CN110995375A - Method and device for extracting fading characteristics of wireless channel - Google Patents

Method and device for extracting fading characteristics of wireless channel Download PDF

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CN110995375A
CN110995375A CN201911132456.2A CN201911132456A CN110995375A CN 110995375 A CN110995375 A CN 110995375A CN 201911132456 A CN201911132456 A CN 201911132456A CN 110995375 A CN110995375 A CN 110995375A
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陈月云
苗杰
买智源
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University of Science and Technology Beijing USTB
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Abstract

The invention provides a method and a device for extracting fading characteristics of a wireless channel, which can improve the real-time performance and the accuracy of channel estimation and reduce the calculation complexity of the channel estimation. The method comprises the following steps: the receiving end constructs an adjacency graph for data containing wireless channel fading characteristics according to whether the received data transmitted through the wireless channel is adjacent in Euclidean space, wherein the received data is the data containing the wireless channel fading characteristics; determining a weight matrix of data containing wireless channel fading characteristics in a low-dimensional space based on the constructed adjacency graph; determining an optimal low-dimensional feature mapping matrix of data containing wireless channel fading features according to the obtained weight matrix; and projecting the data containing the wireless channel fading characteristics to a low-dimensional space through an optimal low-dimensional characteristic mapping matrix to obtain low-dimensional manifold data containing the wireless channel fading characteristics so as to carry out channel estimation. The invention relates to the technical field of wireless communication.

Description

Method and device for extracting fading characteristics of wireless channel
Technical Field
The present invention relates to the field of wireless communication technologies, and in particular, to a method and an apparatus for extracting fading characteristics of a wireless channel.
Background
Communication is one of three major pillars of human life, and is increasingly applied to various fields of life and production, user quantity and data quantity are exponentially increased, and a new generation mobile communication technology requires high transmission rate and rich spectrum resources in the context of big data, and meanwhile, communication quality is guaranteed.
The communication quality of wireless communication depends to a large extent on the accuracy of channel estimation. Channel estimation is a process of estimating model parameters of a certain channel model to be assumed from received data. However, in the new generation mobile communication, the receiving end data contains the wireless channel fading characteristics, and the large increase of the receiving data dimension leads to the significant increase of the channel estimation computation complexity.
Disclosure of Invention
The technical problem to be solved by the present invention is to provide a method and a device for extracting fading characteristics of a wireless channel, so as to solve the problem that in the prior art, the channel estimation calculation complexity is significantly increased due to the large data dimension containing the fading characteristics of the wireless channel.
In order to solve the above technical problem, an embodiment of the present invention provides a method for extracting fading characteristics of a wireless channel, including:
the receiving end constructs an adjacency graph for data containing wireless channel fading characteristics according to whether the received data transmitted through the wireless channel is adjacent in Euclidean space, wherein the received data is the data containing the wireless channel fading characteristics;
determining a weight matrix of data containing wireless channel fading characteristics in a low-dimensional space based on the constructed adjacency graph;
determining an optimal low-dimensional feature mapping matrix of data containing wireless channel fading features according to the obtained weight matrix;
and projecting the data containing the wireless channel fading characteristics to a low-dimensional space through an optimal low-dimensional characteristic mapping matrix to obtain low-dimensional manifold data containing the wireless channel fading characteristics so as to carry out channel estimation.
Further, the step of constructing an adjacency graph for the data containing the fading characteristics of the wireless channel by the receiving end according to whether the received data transmitted through the wireless channel are adjacent in the euclidean space includes:
at the receiving end, the data containing the fading characteristics of the wireless channel is formed into a sample set YbtThe set of samples is denoted as Yb in Euclidean spacet＝{Yt1,Yt2,…YtnWhere n represents the number of samples;
judging sample Y in Euclidean spacetiAnd YtjWhether or not to satisfy Yti-Ytj||2<ε, if satisfied, then sample YtiAnd YtjIs a neighbor, connects the sample Y by an edgetiAnd YtjWhere ε represents a threshold value.
Further, the elements in the weight matrix are represented as:
Figure BDA0002278698870000021
wherein, wijIs a weight value, represents a sample point Yti、YtjThe similarity distance between them; t represents a thermonuclear parameter.
Further, the determining an optimal low-dimensional feature mapping matrix of data containing wireless channel fading features according to the obtained weight matrix includes:
according to the obtained weight matrix, constructing an objective function for solving an optimal low-dimensional feature mapping matrix V of the data containing the wireless channel fading features:
Figure BDA0002278698870000022
wherein Z isti、ZtjRespectively represent Yti、YtjA low-dimensional manifold representation in a low-dimensional space;
converting the objective function into a received data form containing wireless channel fading characteristics:
Figure BDA0002278698870000023
when Y istiAnd YtjWhen the target function is adjacent, the converted target function is deduced to obtain:
Figure BDA0002278698870000024
wherein D is a diagonal matrix formed by the sum of each column of the matrix W, and the elements in D
Figure BDA0002278698870000025
Converting the summation form of the target function obtained by derivation into a matrix form;
and solving the matrix form of the obtained objective function by using a Lagrange multiplier method to obtain an optimal low-dimensional characteristic mapping matrix of the data containing the wireless channel fading characteristics.
Further, the matrix form of the objective function is:
min(VTYtLYt TV)
wherein L is D-W, L is a laplacian matrix, and W represents a weight matrix; y ist＝[Yt1Yt2…Ytn]。
Further, the solving the obtained matrix form of the objective function by using a lagrangian multiplier method to obtain a low-dimensional feature mapping matrix containing wireless channel fading features and having optimal data includes:
adding constraint V when solving the objective functionTYtDYt TAnd V is 1, solving the matrix form of the obtained objective function by using a Lagrange multiplier method: l (V, λ) ═ VTYtLYt TV-λ(VTYtDYt TV-1); wherein, L (V, lambda) represents the corresponding Lagrange function of the target function, and lambda represents the Lagrange multiplier;
the first order partial derivative is calculated for V:
Figure BDA0002278698870000031
then
YtLYt TV＝λYtDYt TV
(YtDYt T)-1·YtLYt TV＝λV
According to (Y)tDYt T)-1·YtLYt TAnd obtaining the first d minimum eigenvectors to form an optimal low-dimensional feature mapping matrix V, wherein d represents the dimension of V.
Further, the low-dimensional manifold characterization of the data containing the wireless channel fading characteristics in the low-dimensional space is represented as: zti＝VTYti。
The embodiment of the present invention further provides a device for extracting fading characteristics of a wireless channel, including:
the building module is used for a receiving end to build an adjacency graph for data containing wireless channel fading characteristics according to whether the received data transmitted through the wireless channel is adjacent in Euclidean space, wherein the received data is the data containing the wireless channel fading characteristics;
the first determining module is used for determining a weight matrix of data containing wireless channel fading characteristics in a low-dimensional space based on the constructed adjacency graph;
the second determining module is used for determining an optimal low-dimensional feature mapping matrix of the data containing the wireless channel fading features according to the obtained weight matrix;
and the projection module is used for projecting the data containing the wireless channel fading characteristics to a low-dimensional space through the optimal low-dimensional characteristic mapping matrix to obtain low-dimensional manifold data containing the wireless channel fading characteristics so as to carry out channel estimation.
The technical scheme of the invention has the following beneficial effects:
in the scheme, a receiving end constructs an adjacency graph for data containing wireless channel fading characteristics according to whether the received data transmitted through a wireless channel are adjacent in Euclidean space; determining a weight matrix of data containing wireless channel fading characteristics in a low-dimensional space based on the constructed adjacency graph so as to ensure that local information of the wireless channel fading characteristics in the low-dimensional space is unchanged; determining an optimal low-dimensional feature mapping matrix of data containing wireless channel fading features according to the obtained weight matrix; projecting the data containing the wireless channel fading characteristics to a low-dimensional space through an optimal low-dimensional characteristic mapping matrix to obtain low-dimensional manifold data containing the wireless channel fading characteristics so as to carry out channel estimation; therefore, the dimensionality reduction of the channel fading characteristics is realized by using the manifold learning algorithm, so that the essence of the wireless channel fading characteristics is searched from the received data containing the wireless channel fading characteristics, the internal rule of the data without the channel fading characteristics is found, the real-time performance and the accuracy of channel estimation are improved, and the calculation complexity of the channel estimation is reduced.
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Fig. 1 is a schematic flowchart of a method for extracting fading characteristics of a wireless channel according to an embodiment of the present invention;
fig. 2 is a detailed flowchart of a method for extracting fading characteristics of a wireless channel according to an embodiment of the present invention;
fig. 3 is a schematic diagram of a mean square error performance curve of the wireless channel fading characteristic extraction method using manifold learning algorithm provided in the embodiment of the present invention after reducing the data characteristic dimension based on the channel estimation algorithm of the extreme learning machine;
fig. 4 is a schematic diagram of an error rate performance curve of the wireless channel fading characteristic extraction method using manifold learning algorithm provided in the embodiment of the present invention after reducing the data characteristic dimension based on the extreme learning machine channel estimation algorithm;
fig. 5 is a schematic structural diagram of an apparatus for extracting fading characteristics of a wireless channel according to an embodiment of the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments.
The invention provides a method and a device for extracting fading characteristics of a wireless channel, aiming at the problem that the existing data containing the fading characteristics of the wireless channel has large dimensionality and obviously improves the channel estimation calculation complexity.
Example one
As shown in fig. 1, the method for extracting fading characteristics of a wireless channel according to an embodiment of the present invention includes:
s101, a receiving end constructs an adjacency graph for data containing wireless channel fading characteristics according to whether the received data transmitted through a wireless channel is adjacent in Euclidean space, wherein the received data is the data containing the wireless channel fading characteristics;
s102, determining a weight matrix of data containing wireless channel fading characteristics in a low-dimensional space based on the constructed adjacency graph;
s103, determining an optimal low-dimensional feature mapping matrix of data containing wireless channel fading features according to the obtained weight matrix;
and S104, projecting the data containing the wireless channel fading characteristics to a low-dimensional space through the optimal low-dimensional characteristic mapping matrix to obtain low-dimensional manifold data containing the wireless channel fading characteristics so as to carry out channel estimation.
According to the method for extracting the fading characteristics of the wireless channel, a receiving end constructs an adjacency graph for data containing the fading characteristics of the wireless channel according to whether the received data transmitted through the wireless channel are adjacent in Euclidean space; determining a weight matrix of data containing wireless channel fading characteristics in a low-dimensional space based on the constructed adjacency graph so as to ensure that local information of the wireless channel fading characteristics in the low-dimensional space is unchanged; determining an optimal low-dimensional feature mapping matrix of data containing wireless channel fading features according to the obtained weight matrix; projecting the data containing the wireless channel fading characteristics to a low-dimensional space through an optimal low-dimensional characteristic mapping matrix to obtain low-dimensional manifold data containing the wireless channel fading characteristics so as to carry out channel estimation; therefore, the dimensionality reduction of the channel fading characteristics is realized by using the manifold learning algorithm, so that the essence of the wireless channel fading characteristics is searched from the received data containing the wireless channel fading characteristics, the internal rule of the data without the channel fading characteristics is found, the real-time performance and the accuracy of channel estimation are improved, and the calculation complexity of the channel estimation is reduced.
It should be noted that: high-dimension and low-dimension are a relative concept, and in this application, the low-dimension is calculated as long as the dimension of the data is reduced.
In this embodiment, the manifold learning algorithm is to obtain a low-dimensional manifold structure from high-dimensional sampling data, obtain a low-dimensional sub-manifold in a high-dimensional space, and perform wireless channel fading feature extraction on data containing channel fading features, so as to perform dimension reduction on the original data containing channel fading features.
For better understanding of the method for extracting fading characteristics of a wireless channel according to an embodiment of the present invention, as shown in fig. 2, the method may include the following steps:
s11, the receiving end constructs an adjacency graph for data containing wireless channel fading characteristics according to whether the received data transmitted through the wireless channel is close in the euclidean space, including:
a1, at the receiving end, forming a sample set Yb by the data containing the wireless channel fading characteristicstThe set of samples is denoted as Yb in Euclidean spacet＝{Yt1,Yt2,…YtnWhere n represents the number of samples; it follows that each data point has its neighbors represented;
a2, when constructing the adjacent map, judging the sample Y in the Euclidean spacetiAnd YtjWhether or not to satisfy Yti-Ytj||2<ε, if satisfied, then sample YtiAnd YtjIs a neighbor, connects the sample Y by an edgetiAnd YtjWherein epsilon represents a threshold value, and the size of epsilon is determined by the actual application scene.
It should be noted that:
in the adjacency graph, one sample is used as a node, and the relationship between the nodes in the adjacency graph is symmetrical, but only a few parts of the nodes in the adjacency graph are connected.
And S12, determining a weight matrix of the data containing the wireless channel fading characteristics in the low-dimensional space based on the constructed adjacency graph so as to ensure that the local information of the wireless channel fading characteristics in the low-dimensional space is unchanged.
In this embodiment, in the adjacency graph, the nodes in the vicinity are connected by edges, assuming that the adjacency graph is connected, to ensure local information of the wireless channel fading characteristics in the low-dimensional space, a thermonuclear method is used to calculate a weight matrix W of data containing the wireless channel fading characteristics in the low-dimensional space, where elements in the weight matrix are represented as:
Figure BDA0002278698870000061
wherein, wijIs a weight value, represents a sample point Yti、YtjThe similarity distance between them; t represents a thermonuclear parameter.
In this embodiment, according to the calculation formula of the weight matrix, when the sample Y is obtainedtiAnd YtjWhen not being neighbors, the weight value wijWhen sample Y is equal to 0tiAnd YtjWhen the neighbor is close, the weighted value is exp (- | | Y)ti-Ytj||2T), when the number n of samples is too large, the thermonuclear parameters can affect the local popular structure of the data of the low-dimensional mapping of the wireless channel fading characteristics, and when n is smaller, the channel fading characteristics extraction does not depend on the size of t.
S13, according to the obtained weight matrix, constructing an objective function for solving an optimal low-dimensional feature mapping matrix V of the data containing the wireless channel fading features:
Figure BDA0002278698870000071
wherein Z isti、ZtjRespectively represent Yti、YtjA low-dimensional manifold representation in a low-dimensional space;
in the present embodiment, in the total sample,
Figure BDA0002278698870000072
for ensuring that two data points Y contain fading characteristics of wireless channelti、YtjAdjacent and smallest in the space of status.
S14, assuming that the low-dimensional mapping of the data containing the wireless channel fading characteristics is the projection relation between the original data containing the channel fading characteristics and the low-dimensional space data, let Zti＝VTYtiThereby converting the objective function into a received data form containing the fading characteristics of the wireless channel:
Figure BDA0002278698870000073
further developed into
Figure BDA0002278698870000074
S15, for
Figure BDA0002278698870000075
And simplifying and deducing.
In this example, when Y istiAnd YtjWhen it is a neighbor, the objective function
Figure BDA0002278698870000076
Can be simplified as follows:
Figure BDA0002278698870000077
further, it is possible to obtain:
Figure BDA0002278698870000078
is equivalent to
Figure BDA0002278698870000081
Wherein D is a diagonal matrix formed by the sum of each column of the matrix W, and the elements in D
Figure BDA0002278698870000082
S16, converting the objective function
Figure BDA0002278698870000083
The form of summation of (a) is converted into a matrix form to solve:
Figure BDA0002278698870000084
Figure BDA0002278698870000085
thus, the matrix form of the objective function is:
min(VTYtDYt TV-VTYtWYt TV)
＝min{VTYt(D-W)Yt TV}
＝min(VTYtLYt TV)
wherein L is D-W, L is a laplacian matrix, and W represents a weight matrix; y ist＝[Yt1Yt2…Ytn]。
S17, adding constraint V when solving the objective functionTYtDYt TV ═ 1 to prevent zero vector and overfitting of the solution process, the objective function can be written as:
min VTYtLYt TV
s.t. VTYtDYt TV＝1
s18, solving the objective function by using a Lagrange multiplier method:
L(V,λ)＝VTYtLYt TV-λ(VTYtDYt TV-1)
wherein, L (V, lambda) represents the corresponding Lagrangian function of the target function, and lambda represents the Lagrangian multiplier;
the first order partial derivative is calculated for V:
Figure BDA0002278698870000091
then
YtLYt TV＝λYtDYt TV
(YtDYt T)-1·YtLYt TV＝λV
It is understood that V is (Y)tDYt T)-1·YtLYt TAnd V, finding the corresponding first d minimum eigenvectors at the moment to form an optimal low-dimensional characteristic mapping matrix V, wherein d represents the dimension of V.
S19, projecting the data containing the wireless channel fading characteristics to a low-dimensional space through the optimal low-dimensional characteristic mapping matrix to obtain low-dimensional manifold data containing the wireless channel fading characteristics:
Zti＝VTYti
in this embodiment, fig. 3 is a schematic diagram of a mean square error performance curve after a data feature dimension (CE-ML-ELM) based on an extreme learning machine channel estimation algorithm is reduced by using a wireless channel fading feature extraction method of a manifold learning algorithm according to an embodiment of the present invention. As shown in fig. 3, among the three channel estimation algorithms, the CE-ML-ELM algorithm adopted in this embodiment has the best mean square error performance, better than the estimation performance of MMSE and LS algorithms in the case of high signal-to-noise ratio, and has an estimation effect close to that of MMSE algorithm in the case of low signal-to-noise ratio.
In this embodiment, fig. 4 is a schematic diagram of an error rate performance curve after a data feature dimension (CE-ML-ELM) based on an extreme learning machine channel estimation algorithm is reduced by using a wireless channel fading feature extraction method of a manifold learning algorithm according to an embodiment of the present invention. As shown in fig. 4, among the three channel estimation algorithms, the CE-ML-ELM algorithm adopted in this embodiment has better bit error rate performance, and better estimation performance than MMSE and LS algorithms under the condition of high signal-to-noise ratio.
In summary, the embodiment of the present invention adopts the method for extracting the fading characteristics of the wireless channel using the manifold learning algorithm, and trains the extreme learning machine (a machine learning algorithm) for channel estimation by using the obtained low-dimensional data containing the fading characteristics of the wireless channel as a training sample, so that the training time of the machine learning algorithm can be reduced, and the trained extreme learning machine can realize channel estimation with higher accuracy, and obtain good performance of mean square error and error rate in channel estimation. The method for extracting the wireless channel fading characteristics by adopting the manifold learning algorithm can be applied to the next generation mobile communication technology, not only can save the design cost and simplify the design flow, but also provides a new idea for extracting the wireless channel fading characteristics, and is suitable for scenes and has generality.
Example two
The present invention also provides a specific embodiment of a fading characteristic extraction apparatus for a wireless channel, which corresponds to the specific embodiment of the aforementioned fading characteristic extraction method for a wireless channel, and can achieve the object of the present invention by executing the flow steps in the specific embodiment of the method, so the explanation in the specific embodiment of the fading characteristic extraction method for a wireless channel is also applicable to the specific embodiment of the fading characteristic extraction apparatus for a wireless channel provided by the present invention, and will not be described in detail in the following specific embodiment of the present invention.
As shown in fig. 5, an embodiment of the present invention further provides an apparatus for extracting fading characteristics of a wireless channel, including:
the building module 11 is configured to build an adjacency graph for data with a wireless channel fading characteristic by a receiving end according to whether the received data transmitted through the wireless channel is adjacent in an euclidean space, where the received data is the data with the wireless channel fading characteristic;
a first determining module 12, configured to determine, based on the constructed adjacency graph, a weight matrix of data in a low-dimensional space, where the data contains fading characteristics of a wireless channel;
a second determining module 13, configured to determine an optimal low-dimensional feature mapping matrix of data containing wireless channel fading features according to the obtained weight matrix;
and the projection module 14 is configured to project the data containing the wireless channel fading characteristics to a low-dimensional space through the optimal low-dimensional characteristic mapping matrix to obtain low-dimensional manifold data containing the wireless channel fading characteristics, so as to perform channel estimation.
According to the device for extracting the fading characteristics of the wireless channel, disclosed by the embodiment of the invention, a receiving end constructs an adjacency graph for data containing the fading characteristics of the wireless channel according to whether the received data transmitted through the wireless channel are adjacent in Euclidean space; determining a weight matrix of data containing wireless channel fading characteristics in a low-dimensional space based on the constructed adjacency graph so as to ensure that local information of the wireless channel fading characteristics in the low-dimensional space is unchanged; determining an optimal low-dimensional feature mapping matrix of data containing wireless channel fading features according to the obtained weight matrix; projecting the data containing the wireless channel fading characteristics to a low-dimensional space through an optimal low-dimensional characteristic mapping matrix to obtain low-dimensional manifold data containing the wireless channel fading characteristics so as to carry out channel estimation; therefore, the dimensionality reduction of the channel fading characteristics is realized by using the manifold learning algorithm, so that the essence of the wireless channel fading characteristics is searched from the received data containing the wireless channel fading characteristics, the internal rule of the data without the channel fading characteristics is found, the real-time performance and the accuracy of channel estimation are improved, and the calculation complexity of the channel estimation is reduced.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (8)

1. A method for extracting fading characteristics of a wireless channel, comprising:
the receiving end constructs an adjacency graph for data containing wireless channel fading characteristics according to whether the received data transmitted through the wireless channel is adjacent in Euclidean space, wherein the received data is the data containing the wireless channel fading characteristics;
determining a weight matrix of data containing wireless channel fading characteristics in a low-dimensional space based on the constructed adjacency graph;
determining an optimal low-dimensional feature mapping matrix of data containing wireless channel fading features according to the obtained weight matrix;
and projecting the data containing the wireless channel fading characteristics to a low-dimensional space through an optimal low-dimensional characteristic mapping matrix to obtain low-dimensional manifold data containing the wireless channel fading characteristics so as to carry out channel estimation.
2. The method of claim 1, wherein the constructing an adjacency graph for the data containing the fading characteristics of the wireless channel by the receiving end according to whether the received data transmitted through the wireless channel are adjacent in euclidean space comprises:
at the receiving end, the data containing the fading characteristics of the wireless channel is formed into a sample set YbtThe set of samples is denoted as Yb in Euclidean spacet＝{Yt1,Yt2,…YtnWhere n represents the number of samples;
judging sample Y in Euclidean spacetiAnd YtjWhether or not to satisfy Yti-Ytj||2<ε, if satisfied, then sample YtiAnd YtjIs a neighbor, connects the sample Y by an edgetiAnd YtjWhere ε represents a threshold value.
3. The method of claim 2, wherein the elements in the weight matrix are represented as:
Figure FDA0002278698860000011
wherein, wijIs a weight value, represents a sample point Yti、YtjThe similarity betweenA degree distance; t represents a thermonuclear parameter.
4. The method of claim 3, wherein determining the optimal low-dimensional feature mapping matrix of the data containing the fading features of the wireless channel according to the obtained weight matrix comprises:
according to the obtained weight matrix, constructing an objective function for solving an optimal low-dimensional feature mapping matrix V of the data containing the wireless channel fading features:
Figure FDA0002278698860000021
wherein Z isti、ZtjRespectively represent Yti、YtjA low-dimensional manifold representation in a low-dimensional space;
converting the objective function into a received data form containing wireless channel fading characteristics:
Figure FDA0002278698860000022
when Y istiAnd YtjWhen the target function is adjacent, the converted target function is deduced to obtain:
Figure FDA0002278698860000023
wherein D is a diagonal matrix formed by the sum of each column of the matrix W, and the elements in D
Figure FDA0002278698860000024
Converting the summation form of the target function obtained by derivation into a matrix form;
and solving the matrix form of the obtained objective function by using a Lagrange multiplier method to obtain an optimal low-dimensional characteristic mapping matrix of the data containing the wireless channel fading characteristics.
5. The method of claim 4, wherein the matrix form of the objective function is:
min(VTYtLYt TV)
wherein L is D-W, L is a laplacian matrix, and W represents a weight matrix; y ist＝[Yt1Yt2…Ytn]。
6. The method for extracting fading characteristics of wireless channel according to claim 5, wherein the obtaining the optimal low-dimensional characteristic mapping matrix containing the fading characteristics of wireless channel by solving the matrix form of the obtained objective function by using the lagrangian multiplier method comprises:
adding constraint V when solving the objective functionTYtDYt TAnd V is 1, solving the matrix form of the obtained objective function by using a Lagrange multiplier method: l (V, λ) ═ VTYtLYt TV-λ(VTYtDYt TV-1); wherein, L (V, lambda) represents the corresponding Lagrange function of the target function, and lambda represents the Lagrange multiplier;
the first order partial derivative is calculated for V:
Figure FDA0002278698860000025
then
YtLYt TV＝λYtDYt TV
(YtDYt T)-1·YtLYt TV＝λV
According to (Y)tDYt T)-1·YtLYt TAnd obtaining the first d minimum eigenvectors to form an optimal low-dimensional feature mapping matrix V, wherein d represents the dimension of V.
7. The method of claim 6, wherein the data containing the fading characteristics of the wireless channel is low in a low dimensional spaceThe dimensional manifold representation is: zti＝VTYti。
8. An apparatus for extracting fading characteristics of a wireless channel, comprising:
the building module is used for a receiving end to build an adjacency graph for data containing wireless channel fading characteristics according to whether the received data transmitted through the wireless channel is adjacent in Euclidean space, wherein the received data is the data containing the wireless channel fading characteristics;
the first determining module is used for determining a weight matrix of data containing wireless channel fading characteristics in a low-dimensional space based on the constructed adjacency graph;
the second determining module is used for determining an optimal low-dimensional feature mapping matrix of the data containing the wireless channel fading features according to the obtained weight matrix;
and the projection module is used for projecting the data containing the wireless channel fading characteristics to a low-dimensional space through the optimal low-dimensional characteristic mapping matrix to obtain low-dimensional manifold data containing the wireless channel fading characteristics so as to carry out channel estimation.
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