A super-nyquist precoding method and system suitable for imperfect channel state information

Abstract

The application discloses a super-Nyquist precoding method and system suitable for imperfect channel state information, and the method comprises the following steps: acquiring a first channel interference matrix composed of an inter-symbol interference matrix caused by a super-Nyquist system and imperfect channel state information; obtaining a first precoding matrix and a decoding matrix for eliminating inter-symbol interference by using the inter-symbol interference matrix; obtaining a second precoding matrix for eliminating channel interference by using the first channel interference matrix based on a minimum mean square error criterion; precoding a sending symbol block by using the first precoding matrix and the second precoding matrix to obtain a coded sending symbol block; processing the coded sending symbol block through cyclic super-Nyquist shaping, a frequency selective fading channel, matched filtering and downsampling to obtain a processed sending symbol block; and decoding the processed sending symbol block by using the decoding matrix to obtain an estimated symbol block, thereby completing precoding of the state information.

Description

Technical Field

[0001] This invention belongs to the field of satellite communication technology, specifically relating to a super Nyquist precoding method and system suitable for imperfect channel state information. Background Technology

[0002] To address the rapidly increasing data transmission demands of mobile broadband services, 6G is expected to achieve peak throughput in the Tbps range. Traditional wireless communication systems typically follow the Nyquist criterion, sacrificing throughput and spectral efficiency for reliable data transmission, which clearly cannot meet the vision of 6G. Furthermore, 6G has ambitious goals for high-throughput satellite communication, aiming to promote an integrated space-ground network architecture and create seamless network coverage for end users. However, existing satellite communication systems, due to their low capacity and inefficient spectrum utilization, cannot meet the demands of 6G. Against this backdrop, super-Nyquist transmission, which deviates from the Nyquist criterion and introduces inter-symbol interference, has attracted academic attention due to its potential to achieve high throughput and high spectral efficiency.

[0003] To ensure the reliability of Super Nyquist (SNN) transmission, many solutions to combat inter-symbol interference (ISI) introduced by SNN systems have been explored, including receiver-only frequency equalization and linear precoding. Both techniques approximate ISI using a finite-tap matrix and eliminate it through matrix operations. The difference lies in the timing of the ISI cancellation: the former performs ISI cancellation at the receiver, which can lead to noise amplification, especially when ISI is severe. The latter, however, effectively mitigates noise amplification by canceling the ISI matrix at the transmitter. Furthermore, frequency equalization struggles to balance resource consumption and bit error rate (BER), while linear precoding better balances these two factors, achieving excellent BER performance while maintaining lower complexity, making it more suitable for SNN transmission. However, existing linear precoding techniques are mainly designed for additive white Gaussian noise channels, while actual satellite communications face frequency-selective fading channels, resulting in channel interference. Therefore, 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 and symbol estimation. However, the frequency domain equalization technique was not very effective in eliminating channel interference. Subsequently, 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 and eliminating channel interference. This algorithm uses a cyclic prefix to avoid inter-block interference and achieves satisfactory bit error rate performance under conditions of mild inter-symbol interference. However, this approach assumes that the transmitter can perfectly obtain the channel state estimated by the receiver. In actual satellite communication, the channel state information obtained by the transmitter is affected by various factors, including estimation errors caused by inaccurate estimation of the channel state information, quantization errors caused by limited feedback, and time delay differences caused by long communication links. These errors result in the channel state information received by the transmitter not accurately reflecting the actual channel state. Therefore, how to perform Super Nyquist precoding under imperfect channel state information remains a challenge. Thus, applying Super Nyquist technology to practical satellite communication and considering a Super Nyquist precoding method suitable for imperfect channel state information is crucial. Summary of the Invention

[0004] This invention aims to address the shortcomings of existing technologies and provides the following solutions:

[0005] A super Nyquist precoding method for imperfect channel state information includes the following steps:

[0006] Obtain the first channel interference matrix composed of the inter-symbol interference matrix caused by the super Nyquist system and the imperfect channel state information;

[0007] The first precoding matrix and decoding matrix for eliminating inter-symbol interference are obtained using the inter-symbol interference matrix;

[0008] Based on the minimum mean square error criterion, the second precoding matrix for eliminating channel interference is obtained using the first channel interference matrix.

[0009] The transmitted symbol block is pre-coded using the first precoding matrix and the second precoding matrix to obtain the encoded transmitted symbol block.

[0010] The encoded transmit symbol block is processed by cyclic super Nyquist shaping, frequency selective fading channel, matched filtering and downsampling to obtain the processed transmit symbol block;

[0011] The processed transmitted symbol block is decoded using the decoding matrix to obtain the estimated symbol block, thus completing the precoding of the state information.

[0012] Preferably, the inter-symbol interference matrix and the first channel interference matrix are:

[0013]

[0014] Where G represents an L×L inter-symbol interference matrix, L represents a natural number, and g i Let v represent the inter-symbol interference factor, v represent the length of the one-sided inter-symbol interference factor, H represent the first channel interference matrix of dimension L×L, and h represent the inter-symbol interference factor. j L represents the tap coefficient of the j-th channel. h Indicates the length of the channel tap.

[0015] Preferably, the method for obtaining the first precoding matrix and the decoding matrix includes:

[0016] Obtain the eigenvalues ​​of the inter-symbol interference matrix, and construct a diagonal matrix using the eigenvalues ​​as diagonal elements;

[0017] The first precoding matrix and decoding matrix are calculated using the diagonal matrix:

[0018]

[0019] Where F represents the first precoding matrix, B represents the decoding matrix, and Q... L Let represent the Fourier transform matrix of dimension L×L, (·) TThis represents the transpose operation, (·). * Represents the conjugate operation, Λ g This represents a diagonal matrix.

[0020] Preferably, the method for obtaining the second precoding matrix includes:

[0021] Using the first channel interference matrix, a cyclic channel interference matrix composed of perfect channel state information is constructed:

[0022]

[0023] in, Let E represent the cyclic channel interference matrix, and E represent the cyclic estimation error matrix.

[0024] The first calculation formula for constructing the second precoding matrix using the cyclic channel interference matrix is ​​as follows:

[0025]

[0026] Where W represents the second precoding matrix, min represents finding the minimum value, and E{·} represents finding the expectation. This indicates the F-norm of a matrix, where I represents the identity matrix;

[0027] Performing matrix operations on the first calculation formula yields the second calculation formula:

[0028]

[0029] Where Re{·} denotes taking the real part, tr(·) denotes the trace of the matrix, and L n This indicates the number of non-zero elements in the first column of E. This represents the variance of the channel estimation error;

[0030] Taking the first derivative of the second calculation formula with respect to W* and setting the derivative to zero, we obtain the second precoding matrix:

[0031]

[0032] in,(·) H This indicates the conjugate transpose operation.

[0033] Preferably, the method for obtaining the encoded transmitted symbol block using the first precoding matrix and the second precoding matrix includes:

[0034] s k =FWa k

[0035] Among them, s k Indicates that the symbol block is sent after encoding, ak This represents the transmitted symbol block after the k-th mapping.

[0036] Preferably, the method for obtaining the processed symbol block includes:

[0037]

[0038] Among them, y k η represents the processed and transmitted symbol block after the kth downsampling, and η represents colored noise.

[0039] Preferably, the method for decoding the processed transmitted symbol block using the decoding matrix to obtain the estimated symbol block includes:

[0040]

[0041] in, represents the estimated symbol block, and n represents Gaussian white noise.

[0042] The present invention also provides a super Nyquist precoding system suitable for imperfect channel state information. The precoding system applies the precoding method described in any of the above-mentioned methods and includes: a matrix acquisition module, a first matrix calculation module, a second matrix calculation module, a precoding module, a symbol block processing module, and a decoding module.

[0043] The matrix acquisition module is used to acquire the first channel interference matrix composed of the inter-symbol interference matrix caused by the super Nyquist system and the imperfect channel state information.

[0044] The first matrix calculation module uses the inter-symbol interference matrix to obtain a first precoding matrix and a decoding matrix to eliminate inter-symbol interference;

[0045] The second matrix calculation module uses the first channel interference matrix to obtain a second precoding matrix that eliminates channel interference, based on the minimum mean square error criterion.

[0046] The precoding module uses the first precoding matrix and the second precoding matrix to precode the transmitted symbol block to obtain the encoded transmitted symbol block.

[0047] The symbol block processing module processes the encoded transmitted symbol block through cyclic super Nyquist shaping, frequency selective fading channel, matched filtering, and downsampling to obtain the processed transmitted symbol block;

[0048] The decoding module uses the decoding matrix to decode the processed transmitted symbol block to obtain the estimated symbol block, thus completing the precoding of the state information.

[0049] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0050] This invention proposes a super-Nyquist precoding method suitable for imperfect channel state information based on the minimum mean square error criterion, achieving satisfactory bit error rate performance under imperfect channel state information. Assuming the transmitter knows the variance of the channel estimation error, a channel interference matrix composed of the inter-symbol interference matrix and the imperfect channel state information is obtained. Based on the minimum mean square error criterion, a precoding matrix and a decoding matrix are designed, and precoding is performed on the mapped transmitted symbol block. Then, the precoded transmitted symbol block undergoes cyclic super-Nyquist shaping, frequency-selective fading, matched filtering, and downsampling. Finally, the downsampled symbol block is decoded using the decoding matrix, thereby eliminating inter-symbol interference and significantly reducing channel interference, resulting in an estimated symbol block. This achieves satisfactory bit error rate performance under imperfect channel state information. Attached Figure Description

[0051] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

[0053] Figure 2 The figures show simulation results of channel estimation errors of different degrees under moderate inter-symbol interference according to an embodiment of the present invention.

[0054] Figure 3 The figures show simulation results of channel estimation errors of different degrees under severe inter-symbol interference according to an embodiment of the present invention. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] 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.

[0057] Example 1

[0058] In this embodiment, as Figure 1As shown, a super Nyquist precoding method suitable for imperfect channel state information includes the following steps:

[0059] S1. Obtain the first channel interference matrix composed of the inter-symbol interference matrix caused by the super Nyquist system and the imperfect channel state information.

[0060] The inter-symbol interference matrix and the first channel interference matrix are as follows:

[0061]

[0062] Where G represents an L×L inter-symbol interference matrix, L is a natural number, and in this formula represents the length of the rows and columns in the matrix, g i In this embodiment, g represents the inter-symbol interference factor. i = g(iτT), where τ represents the packet rate in the super Nyquist system, T represents the symbol spacing, i represents the index value of the inter-symbol interference factor, v represents the length of the one-sided inter-symbol interference factor, H represents the first channel interference matrix of dimension L×L, and h j L represents the tap coefficient of the j-th channel. h Indicates the length of the channel tap.

[0063] S2. Use the inter-symbol interference matrix to obtain the first precoding matrix and decoding matrix to eliminate inter-symbol interference.

[0064] The method for obtaining the first precoding matrix and the decoding matrix includes: obtaining the eigenvalues ​​of the inter-symbol interference matrix and constructing a diagonal matrix using the eigenvalues ​​as diagonal elements; and calculating the first precoding matrix and the decoding matrix using the diagonal matrix.

[0065]

[0066] Where F represents the first precoding matrix, B represents the decoding matrix, and Q... L Let L represent the Fourier transform matrix of dimension L×L, where L represents the length of the rows and columns in the matrix. T This represents the transpose operation, (·). * Represents the conjugate operation, Λ g This represents a diagonal matrix.

[0067] S3. Based on the minimum mean square error criterion, the second precoding matrix for eliminating channel interference is obtained using the first channel interference matrix.

[0068] The method for obtaining the second precoding matrix includes: constructing a cyclic channel interference matrix composed of perfect channel state information using the first channel interference matrix.

[0069]

[0070] in, Let represent the cyclic channel interference matrix, and E represent the cyclic estimation error matrix, where all non-zero elements in E have a zero mean and a variance of . Gaussian distribution; the first calculation formula for constructing the second precoding matrix using the cyclic channel interference matrix:

[0071]

[0072] Where W represents the second precoding matrix, min represents finding the minimum value, and E{·} represents finding the expectation. Let F represent the F-norm of a matrix, and I represent the identity matrix. Performing matrix operations on the first formula yields the second formula:

[0073]

[0074] Where Re{·} denotes taking the real part, tr(·) denotes the trace of the matrix, and in this formula, L represents the length of the symbol block. n This indicates the number of non-zero elements in the first column of E. Represents the variance of the channel estimation error; calculate W using the second formula. * The first derivative is then taken, and the result is set to zero to obtain the second precoding matrix:

[0075]

[0076] in,(·) H This indicates the conjugate transpose operation.

[0077] S4. Use the first precoding matrix and the second precoding matrix to precode the transmitted symbol block to obtain the encoded transmitted symbol block.

[0078] Methods for sending symbol blocks after obtaining the encoding include:

[0079] s k =FWa k

[0080] Among them, s k Indicates that the symbol block is sent after encoding, a k This represents the transmitted symbol block after the k-th mapping.

[0081] S5. The encoded transmitted symbol block is processed by cyclic super Nyquist shaping, frequency selective fading channel, matched filtering and downsampling to obtain the processed transmitted symbol block.

[0082] In this embodiment, the method for obtaining the processed transmission symbol block includes: performing zero-value interpolation on the encoded transmission symbol block, and performing super Nyquist shaping based on the zero-value interpolated transmission frame to obtain the shaped transmission symbol block; passing the shaped transmission symbol block through a frequency-selective fading channel and adding Gaussian white noise, performing matched filtering on the symbol block after adding Gaussian white noise, and downsampling the filtered symbol block to obtain the processed transmission symbol block.

[0083]

[0084] Where yk represents the processed symbol block after the kth downsampling, and η represents colored noise.

[0085] S6. Use the decoding matrix to decode the processed transmitted symbol block to obtain the estimated symbol block, thus completing the precoding of the state information.

[0086] Methods for obtaining estimated symbol blocks include:

[0087]

[0088] in, represents the estimated symbol block, and n represents Gaussian white noise.

[0089] Example 2

[0090] In this embodiment, the effectiveness of the invention is verified through simulation.

[0091] (1) Simulation 1: Considering moderate inter-symbol interference, i.e., packet rate and roll-off factor of 0.8 and 0.25 respectively, symbol estimation is performed using this invention under three channel estimation errors, and the results are as follows. Figure 2 (2) Simulation 2: Considering severe inter-symbol interference, i.e., when the packet rate and roll-off factor are 0.7 and 0.3 respectively, symbol estimation is performed using this invention under three different channel estimation errors, and the results are as follows. Figure 3 . Figure 2 and Figure 3 The horizontal axis represents the bit signal-to-noise ratio of the super Nyquist system, measured in decibels (dB), while the vertical axis represents the bit error rate of the system.

[0092] from Figure 2 It is evident that for moderate inter-symbol interference, as the channel estimation error increases, the present invention requires a higher bit signal-to-noise ratio to achieve the same bit error rate. However, compared to the performance of the Nyquist system, the performance loss of the present invention is within an acceptable range. Furthermore, compared to the JCEP and LPE-FDCE methods, the bit error rate performance of the present invention is the best for each type of channel estimation error. Figure 3It is known that the LPE-FDCE method cannot be applied to severe inter-symbol interference (ISI) due to limitations in packet rate and roll-off factor. While the JCEP method can be used for severe ISI, its bit error rate (BER) performance deteriorates significantly compared to moderate ISI. However, this invention maintains the best BER performance under all three channel estimation error conditions. This demonstrates that this invention can achieve satisfactory BER performance even with imperfect channel state information, ensuring reliable signal detection and physical layer security.

[0093] Example 3

[0094] In this embodiment, a super Nyquist precoding system suitable for imperfect channel state information includes: a matrix acquisition module, a first matrix calculation module, a second matrix calculation module, a precoding module, a symbol block processing module, and a decoding module.

[0095] The matrix acquisition module acquires the first channel interference matrix, which is composed of the inter-symbol interference matrix caused by the super Nyquist system and the imperfect channel state information. The first matrix calculation module uses the inter-symbol interference matrix to obtain the first precoding matrix and the decoding matrix to eliminate inter-symbol interference. The second matrix calculation module uses the minimum mean square error criterion to obtain the second precoding matrix to eliminate channel interference based on the first channel interference matrix. The precoding module uses the first precoding matrix and the second precoding matrix to precode the transmitted symbol block to obtain the encoded transmitted symbol block. The symbol block processing module processes the encoded transmitted symbol block through cyclic super Nyquist shaping, frequency selective fading channel, matched filtering, and downsampling to obtain the processed transmitted symbol block. The decoding module uses the decoding matrix to decode the processed transmitted symbol block to obtain the estimated symbol block, thus completing the precoding of the state information.

[0096] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A super Nyquist precoding method suitable for imperfect channel state information, characterized in that, Includes the following steps: Obtain the first channel interference matrix composed of the inter-symbol interference matrix caused by the super Nyquist system and the imperfect channel state information; The first precoding matrix and decoding matrix for eliminating inter-symbol interference are obtained using the inter-symbol interference matrix; Based on the minimum mean square error criterion, the second precoding matrix for eliminating channel interference is obtained using the first channel interference matrix. The transmitted symbol block is pre-coded using the first precoding matrix and the second precoding matrix to obtain the encoded transmitted symbol block. The encoded transmit symbol block is processed by cyclic super Nyquist shaping, frequency selective fading channel, matched filtering and downsampling to obtain the processed transmit symbol block; The processed transmitted symbol block is decoded using the decoding matrix to obtain the estimated symbol block, thus completing the precoding of the state information. The inter-symbol interference matrix and the first channel interference matrix are: Where G represents an L×L inter-symbol interference matrix, L represents a natural number, and g i Let v represent the inter-symbol interference factor, v represent the length of the one-sided inter-symbol interference factor, H represent the first channel interference matrix of dimension L×L, and h represent the inter-symbol interference factor. j L represents the tap coefficient of the j-th channel. h Indicates the length of the channel tap; The method for obtaining the first precoding matrix and the decoding matrix includes: Obtain the eigenvalues ​​of the inter-symbol interference matrix, and construct a diagonal matrix using the eigenvalues ​​as diagonal elements; The first precoding matrix and decoding matrix are calculated using the diagonal matrix: Where F represents the first precoding matrix, B represents the decoding matrix, and Q... L Let represent the Fourier transform matrix of dimension L×L, (·) T This represents the transpose operation, (·). * Represents the conjugate operation, Λ g This represents a diagonal matrix.

2. The super Nyquist precoding method for imperfect channel state information according to claim 1, characterized in that, The methods for obtaining the second precoding matrix include: Using the first channel interference matrix, a cyclic channel interference matrix composed of perfect channel state information is constructed: in, Let E represent the cyclic channel interference matrix, and E represent the cyclic estimation error matrix. The first calculation formula for constructing the second precoding matrix using the cyclic channel interference matrix is ​​as follows: Where W represents the second precoding matrix, min represents finding the minimum value, and E{·} represents finding the expectation. This indicates the F-norm of a matrix, where I represents the identity matrix; Performing matrix operations on the first calculation formula yields the second calculation formula: Where Re{·} denotes taking the real part, tr(·) denotes the trace of the matrix, and L n This indicates the number of non-zero elements in the first column of E. This represents the variance of the channel estimation error; Find the value of W using the second calculation formula. * The first derivative of the first derivative is then taken, and the result is set to zero to obtain the second precoding matrix: in,(·) H This indicates the conjugate transpose operation.

3. The super Nyquist precoding method for imperfect channel state information according to claim 2, characterized in that, The method for obtaining the encoded transmission symbol block using the first precoding matrix and the second precoding matrix includes: s k =FWa k Among them, s k Indicates that the symbol block is sent after encoding, a k This represents the transmitted symbol block after the k-th mapping.

4. The super Nyquist precoding method for imperfect channel state information according to claim 3, characterized in that, The method for obtaining the processed symbol block includes: Among them, y k η represents the processed and transmitted symbol block after the kth downsampling, and η represents colored noise.

5. The super Nyquist precoding method for imperfect channel state information according to claim 4, characterized in that, The method for decoding the processed transmitted symbol block using the decoding matrix to obtain the estimated symbol block includes: in, represents the estimated symbol block, and n represents Gaussian white noise.

6. A super Nyquist precoding system suitable for imperfect channel state information, wherein the precoding system applies the precoding method according to any one of claims 1-5, characterized in that, include: The system includes a matrix acquisition module, a first matrix calculation module, a second matrix calculation module, a precoding module, a symbol block processing module, and a decoding module. The matrix acquisition module is used to acquire the first channel interference matrix composed of the inter-symbol interference matrix caused by the super Nyquist system and the imperfect channel state information. The first matrix calculation module uses the inter-symbol interference matrix to obtain a first precoding matrix and a decoding matrix to eliminate inter-symbol interference; The second matrix calculation module uses the first channel interference matrix to obtain a second precoding matrix that eliminates channel interference, based on the minimum mean square error criterion. The precoding module uses the first precoding matrix and the second precoding matrix to precode the transmitted symbol block to obtain the encoded transmitted symbol block. The symbol block processing module processes the encoded transmitted symbol block through cyclic super Nyquist shaping, frequency selective fading channel, matched filtering, and downsampling to obtain the processed transmitted symbol block; The decoding module uses the decoding matrix to decode the processed transmitted symbol block to obtain the estimated symbol block, thus completing the precoding of the state information.

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