Pilot efficient super-nyquist system channel estimation method

Abstract

The application discloses a pilot efficient super-Nyquist system channel estimation method, comprising the following steps: obtaining a precoding matrix and a decoding matrix; obtaining a transmission pilot block, and pre-coding the transmission pilot block by using the precoding matrix; obtaining a sending symbol block, and obtaining a transmission frame according to the pre-coded transmission pilot block and the sending symbol block; performing baseband shaping on the transmission frame, and transmitting the baseband-shaped transmission frame on a channel; performing matched filtering and down-sampling on the transmission-received transmission frame to obtain a down-sampled transmission pilot block; and decoding the down-sampled transmission pilot block by using the decoding matrix to obtain channel state information. Through the technical scheme, the pilot cost is reduced, and the estimation precision of the channel state information is improved.

Description

Technical Field

[0001] This invention belongs to the field of satellite communication technology, and in particular relates to a pilot-efficient super Nyquist system channel estimation method. Background Technology

[0002] With the evolution from 5G to 6G, the development of integrated space-air-ground information networks has become an inevitable direction for future communication network construction. Non-terrestrial networks, as the mainstream technology for space-ground converged communication, play a crucial role in the integration of space-air-ground communication systems. The non-terrestrial network technologies considered focus on efficient satellite communication, aiming to achieve seamless global connectivity and promote the realization of the 6G vision. According to the 3G Partnership, existing satellite communication systems struggle to cope with the pressure of massive data transmission through feeder links, urgently requiring improvements in capacity and spectrum efficiency to achieve high-speed data transmission.

[0003] Therefore, the Super Nyquist technique, which can improve capacity and spectral efficiency without additional bandwidth and antennas, has attracted attention in the communications field. However, due to its violation of the Nyquist criterion, Super Nyquist systems introduce inter-symbol interference. Furthermore, integrated air-space-ground information networks rely on low-Earth orbit (LEO) satellite communications, which face frequency-selective fading channels, inevitably introducing multipath interference. Therefore, obtaining accurate channel state information is crucial for eliminating multipath interference.

[0004] To address this, numerous schemes for eliminating inter-symbol interference and channel estimation have been developed, including equalization schemes and linear precoding schemes. Shinya Sugiura et al. utilized soft-decision frequency domain equalization based on the minimum mean square error criterion and proposed a semi-blind iterative joint frequency domain channel estimation and data detection algorithm, using the frequency domain equalization algorithm for channel estimation. Subsequently, Wu Nan et al. from Beijing Institute of Technology proposed a joint frequency domain channel estimation and decoding algorithm based on generalized approximate message passing. This algorithm can approximate the autocorrelation matrix of colored noise as a cyclic matrix without cyclic prefixes and pilots, reducing computational complexity. By treating inter-symbol interference (ISI) and multipath interference separately, Wen Shan from the University of Electronic Science and Technology of China in Chengdu proposed a linear pre-equalization joint frequency domain channel estimation and signal detection method 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). In the transmitter, linear pre-equalization is used to eliminate ISI, and in the receiver, the minimum mean square error criterion is combined with frequency domain equalization technology to estimate channel state information.

[0005] The algorithms mentioned above all utilize equalization techniques to estimate channel state information, which leads to increased noise at the receiver. Linear precoding, however, partially cancels out the interference matrix at the transmitter, effectively mitigating noise amplification. Therefore, Li Qiang from Xi'an University of Electronic Science and Technology, in his paper "Joint Channel Estimation and Precoding for Faster-Than-Nyquist Signaling" (IEEE Transactions on vehicular technology, 2020, 13139-13147), proposed using precoding techniques for channel estimation. This algorithm avoids inter-block interference by using a cyclic prefix and achieves satisfactory mean square error in channel estimation when inter-symbol interference is mild. However, as inter-symbol interference worsens, its mean square error deteriorates sharply.

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

[0007] To address the aforementioned technical problems, this invention proposes a pilot-efficient super Nyquist system channel estimation method that achieves lower channel estimation mean square error with lower pilot overhead, thereby solving the problems existing in the prior art.

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

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

[0010] Obtain the transmission symbol block, and obtain the transmission frame based on the precoded transmission pilot block and the transmission symbol block;

[0011] The baseband shaping of the transmission frame is performed, and the baseband shaped transmission frame is transmitted on the channel. The received transmission frame is subjected to matched filtering and downsampling to obtain the downsampled transmission pilot block.

[0012] Channel state information is obtained by decoding the downsampled transmission pilot block using a decoding matrix.

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

[0014] Obtain the inter-symbol interference matrix, generate a precoding matrix based on the diagonal matrix and Fourier transform matrix of the inter-symbol interference matrix, and generate a decoding matrix based on the diagonal matrix, Fourier transform matrix and transmission pilot block of the inter-symbol interference matrix.

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

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

[0017] Optionally, a cyclic channel matrix is ​​obtained to characterize the channel transmission, 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, It is the estimated channel state information, h is the ideal channel state information, n is Gaussian white noise, and Q is the estimated channel state information. v Let B represent the Fourier transform matrix, and let y represent the decoding matrix. k This represents the downsampled transmission pilot block, v represents the length of the transmission pilot block, diag represents the construction of a diagonal matrix, and p k Represents the k-th transmission pilot block, (·) * Represents conjugate operation.

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

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

[0024] This invention uses circular convolution instead of linear convolution in the super-Nyquist transmission system to construct a cyclic super-Nyquist transmission system, proposing a pilot-efficient channel estimation method for super-Nyquist systems. By obtaining the cyclic inter-symbol interference matrix of the transmission pilot block, a precoding matrix and a decoding matrix are constructed, and the transmission pilot block is precoded. Then, the precoded transmission pilot block and the transmit coincidence block are merged to construct a transmission frame, with a cyclic prefix added as a guard interval before passing through the frequency-selective fading channel. After the transmission frame passes through the channel, matched filtering, and downsampling, the transmission pilot block can be extracted. The decoding matrix is ​​used to decode the downsampled transmission pilot block, thereby estimating the channel state information, improving estimation accuracy, and ensuring reliable signal detection.

[0025] Meanwhile, existing channel estimation techniques require a large number of pilot blocks and cyclic prefixes to transmit a single frame in order to avoid inter-symbol interference. However, this invention introduces cyclic convolution for baseband shaping, which itself avoids inter-symbol interference, thus reducing the number of pilot blocks and cyclic prefixes. A single transmission frame in this invention requires only one pilot block for baseband shaping; and only one cyclic prefix is ​​needed. Therefore, the additional overhead (including pilot overhead) is low. Attached Figure Description

[0026] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0027] Figure 1 This invention relates to a cyclic super Nyquist transport system;

[0028] Figure 2 For the framing process of a cyclic super Nyquist system;

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

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

[0031] Figure 5 The figure shows the simulation results of the mean square error of channel estimation under severe inter-symbol interference according to the present invention. Detailed Implementation

[0032] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

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

[0034] This invention discloses a pilot-efficient super Nyquist system channel estimation method. By replacing the linear convolution of the super Nyquist shaping and matched filtering modules with circular convolution, a circular super Nyquist system model is constructed, and channel state information is estimated by combining linear precoding techniques.

[0035] The channel estimation method proposed in this invention includes: obtaining the inter-symbol 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-symbol interference matrix; performing precoding operation on the transmission pilot block using the precoding matrix; merging the precoded transmission pilot block and the transmitted symbol block to construct the transmission frame of the super-Nyquist system; subjecting the transmission frame to cyclic super-Nyquist shaping, and adding a cyclic prefix to the transmission pilot block in the shaped transmission frame; after the transmission frame with the cyclic prefix passes through a frequency-selective fading channel, removing the cyclic prefix, and performing matched filtering and downsampling operations; obtaining the downsampled transmission pilot block; and decoding the downsampled transmission pilot block using the decoding matrix to obtain channel state information. Through the above technical solution, this invention not only reduces pilot overhead but also improves the estimation accuracy of channel state information.

[0036] To address the problems existing in the prior art, the purpose of this invention is to provide a pilot-efficient super Nyquist system channel estimation method that achieves lower mean square error in channel estimation under severe inter-symbol interference with lower 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] Design the precoding and decoding matrices for the transmission pilot block based on the cyclic inter-symbol interference matrix;

[0040] The transmission pilot block is precoded using a precoding matrix;

[0041] The precoded transmission pilot block and the transmission symbol block are merged to construct a super Nyquist transmission frame;

[0042] Cyclic super Nyquist shaping is achieved using cyclic convolution. After the transmission frame undergoes cyclic super Nyquist shaping, a cyclic prefix is ​​added before the transmission pilot block.

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

[0044] Obtain the downsampled transmission pilot block; use the decoding matrix to decode the downsampled pilot to obtain the channel state information.

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

[0046]

[0047] Where G is a cyclic matrix of dimension v×v. i =g(iτT) represents the inter-symbol interference factor, v represents the length of the one-sided inter-symbol interference factor, where τ represents the packet 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] Where F and B represent the precoding matrix and decoding matrix of the transmission pilot block, respectively, p k Let represent the k-th transmission pilot block, with length v, and diag(p) k ) is a diagonal matrix constructed from the k-th transmission pilot block; Q v Represents a Fourier transform matrix of dimension v×v; (·) * Represents conjugate operation; (·) T Represents the transpose operation; Λ g It is a diagonal matrix, where Λ g The diagonal elements are the eigenvalues ​​of G.

[0051] As one embodiment, the transmission pilot block is precoded using a constructed precoding matrix:

[0052]

[0053] in, This represents the k-th precoded transmission pilot block.

[0054] Preferably, the precoded transmission pilot block and the transmitted symbol block are merged for framing:

[0055]

[0056] Where, d k For the k-th transmission frame, and b k Represents the k-th transmitted symbol block, and [·] indicates a merge operation.

[0057] As one embodiment, cyclic super-Nyquist shaping is implemented using cyclic convolution. Then, after the k-th transmission frame undergoes cyclic super-Nyquist shaping, a cyclic prefix is ​​added before the transmission pilot block.

[0058]

[0059] Where, x k This represents the k-th transmission frame with the inserted cyclic prefix; This 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 A symbol.

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

[0061]

[0062] Where w represents colored noise, and H is a cyclic channel matrix of dimension v×v, denoted as...

[0063]

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

[0065] As one embodiment, channel state information is obtained by decoding the downsampled pilot signals:

[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 cyclic channel matrix; n is Gaussian white noise.

[0068] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0069] The purpose of this invention is to address the shortcomings of the existing technologies by proposing a pilot-efficient super Nyquist system channel estimation method that achieves lower channel estimation mean square error with lower pilot overhead.

[0070] Reference Figure 1 The cyclic super Nyquist transmission system used in this invention includes, in sequence: a data source module, a constellation mapping module, a linear precoding module, a framing module, an upsampling 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 downsampling module, and a channel estimation module. Wherein:

[0071] The data source module generates the transmitted bit data and passes the bit data to the constellation mapping module;

[0072] The constellation mapping module maps bit data into transmission symbols according to constellation mapping rules, and then passes the transmission symbols to the linear precoding module;

[0073] Linear precoding module: Uses the constructed precoding matrix to precode the transmission pilot block, and then passes the precoded transmission pilot block and the transmitted symbol block to the framing module;

[0074] The framing module merges the pre-encoded transmission pilot block and the transmission symbol block to form a transmission frame, and then passes the transmission frame to the upsampling module;

[0075] The upsampling module performs zero-value interpolation on the transmission frame and then passes the zero-value interpolated transmission frame to the cyclic super Nyquist shaping module.

[0076] The cyclic super Nyquist shaping module performs cyclic super Nyquist shaping on the upsampled transmission frame using cyclic convolution, and then passes the shaped transmission frame to the cyclic prefix insertion module.

[0077] The cyclic prefix insertion module inserts a cyclic prefix before the transmission pilot block in the formed transmission frame, and then passes the transmission frame after inserting the cyclic prefix to the frequency selective fading channel module.

[0078] The frequency selective fading channel module passes the transmitted frame after inserting the cyclic prefix through the frequency selective fading channel and adds Gaussian white noise, and then passes the transmitted frame through the channel to the cyclic prefix removal module.

[0079] The cyclic prefix removal module removes the cyclic prefix from the transmitted frames passing through the channel and then passes the cyclic prefix-removed transmitted frames to the matched filtering module.

[0080] The matched filtering module performs matched filtering on the transmission frame after removing the cyclic prefix, and then passes the filtered transmission frame to the downsampling module;

[0081] The downsampling module downsamples the filtered transmission frame and then passes the downsampled transmission frame to the channel estimation module.

[0082] The channel estimation module extracts the transmission pilot block from the downsampled transmission frame and uses the decoding matrix to decode the downsampled pilot block, thereby estimating the channel state information.

[0083] Combining the above-mentioned cyclic super Nyquist transport system, and referring to Figure 3 The steps for channel estimation using the above-mentioned cyclic super Nyquist system are as follows:

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

[0085]

[0086] Where G is a circular matrix of dimension v×v, and the elements g i =g(iτT) represents the inter-symbol interference factor, and v represents the length of the one-sided inter-symbol 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 as follows:

[0088]

[0089] Where F and B represent the precoding matrix and decoding matrix of the transmission pilot block, respectively, p k Let represent the k-th transmission pilot block, with length v, and diag(p) k ) is from p k Constructed diagonal matrix; Q v Represents a Fourier transform matrix of dimension v×v; (·) * Represents conjugate operation; (·) T Represents the transpose operation; Λ g It is a diagonal matrix, where Λ g The diagonal elements are composed of the eigenvalues ​​of G.

[0090] Step 3: Using the constructed precoding matrix, perform precoding operations on the transmission pilot block:

[0091]

[0092] in, This represents the k-th precoded transmission pilot block.

[0093] Step 4, as follows Figure 2 As shown, the precoded transmission pilot block and the transmitted symbol block are merged for framing:

[0094]

[0095] Where, d k For the k-th transmission frame, and b k This represents the k-th transmitted symbol block.

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

[0097]

[0098] Where, x k This represents the k-th transmission frame with the inserted cyclic prefix; This 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.

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

[0100]

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

[0102]

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

[0104] Step 7: Use the decoding matrix to decode the downsampled pilot signal to obtain the 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 effects of this embodiment are further illustrated by simulation experiments;

[0108] 1. Simulation conditions

[0109] The simulation experiment in this embodiment was conducted using MATLAB 2024a software. In the simulation experiment of this embodiment, QPSK was used as the modulation method for the pilot.

[0110] Set three sets of root-raised cosine shaping pulses and matched filter roll-off factors to 0.25, 0.3, and 0.45, respectively. Set three sets of packing ratios to 0.8, 0.7, and 0.6, respectively. Combine the roll-off factors and packing ratios into three groups: 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 (ISI), i.e., a roll-off factor and packet rate combination of 0.8 and 0.25, channel estimation is performed using this invention, and the results are as follows. Figure 4 .

[0113] Simulation 2: Under the above conditions, considering severe inter-symbol interference (ISI), i.e., roll-off factor and packet ratio combinations of 0.7, 0.3 and 0.6, 0.45, the packet ratio is estimated using this 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, measured in decibels (dB), and the vertical axis represents the mean square error (MSE), also measured in decibels (dB).

[0115] from Figure 4 It can be seen that, considering moderate inter-symbol interference, this invention achieves a lower mean square error in channel estimation compared to existing LPE-FDCE and PCE algorithms, and its mean square error performance is close to that of the Nyquist system. From Figure 5 It is evident that the LPE-FDCE algorithm becomes inapplicable as inter-symbol interference (ISI) worsens, while the PCE algorithm, although effective, suffers from decreased estimation accuracy and deteriorated mean square error performance. However, this invention maintains mean square error performance comparable to that under moderate ISI. This demonstrates that this invention can achieve lower channel estimation mean square error with lower overhead, improving estimation accuracy and thus ensuring reliable signal detection.

[0116] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A pilot-efficient super Nyquist system channel estimation method, characterized in that, include: Obtain the precoding matrix and the decoding matrix; Obtain the transmission pilot block and precode the transmission pilot block using a precoding matrix; Obtain the transmission symbol block, and obtain the transmission frame based on the precoded transmission pilot block and the transmission symbol block; wherein the transmission frame contains only one of the precoded transmission pilot blocks; Baseband shaping of the transmission frame is performed using circular convolution. The baseband shaping process includes: adding a cyclic prefix to the baseband-shaped transmission frame; wherein the cyclic prefix is ​​added before the transmission pilot block in the baseband-shaped transmission frame, and the number of cyclic prefixes is one; the transmission frame with the cyclic prefix is ​​transmitted on the channel; and the received transmission frame is subjected to matched filtering and downsampling after removing the cyclic prefix. The baseband shaping of the transmission frame is performed, and the baseband shaped transmission frame is transmitted on the channel. The received transmission frame is subjected to matched filtering and downsampling to obtain the downsampled transmission pilot block. Channel state information is obtained by decoding the downsampled transmission pilot block using a decoding matrix.

2. The method according to claim 1, characterized in that, The process of obtaining the precoding matrix and decoding matrix includes: Obtain the inter-symbol interference matrix, generate a precoding matrix based on the diagonal matrix and Fourier transform matrix of the inter-symbol interference matrix, and generate a decoding matrix based on the diagonal matrix, Fourier transform matrix and 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 merged and framed to obtain a transmission frame.

4. The method according to claim 1, characterized in that, Obtain the cyclic channel matrix used to characterize the channel transmission, 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.

5. The method according to claim 4, characterized in that, The cyclic channel matrix contains different channel tap coefficients.

6. The method according to claim 1, characterized in that, The process of decoding the downsampled transmission pilot block includes: in, It is the estimated channel state information, h is the ideal channel state information, n is Gaussian white noise, and Q is the estimated channel state information. v Let B represent the Fourier transform matrix, and let y represent the decoding matrix. k This represents the downsampled transmission pilot block, v represents the length of the transmission pilot block, diag represents the construction of a diagonal matrix, and p k Represents the k-th transmission pilot block, (·) * Represents conjugate operation.

7. The method according to claim 2, characterized in that, The inter-symbol interference matrix includes the inter-symbol interference factor of the super Nyquist system.

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