Method and device for estimating signal-to-noise ratio of single-carrier super-nyquist transmission system

Abstract

The present application overcomes the shortcomings of the conventional signal-to-noise ratio estimation scheme, and provides a signal-to-noise ratio estimation method and device for a single-carrier super-Nyquist transmission system. The method mainly comprises initialization, cyclic prefix processing, establishment of a received signal structure expression, matrix decomposition operation, calculation of a noise variance estimation value according to an approximate expression of the decomposition cyclic matrix, a white filter output vector, a possible transmission vector combination, the number of all possible transmission vector combinations, and the noise variance estimation value; and conversion of the noise variance estimation value to obtain a signal-to-noise ratio estimation value. The present application solves the problem that the prior art scheme cannot be directly applied to a single-carrier super-Nyquist transmission system, and enables signal-to-noise ratio estimation in an SC-FTN transmission system.

Description

Technical Field

[0001] This invention relates to a signal-to-noise ratio estimation method and apparatus for a single-carrier super Nyquist transmission system, belonging to the field of wireless communication technology. Background Technology

[0002] Signal-to-noise ratio (SNR) estimation is a crucial component of parameter estimation in wireless communication transmission systems. The SNR value measures channel quality and serves as a key indicator for the transmitter to adjust coding and modulation orders in adaptive transmission systems. Single-carrier super-Nyquist (SC-FTN) transmission, a promising technology for sixth-generation (6G) mobile communication, offers higher spectral efficiency. To facilitate the practical application of SC-FTN, SNR estimation techniques can be applied to iterative equalization and adaptive coding and modulation.

[0003] Existing technical solutions primarily address the signal-to-noise ratio (SNR) estimation problem in Nyquist transmission systems under additive white Gaussian noise (CGN) channels. The main approach involves first deriving the expression for noise variance versus signal power based on the maximum likelihood estimation criterion, then finding the extreme points by calculating partial derivatives to ultimately obtain the estimated SNR value. Existing technical solutions have already derived theoretical performance bounds for SNR estimation under different modulation schemes for traditional Nyquist transmission systems and designed corresponding SNR estimation methods.

[0004] The drawback of existing technologies is that traditional signal-to-noise ratio (SNR) estimation algorithms are designed for Nyquist transmission systems. Due to artificially introduced inter-symbol interference (ISI), existing technologies cannot be directly applied to single-carrier super-Nyquist transmission systems. Therefore, to achieve SNR estimation in SC-FTN transmission systems, a non-data-aided SNR estimation method suitable for single-carrier super-Nyquist transmission systems is urgently needed. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a non-data-aided signal-to-noise ratio estimation method applicable to single-carrier super Nyquist transmission systems. This solves the problem that existing technical solutions cannot be directly applied to single-carrier super Nyquist transmission systems and enables signal-to-noise ratio estimation in SC-FTN transmission systems.

[0006] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0007] In a first aspect, the present invention provides a signal-to-noise ratio estimation method suitable for a single-carrier super Nyquist transmission system, comprising the following steps:

[0008] Step 1: Obtain the transmitted signal and its structure; the transmitted signal is a single-carrier super Nyquist signal;

[0009] Step 2: Perform cyclic prefix processing on the transmitted signal to obtain the processed signal;

[0010] Step 3: Based on the processed signal and the transmitted signal structure, establish the received signal structure expression to obtain the output vector of the whitening filter, the cyclic matrix, the possible combinations of transmitted vectors, and the number of all possible combinations of transmitted vectors.

[0011] Step 4: Perform decomposition operations on the cyclic matrix to obtain the decomposed cyclic matrix;

[0012] Step 5: Obtain an approximate expression for the noise variance estimate;

[0013] Step 6: Calculate the noise variance estimate based on the decomposed cyclic matrix, the vector output by the whitening filter, possible combinations of transmission vectors, the number of all possible combinations of transmission vectors, and the approximate expression of the noise variance estimate.

[0014] Step 7: Convert the noise variance estimate to obtain the signal-to-noise ratio estimate.

[0015] Further, step 1: Obtain the transmitted signal and the transmitted signal structure, including:

[0016] The receiving end initializes the initial variables, buffered data, and counters, and then receives the transmission signal and obtains the corresponding transmission signal structure.

[0017] Further, step 2: Perform cyclic prefix processing on the transmitted signal to obtain the processed signal, including:

[0018] By removing the cyclic prefixes at the beginning and end of the transmitted signal, the linear convolution process of the single-carrier super Nyquist signal is transformed into a cyclic convolution process, resulting in the processed signal.

[0019] The transmitted signal is obtained at the transmitting end by adding a cyclic prefix of a certain length to the modulated data, and then performing shaping filtering processing on a single-carrier super Nyquist signal.

[0020] Further, step 3: Based on the processed signal and the transmitted signal structure, establish the received signal structure expression to obtain the whitening filter output vector, cyclic matrix, possible transmission vector combinations, and the number of all possible transmission vector combinations, including:

[0021] Based on the transmitted signal structure, the expression for the received signal structure is established, and the corresponding mathematical expression for the received signal structure is as follows:

[0022]

[0023] in, The vector represents the output of the whitening filter. Vector 'a' represents the modulation symbol transmitted at the transmitter, specifically the constellation point symbol. Vector 'g' represents the combined vector of the shaping filter, matched filter, and whitening filter. (Mathematical notation) Representing a circular convolution operation, matrix G is a circular matrix. The elements in the first column of matrix G are the vector g, padded with zeros. η represents a Gaussian white noise vector with a mean of 0 and a variance of 0.

[0024] Based on the known set of transmitting constellation points, all possible combinations of transmitting vectors are obtained by traversal. The total number of possible combinations is M, and the transmitting vector of the l-th combination is a. l .

[0025] Further, step 4: perform decomposition operations on the cyclic matrix to obtain the decomposed cyclic matrix, including:

[0026] Performing matrix decomposition on a cyclic matrix G, the cyclic matrix can be decomposed into three matrices, as shown in the following expression.

[0027] G = F H ΛF formula (2)

[0028] in,(·) H Let represent the complex conjugate transpose operation. Matrix Λ is a diagonal matrix, and the elements on its diagonal are the Fourier transform values ​​of the elements in the first column of the circular matrix G. F is the normalized discrete Fourier matrix. H It is the conjugate transpose of the normalized discrete Fourier matrix.

[0029] Further, step 5: Obtain an approximate expression for the noise variance estimate, including:

[0030] An expression for obtaining the noise variance estimate;

[0031] Based on the expression for the noise variance estimate, an approximation method is performed to obtain an approximate expression for the noise variance estimate.

[0032] Furthermore, the expression for obtaining the noise variance estimate includes:

[0033] Construct the probability density distribution function of the signal-to-noise ratio, and here we have the probability density distribution function of the signal-to-noise ratio. for

[0034]

[0035] Where M represents the total number of possible combinations of the transmission vectors, a l This represents the transmission vector of the l-th combination, with the superscript H indicating the conjugate transpose;

[0036] By performing a logarithmic operation on the probability density distribution function, then taking the first partial derivative with respect to the noise variance, and setting this first partial derivative to zero, we obtain the expression for the noise variance estimate:

[0037]

[0038] Where M represents the total number of all possible transmission vector combinations, δ l Let represent the standard deviation of the transmission vector of the l-th combination. This represents the standard deviation of the Gaussian white noise vector. This represents the vector output by the whitening filter.

[0039] Furthermore, based on the expression for the noise variance estimate, an approximation method is performed to obtain an approximate expression for the noise variance estimate, including:

[0040] The expression for the noise variance estimate is approximated. Formula (4) can be simplified to the following expression:

[0041]

[0042] in,

[0043] Further, step 6: Calculate the noise variance estimate based on the decomposed cyclic matrix, the vector output by the whitening filter, possible transmission vector combinations, the number of all possible transmission vector combinations, and the approximate expression for the noise variance estimate, including:

[0044] According to the decomposition of the cyclic matrix G = F H ΛF, the vector output by the whitening filter, and the transmit vector a of the l-th combination. l The standard deviation δ of the transmission vector of the l-th combination is calculated according to the following formula. l :

[0045]

[0046] Where Re(·) represents taking the real part of the complex number.

[0047] Based on the vector output by the whitening filter and the standard deviation δ of the transmitted vector of the l-th combination. l The noise variance estimate is calculated using the approximate expression for the noise variance estimate, along with the number of all possible transmission vector combinations:

[0048]

[0049] Wherein, the superscript H indicates the conjugate transpose; δ 2 This is the noise variance estimate.

[0050] Further, step 7: Obtaining a signal-to-noise ratio estimate based on the noise variance estimate includes:

[0051] By combining the obtained noise variance estimate with a division operation and converting the ratio into logarithmic form, the final signal-to-noise ratio estimate can be obtained.

[0052] SNR = 10log 10 (1 / δ 2 ) Formula (6)

[0053] Wherein, SNR is the estimated signal-to-noise ratio.

[0054] Furthermore, the method also includes:

[0055] The obtained signal-to-noise ratio (SNR) estimate can be saved or output for subsequent signal demodulation.

[0056] In a second aspect, the present invention provides a signal-to-noise ratio estimation device suitable for a single-carrier super Nyquist transmission system, comprising a processor and a storage medium;

[0057] The storage medium is used to store instructions;

[0058] The processor is configured to operate according to the instructions to perform the steps of the method according to the first aspect.

[0059] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0060] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0061] 1. This invention provides a specific method for signal-to-noise ratio (SNR) estimation in a single-carrier super Nyquist transmission system. The method involves initialization, processing of the cyclic prefix, establishing the received signal structure expression, matrix decomposition, obtaining a noise variance estimate, approximating the mathematical expression, converting it into an SNR estimate, and finally outputting the SNR estimate for the single-carrier super Nyquist transmission system. This solves the problem that existing technical solutions cannot be directly applied to single-carrier super Nyquist transmission systems, and enables SNR estimation in SC-FTN transmission systems.

[0062] 2. This invention performs matrix decomposition on the cyclic matrix G and applies the decomposed cyclic matrix to the solution of the standard deviation of the signal. The computational complexity can be reduced by using the fast Fourier transform.

[0063] 3. This invention removes the cyclic prefixes at the beginning and end of the transmitted signal, transforming the linear convolution process inherent in the single-carrier super Nyquist transmission system into a cyclic convolution process, which facilitates signal processing. Attached Figure Description

[0064] Figure 1 Flowchart of the signal-to-noise ratio estimation algorithm for a single-carrier super Nyquist transmission system;

[0065] Figure 2 The signal flow diagram for a single-carrier super Nyquist transmission system;

[0066] Figure 3 The graph shows the signal-to-noise ratio estimation performance of the proposed method when the compression factor and data length are different. Detailed Implementation

[0067] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0068] Example 1:

[0069] This embodiment proposes a signal-to-noise ratio estimation method and apparatus for a single-carrier super Nyquist transmission system. For specific implementation steps of this invention, please refer to [link to relevant documentation]. Figure 1 The detailed workflow is as follows:

[0070] Step 1: Initialization

[0071] The signal-to-noise ratio (SNR) estimation of a single-carrier super Nyquist transmission system is completed at the receiver. Initial variables, buffered data, counters, etc., need to be initialized at the receiver before the next SNR estimation process can begin.

[0072] Step 2: Processing the cyclic prefix

[0073] At the transmitting end, a cyclic prefix of a certain length is added to the modulated data before shaping and filtering the single-carrier super-Nyquist signal. At the receiving end, removing the leading and trailing cyclic prefixes transforms the linear convolution process inherent in the single-carrier super-Nyquist transmission system into a cyclic convolution process.

[0074] Step 3: Establish the received signal structure expression

[0075] After receiving data, the receiving end needs to store it in its buffer. Furthermore, in wireless communication systems, since the receiving and transmitting ends are partners, the receiving end typically knows the transmitting signal structure of the transmitting end. For example... Figure 2 As shown, after the receiving end receives the data, it can establish the expression for the received signal structure based on the transmitted signal structure. The corresponding mathematical expression for the received signal structure can be written in the following form:

[0076]

[0077] in, The vector represents the output of the whitening filter, vector 'a' represents the modulation symbol transmitted at the transmitter, and vector 'g' represents the combined vector of the shaping filter, matched filter, and whitening filter. (Mathematical symbols) Representing a circular convolution operation, matrix G is a circular matrix, where the elements in the first column of matrix G are the vector g, padded with zeros. η represents a Gaussian white noise vector with a mean of 0 and a variance of .

[0078] Step 4: Matrix decomposition operation

[0079] According to matrix factorization theory, a cyclic matrix can be decomposed into three matrices, and the expression after decomposition is as follows:

[0080] G = F H ΛF formula (2)

[0081] in,(·) H Let represent the complex conjugate transpose operation. Matrix Λ is a diagonal matrix, and the elements on its diagonal are the Fourier transform values ​​of the elements in the first column of the circular matrix G. F is the normalized discrete Fourier matrix. H It is the conjugate transpose of the normalized discrete Fourier matrix.

[0082] Step 5: Noise Variance Estimate

[0083] Based on statistical signal processing theory, a probability density function for the signal-to-noise ratio is constructed. The logarithm of this function is then calculated, and the first partial derivative with respect to the noise variance is taken, set to zero. Analysis reveals that the first partial derivative equation contains only one unknown: the noise variance. Simplification yields an expression for the noise variance estimate.

[0084] Based on statistical signal processing theory, a probability density function for the signal-to-noise ratio (SNR) is constructed. The logarithm of this probability density function is then calculated, and the first partial derivative with respect to the noise variance is taken, set to zero. Here, the probability density function for the SNR is... for

[0085]

[0086] Where M represents the total number of possible combinations of the transmission vectors, a l Let a represent the transmission vector of the l-th combination. The receiver knows the set of transmission constellation points and obtains a by traversing the set. l The superscript H indicates conjugate transpose;

[0087] Analysis revealed that the first-order partial derivative equation contained only one unknown: the noise variance. Simplification yields the expression for the noise variance estimate.

[0088]

[0089] in, Substituting formula (2) here, the computational complexity can be reduced by using the Fast Fourier Transform. Re(·) represents taking the real part of the complex number. M represents the total number of possible combinations of the sending vectors, δ l This represents the standard deviation of the l-th signal. This represents the standard deviation of the Gaussian white noise vector. This represents the vector output by the whitening filter.

[0090] Step Six: Approximation Method

[0091] To obtain a specific expression for the noise variance estimate, it is also necessary to perform an expectation operation on the transmitted modulation symbols. At this point, the properties of the circulant matrix G are needed to simplify the computational complexity.

[0092] To obtain a specific expression for the noise variance estimate, an approximation is performed here, yielding: Equation (4) can be simplified to an approximate expression for the noise variance estimate:

[0093]

[0094] The specific steps for calculating the noise variance estimate using the approximate expression for the noise variance estimate – formula (5) – are as follows:

[0095] Based on the decomposed cyclic matrix, the vector output by the whitening filter, and the possible combinations of transmit vectors, the standard deviation δ of the transmit vector for the l-th combination is calculated according to the following formula. l :

[0096] G = F H ΛF

[0097]

[0098] Where Re(·) represents taking the real part of the complex number.

[0099] Based on the vector output by the whitening filter and the standard deviation δ of the transmitted vector of the l-th combination. l The noise variance estimate is calculated using the approximate expression for the noise variance estimate, along with the number of all possible transmission vector combinations:

[0100]

[0101] Wherein, the superscript H indicates the conjugate transpose; δ 2 This is the noise variance estimate.

[0102] Step 7: Convert to signal-to-noise ratio estimate

[0103] In practical wireless communication transmission systems, the power of the transmitted signal is usually normalized or estimated at the receiver. Combining the noise variance estimate obtained in the previous step with a division operation and converting the ratio to logarithmic form, the final signal-to-noise ratio estimate can be obtained:

[0104] SNR = 10log 10 (1 / δ 2 ) Formula (6)

[0105] Wherein, SNR is the estimated signal-to-noise ratio.

[0106] Step 8: Output Results

[0107] Once the signal-to-noise ratio estimate is obtained, it can be saved or output to the subsequent signal demodulation module for signal demodulation.

[0108] This embodiment proposes a non-data-aided signal-to-noise ratio (SNR) estimation mathematical model for single-carrier super-Nyquist transmission systems. A non-data-aided SNR estimation algorithm suitable for single-carrier super-Nyquist transmission systems is then proposed. By using a cyclic prefix, the linear convolutional structure of inter-symbol interference (ISI) is transformed into a cyclic convolutional structure. The Fast Fourier Transform (FFT) is fully utilized to achieve matrix decomposition, reducing the computational complexity of SNR estimation. Simulation results demonstrate that the proposed SNR estimation algorithm achieves good performance.

[0109] exist Figure 1 The algorithm flowchart describes the various steps of signal-to-noise ratio estimation in a single-carrier super Nyquist transmission system. These steps include initialization, processing of the cyclic prefix, establishing the received signal structure expression, matrix decomposition operations, obtaining noise variance estimates, approximating the mathematical expression, converting it into a signal-to-noise ratio estimate, and finally outputting the signal-to-noise ratio estimate of the single-carrier super Nyquist transmission system.

[0110] Figure 2The signal flow diagram for a single-carrier super Nyquist transmission system; Figure 2 In M-QAM (M-ary Quadrature Amplitude Modulation), an M-ary quadrature amplitude modulation is applied. After quadrature amplitude modulation, a cyclic prefix (CP) is inserted, followed by Faster-than-Nyquist (FTN) transmission. The transmitted signal reaches the receiver after being affected by noise. The receiver first performs matched filtering (MF) followed by whitening matched filtering (WMF). Then, the cyclic prefix is ​​removed (Remove CP), and signal-to-noise ratio (SNR) estimation is performed.

[0111] To verify the technical effectiveness of this invention, simulations and verifications were performed on the proposed noise variance estimation method. In the simulations, the shaping filter used was the root-raised cosine waveform after energy normalization, with a time truncation length of six symbol time intervals on both sides. The length of the cyclic prefix was 10. Since existing literature does not derive the theoretical performance bound for signal-to-noise ratio estimation in single-carrier super Nyquist transmission systems, simulations were conducted to compare the proposed algorithm under different data lengths and different time-domain compression factors.

[0112] Figure 3 This indicates the signal-to-noise ratio estimation performance of the proposed method when the compression factor and data length are different; Figure 3 The horizontal axis Es / No represents the symbol signal-to-noise ratio. Figure 3 The ordinate MSE (Mean Square Error) represents the mean square error of the signal-to-noise ratio estimation. The time-domain compression factor is τ, and the symbol length used for signal-to-noise ratio estimation is N.

[0113] Figure 3The performance of the proposed noise variance estimation method under binary phase modulation in a single-carrier super-Nyquist transmission system was simulated. In the simulation, the time-domain compression factor was set to τ = 0.7, 0.8, and 0.9, and the data length was set to N = 256 and N = 2048, respectively. The performance of the proposed noise variance estimation method improves with increasing symbol signal-to-noise ratio (SNR). However, when the symbol SNR exceeds a certain value, a plateau in the noise variance estimation performance occurs. This phenomenon is caused by two factors: firstly, the single-carrier super-Nyquist transmission method introduces artificial inter-symbol interference (ISI), which, when sufficiently numerous, can be approximated as Gaussian noise; secondly, the proposed noise variance estimation algorithm derives its final analytical expression under the assumption of a low SNR region. Simulation results show that the noise variance estimation performance of the proposed algorithm gradually improves as the compression factor of the single-carrier super-Nyquist transmission system changes from τ = 0.7 to τ = 0.9.

[0114] Example 2:

[0115] This embodiment provides a signal-to-noise ratio estimation device suitable for a single-carrier super Nyquist transmission system, including a processor and a storage medium;

[0116] The storage medium is used to store instructions;

[0117] The processor is configured to operate according to the instructions to perform the steps of the method according to Embodiment 1.

[0118] Example 3:

[0119] This embodiment provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in Embodiment 1.

[0120] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0121] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0122] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0123] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0124] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A signal-to-noise ratio estimation method applicable to single-carrier super Nyquist transmission systems, characterized in that, Includes the following steps: Acquire the transmitted signal and its structure; the transmitted signal is a single-carrier super Nyquist signal. The transmitted signal is processed by a cyclic prefix to obtain the processed signal; Based on the processed signal and the transmitted signal structure, establish the received signal structure expression to obtain the whitening filter output vector, cyclic matrix, possible transmission vector combinations, and the number of all possible transmission vector combinations; The cyclic matrix is ​​decomposed to obtain the decomposed cyclic matrix; To obtain an approximate expression for the noise variance estimate; The noise variance estimate is calculated based on the decomposed cyclic matrix, the vector output by the whitening filter, possible combinations of transmission vectors, the number of all possible combinations of transmission vectors, and the approximate expression for the noise variance estimate. The signal-to-noise ratio estimate is obtained by converting the noise variance estimate.

2. The signal-to-noise ratio estimation method for single-carrier super Nyquist transmission systems according to claim 1, characterized in that, Obtain the transmitted signal and the transmitted signal structure, including: The receiving end initializes the initial variables, buffered data, and counters, and then receives the transmission signal and obtains the corresponding transmission signal structure.

3. The signal-to-noise ratio estimation method for single-carrier super Nyquist transmission systems according to claim 1, characterized in that, The transmitted signal is subjected to cyclic prefix processing to obtain a processed signal, including: By removing the cyclic prefixes at the beginning and end of the transmitted signal, the linear convolution process of the single-carrier super Nyquist signal is transformed into a cyclic convolution process, resulting in the processed signal. The transmitted signal is obtained at the transmitting end by adding a cyclic prefix of a certain length to the modulated data, and then performing shaping filtering processing on a single-carrier super Nyquist signal.

4. The signal-to-noise ratio estimation method for single-carrier super Nyquist transmission systems according to claim 1, characterized in that, Based on the processed signal and the transmitted signal structure, an expression for the received signal structure is established, yielding the whitening filter output vector, cyclic matrix, possible combinations of transmitted vectors, and the number of all possible combinations of transmitted vectors, including: Based on the transmitted signal structure, the expression for the received signal structure is established, and the corresponding mathematical expression for the received signal structure is as follows: in, The vector representing the output of the whitening filter; vector a represents the modulation symbol transmitted at the transmitting end, referring to the constellation point symbol; vector g represents the combined vector of the shaping filter, matched filter, and whitening filter; mathematical symbols. Representing a circular convolution operation, matrix G is a circular matrix. The elements in the first column of matrix G are the vector g, padded with zeros. η represents a Gaussian white noise vector with a mean of 0 and a variance of 0. Based on the known set of transmitting constellation points, all possible combinations of transmitting vectors are obtained by traversal. The total number of possible combinations is M, and the transmitting vector of the l-th combination is a. l .

5. The signal-to-noise ratio estimation method for single-carrier super Nyquist transmission systems according to claim 1, characterized in that, The cyclic matrix is ​​decomposed to obtain the decomposed cyclic matrix, including: Performing matrix decomposition on a cyclic matrix G, the cyclic matrix can be decomposed into three matrices, as shown in the following expression. G = F H ΛF formula (2) in,(·) H Let represent the complex conjugate transpose operation. Matrix Λ is a diagonal matrix, and the elements on its diagonal are the Fourier transform values ​​of the elements in the first column of the circulant matrix G; F is the normalized discrete Fourier matrix. H It is the conjugate transpose of the normalized discrete Fourier matrix.

6. The signal-to-noise ratio estimation method for a single-carrier super Nyquist transmission system according to claim 5, characterized in that, An approximate expression for obtaining the noise variance estimate includes: An expression for obtaining the noise variance estimate; Based on the expression for the noise variance estimate, an approximation method is performed to obtain an approximate expression for the noise variance estimate.

7. The signal-to-noise ratio estimation method for a single-carrier super Nyquist transmission system according to claim 6, characterized in that, The expression for obtaining the noise variance estimate includes: Construct the probability density distribution function of the signal-to-noise ratio, and here we have the probability density distribution function of the signal-to-noise ratio. for Where M represents the total number of possible combinations of the transmission vectors, a l This represents the transmission vector of the l-th combination, with the superscript H indicating the conjugate transpose; By performing a logarithmic operation on the probability density distribution function, then taking the first partial derivative with respect to the noise variance, and setting this first partial derivative to zero, we obtain the expression for the noise variance estimate: Where M represents the total number of all possible transmission vector combinations, δ l This represents the standard deviation of the transmission vector for the l-th combination; The standard deviation of the Gaussian white noise vector; This represents the vector output by the whitening filter; Based on the expression for the noise variance estimate, an approximation method is performed to obtain an approximate expression for the noise variance estimate, including: The expression for the noise variance estimate is approximated. Formula (4) can be simplified to the following expression: Wherein, the standard deviation of the transmission vector of the l-th combination 8. The signal-to-noise ratio estimation method for a single-carrier super Nyquist transmission system according to claim 7, characterized in that, The noise variance estimate is calculated based on the decomposed cyclic matrix, the vector output by the whitening filter, possible combinations of transmitted vectors, the number of all possible combinations of transmitted vectors, and the approximate expression for the noise variance estimate, including: According to the decomposition of the cyclic matrix G = F H ΛF, the vector output of the whitening filter The transmission vector a of the l-th combination l The standard deviation δ of the transmission vector of the l-th combination is calculated according to the following formula. l : Where Re(·) denotes taking the real part of the complex number; Based on the vector output by the whitening filter and the standard deviation δ of the transmitted vector of the l-th combination. l The noise variance estimate is calculated using the approximate expression for the noise variance estimate, along with the number of all possible transmission vector combinations: Wherein, the superscript H indicates the conjugate transpose; δ 2 This is the noise variance estimate.

9. The signal-to-noise ratio estimation method for a single-carrier super Nyquist transmission system according to claim 1, characterized in that, The signal-to-noise ratio (SNR) estimate is obtained by converting the noise variance estimate into a signal-to-noise ratio estimate, including: By combining the obtained noise variance estimate, performing a division operation, and converting the ratio to logarithmic form, the final signal-to-noise ratio estimate can be obtained. SNR = 10 log 10 (1 / δ 2 ) Formula (6) Where, δ 2 is the noise variance estimate, and SNR is the signal-to-noise ratio estimate.

10. A signal-to-noise ratio estimation device suitable for a single-carrier super Nyquist transmission system, characterized in that, Including processor and storage media; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method according to any one of claims 1-9.

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