CN114143146B - OFDM system channel estimation system and method based on graph signal method - Google Patents
OFDM system channel estimation system and method based on graph signal method Download PDFInfo
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Abstract
The invention discloses an OFDM system channel estimation system and method based on a graph signal method; the method is a pilot frequency-based non-blind estimation algorithm, in which each resource block of an OFDM time-frequency dual-selection channel with structural characteristics is regarded as a node of a graph signal, wherein the topological structure of the graph signal is not only determined by a spatial structure, but also influenced by time selective fading and frequency selective fading. Modeling is performed by using smoothness constraint, and the signal recovery problem is mathematically modeled as an optimization problem to be solved. Meanwhile, the design of the pilot frequency position is carried out by using a graph sampling method, and a better pilot frequency placement position is found out, so that the accuracy of channel estimation is improved.
Description
Technical Field
The invention belongs to the technical field of graph signal processing, and particularly relates to an OFDM system channel estimation system and method based on a graph signal method.
Background
In a conventional data transmission system, data is generally transmitted in serial, each symbol occupies all frequency bands, channel spectrums of the carriers are not overlapped, and the frequency band utilization rate is low. In a multi-carrier system, however, when transmitting data symbols, a data stream to be transmitted is first divided into a plurality of groups of sub-data streams, and then the sub-data streams are simultaneously transmitted by a parallel transmission method. Orthogonal Frequency Division Multiplexing (OFDM) is a multi-carrier digital communication technology suitable for high-speed data transmission. OFDM techniques divide a given frequency band into more subchannels by overlapping the frequency spectrum of each subchannel. The OFDM system can reduce inter-symbol interference caused by time dispersion by converting a high-speed data stream of serial transmission into a sub-data stream of parallel transmission at a low speed. Meanwhile, the orthogonality among the subcarriers can improve the spectrum utilization rate of the system.
With the rapid development of society, more complex communication environments and more advanced vehicles are brought. The high-rise is erected, and the high-speed shuttle automobiles and the high-speed train running in the middle of the high-rise have great influence on the channel change of communication. During signal transmission, frequency selective fading caused by multipath effect causes frequency spectrum distortion of the signal at the receiving end. The Doppler effect generated by the transmitting end and the receiving end moving at high speed can also generate time selective fading. These have a large impact on the transmission performance of the communication system band. Therefore, the change characteristics of the system in the whole signal transmission process are analyzed, a time-frequency double-selection channel is established, and the accuracy of channel estimation is improved as much as possible by combining an optimal channel estimation technology, so that the performance of the whole communication system is improved.
There are two main types of channel estimation algorithms, one is a non-blind estimation algorithm, which implements channel estimation through pilot and training sequences. And the other is a blind estimation algorithm, which realizes channel estimation by utilizing the characteristics of the signal without prior knowledge. Comparing the two algorithms, a non-blind estimation algorithm is typically used.
Among the non-blind estimation algorithms, the least squares channel estimation (LS), the minimum mean square error channel estimation algorithm (MMSE) and the linear minimum mean square error algorithm (LMMSE) are the most common. The LS algorithm does not need to know channel state information a priori when performing channel estimation, and does not consider the influence of noise, so that the accuracy of estimation is poor. The MMSE algorithm combines the related information of the channel, requires that the state information of the channel is known, and has a great amount of operation for inversion after calculating an autocorrelation matrix, and is not commonly used in practice although the accuracy is improved. LMMSE is an improvement of MMSE algorithm, but requires channel part a priori information, knowing the autocorrelation function of the channel's time domain impulse response and the average power of the noise. In general, the LS algorithm is the most commonly used, which is simple to implement, and the LMMSE algorithm, which is accurate.
After estimating the channel of part of the positions based on the pilot frequency, the channel estimation of the whole system is usually realized by a first-order linear interpolation method and a second-order linear interpolation method, or the channel estimation is realized on the channel in a high-speed environment by a compressed sensing method by utilizing the characteristics of the system. Considering simple linear interpolation, there is no influence caused by time selective fading and frequency selective fading, and the channel estimation performance is insufficient.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides an OFDM system channel estimation system and method based on a graph signal method, which are used for solving the problem of inaccurate channel estimation value in the prior art.
In order to achieve the purpose, the invention is realized by adopting the following technical scheme:
an OFDM system channel estimation method based on a graph signal method comprises the following steps:
step 1, converting a channel of an OFDM system into a signal with a size of n x k, wherein n represents the number of carriers, and k represents the number of OFDM symbols;
step 2, determining the topological structure of the graph signals;
step 3, obtaining the band limit of channel data based on the topological structure of the image signal, selecting pilot frequency according to the band limit signal sampling theorem, designing a pilot frequency pattern based on a method of maximizing the minimum characteristic value, obtaining a sampling matrix, and establishing a sampling recovery problem of the image signal through the sampling matrix;
step 4, determining a smoothness constraint term of the sampling recovery problem;
and step 5, solving a sampling recovery problem based on the smoothness constraint term to obtain a channel estimation result of the OFDM system.
Further improvements of the invention are described in:
preferably, in step 1, the map signal is channel H:
where H is a channel of length n×k, W is a noise vector, and X is the nth OFDM symbol transmitted on the kth subcarrier.
Preferably, in step 2, the topology is as follows:
0＜α＜1 (8)
where α is the distance overall weighting coefficient, γ is the influencing factor, and the magnitude of γ is determined by the actual velocity V and the threshold velocity V.
Preferably, in step 3, the process of obtaining the channel data band limit based on the topology of the graph signal is:
the fourier transform of the plot signal x is:
s＝U T x (10)
the inverse fourier transform of the map is expressed as:
x＝Us (11)
when the plot Fourier coefficient s of plot signal x is non-zero for only the first k elements or only the first k plot Fourier components { u } 1 ,u 2 ,...,u k When linearly combined, the graph signal x is defined as k band-limited.
Preferably, in step 3, the sampling matrix obtained based on the method of maximizing the minimum eigenvalue is:
preferably, in step 3, the sampling recovery problem is:
Y＝Ψ opt °X+V (20)
where X represents channel data H and Y represents channel data at pilot estimated using LS algorithm
Preferably, the sample recovery problem is transformed into:
preferably, in step 4, the smoothness constraint term is:
wherein w is ij Representing the connection weights between nodes.
Preferably, in step 5, based on the smoothness constraint, the sample recovery problem forms the following optimization problem:
min H ‖SH-H P ‖ 2 +αH T LH (27)
where H represents the channel estimation vector, L represents the Laplace matrix, S is the sampling matrix ψ opt I.e. pilot pattern design, H P Is the channel estimate at the pilot;
the solution of the optimization problem is as follows:
H＝(S T S+αL) -1 S T H P (28)。
an OFDM system channel estimation based on a graph signal method, comprising:
the image signal conversion module is used for converting a channel of the OFDM system into an image signal with the size of n x k, wherein n represents the number of carriers, and k represents the number of OFDM symbols;
the topological structure acquisition module is used for determining the topological structure of the graph signals;
the sampling recovery problem establishing module is used for obtaining the band limit of the channel data based on the topological structure of the image signal, selecting pilot frequency according to the band limit signal sampling theorem, designing a pilot frequency pattern based on a method of maximizing the minimum characteristic value, obtaining a sampling matrix, and establishing the sampling recovery problem of the image signal through the sampling matrix;
the constraint item establishing module is used for determining a smoothness constraint item of the sampling recovery problem;
and the solving module is used for solving the sampling recovery problem based on the smoothness constraint term to obtain a channel estimation result of the OFDM system.
Compared with the prior art, the invention has the following beneficial effects:
the invention discloses an OFDM system channel estimation method based on a graph signal method; the method is a pilot frequency-based non-blind estimation algorithm, in which each resource block of an OFDM time-frequency dual-selection channel with structural characteristics is regarded as a node of a graph signal, wherein the topological structure of the graph signal is not only determined by a spatial structure, but also influenced by time selective fading and frequency selective fading. Modeling is performed by using smoothness constraint, and the signal recovery problem is mathematically modeled as an optimization problem to be solved. Meanwhile, the design of the pilot frequency position is carried out by using a graph sampling method, and a better pilot frequency placement position is found out, so that the accuracy of channel estimation is improved. Based on the time-frequency double-selection channel, each resource block of the time-frequency double-selection channel of the OFDM signal is modeled into a node of a graph, a proper graph topological structure is constructed, a graph Laplace matrix is constructed by utilizing the smoothness of channel data and combining the characteristics of time delay and Doppler frequency shift of the channel, and the OFDM channel estimation is performed by utilizing a graph signal method. And modeling the design of the pilot pattern as a sampling design problem of a smooth graph signal by combining a graph sampling theory, and performing self-adaption of the pilot pattern by utilizing a graph sampling method.
Further, for the OFDM time-frequency dual-selection channel, the channel estimation is performed by taking the overall correlation of the channel into consideration by taking the smoothness of the channel data into consideration and taking the method of using the map signal from a new perspective.
Further, the influence of fading is described by using a weighting coefficient, and the characteristics of the channel are combined, which are the results brought by a plurality of experiments under the environment suitable for the invention.
Further, for channel estimation in a high-speed motion scene, the correlation of signals is considered, and the channel estimation can be performed by training parameters by utilizing the relation between nodes.
Further, in a gentle motion scene, modeling the channel data into a band-limited graph signal by using a graph signal modeling method, and obtaining the minimum pilot frequency number according to the bandwidth size to place the pilot frequency, so as to obtain a scheme for saving the pilot frequency number.
The invention also discloses an OFDM system channel estimation system based on the graph signal method, which considers each resource block of the modeling time-frequency double-selection channel, namely each channel value to be estimated, utilizes the physical position information of the resource blocks and the relativity among the resource blocks, and simultaneously considers the size of the resource blocks affected by time delay and speed shifting. When channel estimation is carried out, the integral structural characteristics can be considered, a channel estimation method based on graph signal processing is provided, the problem that the channel characteristics are not reflected in the simple linear interpolation channel estimation process is solved, and a proper model is utilized to find out a proper parameter to reflect time selective fading and frequency selective fading of a channel, so that the channel estimation is carried out better. Meanwhile, the problem of pilot frequency position pattern design of channel estimation is solved, the number and the positions of the traditional pilot frequency patterns are fixed, the method of the image signal is utilized to self-adaptively find a non-fixed pilot frequency pattern, and the pattern scheme can self-adaptively change the placement position according to different environments of the channel, so that the accuracy of channel estimation is improved.
Drawings
Fig. 1 is a schematic diagram of the signal model of the drawing.
Fig. 2 is a schematic diagram of modeling resource blocks as graph signals.
Fig. 3 is a graph of normalized orthonormal basis correspondence eigenvalues of channel data modeled as a graph signal.
Fig. 4 is a plot of v=100 km/h channel estimation BER.
Fig. 5 is a plot of v=100 km/h channel estimation MSE.
Fig. 6 is a plot of v=300 km/h channel estimation BER.
Fig. 7 is a plot of v=300 km/h channel estimation MSE.
Fig. 8 is a plot of v=500 km/h channel estimation BER.
Fig. 9 is a plot of v=500 km/h channel estimation MSE.
Fig. 10 shows v=300 fixed position pilot patterns and pilot pattern patterns after design based on the new and good method of the figure.
Wherein (a) the figure is a fixed position pattern; (b) pattern signal processing method pilot pattern.
Detailed Description
The invention is described in further detail below with reference to the attached drawing figures:
the channel estimation is carried out by using a method of the image signal, firstly, the channel estimation problem is needed to be modeled into a sampling recovery problem of the image signal, and the research of the image signal is based on a digital signal processing theory, so that a perfect theoretical knowledge system exists.
Referring to fig. 1, the graph signal is represented by G (V, epsilon, W), where V represents a set of N nodes, epsilon represents a set of all edges, and the symmetric non-negative matrix W represents the weight matrix of the undirected weighted graph. Element W of the ith row and jth column in matrix W ij Defined as the weight of the edge connecting the ith node with the jth node. When there is an edge between the ith node and the jth node, w ij Is not 0; otherwise w ij Is 0. The degree matrix of the graph is defined as:
D＝diag(d 1 ,…,d N ) (1)
wherein,,defined as the degree of the ith node, and the laplacian matrix of the graph is defined as:
L＝D-W (2)
the problem of sampling and recovering the graph signals is that for the undirected weighted graph G, the collected graph signals of M nodes are defined as y= [ Y ] 1 ,y 2 ,…,y m ]. Restoration of the plot signal is the restoration of the complete signal from its samples:
Y＝S°X+V (3)
wherein X is an original image signal, Y is a sampling signal, V is Gaussian noise with small variance, S is defined as a sampling operator, and O is the Hadamard product of a matrix.
In the channel estimation problem, channel estimation is generally performed by a method such as linear interpolation based on the channel estimation result based on the pilot position. After the channel value of the pilot frequency position is known, the problem of channel estimation is a problem of data recovery, the channel value of the known partial channel position is utilized to estimate the whole channel, the process and the sampling and recovery of the signal are hardly different, if the channel data can be modeled into a graph signal with a structure, the problem of channel estimation can be converted into the problem of sampling and recovery of the graph signal, at the moment, S in the formula y=s° x+v is the pattern of pilot frequency placement, X is the channel data to be recovered, Y is the channel data of pilot frequency position estimation, and V is still noise.
How to transform the channel estimation model into the graph signal sampling and recovery problem model focuses on modeling the graph signal, that is, learning the graph topology, and finding a suitable L matrix.
Step 1, combining time-frequency double-selection channel characteristics, and regarding a channel as a picture signal;
the signal transmission of OFDM has its unique feature that it converts the OFDM symbols transmitted in serial at high speed into symbols in parallel at low speed and then transmits them to different orthogonal sub-carriers. The characteristics of its channel structure are created, each channel being described by a resource block.
In the time-frequency dual-selection channel, the nth OFDM symbol transmitted on the kth subcarrier is denoted as X (n, k), and the signal Y received by the receiving end may be denoted as:
Y＝HX+W (4)
where H is a channel of length n x k and W is the noise vector.
Wherein H (N, K) represents an nth OFDM symbol, a channel resource block of a kth subcarrier, L is a multipath number, M is a maximum doppler shift, K is a total number of subcarriers, and H (L, M) represents a channel tap coefficient.
For a resource block of size n x k, the channel data of adjacent resource blocks is considered to be smooth due to the correlation that they have with respect to their structural features. Considering each resource block as a node of the mapping signal, the value of the node is equal to the channel value of the resource block, as shown in fig. 2, a time-frequency dual-selection channel is regarded as a mapping signal with the size of n x k.
And step 2, finding a topological structure of a suitable adaptive fading channel of the picture signal.
In graph signal theory, there are many ways to learn the topology of a set of graph signals. The invention utilizes a method based on physical location to establish an initial graph topology, namely the physical distance between resource blocks. A coordinate is given to each node, the coordinate value corresponds to the subcarrier where the node is located and the number of the transmitted symbols, and the calculation is carried out according to a distance formula:
where k represents the number of subcarriers and n represents the number of OFDM symbols.
Through calculation, a distance value exists between every two nodes to describe the correlation before the nodes, and the weight value forms a weight matrix W of nk, so that the matrix L can be calculated by using the formula to obtain the structure of the graph signal. However, the obtained topology structure simply describes the physical position relation between the nodes and cannot fully reflect the channel characteristics, the invention introduces parameters according to the influence of fading to correct the topology structure, and the connection weight between the nodes is modified by the following formula (7), specifically, the distance between the nodes is weighted by considering the influence of time and frequency selective fading, and the weighting coefficient is an experimental coefficient, so that a proper topology structure can be obtained.
0＜α＜1 (8)
Where α is the distance overall weighting coefficient, γ is the influencing factor, and the magnitude of γ is determined by the actual velocity V and the threshold velocity V. After the calculated Dist matrix, namely the weight matrix W, is processed by a simple K-nearest method, only K most relevant nodes of each node are reserved as the last weight matrix W, and after the corresponding L matrix is calculated, the topological structure of the graph is found.
And step 3, combining the graph sampling theory to design a pilot pattern.
In conventional DSP signals are often considered band limited or real signals can be approximated by a low band limited signal, which still holds in GSP theory. A Laplace matrix L is used as a graph shift operator, and lambda is assumed 1 ≤λ 2 ≤...λ N . The fourier transform and the inverse fourier transform of a plot signal x can be expressed as:
s＝U T x (10)
x＝Us (11)
when the plot Fourier coefficient s of plot signal x is non-zero for only the first k elements or only the first k plot Fourier components { u } 1 ,u 2 ,...,u k When linearly combined, the plot signal is defined as a k-band limit.
After a suitable topology matrix is established, the result shown in fig. 4 appears, and the channel data band limit can be seen, at this time, pilot frequency selection can be performed by using the band-limited signal sampling theorem, and pilot frequency pattern, that is, the design of the sampling matrix, is performed by using a method based on the maximized minimum eigenvalue.
Based on the method of maximizing the minimum eigenvalue, a sampling pattern based on the graph signal method is designed. Decomposing L:
L＝U T ΛU (12)
wherein U is a Fourier base matrix, and Λ is a diagonal matrix composed of eigenvalues.
In the graph signal processing, there is a method that can realize signal recovery for band-limited signals:
x M ＝Ψx+e (13)
wherein,,is a sampled signal, ψ represents a sample set, its diagonal elements are 0,1, x represents the original signal, and e is noise. Perfect recovery can be achieved if the sample set satisfies the following theorem:
rank(ΨV (K) )＝K (14)
where K represents the bandwidth of the signal, V (K) Is the first K columns of the base matrix U after laplace matrix decomposition, and if perfect recovery is to be achieved, the following formula needs to be satisfied
x＝ΦΨx (15)
The recovery matrix Φ is defined as:
Φ＝V (K) U (16)
wherein U psi V (K) Is a K x K identity matrix.
Assuming that the defined sampling matrix is a qualified sampling operator, the signal is recovered:
x′ e ＝Φx M ＝ΦΨx+Φe＝x+Φe (17)
in order to make the noise of the recovered signal as small as possible, make:
wherein II V (K) ‖ 2 And II e II 2 Is of fixed size, then the problem translates to having U with as small a spectral norm as possible, and finally the problem translates to:
wherein ψ is opt I.e. a sampling matrix obtained by maximizing the minimum eigenvalues. After the Fourier transform of the graph Fourier basis obtained after the weighted adjacency matrix is decomposed, the channel data is approximately band limited, and the method can be used for designing beliefsChannel estimation pilot patterns.
Based on the method, the psi is obtained opt As a sampling operator, then the problem of sample recovery of the graph signal is:
Y＝Ψ opt °x+V (20)
where X represents channel data H and Y represents channel data at pilot estimated using LS algorithmV is noise. The problem can be written as:
for channel data at pilotUsing the classical LS algorithm. Sampling pattern ψ obtained by a method of maximizing a minimum feature value opt Placing pilots, channel data at the point where the pilots are received:
at this time, the LS algorithm is used forAnd (3) derivative:
and obtaining a channel estimation value of a final pilot frequency position through calculation so as to carry out overall channel estimation subsequently:
step 4, establishing a smooth mathematical representation of the graph signal matrix
Setting the sampling recovery problem of the image signal as a target problem, and the target problemAfter the establishment, constraint items are needed to be found to constrain the target problem, so that the solution is realized.
In recovering the image signal, the correlation of the image signal itself is generally used. The correlation is divided into two parts, the first part being a global correlation, i.e. the signal from each observation comes from a finite pattern, mathematically representing the whole original space-time signal X as a low rank matrix, and the second part being a local correlation, i.e. smoothness. Smoothness indicates that the graph signal should be slowly varying in space, i.e., smooth, based on a given topology. Smoothing is a qualitative representation that requires finding a mathematical representation of the smoothness to mathematically model the signal recovery problem. For a signal sampled at a single instant, a typical mathematical representation of smoothness is:
the smaller S (a), the smoother the signal.
In the present embodiment, αh is used T LH as a smoothness constraint:
wherein w is ij Representing the connection weights between nodes.
And 5, establishing the problem of channel estimation as a mathematical optimization problem, and carrying out channel estimation.
Modeling the problem of channel estimation as the problem of sampling and recovering the graph signals by using the constraint condition of the correlation of the graph signals and combining the smoothness constraint terms proposed in the previous steps, and finally forming the following optimization problem:
min H ‖SH-H P ‖ 2 +αH T LH (27)
where H represents the target channel estimation vector to be estimated, L represents the Laplacian matrix, S is the sampling matrix ψ we design opt I.e. pilot pattern design, H P Is the channel estimation value at the pilot frequency estimated in the step 3
The problem is a closed-form solution, and the matrix inversion operation is not very complex under the condition of less subcarriers and OFDM symbols, so that the solution can be carried out by using a simple closed-form solution:
H＝(S T S+αL) -1 S T H P (28)
example 1
The invention is described in further detail below with reference to the drawings and examples.
In order to verify the estimation performance of the proposal provided by the invention, OFDM channel estimation is carried out under different shift speeds, 14 symbols are shared in one frame of OFDM, each symbol is modulated onto 24 subcarrier numbers, and 16 pilot frequencies which are equidistantly arranged are used for carrying out channel estimation at the shift speeds of 100km/h,300km/h and 500km/h respectively. And under each different shift scene, designing the topological structure of the graph according to a designed weighting method, and carrying out sampling recovery according to a method for maximizing the minimum eigenvalue.
Fig. 2 shows a schematic diagram of modeling a time-frequency dual-channel as a graph signal when v=300 km/h, and as can be seen from fig. 2, topology is obtained under the weighted distance scheme designed in this embodiment, and the illustrated graph signal is relatively smooth and can be sampled and recovered. Fig. 3 shows a graph of eigenvalues corresponding to orthonormal bases after modeling of channel data into a graph signal, the abscissa is the eigenvalues corresponding to each orthonormal base, and the ordinate is the value after the fourier transform of the channel data, and it can be found that almost all GFT components are concentrated on frequency components with eigenvalues less than 0.1, so that the channel data can be considered as a band limited signal.
Fig. 3-9 show BER and MSE results for channel estimation at different shift speeds. The square dotted line and the black dot solid line are simulation result graphs for realizing channel estimation by carrying out LS estimation on equidistant placement of pilot frequencies and then carrying out one-dimensional and two-dimensional linear interpolation, the triangular solid line is a simulation result obtained by carrying out channel estimation by using a graph signal method after carrying out LS estimation on equidistant placement of pilot frequencies, the dot solid line is a result obtained by selecting 16 pilot frequencies by using a minimum eigenvalue maximizing method, estimating positions of the pilot frequencies by using LS, and realizing channel estimation by using a graph signal method. It can be seen that, with the increase of the shift speed, the effect of the method for performing channel estimation by using the method for performing the smoothness-based graph signal at the designed pilot frequency position of the sampling graph sampling method is obviously better than that of the linear interpolation, and the higher the shift speed is, the worse the channel environment is, whether the MSE or the BER is, the greater the effect of the method of the embodiment is better than that of the linear interpolation method.
Fig. 10 shows v=300 fixed position pilot patterns and pilot pattern patterns designed based on the new and good method, it can be seen that the pilot positions of the fixed patterns are not the optimal choice for recovery according to the characteristics of the channel, and the adaptive pilot patterns based on the maximized minimum feature of the present invention are more suitable schemes.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.
Claims (6)
1. An OFDM system channel estimation method based on a graph signal method is characterized by comprising the following steps:
step 1, converting a channel of an OFDM system into a signal with a size of n x k, wherein n represents the number of carriers, and k represents the number of OFDM symbols;
the graph signal is channel H:
wherein, H is a channel with length n×k, W is a noise vector, and X is an nth OFDM symbol transmitted on a kth subcarrier; l means the multipath number, M means the maximum Doppler shift, h () means the channel tap coefficient, N means the OFDM symbol number of one frame, K means the total number of subcarriers;
step 2, determining the topological structure of the graph signals;
step 3, obtaining the band limit of channel data based on the topological structure of the image signal, selecting pilot frequency according to the band limit signal sampling theorem, designing a pilot frequency pattern based on a method of maximizing the minimum characteristic value, obtaining a sampling matrix, and establishing a sampling recovery problem of the image signal through the sampling matrix;
the process of obtaining the channel data band limit based on the topological structure of the graph signal is as follows:
the fourier transform of the plot signal x is:
s＝U T x (10)
the inverse fourier transform of the map is expressed as:
x＝Us (11)
when the plot Fourier coefficient s of plot signal x is non-zero for only the first k elements or only the first k plot Fourier components { u } 1 ，u 2 ，...，u k Defining the graph signal x as a k band-limit when linearly combined; u is a Fourier base matrix;
the sampling matrix obtained based on the method for maximizing the minimum eigenvalue is as follows:
wherein, the meaning of ψ is that it represents a sampling set, V (K) Meaning the first K columns of the base matrix after the laplace matrix decomposition;
the sampling recovery problem is as follows:
wherein X represents channel data H, Y represents channel data at pilot estimated using LS algorithm
Step 4, determining a smoothness constraint term of the sampling recovery problem;
and step 5, solving a sampling recovery problem based on the smoothness constraint term to obtain a channel estimation result of the OFDM system.
2. The method for estimating a channel of an OFDM system based on the graph signal method according to claim 1, wherein in step 2, the topology is:
0＜α＜1 (8)
wherein alpha is a distance overall weighting coefficient, gamma is an influence factor, and the magnitude of gamma is determined by an actual speed V and a threshold speed V; k indicates the number of subcarriers, and n indicates the number of OFDM symbols.
3. The method for estimating a channel of an OFDM system based on the graph signal method according to claim 1, wherein the sample recovery problem is transformed into:
4. the method for estimating a channel of an OFDM system based on the graph signal method according to claim 1, wherein in step 4, the smoothness constraint term is:
wherein w is ij Representing the connection weights between nodes.
5. The method for estimating a channel of an OFDM system based on the graph signal method according to claim 1, wherein in step 5, based on the smoothness constraint, the sample recovery problem forms the following optimization problem:
min H ||SH-H P || 2 +αH T LH (27)
where H represents the channel estimation vector, L represents the Laplace matrix, S is the sampling matrix ψ opt I.e. pilot pattern design, H P Is the channel estimate at the pilot;
the solution of the optimization problem is as follows:
H＝(S T S+αL) -1 S T H P (28)。
6. a system for implementing the graph signal method-based OFDM system channel estimation method of claim 1, comprising:
the image signal conversion module is used for converting a channel of the OFDM system into an image signal with the size of n x k, wherein n represents the number of carriers, and k represents the number of OFDM symbols;
the topological structure acquisition module is used for determining the topological structure of the graph signals;
the sampling recovery problem establishing module is used for obtaining the band limit of the channel data based on the topological structure of the image signal, selecting pilot frequency according to the band limit signal sampling theorem, designing a pilot frequency pattern based on a method of maximizing the minimum characteristic value, obtaining a sampling matrix, and establishing the sampling recovery problem of the image signal through the sampling matrix;
the constraint item establishing module is used for determining a smoothness constraint item of the sampling recovery problem;
and the solving module is used for solving the sampling recovery problem based on the smoothness constraint term to obtain a channel estimation result of the OFDM system.
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