Faster-Nyquist precoding method and system suitable for imperfect channel state information

Abstract

The invention discloses a super-Nyquist precoding method and system suitable for imperfect channel state information. The method comprises the following steps: acquiring an intersymbol interference matrix caused by a super-Nyquist system and a first channel interference matrix formed by the imperfect channel state information; obtaining a first precoding matrix and a decoding matrix for eliminating the inter-symbol interference by using the inter-symbol interference matrix; based on a minimum mean square error criterion, using the first channel interference matrix to obtain a second precoding matrix for eliminating channel interference; pre-coding the sending symbol block by using the first pre-coding matrix and the second pre-coding 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 down-sampling 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, and completing the precoding of the state information.

Description

Technical Field

[0001] The invention belongs to the technical field of satellite communications, and in particular relates to a super-Nyquist precoding method and system suitable for imperfect channel state information. Background Art

[0002] In response to the sharply rising demand for data transmission for mobile broadband services, 6G is expected to achieve a peak throughput of Tbps. Traditional wireless communication systems usually follow the Nyquist criterion, sacrificing throughput and spectrum efficiency in exchange for reliable information transmission, which obviously cannot meet the vision of 6G. In addition, 6G is also ambitious in its goals for high-throughput satellite communications. It will promote a satellite-ground integrated network architecture and create seamless network coverage for end users. However, existing satellite communication systems cannot meet the needs of 6G due to their low capacity and low spectrum utilization. In this context, super-Nyquist transmission, which deviates from the Nyquist criterion and introduces inter-symbol interference, has attracted the attention of the academic community because it can achieve high throughput and high spectrum utilization.

[0003] In order to ensure the reliability of super-Nyquist transmission, many solutions to combat the inter-symbol interference introduced by super-Nyquist systems have been explored, including frequency domain equalization technology and linear precoding technology located only in the receiver. These technologies all use a finite tap matrix to approximate inter-symbol interference and eliminate inter-symbol interference through matrix operations. The difference is that the former performs inter-symbol interference elimination operations at the receiver, which will lead to noise amplification, especially when the inter-symbol interference is severe, the noise amplification phenomenon is more significant. The latter effectively alleviates the noise amplification phenomenon because the inter-symbol interference matrix is ​​offset at the transmitter. In addition, frequency domain equalization technology is difficult to strike a balance between resource consumption and bit error rate, while linear precoding technology can better compromise the two, thereby achieving excellent bit error rate performance while maintaining low complexity, so it is more suitable for super-Nyquist transmission. However, the existing linear precoding technology is mainly aimed at additive white Gaussian noise channels, while actual satellite communications will face frequency selective fading channels, which will cause channel interference. Therefore, Shinya Sugiura et al. used 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 and symbol estimation. However, the frequency domain equalization technology is not very effective in eliminating channel interference. Subsequently, Li Qiang from Xidian University proposed the use of precoding technology to perform channel estimation and eliminate channel interference 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 bit error rate performance when inter-code interference is relatively mild. However, it assumes that the transmitter can perfectly obtain the channel state estimated by the receiver. In actual satellite communications, the channel state information obtained by the transmitter is affected by many factors, including estimation errors caused by inaccurate estimation of channel state information, quantization errors caused by limited feedback, and delay differences caused by the long distance of the communication link. These errors cause the channel state information received by the transmitter to be unable to accurately reflect the actual channel state. Therefore, how to perform super-Nyquist precoding in the case of imperfect channel state information is still a difficult problem. Therefore, in order to apply super-Nyquist technology to actual satellite communications, it is crucial to consider a super-Nyquist precoding method suitable for imperfect channel state information. Summary of the invention

[0004] The present invention aims to solve the deficiencies of the prior art and provides the following solutions:

[0005] A super-Nyquist precoding method applicable to imperfect channel state information comprises the following steps:

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

[0007] Using the inter-symbol interference matrix to obtain a first precoding matrix and a decoding matrix to eliminate inter-symbol interference;

[0008] Based on a minimum mean square error criterion, using the first channel interference matrix to obtain a second precoding matrix that eliminates channel interference;

[0009] Precoding a transmission symbol block using the first precoding matrix and the second precoding matrix to obtain a coded transmission symbol block;

[0010] Processing the encoded transmission symbol block through cyclic super-Nyquist shaping, frequency selective fading channel, matched filtering and down sampling to obtain a processed transmission symbol block;

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

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

[0013]

[0014] Where G represents the inter-symbol interference matrix with dimension L×L, L represents a natural number, and g i represents the inter-code interference factor, v represents the length of the unilateral inter-code interference factor, H represents the first channel interference matrix with dimension L×L, and h j represents the jth channel tap coefficient, L h Indicates the length of the channel tap.

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

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

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

[0018]

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

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

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

[0022]

[0023] in, represents the cyclic channel interference matrix, E represents the found estimation error cyclic matrix;

[0024] A first calculation formula for constructing the second precoding matrix by using the cyclic channel interference matrix is:

[0025]

[0026] Wherein, W represents the second precoding matrix, min represents the minimum value, and E{·} represents the expectation value. It means to find the F norm of the matrix, and I means the identity matrix;

[0027] Performing matrix operations on the first calculation formula, a second calculation formula is obtained:

[0028]

[0029] Among them, Re{·} means taking the real part, tr(·) means the trace of the matrix, L n represents the number of non-zero elements in the first column of E, represents the variance of the channel estimation error;

[0030] The first-order derivative of the second calculation formula with respect to W* is calculated, and the derivative result is set to zero to obtain the second precoding matrix:

[0031]

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

[0033] Preferably, the method of 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 the symbol block sent after encoding, ak Represents the kth mapped transmitted symbol block.

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

[0037]

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

[0039] Preferably, the method of 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 applicable to imperfect channel state information, wherein the precoding system applies any of the precoding methods described above, including: 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 a first channel interference matrix composed of an inter-symbol interference matrix caused by a super-Nyquist system and 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 that eliminate inter-symbol interference;

[0045] The second matrix calculation module obtains a second precoding matrix that eliminates channel interference using the first channel interference matrix based on a minimum mean square error criterion;

[0046] The precoding module precodes the transmission symbol block using the first precoding matrix and the second precoding matrix to obtain a coded transmission symbol block;

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

[0048] The decoding module decodes the processed transmission symbol block using the decoding matrix to obtain an estimated symbol block, thereby completing the precoding of the state information.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] The present invention proposes a super-Nyquist precoding method suitable for imperfect channel state information based on the minimum mean square error criterion, which can achieve satisfactory bit error rate performance under imperfect channel state information. Assuming that the transmitter knows the variance of the channel estimation error, the channel interference matrix composed of the inter-symbol interference matrix and the imperfect channel state information is obtained, and the precoding matrix and the decoding matrix are designed based on the minimum mean square error criterion, and the mapped transmission symbol block is precoded. Then, the precoded transmission symbol block is subjected to cyclic super-Nyquist shaping, frequency selective fading channel, matched filtering and downsampling, and the downsampled symbol block is decoded using the decoding matrix, thereby eliminating inter-symbol interference and channel interference to a great extent, obtaining an estimated symbol block, and achieving satisfactory bit error performance under imperfect channel state information. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0052] Figure 1 A schematic diagram of a method flow of an embodiment of the present invention;

[0053] Figure 2 Graphs showing simulation results of an embodiment of the present invention under different degrees of channel estimation errors under moderate inter-symbol interference;

[0054] Figure 3 It is a simulation result diagram of the embodiment of the present invention under different degrees of channel estimation error under severe inter-symbol interference. DETAILED DESCRIPTION

[0055] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0056] 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.

[0057] Embodiment 1

[0058] In this embodiment, if Figure 1As shown, a super-Nyquist precoding method applicable to imperfect channel state information includes the following steps:

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

[0060] The inter-code interference matrix and the first channel interference matrix are:

[0061]

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

[0063] S2. Using the inter-code interference matrix, obtain a first precoding matrix and a decoding matrix for eliminating inter-code interference.

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

[0065]

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

[0067] S3. Based on the minimum mean square error criterion, the first channel interference matrix is ​​used to obtain a second precoding matrix that eliminates channel interference.

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

[0069]

[0070] in, represents the cyclic channel interference matrix, E represents the estimated error cyclic matrix, and all non-zero elements in E obey zero mean and variance Gaussian distribution; construct the first calculation formula of the second precoding matrix by cyclic channel interference matrix:

[0071]

[0072] Wherein, W represents the second precoding matrix, min represents the minimum value, and E{·} represents the expectation value. Indicates the F norm of the matrix, I represents the identity matrix; perform matrix operation on the first calculation formula to obtain the second calculation formula:

[0073]

[0074] Where Re{·} represents the real part, tr(·) represents the trace of the matrix, and in this formula, L represents the length of the symbol block, L n represents the number of non-zero elements in the first column of E, represents the variance of the channel estimation error; the second calculation formula is calculated about W * The first-order derivative of and set the derivative result to zero to obtain the second precoding matrix:

[0075]

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

[0077] S4. Precode the transmission symbol block using the first precoding matrix and the second precoding matrix to obtain a coded transmission symbol block.

[0078] The method of obtaining the encoded and transmitted symbol block includes:

[0079] s k =FWa k

[0080] Among them, s k Indicates the symbol block sent after encoding, a k Represents the kth mapped transmitted symbol block.

[0081] S5. Process the encoded transmission symbol block through cyclic super-Nyquist shaping, frequency selective fading channel, matched filtering and down sampling to obtain a processed transmission symbol block.

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

[0083]

[0084] Wherein, yk represents the processed transmitted 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 an estimated symbol block, thereby 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] Embodiment 2

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

[0091] (1) Simulation 1, when considering moderate inter-symbol interference, that is, when the packing rate and roll-off factor are 0.8 and 0.25 respectively, the present invention is used to perform symbol estimation under three channel estimation errors. The results are as follows: Figure 2 (2) Simulation 2, when severe inter-symbol interference is considered, that is, when the packing rate and roll-off factor are 0.7 and 0.3 respectively, the present invention is used to perform symbol estimation under three channel estimation errors. 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, and its unit is decibel dB (decibel), and the vertical axis represents the bit error rate of the system.

[0092] from Figure 2 It can be seen that for moderate inter-symbol interference, as the channel estimation error increases, the present invention needs a higher bit signal-to-noise ratio to achieve the same bit error rate, but compared with the performance of the Nyquist system, the performance loss of the present invention is within an acceptable range. In addition, compared with the JCEP method and the LPE-FDCE method, the bit error rate performance of the present invention is the best under each channel estimation error. Figure 3It can be seen that for severe inter-symbol interference, the LPE-FDCE method cannot be applied to severe inter-symbol interference due to the limitations of the packing rate and the roll-off factor, and although the JCEP method can be used for severe inter-symbol interference, its bit error rate performance is seriously deteriorated compared to moderate inter-symbol interference, and the present invention can still maintain the best bit error rate performance under three channel estimation errors. This shows that the present invention can achieve satisfactory bit error rate performance under imperfect channel state information, ensuring the reliable implementation of signal detection and physical layer security.

[0093] Embodiment 3

[0094] In this embodiment, a super-Nyquist precoding system applicable to 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 is used to obtain the first channel interference matrix composed of the inter-code interference matrix caused by the super-Nyquist system and the imperfect channel state information; the first matrix calculation module uses the inter-code interference matrix to obtain the first precoding matrix and decoding matrix for eliminating inter-code interference; the second matrix calculation module uses the first channel interference matrix to obtain the second precoding matrix for eliminating 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 transmission symbol block to obtain the encoded transmission symbol block; the symbol block processing module processes the encoded transmission symbol block through cyclic super-Nyquist shaping, frequency selective fading channel, matched filtering and downsampling to obtain the processed transmission symbol block; the decoding module uses the decoding matrix to decode the processed transmission symbol block to obtain the estimated symbol block, and completes the precoding of the state information.

[0096] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A super-Nyquist precoding method for imperfect channel state information, characterized in that: The following steps are involved: Obtaining a first channel interference matrix composed of an inter-symbol interference matrix caused by a super-Nyquist system and imperfect channel state information; Using the inter-symbol interference matrix to obtain a first precoding matrix and a decoding matrix to eliminate inter-symbol interference; Based on a minimum mean square error criterion, using the first channel interference matrix to obtain a second precoding matrix that eliminates channel interference; Precoding a transmission symbol block using the first precoding matrix and the second precoding matrix to obtain a coded transmission symbol block; Processing the encoded transmission symbol block through cyclic super-Nyquist shaping, frequency selective fading channel, matched filtering and down sampling to obtain a processed transmission symbol block; The processed transmission symbol block is decoded using the decoding matrix to obtain an estimated symbol block, thereby completing the precoding of the state information.

2. The super-Nyquist precoding method for imperfect channel state information according to claim 1, characterized in that: The inter-symbol interference matrix and the first channel interference matrix are: Where G represents the inter-symbol interference matrix with dimension L×L, L represents a natural number, and g i represents the inter-code interference factor, v represents the length of the unilateral inter-code interference factor, H represents the first channel interference matrix with dimension L×L, and h j represents the jth channel tap coefficient, L h Indicates the length of the channel tap.

3. A super-Nyquist precoding method applicable to imperfect channel state information according to claim 2, characterized in that: The method of obtaining the first precoding matrix and the decoding matrix includes: Obtaining eigenvalues ​​of the inter-symbol interference matrix, and constructing a diagonal matrix using the eigenvalues ​​as diagonal elements; The first precoding matrix and the decoding matrix are calculated by the diagonal matrix: Where F represents the first precoding matrix, B represents the decoding matrix, Q L represents the Fourier transform matrix of dimension L×L, (·) T represents the transpose operation, (·) * represents the conjugate operation, Λ g represents a diagonal matrix.

4. The super-Nyquist precoding method for imperfect channel state information according to claim 3, characterized in that: The method for obtaining the second precoding matrix includes: Through the first channel interference matrix, a cyclic channel interference matrix consisting of perfect channel state information is constructed: in, represents the cyclic channel interference matrix, E represents the found estimation error cyclic matrix; A first calculation formula for constructing the second precoding matrix by using the cyclic channel interference matrix is: Wherein, W represents the second precoding matrix, min represents the minimum value, and E{·} represents the expectation value. It means to find the F norm of the matrix, and I means the identity matrix; Performing matrix operations on the first calculation formula, a second calculation formula is obtained: Among them, Re{·} means taking the real part, tr(·) means the trace of the matrix, L n represents the number of non-zero elements in the first column of E, represents the variance of the channel estimation error; The first-order derivative of the second calculation formula with respect to W* is calculated, and the derivative result is set to zero to obtain the second precoding matrix: in,(·) H Represents the conjugate transpose operation.

5. The super-Nyquist precoding method applicable to imperfect channel state information according to claim 4, characterized in that: The method of obtaining the encoded transmitted symbol block by using the first precoding matrix and the second precoding matrix includes: s k =FWa k Among them, s k Indicates the symbol block sent after encoding, a k Represents the kth mapped transmitted symbol block.

6. The super-Nyquist precoding method applicable to imperfect channel state information according to claim 5, characterized in that: The method for obtaining the processed sending symbol block includes: Wherein, yk represents the processed transmitted symbol block after the kth downsampling, and η represents colored noise.

7. The super-Nyquist precoding method applicable to imperfect channel state information according to claim 6, characterized in that: The method of 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.

8. A super-Nyquist precoding system applicable to imperfect channel state information, the precoding system applying the precoding method according to any one of claims 1 to 7, characterized in that: include: 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 a first channel interference matrix composed of an inter-symbol interference matrix caused by a super-Nyquist system and 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 that eliminate inter-symbol interference; The second matrix calculation module obtains a second precoding matrix that eliminates channel interference using the first channel interference matrix based on a minimum mean square error criterion; The precoding module precodes the transmission symbol block using the first precoding matrix and the second precoding matrix to obtain a coded transmission symbol block; The symbol block processing module processes the encoded transmission symbol block through cyclic super-Nyquist shaping, frequency selective fading channel, matched filtering and down sampling to obtain a processed transmission symbol block; The decoding module decodes the processed transmission symbol block using the decoding matrix to obtain an estimated symbol block, thereby completing the precoding of the state information.

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