail with reference to the accompanying drawings.
Drawings
FIG. 1 is a flow chart of a method for estimating a super-large MIMO channel based on Newton-orthogonal matching pursuit in a preferred embodiment of the present invention;
FIG. 2 is a schematic diagram of a very large scale multiple input multiple output system in accordance with a preferred embodiment of the present invention;
FIG. 3 is a graph comparing normalized mean square error of the Newtonian orthogonal matching pursuit algorithm and the conventional orthogonal matching pursuit algorithm in the present invention;
fig. 4 is a graph comparing channel capacities of the newtonian orthogonal matching pursuit algorithm of the present invention and the conventional orthogonal matching pursuit algorithm.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
As shown in fig. 1, the method for estimating a very large MIMO channel based on newton-orthogonal matching pursuit in the preferred embodiment of the present invention includes the following steps:
and S10, establishing a signal model according to the space non-stationary characteristic and the near field effect.
Optionally, step S10 includes:
and S11, establishing a visible relation between the scatterer and the antenna according to the spatial non-stationary characteristic.
As shown in fig. 2, the super-large-scale mimo system includes a base station end that employs a uniform linear array and has M antennas, a user end that employs a single antenna only considers a downlink, a link that includes multiple scattering points, and in the super-large-scale mimo channel, scattering hypotheses are all poisson distribution, and the survival probability of scatterers between different antennas can be expressed as:
Figure BDA0002823463570000071
wherein λrIs the survival rate of the scatterers, D is an environment-dependent coherence factor, δ represents the spacing between different antenna elements;
the average number of newly generated scatterers may be expressed as:
is composed of
Figure BDA0002823463570000072
Wherein λ isgRepresenting the regeneration rate of the scatterers;
to express more intuitively the visible relationship between scatterers and arrays, bynArray psi indicating that scatterers are visiblen＝{sn,1,...,sn,m},m∈{1,2,...,M}，sn,mRepresenting the mth visible antenna relative to the scatterer n, the visible relationship between the scatterer and all antennas can be expressed as
Figure BDA0002823463570000073
If s isn,mIn the set psinIn (1),
Figure BDA0002823463570000074
note:
Figure BDA0002823463570000075
the representation a is a matrix of m rows and n columns.
And S12, establishing a signal model according to the near field effect and the visible relation between the scatterer and the antenna.
Specifically, the channel impulse response is characterized by a spherical wave model considering the near-field effect, and the response between the scatterer and the antenna is as follows:
Figure BDA0002823463570000076
wherein the content of the first and second substances,
Figure BDA0002823463570000077
representing the distance between the scatterer and the center of the array,
Figure BDA0002823463570000078
representing the distance between the scatterer and the array element m;
in the spherical wave model, the phase change and path loss change on the array are nonlinear, and the channel matrix of the downlink is
Figure BDA0002823463570000079
Wherein (x)n,yn) Coordinates representing the nth scatterer, N being the number of scatterers; gnRepresents the complex path gain; an indication of a hadamard product;
representing the signal model as a matrix representation
Figure BDA00028234635700000710
Wherein
Figure BDA00028234635700000711
w is additive white Gaussian noise satisfying
Figure BDA00028234635700000712
And (4) distribution.
And S20, obtaining the maximum likelihood estimation of the gain and the position of the scatterer by minimizing the residual power according to the signal model.
Wherein the maximum likelihood estimation is:
Figure BDA0002823463570000081
to obtain the optimal solution of the objective function, the objective problem is further transformed as follows:
Figure BDA0002823463570000082
wherein the content of the first and second substances,
Figure BDA0002823463570000083
are the scatterer coordinates obtained after the estimation,
Figure BDA0002823463570000084
the path gain is expressed as:
Figure BDA0002823463570000085
however, S (x) is optimized directly by all gains and scatterer positionsn,yn) It is difficult to solve the above optimization problem by proposing newton iterative optimization based on the orthogonal matching pursuit algorithm, which is divided into two steps, see steps S30, S40.
And S30, dividing the initial grid, searching grid points by using an orthogonal matching pursuit algorithm, and roughly estimating the position of the scatterer and the path gain.
Specifically, it is assumed that the positional information of the target scatterer satisfies Xmin＜xn＜Xmax，Ymin＜yn＜Ymax，Xmin、Xmax、YminAnd YmaxThe minimum and maximum values of the scatterer position within the visible range of the array are represented separately, and the grid is divided as follows:
Z＝{(x,y)|x＝Xmin,Xmin+Δx,...,Xmax；y＝Ymin,Ymin+Δy,...,Ymax}
where Δ x and Δ y are the step sizes on the x-axis and y-axis, respectively;
the roughly estimated scatterer position and path gain are obtained by searching grid points in detail, only one path is extracted in each iteration, and the residual error obtained after the (s-1) th iteration is as follows:
Figure BDA0002823463570000086
coarse estimation of scatterer position
Figure BDA0002823463570000091
And S40, performing accurate estimation by using a Newton iterative optimization method according to the initial value obtained by the rough estimation.
Specifically, g isnAs a redundancy parameter, assume
Figure BDA0002823463570000092
Is the current estimated value, the iteration step is:
Figure BDA0002823463570000093
wherein the content of the first and second substances,
Figure BDA0002823463570000094
is a first order partial derivative vector, the second order partial derivative matrix is:
Figure BDA0002823463570000095
according to
Figure BDA0002823463570000096
Handle
Figure BDA0002823463570000097
The first partial derivative of (d) is written as:
Figure BDA0002823463570000098
Figure BDA0002823463570000099
the second partial derivative of (c) is calculated as follows:
Figure BDA00028234635700000910
Figure BDA00028234635700000911
obtained by the same method
Figure BDA00028234635700000912
When the remaining power is less than the total noise power, the iterative process terminates and the threshold is set to:
Figure BDA00028234635700000913
where F { a } is a Discrete Fourier Transform (DFT) of a, and PfaIs the false alarm rate and can obtain (x)n,yn) The generalized likelihood ratio test estimate of (1), the path gain is expressed as:
Figure BDA0002823463570000101
the modified NOMP algorithm is described as follows:
Figure BDA0002823463570000102
next, the proposed super-large-scale multiple-input multiple-output channel algorithm was verified by numerical simulation. The simulation parameter settings are shown in table 1.
Parameter Value Parameter Value
M 1024 Xmin，Xmax 0,200
δ 0.5 Ymin，Ymax -500,500
D 100 Δx, Δy 4,4
λr,λ g 8,4 Pfa 0.01
TABLE 1
The Signal-to-Noise Ratio (SNR) is defined as SNR | | | x (ω) | non-magnetic circuit2/σ2＝1/σ2. To evaluate the performance of the proposed algorithm, Normalized Mean Square Error (NMSE) is used as a metric.
Figure BDA0002823463570000103
As an estimate of the true channel h, for NMSE
Figure BDA0002823463570000104
Numerical calculations were performed. FIG. 3 is a drawingCompared with the normalized mean square error comparison graph of the Newton orthogonal matching tracking algorithm and the traditional orthogonal matching tracking algorithm, the result shows that the Newton orthogonal matching tracking algorithm has lower NMSE. This is because the addition of the newton's cycle refinement step in the proposed algorithm not only avoids the off-net effect, but also improves performance by inputting previously estimated atoms in each iteration.
Fig. 4 compares the channel capacity difference between the newtonian orthogonal matching pursuit algorithm of the present invention and the conventional orthogonal matching pursuit algorithm. The channel capacity is defined as
Figure BDA0002823463570000111
Channel capacity tends to increase as the signal-to-noise ratio increases. It is clear that the channel capacity of the proposed algorithm is closer to perfect channel state information, since the accuracy of the channel estimation is improved.
Table 2 summarizes the complexity of the Newtonian orthogonal matching pursuit algorithm of the present invention and compares it with the conventional orthogonal matching pursuit algorithm, where S is the number of iterations, Z is the number of iterationsHAnd ZLRespectively, the size of the grid partition. The comparison result shows that the computational complexity of the Newton orthogonal matching pursuit algorithm is lower than that of the orthogonal matching pursuit algorithm.
Figure BDA0002823463570000112
TABLE 2
The ultra-large-scale MIMO channel estimation method based on Newton-orthogonal matching pursuit considers the near field effect and the spatial non-stationary characteristic, increases the scattering body extinction process, simulates the appearance and disappearance of scattering bodies on an array and a time axis, increases Newton iteration on the basis of the orthogonal matching pursuit algorithm to improve the channel estimation precision and reduce the calculation complexity, and can accurately position the scattering bodies and determine the non-stationary channel.
The above embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.

Claims (4)

1. The super-large-scale MIMO channel estimation method based on Newton-orthogonal matching pursuit is characterized by comprising the following steps:
establishing a signal model according to the space non-stationary characteristic and the near field effect;
obtaining a maximum likelihood estimate of the gain and position of the scatterers by minimizing the residual power according to the signal model;
dividing an initial grid, searching a grid point by using an orthogonal matching pursuit algorithm, and roughly estimating the position of a scatterer and path gain;
carrying out accurate estimation by using a Newton iterative optimization method according to an initial value obtained by rough estimation;
the signal model is established based on the space non-stationary characteristic and the near-field effect, and comprises the following steps:
establishing a visible relation between a scatterer and an antenna according to the spatial non-stationary characteristic;
establishing a signal model according to the near field effect and the visible relation between the scatterer and the antenna;
the establishing of the visible relationship between the scatterer and the antenna according to the spatial non-stationary characteristic includes:
the base station end adopts a uniform linear array and is provided with M antennas, the user end adopts a single antenna, only a downlink is considered, a plurality of scattering points exist in a link, in a super-large-scale multi-input multi-output channel, scattering assumptions are Poisson distribution, and the survival probability of scatterers among different antennas can be expressed as follows:
Figure FDA0003252069650000011
wherein λrIs the survival rate of the scatterers, D is an environment-dependent coherence factor, δ represents the spacing between different antenna elements;
the average number of newly generated scatterers may be expressed as:
is composed of
Figure FDA0003252069650000012
Wherein λ isgRepresenting the regeneration rate of the scatterers;
by psinArray psi indicating that scatterers are visiblen＝{sn,1,...,sn,m},m∈{1,2,...,M}，sn,mRepresenting the mth visible antenna relative to the scatterer n, the visible relationship between the scatterer and all antennas can be expressed as
Figure FDA0003252069650000021
If s isn,mIn the set psinIn (1),
Figure FDA0003252069650000022
the establishing of the signal model according to the near field effect and the visible relation between the scatterer and the antenna comprises the following steps:
the channel impulse response is characterized using a spherical wave model considering the near field effect, the response between the scatterers and the antenna is as follows:
Figure FDA0003252069650000023
wherein the content of the first and second substances,
Figure FDA0003252069650000024
representing the distance between the scatterer and the center of the array,
Figure FDA0003252069650000025
representing the distance between the scatterer and the array element m;
in the spherical wave model, the phase change and path loss change on the array are nonlinear, and the channel matrix of the downlink is
Figure FDA0003252069650000026
Wherein (x)n,yn) Coordinates representing the nth scatterer, N being the number of scatterers; gnRepresents the complex path gain; an indication of a hadamard product;
representing the signal model as a matrix representation
Figure FDA0003252069650000027
Wherein
Figure FDA0003252069650000028
w is additive white Gaussian noise satisfying
Figure FDA0003252069650000029
And (4) distribution.
2. The method of claim 1, wherein the maximum likelihood estimation of the gain and position of scatterers is obtained by minimizing the residual power according to the signal model, wherein the maximum likelihood estimation is:
Figure FDA00032520696500000210
to obtain the optimal solution of the objective function, the objective problem is further transformed as follows:
Figure FDA00032520696500000211
wherein the content of the first and second substances,
Figure FDA00032520696500000212
are the scatterer coordinates obtained after the estimation,
Figure FDA00032520696500000213
the path gain is expressed as:
Figure FDA00032520696500000214
3. the method of claim 2, wherein the dividing the initial grid, searching the grid points using the orthogonal matching pursuit algorithm, and roughly estimating the scatterer position and the path gain comprises:
assuming that the position information of the target scatterer satisfies Xmin＜xn＜Xmax，Ymin＜yn＜Ymax，Xmin、Xmax、YminAnd YmaxThe minimum and maximum values of the scatterer position within the visible range of the array are represented separately, and the grid is divided as follows:
Z＝{(x,y)|x＝Xmin,Xmin+Δx,...,Xmax；y＝Ymin,Ymin+Δy,...,Ymax}
where Δ x and Δ y are the step sizes on the x-axis and y-axis, respectively;
the roughly estimated scatterer position and path gain are obtained by searching grid points in detail, only one path is extracted in each iteration, and the residual error obtained after the (s-1) th iteration is as follows:
Figure FDA0003252069650000031
coarse estimation of scatterer position
Figure FDA0003252069650000032
4. The method of claim 3, wherein the initial value obtained from the rough estimation is used for the precise estimation by using a Newton iterative optimization method, and the method comprises:
handle gnAs a redundancy parameter, assume
Figure FDA0003252069650000033
Is the current estimated value, the iteration step is:
Figure FDA0003252069650000034
wherein the content of the first and second substances,
Figure FDA0003252069650000035
is a first order partial derivative vector, the second order partial derivative matrix is:
Figure FDA0003252069650000036
according to
Figure FDA0003252069650000041
Handle
Figure FDA0003252069650000042
The first partial derivative of (d) is written as:
Figure FDA0003252069650000043
Figure FDA0003252069650000044
the second partial derivative of (c) is calculated as follows:
Figure FDA0003252069650000045
Figure FDA0003252069650000046
obtained by the same method
Figure FDA0003252069650000047
When the remaining power is less than the total noise power, the iterative process terminates and the threshold is set to:
Figure FDA0003252069650000048
where F { a } is a discrete Fourier transform of a, and PfaIs the false alarm rate and can obtain (x)n,yn) The generalized likelihood ratio test estimate of (1), the path gain is expressed as:
Figure FDA0003252069650000049
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