A robust and high-precision method for estimating packing rate of super-Nyquist systems

Abstract

The present invention discloses a robust and high-precision super-Nyquist system packing rate estimation method, including: obtaining a transmission pilot block, constructing a transmission frame according to the transmission pilot block; simulating transmission of the transmission frame based on the super-Nyquist system, setting a number of downsampling factors, inputting the several downsampling factors into a downsampling symbol generation model respectively, obtaining downsampling symbols, and generating a number of decision values ​​corresponding to the downsampling factors through a differential generalized a posteriori accumulation algorithm based on the downsampled pilot block and the transmission pilot block extracted from the downsampling symbol; extracting the downsampling factor corresponding to the decision value with the largest value, and obtaining the packing rate of the super-Nyquist system according to the extracted downsampling factor. Through the above technical scheme, the present invention can resist high-frequency bias and phase noise, obtain a better performance of random packing rate, and improve the packing rate estimation accuracy of the super-Nyquist system.

Description

Technical Field

[0001] The present invention relates to the field of communication technology, and in particular to a robust and high-precision super-Nyquist system packing rate estimation method. Background Art

[0002] As a physical layer technology, the Faster-Than-Nyquist system can improve capacity and spectrum efficiency without requiring additional bandwidth and antennas, and has attracted attention in the communications field. However, due to the deviation from the Nyquist criterion, the Faster-Than-Nyquist system intentionally introduces inter-symbol interference. This naturally leads to two aspects of the study of the Faster-Than-Nyquist system.

[0003] On the one hand, signal detection algorithm is a necessary means to ensure the reliability of super-Nyquist system. Signal detection algorithms in super-Nyquist system mainly include Bahl-Cocke-Jelinek-Raviv (BCJR), iterative interference cancellation, equalization and precoding. By inserting a cyclic suffix for each transmitted symbol block, Shinya Sugiura converted the inter-symbol interference matrix caused by super-Nyquist system into a cyclic matrix and proposed a frequency domain equalization algorithm. The precoding algorithm uses the inter-symbol interference matrix decomposition to pre-process the mapped symbols, and performs corresponding decoding at the receiving end to recover the transmitted symbols. Except for the time domain equalization algorithm, all signal detection algorithms for super-Nyquist system assume that the packet rate is accurately known at the receiver and transmitter through control frames or preset methods.

[0004] On the other hand, the inter-symbol interference caused by super-Nyquist is regarded as artificial noise, and the super-Nyquist system is used to achieve physical layer security. Wang Jianquan from Chengdu University of Electronic Science and Technology considered the pulse shaping filter in the transmitter changing over time in the super-Nyquist system in his paper "Filter Hopping Based Faster-Than-Nyquist Signaling for Physical Layer Security" (IEEE Wireless Communications Letters, 2018, 894-897). The filter hopping pattern is pre-shared between the transmitter and the legitimate receiver. On this basis, Yuan Li from Chengdu University of Electronic Science and Technology proposed a super-Nyquist system scheme based on variable packetization rate for physical layer security in his paper "A Variable Symbol Duration Based FTNSignaling Scheme for PLS" (International Conference on Wireless Communications and Signal Processing, 2019, 1-5), in which the information rate of cooperative links and non-cooperative links was derived. In addition, Shinya Sugiura proposed in his paper "Secrecy performance of eigendecomposition-based super-Nyquist signaling and NOFDM in Quasi-static fading channels" (IEEE Transactions on Wireless Communications, 2021, 5872-5882) to extend the confidentiality rate and confidentiality interruption probability of fading eavesdropping channels to eigendecomposition-based super-Nyquist of quasi-static frequency-flat Rayleigh fading channels. These studies are based on the assumption that when the super-Nyquist system is established, the packet rate pattern between the receiver and the transmitter has been determined or synchronized.

[0005] In view of the above considerations, packing rate estimation methods for super-Nyquist systems are essential to realize the full potential of super-Nyquist systems. In addition, since most frequency offset estimation algorithms are semi-blind and use pilot blocks after downsampling, they require accurate packing rates. Therefore, it is necessary to perform packing rate estimation before frequency offset estimation and resist frequency offset. Based on deep learning, Song Peiyang of Xidian University proposed a blind packing rate estimation for super-Nyquist systems in his paper "For security and higher spectrum efficiency: A variable packing ratio transmission system based on Faster-Than-Nyquist and deep learning" (IEEE Transactions on Wireless Communications, 2023, 5898-5913). However, its sensitivity to frequency offset and phase noise makes it unsuitable for super-Nyquist systems. Therefore, for super-Nyquist systems, a robust and high-precision packing rate estimation method is crucial. Summary of the invention

[0006] In order to solve the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a robust and high-precision super-Nyquist system packing rate estimation method to resist high-frequency bias and phase noise and improve the estimation accuracy of the super-Nyquist system packing rate.

[0007] To achieve the above object, the present invention provides a robust and high-precision super-Nyquist system packing rate estimation method, comprising the following steps:

[0008] Acquire a transmission pilot block, and construct a transmission frame according to the transmission pilot block; perform simulation transmission on the transmission frame based on the super-Nyquist system, and generate a down-sampling symbol generation model with a down-sampling factor as a variable;

[0009] Setting a number of downsampling factors, inputting the several downsampling factors into the downsampling symbol generation model respectively to obtain downsampling symbols, and generating decision values ​​corresponding to the several downsampling factors through a differential generalized a posteriori accumulation algorithm based on downsampled pilot blocks and transmission pilot blocks extracted from the downsampled symbols;

[0010] A downsampling factor corresponding to the decision value with the largest value is extracted, and a packing rate of the super-Nyquist system is obtained according to the extracted downsampling factor.

[0011] Optionally, the process of constructing the transmission frame includes:

[0012] The mapped symbols transmitted by the super-Nyquist system are acquired, and pilot blocks are inserted into the mapped symbols to generate a transmission frame.

[0013] Optionally, the simulation transmission process includes:

[0014] The transmission frame is sequentially simulated by upsampling, baseband shaping, adding frequency offset and noise, matched filtering and downsampling, and a downsampling symbol generation model is constructed according to the simulation process.

[0015] Optionally, the down-sampling symbol generation model is:

[0016]

[0017] Among them, y k represents the kth down-sampled symbol, E s is the average power of the signal after framing, represents the assumed downsampling factor, which is not greater than the upsampling parameter Q of the root raised cosine shaped pulse, represents the frequency deviation and phase noise after downsampling, Δf is the frequency deviation, is the phase noise at time t, T is the symbol period of the root raised cosine shaped pulse, is the colored noise after downsampling.

[0018] Optionally, the process of generating the decision value includes:

[0019]

[0020] Among them, Λ represents the decision value corresponding to a downsampling factor, L is the pilot block length, is the ith symbol of the kth pilot block after downsampling, p i is the i-th symbol of the transmitted pilot block, l is the time span, i represents the symbol number in the pilot block, and the superscript “*” represents matrix conjugation.

[0021] Optionally, the process of obtaining the packing rate of the super-Nyquist system includes:

[0022]

[0023] Among them, τ is the packing rate, It is the downsampling factor corresponding to the decision value with the largest value.

[0024] Optionally, a simulation model for sequentially upsampling and baseband shaping the transmission frame is:

[0025]

[0026] Among them, s(t) represents the transmission signal, that is, the transmission frame after baseband shaping, E s is the average power of the signal after framing, N is the symbol length after framing, b n represents the nth symbol of the transmission frame, n represents the symbol number in the transmission frame, c(t) is the root raised cosine shaped pulse of unit energy corresponding to time t, and T is the symbol period of the root raised cosine shaped pulse.

[0027] Optionally, the simulation model for sequentially adding frequency deviation and noise and matching filtering to the transmission frame after baseband shaping is:

[0028]

[0029] Among them, r k is the kth received symbol, k represents the received symbol number, g(t) represents the impulse response of the super-Nyquist system transfer function corresponding to time t, M represents the upsampling multiple of the super-Nyquist system, Q is the upsampling parameter of the root raised cosine shaped pulse, Δf is the frequency deviation, is the phase noise at time t, η k Represents colored noise.

[0030] Compared with the prior art, the present invention has the following advantages and technical effects:

[0031] The present invention discloses the following technical effects: A super-Nyquist transmission system constructed by transmission pilot blocks is proposed in the present invention. A robust and high-precision super-Nyquist system packing rate estimation method is proposed, and the packing rate estimation problem is converted into a downsampling factor estimation problem. In order to combat high-frequency deviation, the present invention introduces a differential generalized a posteriori accumulation algorithm into the packing rate estimation, overcomes phase rotation and phase noise, improves the packing rate estimation accuracy of the super-Nyquist system, and ensures the reliable implementation of signal detection and physical layer security. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0033] Figure 1 A schematic diagram of a super-Nyquist transmission system constructed using a transmission pilot block according to the present invention;

[0034] Figure 2 It is a schematic diagram of the framing process of the super-Nyquist system;

[0035] Figure 3 A flowchart of a robust and high-precision super-Nyquist system packing rate estimation method according to the present invention;

[0036] Figure 4It is a simulation result diagram of the present invention for estimating the packing rate when the packing rate changes slowly and the normalized frequency deviation is 0 and there is no phase noise, the normalized frequency deviation is 0.1 and there is phase noise, and the normalized frequency deviation is 0.2 and there is phase noise;

[0037] Figure 5 This is a simulation result diagram of the present invention for estimating the packing rate when there is frequency deviation and phase noise and the packing rate is randomly and evenly distributed. DETAILED DESCRIPTION

[0038] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0039] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0040] In order to solve the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a robust and high-precision super-Nyquist system packing rate estimation method to resist high-frequency offset and phase noise and improve the estimation accuracy of the super-Nyquist system packing rate.

[0041] To achieve the above technical objectives, the present invention provides the following solutions: The present invention provides a robust and high-precision super-Nyquist system packing rate estimation method, comprising: simulating the signal transmission process of the super-Nyquist system, wherein the signal transmission process comprises: subjecting the constructed transmission frame to super-Nyquist shaping to obtain a pilot-based transmission signal; subjecting the transmission signal to frequency offset, phase noise, channel and matched filtering to simulate the transmission process to obtain a received signal; downsampling the received signal by using different downsampling factors to obtain a downsampled pilot block, and constructing a simulation model according to the above signal transmission process; and generating downsampled pilot blocks corresponding to different downsampling factors according to the simulation model, performing an incoherent correlated differential generalized a posteriori accumulation operation on the transmission pilot block and the downsampled pilot block to obtain a decision value corresponding to the downsampling factor; iterating the downsampling operation and the decision value acquisition operation for each downsampling factor; finding the downsampling factor corresponding to the decision value with the largest correlation, and calculating the packing rate of the super-Nyquist system.

[0042] As some embodiments, in the construction of the simulation model of symbol generation after downsampling, the transmission frame is upsampled and super-Nyquist shaped and transmitted to obtain a transmission signal, that is, a transmission frame after baseband shaping, wherein the simulation model corresponding to the process is:

[0043]

[0044] Among them, s(t) represents the transmitted signal, E s is the average power of the signal after framing, N is the symbol length after framing, b n represents the nth symbol of the transmission frame, n represents the symbol number in the transmission frame, c(t) is the root raised cosine shaped pulse of unit energy corresponding to time t, and T is the symbol period of the root raised cosine shaped pulse.

[0045] As some embodiments, in the construction of the symbol generation simulation model after downsampling, the transmitted signal is subjected to frequency deviation, phase noise, channel and matched filtering to obtain a received signal, wherein the simulation model corresponding to the process is:

[0046]

[0047] Among them, r k is the kth received symbol, k represents the received symbol number, g(t) represents the impulse response of the super-Nyquist system transfer function corresponding to time t, M represents the upsampling multiple of the super-Nyquist system, Q is the upsampling parameter of the root raised cosine shaped pulse, e represents a natural constant, superscript j is an imaginary unit, Δf is the frequency deviation, is the phase noise at time t, η k Represents colored noise.

[0048] As some embodiments, in the construction of the symbol generation simulation model after downsampling, when the selected downsampling factor does not exceed the upsampling parameter of the root raised cosine shaped pulse, the received signal is downsampled using the assumed downsampling factor, wherein the simulation model corresponding to the process, i.e., the downsampling symbol generation model, is:

[0049]

[0050] Among them, y k represents the kth down-sampled symbol, represents the assumed downsampling factor, which is not greater than the upsampling parameter Q of the root raised cosine shaped pulse, represents the frequency deviation and phase noise after downsampling, is the colored noise after downsampling.

[0051] For the transmission pilot block p = [p0, p1, p2, ..., p L-1 ] and the downsampled pilot block Perform the differential generalized a posteriori accumulation algorithm to obtain the decision value corresponding to the downsampling factor used:

[0052]

[0053] Among them, Λ represents the decision value corresponding to a downsampling factor, L is the pilot block length, is the ith symbol of the kth pilot block after downsampling, p i is the i-th symbol of the transmitted pilot block, l is the time span, i represents the symbol number in the pilot block, and the superscript “*” represents matrix conjugation.

[0054] Within a certain range, select several downsampling factor values, input each selected downsampling factor into the downsampling factor generation model, and perform downsampling pilot block operations and accumulation algorithm operations in sequence, and generate different decision values ​​for different downsampling factors. The decision values ​​generated by different downsampling factors are stored, and the iteration stops.

[0055] At the same time, in order to expand the search range, within a certain range, the value of the downsampling factor is continuously adjusted through iterative updating. Based on each downsampling factor adjusted in the iterative updating process, each downsampling factor is input into the downsampling symbol generation model for simulation, and the downsampling pilot block is extracted from the downsampling symbol corresponding to the downsampling factor. The downsampling pilot block operation and related operations are iterated in turn, and the decision values ​​corresponding to different downsampling factors generated in the iterative process are stored until the downsampling factor is greater than the upsampling parameter of the root raised cosine shaped pulse, and the iteration stops.

[0056] As some embodiments, the downsampling factor corresponding to the maximum decision value is found, and the packing rate of the super-Nyquist system is calculated:

[0057]

[0058] Among them, τ is the packing rate, is the assumed downsampling factor corresponding to the decision value with the largest value.

[0059] The above contents are described in detail below with reference to the accompanying drawings.

[0060] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and to propose a robust and high-precision super-Nyquist system packing rate estimation method to combat high-frequency bias and improve the packing rate estimation accuracy of the super-Nyquist system.

[0061] 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.

[0062] Reference Figure 1-2 The super-Nyquist transmission system constructed by using transmission pilot blocks and frequency deviation adopted by the present invention is mainly composed of a data source module, a constellation mapping module, a framing module, an upsampling module, a baseband shaping module, a frequency deviation module, a phase noise module, a channel module, a matched filtering module and a packing rate estimation module, wherein:

[0063] A data source module generates bit data required to be transmitted by the super-Nyquist system and transmits the bit data to the constellation mapping module;

[0064] A constellation mapping module maps bit data into symbols according to the constellation mapping rules and passes the mapped symbols to the framing module;

[0065] A framing module, which inserts a known transmission pilot block before each mapped symbol block to form a transmission frame so as to construct a transmission frame based on the transmission pilot block and the mapped symbols, and passes the transmission frame to the upsampling module;

[0066] An up-sampling module performs zero-value interpolation on a transmission frame to perform up-sampling of the transmission frame, and transmits the zero-value interpolated transmission frame to a baseband shaping module;

[0067] The baseband shaping module performs super-Nyquist shaping on the upsampled transmission frame to perform baseband shaping of the transmission frame, and transmits the transmission frame after baseband shaping, i.e., the transmission signal, to the channel module;

[0068] The frequency deviation module performs frequency deviation on the transmission frame after baseband shaping and passes the deviation transmission frame to the phase noise module;

[0069] The phase noise module adds phase noise to the frequency-shifted transmission frame and passes the transmission frame with phase noise added to the channel module;

[0070] The channel module adds Gaussian white noise to the transmission frame after adding the phase noise, and passes the transmission frame after adding the Gaussian white noise to the matched filter module;

[0071] A matched filtering module performs matched filtering on the transmission frame after adding Gaussian white noise, that is, the received signal, and transmits the filtered transmission frame to the packing rate estimation module;

[0072] The packing rate estimation module downsamples the received signal after matched filtering by using different downsampling factors to obtain the downsampled pilot block, and performs incoherent correlation differential generalized a posteriori accumulation operation on the transmission pilot block and the downsampled pilot block to obtain the decision value corresponding to the downsampling factor used; it iterates the downsampling operation and the decision value acquisition operation to find the downsampling factor corresponding to the decision value with the largest correlation, and calculates the packing rate of the super-Nyquist system.

[0073] Reference Figure 3 The steps of using the super-Nyquist system to estimate the packing rate in the present invention are as follows:

[0074] Step 1, in the construction of the simulation model of symbol generation after downsampling, the transmission frame is upsampled and super-Nyquist shaped and transmitted to obtain a transmission signal, that is, a transmission frame after baseband shaping, wherein the simulation model corresponding to the process is:

[0075]

[0076] Among them, s(t) represents the transmitted signal, E s is the average power of the signal after framing, N is the symbol length after framing, b n represents the nth symbol of the transmission frame, n represents the symbol number in the transmission frame, c(t) is the root raised cosine shaped pulse of unit energy corresponding to time t, and T is the symbol period of the root raised cosine shaped pulse.

[0077] Step 2, as some embodiments, in the construction of the symbol generation simulation model after downsampling, the transmitted signal is subjected to frequency deviation, phase noise, channel and matched filtering to obtain a received signal, wherein the simulation model corresponding to the process is:

[0078]

[0079] Among them, r k is the kth received symbol, k represents the received symbol number, g(t) represents the impulse response of the super-Nyquist system transfer function corresponding to time t, M represents the upsampling multiple of the super-Nyquist system, Q is the upsampling parameter of the root raised cosine shaped pulse, Δf is the frequency deviation, is the phase noise at time t, η k Represents colored noise.

[0080] Step 3, in the construction of the symbol generation simulation model after downsampling, when the selected downsampling factor does not exceed the upsampling parameter of the root raised cosine shaped pulse, the received signal is downsampled using the assumed downsampling factor, wherein the simulation model corresponding to the process, i.e., the downsampling symbol generation model, is:

[0081]

[0082] Among them, y k represents the kth downsampled symbol, M represents the assumed downsampling factor, which is not greater than the upsampling parameter Q of the root raised cosine shaped pulse, represents the frequency deviation and phase noise after downsampling, is the colored noise after downsampling.

[0083] For the transmission pilot block p = [p0, p1, p2, ..., p L-1 ] and the downsampled pilot block Perform the differential generalized a posteriori accumulation algorithm to obtain the decision value corresponding to the downsampling factor used:

[0084]

[0085] Among them, Λ represents the decision value corresponding to a downsampling factor, L is the pilot block length, is the ith symbol of the kth pilot block after downsampling, p i is the i-th symbol of the transmitted pilot block, and l is the time span.

[0086] Within a certain range, several values ​​of downsampling factors are selected. For each selected downsampling factor, when the relevant simulation parameters and transmission frames in the super-Nyquist system are determined, they are input into the above-mentioned downsampling factor generation model, and the downsampling pilot block operation and the accumulation algorithm operation are performed in sequence. Different decision values ​​are generated for different downsampling factors, and the decision values ​​generated by different downsampling factors are stored, and the iteration stops.

[0087] At the same time, in order to expand the search range, within a certain range, the value of the downsampling factor is continuously adjusted through iterative updating. Based on each downsampling factor adjusted in the iterative updating process, the downsampling factor is input into the downsampling symbol generation model for simulation, and the downsampling pilot block is extracted from the downsampling symbol corresponding to the downsampling factor. The downsampling pilot block operation and related operations are iterated in turn, and the decision values ​​corresponding to different downsampling factors generated in the iterative process are stored until the downsampling factor is greater than the upsampling parameter of the root raised cosine shaped pulse, and the iteration stops.

[0088] During the iterative update process of the downsampling factor, the downsampling factor of the previous iteration is increased by a fixed step size for iterative update, wherein the initial value and the fixed step size of the initial downsampling factor are set according to the upsampling parameters of the root raised cosine shaped pulse, the initial value of the initial downsampling factor is less than the upsampling parameters of the root raised cosine shaped pulse, and the fixed step size is set to 1.

[0089] Step 4: Find the downsampling factor corresponding to the maximum decision value, i.e., the decision value with the largest correlation, and calculate the packing rate of the super-Nyquist system:

[0090]

[0091] Among them, τ is the packing rate, It is the downsampling factor corresponding to the decision value with the largest value.

[0092] In this embodiment, the effect of this embodiment is further explained in combination with simulation experiments;

[0093] 1. Simulation conditions

[0094] The simulation experiment of this embodiment is carried out under MATLAB 2022B software. In the simulation experiment of this embodiment, BPSK is used as the modulation mode of the pilot block, the length of a single pilot block is 32, and the frequency offset is normalized.

[0095] Set the root raised cosine pulse shaping and the matched filter roll-off factor to 0.3.

[0096] Sets the phase noise to be randomly distributed between 0 and 2π, but changes quite slowly.

[0097] 2. Simulation content and result analysis

[0098] Simulation 1, under the above conditions, considering the packing rate changes slowly and the normalized frequency deviation is 0 and there is no phase noise, the normalized frequency deviation is 0.1 and there is phase noise, and the normalized frequency deviation is 0.2 and there is phase noise, the present invention and the coherent correlation algorithm are used to estimate the packing rate respectively, and the results are as follows: Figure 4 .

[0099] Simulation 2, under the above conditions, considering the presence of frequency offset and phase noise and the packing rate is randomly and uniformly distributed in [0.6, 0.7, 0.8, 0.9, 1], the packing rate is estimated using the present invention and the coherent correlation algorithm, respectively. The results are as follows: Figure 5 .

[0100] Figure 4 and Figure 5 The horizontal axis represents the bit signal-to-noise ratio of the super-Nyquist system, and its unit is decibel dB (decibel), and the vertical axis represents the probability of false alarm PFA (Probability of False Alarm).

[0101] from Figure 4 It can be seen that when the packet rate changes slowly, when the normalized frequency deviation is 0, the coherent correlation algorithm can achieve accurate packet rate estimation with a lower bit signal-to-noise ratio, and its false alarm probability is lower than the false alarm probability of the present invention. However, when the normalized frequency deviation is 0.1 and 0.2, the false alarm probability of the coherent correlation algorithm deteriorates, and the false alarm probability of the present invention is significantly lower than the false alarm probability of the coherent correlation algorithm. Figure 5 It can be seen that when the packing rate is randomly and uniformly distributed, the false alarm probability of both algorithms increases with the increase of frequency deviation. However, compared with the coherent correlation algorithm, the packing rate estimation accuracy of the present invention is higher. This shows that the present invention can resist high-frequency deviation and phase noise, obtain high accuracy of random packing rate, and ensure the reliable implementation of signal detection and physical layer security.

[0102] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A robust and high-precision method for estimating the packing rate of a super-Nyquist system, characterized in that: The following steps are involved: Acquire a transmission pilot block, and construct a transmission frame according to the transmission pilot block; perform simulation transmission on the transmission frame based on the super-Nyquist system, and generate a down-sampling symbol generation model with a down-sampling factor as a variable; Setting a number of downsampling factors, inputting the several downsampling factors into the downsampling symbol generation model respectively to obtain downsampling symbols, and generating decision values ​​corresponding to the several downsampling factors through a differential generalized a posteriori accumulation algorithm based on downsampled pilot blocks and transmission pilot blocks extracted from the downsampled symbols; A downsampling factor corresponding to the decision value with the largest value is extracted, and a packing rate of the super-Nyquist system is obtained according to the extracted downsampling factor.

2. The method according to claim 1, characterized in that The process of constructing the transmission frame includes: The mapped symbols transmitted by the super-Nyquist system are acquired, and pilot blocks are inserted into the mapped symbols to generate a transmission frame.

3. The method according to claim 1, characterized in that The simulation transmission process includes: The transmission frame is sequentially simulated by upsampling, baseband shaping, adding frequency offset and noise, matched filtering and downsampling, and a downsampling symbol generation model is constructed according to the simulation process.

4. The method according to claim 1, characterized in that: The down-sampling symbol generation model is: Among them, y k represents the kth down-sampled symbol, E s is the average power of the signal after framing, represents the assumed downsampling factor, which is not greater than the upsampling parameter Q of the root raised cosine shaped pulse, represents the frequency deviation and phase noise after downsampling, Δf is the frequency deviation, is the phase noise at time t, T is the symbol period of the root raised cosine shaped pulse, is the colored noise after downsampling, b n represents the nth symbol of the transmission frame, n represents the symbol number in the transmission frame, g(t) represents the impulse response of the super-Nyquist system transfer function corresponding to time t, and M represents the upsampling multiple of the super-Nyquist system.

5. The method according to claim 1, characterized in that The generation process of the decision value includes: Among them, Λ represents the decision value corresponding to a downsampling factor, L is the pilot block length, is the ith symbol of the kth pilot block after downsampling, p i is the i-th symbol of the transmitted pilot block, l is the time span, i represents the symbol number in the pilot block, and the superscript "*" represents matrix conjugation.

6. The method according to claim 4, characterized in that The process of obtaining the packing rate of the super-Nyquist system includes: Among them, τ is the packing rate, It is the downsampling factor corresponding to the decision value with the largest value.

7. The method according to claim 3, characterized in that The simulation model for sequentially up-sampling and baseband shaping the transmission frame is: Among them, s(t) represents the transmission signal, that is, the transmission frame after baseband shaping, E s is the average power of the signal after framing, N is the symbol length after framing, b n represents the nth symbol of the transmission frame, n represents the symbol number in the transmission frame, c(t) is the root raised cosine shaped pulse of unit energy corresponding to time t, and T is the symbol period of the root raised cosine shaped pulse.

8. The method according to claim 7, characterized in that The simulation model of adding frequency deviation, noise and matched filtering to the transmission frame after baseband shaping is as follows: Among them, r k is the kth received symbol, k represents the received symbol number, g(t) represents the impulse response of the super-Nyquist system transfer function corresponding to time t, M represents the upsampling multiple of the super-Nyquist system, Q is the upsampling parameter of the root raised cosine shaped pulse, Δf is the frequency deviation, is the phase noise at time t, η k Represents colored noise.

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