Pilot-frequency-efficient super-Nyquist system channel estimation method

Abstract

The invention discloses a pilot-frequency-efficient channel estimation method for a super-Nyquist system. The method comprises the following steps: acquiring a pre-coding matrix and a decoding matrix; acquiring a transmission pilot frequency block, and pre-coding the transmission pilot frequency block by using the pre-coding matrix; obtaining a sending symbol block, and obtaining a transmission frame according to the pre-coded transmission pilot frequency block and the sending symbol block; the method comprises the following steps: carrying out baseband forming on a transmission frame, transmitting the transmission frame subjected to baseband forming on a channel, and carrying out matched filtering and down-sampling on the received transmission frame to obtain a transmission pilot frequency block subjected to down-sampling; and decoding the down-sampled transmission pilot frequency block through the decoding matrix to obtain channel state information. According to the technical scheme, the pilot frequency overhead is reduced, and the estimation precision of the channel state information is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of satellite communications, and in particular relates to a super-Nyquist system channel estimation method with efficient pilot frequency. Background Art

[0002] With the evolution from 5G to 6G, the development of an integrated space-ground information network has become an inevitable direction for the construction of future communication networks. As the mainstream technology of satellite-ground integrated communications, non-terrestrial networks play a vital role in the integration of space-ground communication systems. The non-terrestrial network technologies considered focus on efficient satellite communications, aiming to achieve seamless connectivity worldwide and promote the realization of the 6G vision. According to the Third Generation Partnership Project, the existing satellite communication system is unable to cope with the pressure of massive data transmission on the feeder link, and it is urgent to improve capacity and spectrum efficiency to achieve high-speed data transmission.

[0003] Therefore, super-Nyquist technology, which can improve capacity and spectrum efficiency without additional bandwidth and antennas, has attracted attention in the communications field. However, due to the violation of the Nyquist criterion, super-Nyquist systems introduce inter-symbol interference. In addition, the integrated space-ground information network relies on low-orbit satellite communications, which face frequency selective fading channels and inevitably introduce multipath interference. Therefore, obtaining accurate channel state information is crucial to eliminate multipath interference.

[0004] To this end, many schemes for eliminating inter-symbol interference and channel estimation have been developed, including equalization schemes and linear precoding schemes. Shinya Sugiura et al. used the soft decision frequency domain equalization technology based on the minimum mean square error criterion, and proposed a semi-blind iterative joint frequency domain channel estimation and data detection algorithm, and used the frequency domain equalization algorithm for channel estimation. Subsequently, Wu Nan et al. from Beijing Institute of Technology proposed a frequency domain joint channel estimation and decoding algorithm based on generalized approximate message passing. In the absence of cyclic prefixes and pilots, the algorithm can approximate the autocorrelation matrix of colored noise as a circulant matrix, reducing the computational complexity. By processing inter-symbol interference and multipath interference separately, Wen Shan from Chengdu University of Electronic Science and Technology proposed linear pre-equalization joint frequency domain channel estimation and signal detection in his paper "Joint Precoding and Pre-Equalization for Faster-Than-Nyquist Transmission Over Multipath Fading Channels" (IEEE Transactions on vehicular technology, 2022, 3948-3963). Linear pre-equalization is used in the transmitter to eliminate inter-symbol interference, and the minimum mean square error criterion is combined with frequency domain equalization technology in the receiver to estimate channel state information.

[0005] The algorithms mentioned above all use equalization technology to estimate channel state information, which will lead to increased noise at the receiving end. The linear precoding technology partially offsets the interference matrix at the transmitter, effectively alleviating the noise amplification phenomenon. Therefore, Li Qiang from Xidian University proposed using precoding technology for channel estimation in his paper "Joint Channel Estimation and Precoding for Faster-Than-Nyquist Signaling" (IEEE Transactions on vehicular technology, 2020, 13139-13147). The algorithm uses cyclic prefixes to avoid inter-block interference and obtains satisfactory channel estimation mean square error when inter-code interference is relatively mild. However, as inter-code interference becomes severe, the mean square error of its channel estimation will deteriorate sharply.

[0006] The channel estimation algorithms mentioned above have two main disadvantages: first, the additional overhead is large (including pilot overhead); second, under severe inter-symbol interference, the mean square error performance of channel estimation is poor. Summary of the invention

[0007] To solve the above technical problems, the present invention proposes a pilot-efficient super-Nyquist system channel estimation method, which achieves lower channel estimation mean square error with lower pilot overhead, so as to solve the above problems in the prior art.

[0008] To achieve the above object, the present invention provides a pilot-efficient super-Nyquist system channel estimation method, comprising:

[0009] Obtain a precoding matrix and a decoding matrix; obtain a transmission pilot block, and precode the transmission pilot block using the precoding matrix;

[0010] Acquire a transmission symbol block, and obtain a transmission frame according to the precoded transmission pilot block and the transmission symbol block;

[0011] Performing baseband shaping on the transmission frame, transmitting the transmission frame after baseband shaping on the channel, performing matched filtering and down-sampling on the transmission frame received, and obtaining a down-sampled transmission pilot block;

[0012] The downsampled transmission pilot block is decoded through a decoding matrix to obtain channel state information.

[0013] Optionally, the process of obtaining the precoding matrix and the decoding matrix includes:

[0014] An inter-symbol interference matrix is ​​obtained, a precoding matrix is ​​generated according to a diagonal matrix and a Fourier transform matrix of the inter-symbol interference matrix, and a decoding matrix is ​​generated according to the diagonal matrix, the Fourier transform matrix and a transmission pilot block of the inter-symbol interference matrix.

[0015] Optionally, the precoded transmission pilot block and the transmission symbol block are combined and framed to obtain a transmission frame.

[0016] Optionally, circular convolution is used to perform baseband shaping on the transmission frame, wherein the baseband shaping of the transmission frame includes: adding a cyclic prefix to the transmission frame after baseband shaping, wherein the cyclic prefix is ​​added before the transmission pilot block in the transmission frame after baseband shaping; transmitting the transmission frame with the cyclic prefix added on the channel, and performing matched filtering and down-sampling on the received transmission frame after removing the cyclic prefix.

[0017] Optionally, a cyclic channel matrix for characterizing channel transmission is obtained, wherein the downsampled transmission pilot block is associated with the Fourier transform matrix, the cyclic channel matrix, the diagonal matrix of the inter-symbol interference matrix, the transmission pilot block and the colored noise.

[0018] Optionally, the cyclic channel matrix contains different channel tap coefficients.

[0019] Optionally, the process of decoding the downsampled transmission pilot block includes:

[0020]

[0021] in, is the estimated channel state information, h is the ideal channel state information, n is Gaussian white noise, Q v represents the Fourier transform matrix, B represents the decoding matrix, y k represents the downsampled transmission pilot block, v represents the length of the transmission pilot block, diag represents the diagonal matrix constructor, p k represents the kth transmission pilot block, (·) * Represents the conjugate operation.

[0022] Optionally, the inter-symbol interference matrix includes an inter-symbol interference factor of a super-Nyquist system.

[0023] Compared with the prior art, the present invention has the following advantages and technical effects:

[0024] In the present invention, a cyclic convolution is used to replace the linear convolution of a super-Nyquist transmission system to construct a cyclic super-Nyquist transmission system. The present invention proposes a super-Nyquist system channel estimation method with high pilot efficiency. By obtaining the cyclic inter-code interference matrix of the transmission pilot block, a precoding matrix and a decoding matrix are constructed, and a precoding operation is performed on the transmission pilot block. Then the precoded transmission pilot block and the transmission symbol block are combined to construct a transmission frame, and a cyclic prefix is ​​added as a protection interval before passing through a frequency selective fading channel. After the transmission frame passes through the channel, matched filtering and down-sampling, the transmission pilot block can be taken out, and the down-sampled transmission pilot block is decoded using a decoding matrix, thereby estimating the channel state information, improving the estimation accuracy, and ensuring the reliable implementation of signal detection.

[0025] At the same time, in order to avoid interference between symbol blocks, the existing channel estimation technology requires more pilot blocks and more cyclic prefixes for a transmission frame. However, the present invention introduces cyclic convolution for baseband shaping, and the cyclic convolution itself can avoid interference between symbol blocks, thereby reducing the number of pilot blocks and cyclic prefixes. A transmission frame of the present invention only needs one pilot block during baseband shaping; and the cyclic prefix required in the present invention is also only one. Therefore, the additional overhead (including pilot overhead) is low. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0027] Figure 1 The cyclic super-Nyquist transmission system of the present invention;

[0028] Figure 2 The framing process for the cyclic super-Nyquist system;

[0029] Figure 3 The present invention is a flowchart of the implementation of the super-Nyquist system channel estimation method with efficient pilot signal.

[0030] Figure 4 This is a simulation result diagram of the mean square error of channel estimation under moderate inter-symbol interference of the present invention;

[0031] Figure 5 This is a simulation result diagram of the mean square error of channel estimation under severe inter-symbol interference of the present invention. DETAILED DESCRIPTION

[0032] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0033] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0034] The invention discloses a pilot-efficient super-Nyquist system channel estimation method. By replacing the linear convolution of super-Nyquist shaping and matched filter modules with circular convolution, a circular super-Nyquist system model is constructed, and the estimation of channel state information is realized in combination with linear precoding technology.

[0035] The channel estimation method proposed in the present invention includes: obtaining the inter-code interference matrix of the transmission pilot block caused by the cyclic super-Nyquist system; designing the precoding matrix and decoding matrix of the transmission pilot block based on the inter-code interference matrix; using the precoding matrix to precode the transmission pilot block; merging the precoded transmission pilot block and the transmission symbol block to construct the transmission frame of the super-Nyquist system; the transmission frame is shaped by the cyclic super-Nyquist, and a cyclic prefix is ​​added before the transmission pilot block in the shaped transmission frame; after the transmission frame with the cyclic prefix passes through the frequency selective fading channel, the cyclic prefix is ​​removed, and matched filtering and downsampling operations are performed; the downsampled transmission pilot block is obtained; the downsampled transmission pilot block is decoded using the decoding matrix to obtain the channel state information. Through the above technical solution, the present invention not only reduces the pilot overhead, but also improves the estimation accuracy of the channel state information.

[0036] To solve the above problems in the prior art, the present invention aims to provide a pilot-efficient super-Nyquist system channel estimation method, which achieves lower channel estimation mean square error under severe inter-symbol interference with lower additional overhead.

[0037] To achieve the above technical objectives, the present invention provides the following solution: The present invention provides a pilot-efficient super-Nyquist system channel estimation method, comprising:

[0038] Obtain the cyclic inter-symbol interference matrix caused by the cyclic super-Nyquist system;

[0039] Designing a precoding matrix and a decoding matrix for a transmission pilot block based on a cyclic inter-symbol interference matrix;

[0040] Using a precoding matrix, a precoding operation is performed on the transmission pilot block;

[0041] Combining the precoded transmission pilot block and the transmission symbol block to construct a super-Nyquist transmission frame;

[0042] Circular super-Nyquist shaping is realized by using cyclic convolution. After the transmission frame is cyclic super-Nyquist shaped, a cyclic prefix is ​​added before the transmission pilot block.

[0043] After the transmission frame with cyclic prefix passes through the frequency selective fading channel, the cyclic prefix is ​​removed, and matched filtering and downsampling operations are performed;

[0044] A downsampled transmission pilot block is obtained; and channel state information is obtained by decoding the downsampled pilot block using a decoding matrix.

[0045] As some embodiments, the transmission pilot block inter-symbol interference matrix caused by the cyclic super-Nyquist system is obtained as:

[0046]

[0047] Where G is a circulant matrix of dimension v×v. i =g(iτT) represents the inter-symbol interference factor, and v represents the length of the unilateral inter-symbol interference factor, wherein τ represents the packing rate in the super-Nyquist system, T represents the symbol interval, and i represents the index value of the inter-symbol interference factor.

[0048] As some embodiments, the precoding matrix and decoding matrix of the transmission pilot block are designed based on the cyclic inter-symbol interference matrix:

[0049]

[0050] Among them, F and B represent the precoding matrix and decoding matrix of the transmission pilot block respectively, p k represents the kth transmission pilot block, whose length is v, and diag(p k ) is a diagonal matrix constructed by the kth transmission pilot block; Q v represents the Fourier transform matrix of dimension v×v; (·) * represents the conjugate operation; (·) T represents the transpose operation; Λ g is a diagonal matrix, where Λ g The diagonal elements of are the eigenvalues ​​of G.

[0051] As some embodiments, a precoding operation is performed on the transmission pilot block using the constructed precoding matrix:

[0052]

[0053] in, represents the kth precoded transmission pilot block.

[0054] Preferably, the precoded transmission pilot block and the transmission symbol block are combined to perform a framing operation:

[0055]

[0056] Among them, d k is the kth transmission frame, and b k represents the kth transmitted symbol block, and [·] represents the combining operation.

[0057] As some embodiments, cyclic super-Nyquist shaping is implemented by using cyclic convolution, and a cyclic prefix is ​​added before the transmission pilot block of the k-th transmission frame after cyclic super-Nyquist shaping:

[0058]

[0059] Among them, x k represents the kth transmission frame with a cyclic prefix inserted; is the cyclic prefix added before the transmission pilot block after cyclic super-Nyquist shaping; Represents d k The transmission frame after cyclic super-Nyquist shaping, where the cyclic prefix refers to the last L in the shaped transmission pilot block h symbol.

[0060] As some embodiments, after the k-th transmission frame with a cyclic prefix passes through a frequency selective fading channel, the cyclic prefix is ​​removed, and matched filtering and downsampling operations are performed to obtain the k-th transmission pilot block y after downsampling. k for

[0061]

[0062] Where w represents colored noise, H is a circulant channel matrix with dimension v×v, expressed as

[0063]

[0064] Among them, h j represents the jth channel tap coefficient, L h is the length of the channel tap, Λ h is a diagonal matrix, where Λ h The diagonal elements of are the eigenvalues ​​of the circulant matrix H.

[0065] As some embodiments, the channel state information is obtained by decoding the downsampled pilot:

[0066]

[0067] in, is the estimated channel state information; h is the ideal channel state information, specifically a one-dimensional matrix of the first row elements in the circulant channel matrix; n is Gaussian white noise.

[0068] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0069] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and to propose a pilot-efficient super-Nyquist system channel estimation method to achieve lower channel estimation mean square error with lower pilot overhead.

[0070] Reference Figure 1 The cyclic super-Nyquist transmission system adopted by the present invention comprises: a data source module, a constellation mapping module, a linear precoding module, a framing module, an up-sampling module, a cyclic super-Nyquist shaping module, a cyclic prefix insertion module, a frequency selective fading channel module, a cyclic prefix removal module, a matched filtering module, a down-sampling module and a channel estimation module connected in sequence. Among them:

[0071] A data source module generates bit data for transmission and passes the bit data to the constellation mapping module;

[0072] A constellation mapping module maps bit data into transmission symbols according to the constellation mapping rule, and transmits the transmission symbols to the linear precoding module;

[0073] Linear precoding module: performs precoding operation on the transmission pilot block using the constructed precoding matrix, and passes the precoded transmission pilot block and transmission symbol block to the framing module;

[0074] A framing module combines the precoded transmission pilot block and the transmission symbol block to form a transmission frame, and passes the transmission frame to the upsampling module;

[0075] An up-sampling module performs zero-value interpolation on the transmission frame and passes the zero-value interpolated transmission frame to a cyclic super-Nyquist shaping module;

[0076] A cyclic super-Nyquist shaping module performs cyclic super-Nyquist shaping on the upsampled transmission frame by using cyclic convolution, and transmits the shaped transmission frame to the cyclic prefix insertion module;

[0077] A cyclic prefix insertion module inserts a cyclic prefix before a transmission pilot block in a formed transmission frame, and transmits the transmission frame after the cyclic prefix is ​​inserted to a frequency selective fading channel module;

[0078] The frequency selective fading channel module passes the transmission frame after the cyclic prefix is ​​inserted through the frequency selective fading channel and adds Gaussian white noise, and passes the transmission frame passing through the channel to the cyclic prefix removal module;

[0079] The cyclic prefix removal module removes the cyclic prefix from the transmission frame passing through the channel, and passes the transmission frame with the cyclic prefix removed to the matched filtering module.

[0080] A matched filtering module performs matched filtering on the transmission frame after the cyclic prefix is ​​removed, and passes the filtered transmission frame to the downsampling module;

[0081] A down-sampling module down-samples the filtered transmission frame and transmits the down-sampled transmission frame to the channel estimation module;

[0082] The channel estimation module extracts the transmission pilot block from the downsampled transmission frame and decodes the downsampled pilot block using a decoding matrix to estimate the channel state information.

[0083] Combined with the above cyclic super-Nyquist transmission system, and referring to Figure 3 The steps of using the above-mentioned cyclic super-Nyquist system to perform channel estimation in the present invention are as follows:

[0084] Step 1: The obtained transmission pilot block inter-code interference matrix caused by the cyclic super-Nyquist system is:

[0085]

[0086] Where G is a circulant matrix of dimension v×v, where the element g i =g(iτT) represents the inter-code interference factor, and v represents the length of the unilateral inter-code interference factor.

[0087] Step 2: The precoding matrix and decoding matrix of the transmission pilot block constructed based on the cyclic inter-symbol interference matrix are:

[0088]

[0089] Among them, F and B represent the precoding matrix and decoding matrix of the transmission pilot block respectively, p k represents the kth transmission pilot block, whose length is v, and diag(p k ) is composed of p k Constructed diagonal matrix; Q v represents the Fourier transform matrix of dimension v×v; (·) * represents the conjugate operation; (·) T represents the transpose operation; Λ g is a diagonal matrix, where Λ g The diagonal elements of consist of the eigenvalues ​​of G.

[0090] Step 3: Use the constructed precoding matrix to perform precoding operation on the transmission pilot block:

[0091]

[0092] in, represents the kth precoded transmission pilot block.

[0093] Step 4, such as Figure 2 As shown, the precoded transmission pilot block and the transmission symbol block are combined to perform a framing operation:

[0094]

[0095] Among them, d k is the kth transmission frame, and b k Represents the kth transmitted symbol block.

[0096] Step 5: After cyclic super-Nyquist shaping, add a cyclic prefix before the transmission pilot block of the kth transmission frame:

[0097]

[0098] Among them, x k represents the kth transmission frame with a cyclic prefix inserted; is the cyclic prefix added before the transmission pilot block after cyclic super-Nyquist shaping; Represents d k Transmission frame after cyclic super-Nyquist shaping.

[0099] Step 6: After the kth transmission frame passes through the frequency selective fading channel, the cyclic prefix is ​​first removed, and then matched filtering and downsampling are performed to obtain the kth transmission pilot block after downsampling:

[0100]

[0101] Where w represents colored noise, H is a cyclic channel matrix with dimension v×v, which represents the transmission process of an ideal channel and is expressed as

[0102]

[0103] Among them, h j represents the jth channel tap coefficient, L h is the length of the channel tap, Λ h is a diagonal matrix, where Λ h The diagonal elements of are the eigenvalues ​​of the circulant matrix H.

[0104] Step 7: Use the decoding matrix to decode the downsampled pilot to obtain channel state information:

[0105]

[0106] in, is the estimated channel state information; h is the ideal channel state information; n is Gaussian white noise.

[0107] In this embodiment, the effect of this embodiment is further explained in combination with simulation experiments;

[0108] 1. Simulation conditions

[0109] The simulation experiment of this embodiment is carried out under MATLAB 2024a software. In the simulation experiment of this embodiment, QPSK is used as the modulation mode of the pilot.

[0110] Set three groups of root raised cosine shaped pulses and matched filter roll-off factors to 0.25, 0.3, and 0.45, respectively. Set three groups of packing rates to 0.8, 0.7, and 0.6, respectively. Combine the roll-off factors and packing rates into three groups, namely 0.8, 0.25; 0.7, 0.3; 0.6, 0.45.

[0111] 2. Simulation content and result analysis

[0112] Simulation 1, under the above conditions, considering moderate inter-symbol interference, that is, the roll-off factor and the packing rate are combined to be 0.8 and 0.25, the present invention is used to perform channel estimation, and the results are as follows: Figure 4 .

[0113] Simulation 2, under the above conditions, considering severe inter-symbol interference, that is, the roll-off factor and the packing rate combination are 0.7, 0.3 and 0.6, 0.45, the packing rate is estimated by the present invention, and the results are as follows: Figure 5 .

[0114] Figure 4 and Figure 5 The horizontal axis represents the bit signal-to-noise ratio of the super-Nyquist system, and its unit is decibel dB (decibel), and the vertical axis represents the mean square error MSE (Mean Square Error), and its unit is decibel dB.

[0115] from Figure 4 It can be seen that when considering moderate inter-symbol interference, compared with the existing LPE-FDCE and PCE algorithms, the present invention achieves a lower channel estimation mean square error and is close to the mean square error performance of the Nyquist system. Figure 5 It can be seen that as the inter-symbol interference becomes more serious, the LPE-FDCE algorithm is no longer applicable, and although the PCE algorithm is effective, the estimation accuracy becomes worse and the mean square error performance deteriorates. However, the present invention still maintains the mean square error performance equivalent to that under moderate inter-symbol interference. This shows that the present invention can achieve lower channel estimation mean square error with lower additional overhead, improve estimation accuracy, and thus ensure reliable implementation of signal detection.

[0116] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A pilot-efficient super-Nyquist system channel estimation method, characterized in that: include: Obtaining a precoding matrix and a decoding matrix; Obtaining a transmission pilot block, and precoding the transmission pilot block using a precoding matrix; Acquire a transmission symbol block, and obtain a transmission frame according to the precoded transmission pilot block and the transmission symbol block; Performing baseband shaping on the transmission frame, transmitting the transmission frame after baseband shaping on the channel, performing matched filtering and down-sampling on the transmission frame received, and obtaining a down-sampled transmission pilot block; The downsampled transmission pilot block is decoded through a decoding matrix to obtain channel state information.

2. The method according to claim 1, characterized in that The process of obtaining the precoding matrix and the decoding matrix includes: An inter-symbol interference matrix is ​​obtained, a precoding matrix is ​​generated according to a diagonal matrix and a Fourier transform matrix of the inter-symbol interference matrix, and a decoding matrix is ​​generated according to the diagonal matrix, the Fourier transform matrix and a transmission pilot block of the inter-symbol interference matrix.

3. The method according to claim 1, characterized in that The precoded transmission pilot block and the transmission symbol block are combined to perform a framing operation to obtain a transmission frame.

4. The method according to claim 1, characterized in that The transmission frame is baseband shaped by using circular convolution, wherein the baseband shaping of the transmission frame includes: adding a cyclic prefix to the transmission frame after baseband shaping, wherein the cyclic prefix is ​​added before the transmission pilot block in the transmission frame after baseband shaping; transmitting the transmission frame with the cyclic prefix added on a channel, and performing matched filtering and down-sampling on the transmission frame received after removing the cyclic prefix.

5. The method according to claim 1, characterized in that A cyclic channel matrix for characterizing channel transmission is obtained, wherein the downsampled transmission pilot block is associated with the Fourier transform matrix, the cyclic channel matrix, the diagonal matrix of the inter-symbol interference matrix, the transmission pilot block and the colored noise.

6. The method according to claim 5, characterized in that The cyclic channel matrix contains different channel tap coefficients.

7. The method according to claim 1, characterized in that The process of decoding the downsampled transmission pilot block includes: in, is the estimated channel state information, h is the ideal channel state information, n is Gaussian white noise, Q v represents the Fourier transform matrix, B represents the decoding matrix, y k represents the downsampled transmission pilot block, v represents the length of the transmission pilot block, diag represents the diagonal matrix constructor, p k represents the kth transmission pilot block, (·) * Represents the conjugate operation.

8. The method according to claim 2, characterized in that: The inter-symbol interference matrix includes inter-symbol interference factors of a super-Nyquist system.

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