A low-complexity method for estimating packing rate of super-Nyquist systems

Abstract

The present invention discloses a low-complexity super-Nyquist system packing rate estimation method, including: constructing a transmission frame based on a transmission pilot block and a mapped symbol; generating a transmission signal based on the transmission frame; adding noise and filtering the transmission signal to generate a received signal; obtaining an initial assumed downsampling factor, iteratively updating the initial assumed downsampling factor, downsampling the received signal based on each assumed downsampling factor in the iterative update process, obtaining a downsampled pilot block, and coherently correlating the downsampled pilot block and the transmission pilot block to obtain a decision value corresponding to each assumed downsampling factor; extracting the assumed downsampling factor corresponding to the maximum decision value, and generating the packing rate of the super-Nyquist system according to the extracted assumed downsampling factor. Through the above technical solution, the present invention can estimate the packing rate of a random super-Nyquist system, and achieve low complexity.

Description

Technical Field

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

[0002] With the urgent demand for high-speed, high-quality communication services, communication systems with higher spectrum efficiency and large capacity have become an urgent need. Therefore, super-Nyquist systems, as a physical layer technology, can improve capacity and spectrum efficiency without the need for additional bandwidth and antennas, and thus have attracted attention in the communication field. However, due to the violation of the Nyquist criterion, super-Nyquist systems introduce inter-symbol interference. This naturally leads to two aspects of research on super-Nyquist systems.

[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] As mentioned above, it can be concluded that for most studies beyond Nyquist, an accurate packing rate is necessary, otherwise it is difficult to achieve signal detection and physical layer security. Based on deep learning, Song Peiyang of Xidian University proposed a blind packing rate estimation for beyond 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 high complexity makes it unsuitable for beyond Nyquist systems. Therefore, for beyond Nyquist systems, a low-complexity packing rate estimation method is urgently needed. Summary of the invention

[0006] In order to solve the problems existing in the above-mentioned prior art, an object of the present invention is to provide a low-complexity super-Nyquist system packing rate estimation method to estimate the packing rate of a random super-Nyquist system and reduce the implementation complexity.

[0007] To achieve the above object, the present invention provides a low-complexity super-Nyquist system packing rate estimation method, comprising:

[0008] Acquire a transmission pilot block and a mapped symbol in a super-Nyquist system, and construct a transmission frame based on the transmission pilot block and the mapped symbol; perform upsampling and baseband shaping on the transmission frame to generate a transmission signal; perform noise addition and filtering on the transmission signal to generate a received signal;

[0009] Acquire an initial assumed downsampling factor, iteratively update the initial assumed downsampling factor, downsample the received signal based on each assumed downsampling factor in the iterative update process, obtain a downsampled pilot block, and perform coherent correlation processing on the downsampled pilot block and the transmission pilot block until the last updated assumed downsampling factor is greater than the upsampling parameter in the upsampling process, and obtain a decision value corresponding to each assumed downsampling factor;

[0010] The assumed downsampling factor corresponding to the maximum decision value is extracted, and the packing rate of the super-Nyquist system is generated according to the extracted assumed downsampling factor.

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

[0012]

[0013] Among them, b k represents the kth transmission frame, b n represents the nth symbol in the corresponding transmission frame, p is the transmission pilot block, p=[p0,p1,p2,…,p L-1 ], L represents the length of the transmission pilot block, Represents the length of the symbol after mapping, a n is the nth symbol after mapping.

[0014] Optionally, the generation process of the transmission signal includes:

[0015]

[0016] Among them, s(t) represents the transmitted signal, E s is the average power of the signal in the transmission frame, N is the symbol length in the transmission frame, b n It represents the nth symbol in the corresponding transmission frame, n is the index of 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.

[0017] Optionally, the generation process of the received signal includes:

[0018]

[0019] Among them, r k represents the kth received symbol in the received signal, g(t) represents the impulse response of the super-Nyquist system transfer function corresponding to time t, and E s is the average power of the signal in the transmission frame, N is the symbol length in the transmission frame, b n represents the nth symbol in the corresponding transmission frame, n is the number of the transmission frame, M represents the upsampling multiple of the super-Nyquist system, T is the symbol period of the root raised cosine shaped pulse, Q is the upsampling parameter of the root raised cosine shaped pulse, η k is colored noise.

[0020] Optionally, the process of downsampling the received signal includes:

[0021]

[0022] Among them, y k represents the kth downsampled symbol, g(t) represents the impulse response of the super-Nyquist system transfer function corresponding to time t, and E s is the average power of the signal in the transmission frame, N is the symbol length in the transmission frame, b nIndicates the nth symbol in the corresponding transmission frame, n is the index of the transmission frame, M represents the upsampling multiple of the super-Nyquist system, T is the symbol period of the root raised cosine shaped pulse, Q is the upsampling parameter of the root raised cosine shaped pulse, represents the assumed downsampling factor, is the colored noise after downsampling.

[0023] Optionally, the process of performing coherent correlation processing on the downsampled pilot block and the transmission pilot block includes:

[0024]

[0025] in, represents the ith symbol of the kth pilot block after downsampling, p i is the i-th symbol of the transmission pilot block, L represents the length of the transmission pilot block, and i represents the symbol number in the transmission pilot block.

[0026] Optionally, the generation process of the packing rate of the super-Nyquist system includes:

[0027]

[0028] Where τ is the packing rate, Q is the upsampling parameter of the root raised cosine shaped pulse, is the assumed downsampling factor corresponding to the maximum decision value.

[0029] Compared with the prior art, the present invention has the following advantages and technical effects:

[0030] Using a pilot-based super-Nyquist transmission model, the present invention proposes a low-complexity super-Nyquist system packing rate estimation method, which can transform the packing rate estimation problem into a downsampling factor estimation problem. By using different assumed downsampling factors to downsample the matched filtered signal, the downsampled pilot block corresponding to each assumed downsampling factor is obtained, and then the transmission pilot block and the downsampled pilot block are subjected to a coherent correlation operation to obtain a decision value corresponding to the assumed downsampling factor, and the assumed downsampling factor corresponding to the maximum decision value is found, thereby calculating the corresponding super-Nyquist system packing rate. The corresponding packing rate can be used to design the transmission scheme for the corresponding random super-Nyquist system, ensuring the reliable implementation of signal detection and physical layer security, and the implementation complexity is low. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] 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:

[0032] Figure 1A super-Nyquist transmission system based on pilot of the present invention;

[0033] Figure 2 The framing process for the super-Nyquist system;

[0034] Figure 3 It is a flow chart of the implementation of the low-complexity super-Nyquist system packing rate estimation method of the present invention;

[0035] Figure 4 This is a simulation result diagram of the present invention for estimating the packing rate when the packing rate changes slowly;

[0036] Figure 5 This is a simulation result diagram of the present invention for estimating the packing rate when the packing rate is randomly and evenly distributed. DETAILED DESCRIPTION

[0037] 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.

[0038] 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.

[0039] In order to solve the problems existing in the above-mentioned prior art, an object of the present invention is to provide a low-complexity super-Nyquist system packing rate estimation method to estimate the packing rate of a random super-Nyquist system and reduce the implementation complexity.

[0040] To achieve the above technical objectives, the present invention provides the following solutions: The present invention provides a low-complexity super-Nyquist system packing rate estimation method, comprising: performing a framing operation on the mapped symbols to construct a pilot-based super-Nyquist transmission frame, using the super-Nyquist transmission model, the packing rate estimation problem can be converted into a downsampling factor estimation problem; upsampling and baseband shaping the transmission frame to obtain a transmission signal; the transmission signal passes through an additive Gaussian white noise channel and matched filtering to describe the transmission process of the transmission signal to obtain a received signal; downsampling the matched filtered received signal using different assumed downsampling factors to generate downsampled symbols; extracting and obtaining a downsampled pilot block from the downsampled symbols; performing a coherent correlation operation on the transmission pilot block and the downsampled pilot block to obtain decision values ​​corresponding to different assumed downsampling factors; finding the assumed downsampling factor corresponding to the maximum decision value; calculating the packing rate of the super-Nyquist system according to the found assumed downsampling factor to obtain an estimated packing rate.

[0041] As some embodiments, the construction of the pilot-based super-Nyquist k-th transmission frame includes constructing a transmission frame based on a transmission pilot block and mapped symbols:

[0042]

[0043] Among them, b k represents the kth transmission frame, k is the label corresponding to the transmission frame, b n Indicates the nth symbol in the corresponding transmission frame, p = [p0, p1, p2, ..., p L-1 ] is the transmission pilot block, L represents the length of the transmission pilot block, Represents the length of the symbol block after mapping, a n is the nth symbol after mapping.

[0044] As some embodiments, the transmission frame is up-sampled and baseband-shaped and transmitted to obtain a transmission signal:

[0045]

[0046] Among them, s(t) represents the transmitted signal, E s is the average power of the transmission frame signal, n is the symbol number in the transmission frame, N is the length of the symbol in the transmission frame, c(t) is the root raised cosine shaped pulse with unit energy corresponding to time t, and T is the symbol period of the root raised cosine shaped pulse.

[0047] As some embodiments, the transmitted signal is subjected to an additive white Gaussian noise channel and matched filtering to obtain a received signal:

[0048]

[0049] Among them, r k represents the kth received symbol in the received signal, g(t) represents the impulse response of the super-Nyquist system transfer function corresponding to time t, and E s is the average power of the signal in the transmission frame, N is the symbol length in the transmission frame, b n represents the nth symbol in the corresponding transmission frame, n is the number of the transmission frame, M represents the upsampling multiple of the super-Nyquist system, T is the symbol period of the root raised cosine shaped pulse, Q is the upsampling parameter of the root raised cosine shaped pulse, η k is colored noise.

[0050] The specific acquisition process of the received signal is:

[0051]

[0052] Where r(t) represents the received signal, represents linear convolution, represents the impulse response of the super-Nyquist system transfer function corresponding to time t, and n(t) represents white noise represents the matched filtered colored noise.

[0053] When the assumed downsampling factor is not greater than Q, that is, Then the received signal is downsampled using the assumed downsampling factor to obtain the downsampled symbols:

[0054]

[0055] Among them, y k represents the symbol after the kth downsampling, M represents the upsampling multiple of the super-Nyquist system, Q is the upsampling parameter of the root raised cosine shaped pulse, represents the assumed downsampling factor, which is not greater than the upsampling parameter Q of the root raised cosine shaped pulse, is the colored noise after downsampling.

[0056] Extract the pilot block from the corresponding position of the downsampled symbol to obtain the downsampled pilot block

[0057]

[0058] A coherent correlation operation is performed on the transmission pilot block and the downsampled pilot block to obtain a decision value corresponding to the assumed downsampling factor:

[0059]

[0060] Where Λ represents the decision value corresponding to the assumed downsampling factor, represents the ith symbol of the kth pilot block after downsampling, p i is the i-th symbol of the transmission pilot block.

[0061] Within a certain range, the value of the assumed downsampling factor is continuously adjusted through iterative updating. Based on each assumed downsampling factor adjusted in the iterative updating process, the downsampling operation, the downsampling pilot block acquisition operation and the related operations are sequentially performed on the received signal after matched filtering, and the decision value generated in the iterative process is stored until the assumed downsampling factor is greater than the upsampling parameter of the root raised cosine shaped pulse, and the iteration stops.

[0062] As some embodiments, among the decision values ​​corresponding to different assumed downsampling factors stored, the assumed downsampling factor corresponding to the maximum decision value is found, and the packing rate τ of the super-Nyquist system is calculated:

[0063]

[0064] in, is the assumed downsampling factor corresponding to the maximum decision value.

[0065] The present invention discloses the following technical effects: using a pilot-based super-Nyquist transmission model, the present invention proposes a low-complexity super-Nyquist system packing rate estimation method, which can transform the packing rate estimation problem into a downsampling factor estimation problem. By using different assumed downsampling factors to downsample the matched filtered signal, the downsampled pilot block corresponding to each assumed downsampling factor is obtained, and then a coherent correlation operation is performed on the transmission pilot block and the downsampled pilot block to obtain a decision value corresponding to the assumed downsampling factor, and the assumed downsampling factor corresponding to the maximum decision value is found, thereby calculating the packing rate of the super-Nyquist system, ensuring the reliable implementation of signal detection and physical layer security, and the implementation complexity is low.

[0066] The above contents are described in detail with reference to the accompanying drawings:

[0067] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and propose a low-complexity super-Nyquist system packing rate estimation method to obtain the super-Nyquist packing rate and reduce the implementation complexity.

[0068] 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.

[0069] Reference Figure 1-2 The pilot-based super-Nyquist transmission system 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 channel module, a matched filtering module and a packing rate estimation module, wherein:

[0070] 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;

[0071] A constellation mapping module maps bit data into symbols according to the constellation mapping rules and passes the mapped symbols to the framing module;

[0072] 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;

[0073] 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;

[0074] 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;

[0075] The channel module adds Gaussian white noise to the transmission frame after baseband shaping, and passes the transmission frame after adding Gaussian white noise to the matched filter module;

[0076] 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 received signal to the packing rate estimation module;

[0077] The packing rate estimation module downsamples the filtered received signal using different assumed downsampling factors to obtain the downsampled pilot block, and performs coherent correlation operation on the transmission pilot block and the downsampled pilot block to obtain the decision value corresponding to the assumed downsampling factor. The downsampling operation and the correlation operation are iterated in sequence to find the assumed downsampling factor corresponding to the maximum decision value and calculate the packing rate of the super-Nyquist system.

[0078] Reference Figure 3 The steps of using the super-Nyquist system to estimate the packing rate in the present invention are as follows:

[0079] Step 1, the construction of the pilot-based super-Nyquist k-th transmission frame includes transmitting a pilot block and a mapped symbol:

[0080]

[0081] Among them, b k represents the kth transmission frame, k is the label corresponding to the transmission frame, b n Indicates the nth symbol in the corresponding transmission frame, p = [p0, p1, p2, ..., p L-1 ] is the transmission pilot block, L represents the length of the transmission pilot block, Represents the length of the symbol block after mapping, a n is the nth symbol after mapping.

[0082] Step 2: Upsample and baseband shape the transmission frame and transmit it to obtain the transmission signal:

[0083]

[0084] Among them, s(t) represents the transmitted signal, E s is the average power of the transmission frame signal, n is the symbol number in the transmission frame, N is the length of the symbol in the transmission frame, c(t) is the root raised cosine shaped pulse with unit energy corresponding to time t, and T is the symbol period of the root raised cosine shaped pulse.

[0085] Step 3: The transmitted signal passes through the additive white Gaussian noise channel and matched filtering to obtain the received signal:

[0086]

[0087] Among them, r k represents the kth received symbol in the received signal, g(t) represents the impulse response of the super-Nyquist system transfer function corresponding to time t, and E s is the average power of the signal in the transmission frame, N is the symbol length in the transmission frame, b n represents the nth symbol in the corresponding transmission frame, n is the number of the transmission frame, M represents the upsampling multiple of the super-Nyquist system, T is the symbol period of the root raised cosine shaped pulse, Q is the upsampling parameter of the root raised cosine shaped pulse, η k is colored noise.

[0088] The specific acquisition process of the received signal is:

[0089]

[0090] Where r(t) represents the received signal, represents linear convolution, represents the impulse response of the super-Nyquist system transfer function corresponding to time t, n(t) represents white noise, represents the colored noise after matched filtering. When the assumed downsampling factor is not greater than Q, the received signal after matched filtering is downsampled using the assumed downsampling factor to obtain the downsampled symbol:

[0091]

[0092] Among them, y k represents the symbol after the kth downsampling, M represents the upsampling multiple of the super-Nyquist system, Q is the upsampling parameter of the root raised cosine shaped pulse, represents the assumed downsampling factor, which is not greater than the upsampling parameter Q of the root raised cosine shaped pulse, is the colored noise after downsampling.

[0093] Extract the pilot block from the corresponding position of the downsampled symbol to obtain the downsampled pilot block

[0094]

[0095] A coherent correlation operation is performed on the transmission pilot block and the downsampled pilot block to obtain a decision value corresponding to the assumed downsampling factor:

[0096]

[0097] Where Λ represents the decision value corresponding to the assumed downsampling factor, represents the ith symbol of the kth pilot block after downsampling, p i is the i-th symbol of the transmission pilot block.

[0098] Within a certain range, the value of the assumed downsampling factor is continuously adjusted through iterative updating. Based on each adjusted assumed downsampling factor in the iterative updating process, the downsampling operation, the acquisition of the downsampling pilot block operation and the related operations are iterated in sequence on the received signal of the matched filter, and the decision value generated in the iterative process is stored until the assumed downsampling factor is greater than the upsampling parameter of the root raised cosine shaped pulse, and the iteration stops.

[0099] It should be noted that the above-mentioned transmitted signal, received signal and downsampled symbols are all simulation signal models for signal transmission, wherein the simulation signal model corresponding to the downsampled symbol only includes the "assumed downsampling factor" as a variable, and when the parameters of the super-Nyquist system and the transmission frame are determined, different assumed downsampling factors can generate corresponding downsampled symbols, wherein the value of the assumed downsampling factor obtained through each iteration is substituted into the calculation formula of the downsampled symbol, and then the downsampled pilot block can be extracted and determined, and the decision value is further calculated through related operations. After several groups of iterations, several groups of different downsampling factors will be obtained, and then several groups of different decision values ​​will be obtained, from which the maximum decision value is selected, and finally the packing rate is calculated using the downsampling factor corresponding to the maximum decision value.

[0100] During the iterative update process of the assumed downsampling factor, the iterative update is performed by increasing the value of the assumed downsampling factor of the previous iteration by a fixed step, wherein the initial value and the fixed step of the initial assumed downsampling factor are set according to the upsampling parameters of the root raised cosine shaped pulse, the initial value of the downsampling factor is less than the upsampling parameters of the root raised cosine shaped pulse, and the fixed step is 1.

[0101] Step 4, find the assumed downsampling factor corresponding to the maximum decision value and calculate the packing rate τ of the super-Nyquist system:

[0102]

[0103] in, is the assumed downsampling factor corresponding to the maximum decision value.

[0104] In this embodiment, the effect of this embodiment is further explained in combination with simulation experiments;

[0105] 1. Simulation conditions

[0106] 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, and the length of a single pilot block is 32.

[0107] Set the root raised cosine pulse shaping and the matched filter roll-off factor to 0.3.

[0108] 2. Simulation content and result analysis

[0109] Simulation 1, under the above conditions, considering the slow change of packing rate, the packing rate is estimated by the present invention, and the result is as follows: Figure 4 .

[0110] Simulation 2, under the above conditions, considering that the packing rate is randomly and uniformly distributed in [0.6, 0.7, 0.8, 0.9, 1], the packing rate is estimated by the present invention, and the results are as follows: Figure 5 .

[0111] 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).

[0112] from Figure 4 It can be seen that when the packing rate changes slowly, the present invention has the highest estimation accuracy for a packing rate of 1 at a low bit signal-to-noise ratio. As the bit signal-to-noise ratio increases, the estimation accuracy for a packing rate of 0.8 is the highest. Regardless of the bit signal-to-noise ratio, the estimation accuracy for a packing rate of 0.6 is the lowest. Figure 5 It can be seen that under the same bit signal-to-noise ratio, the false alarm probability when the packing rate is randomly and evenly distributed is higher than the false alarm probability when the packing rate changes slowly, and the estimation accuracy is lower than when the packing rate changes slowly. This shows that the present invention can estimate the packing rate of a random super-Nyquist system, ensuring the reliable implementation of signal detection and physical layer security.

[0113] 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 low-complexity super-Nyquist system packing rate estimation method, characterized in that: include: Acquire a transmission pilot and a mapped symbol in a super-Nyquist system, and construct a transmission frame based on the transmission pilot and the mapped symbol; Performing up-sampling and baseband shaping on the transmission frame to generate a transmission signal; Adding noise and filtering to the transmission signal to generate a reception signal; Acquire an initial assumed downsampling factor, iteratively update the initial assumed downsampling factor, downsample the received signal based on each assumed downsampling factor in the iterative update process, obtain a downsampled pilot, and perform coherent correlation processing on the downsampled pilot and the transmission pilot until the last updated assumed downsampling factor is greater than the upsampling parameter in the upsampling process, and obtain a decision value corresponding to each assumed downsampling factor; Extracting an assumed downsampling factor corresponding to the maximum decision value, and generating a packing rate of a super-Nyquist system according to the extracted assumed downsampling factor; The construction process of the transmission frame includes: Among them, b k represents the kth transmission frame, b n Indicates the nth symbol in the corresponding transmission frame, p is the transmission pilot, p = [p0, p1, p2, ..., p L-1 ], L represents the length of the transmission pilot, Represents the length of the symbol after mapping, a n is the nth symbol after mapping; The generation process of the transmission signal includes: Among them, s(t) represents the transmitted signal, τ is the packet rate, E s is the average power of the signal in the transmission frame, N is the symbol length in the transmission frame, b n represents the nth symbol in the corresponding transmission frame, n is the index of 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; The generation process of the received signal includes: Among them, r k represents the kth received symbol, g(t) represents the impulse response of the super-Nyquist system transfer function corresponding to time t, τ is the packing rate, E s is the average power of the signal in the transmission frame, N is the symbol length in the transmission frame, b n represents the nth symbol in the corresponding transmission frame, n is the number of the transmission frame, M represents the upsampling multiple of the super-Nyquist system, T is the symbol period of the root raised cosine shaped pulse, Q is the upsampling parameter of the root raised cosine shaped pulse, η k is colored noise; The process of downsampling the received signal includes: Among them, y k represents the kth downsampled symbol, g(t) represents the impulse response of the super-Nyquist system transfer function corresponding to time t, τ is the packing rate, E s is the average power of the signal in the transmission frame, N is the symbol length in the transmission frame, b n Indicates the nth symbol in the corresponding transmission frame, n is the index of the transmission frame, M represents the upsampling multiple of the super-Nyquist system, T is the symbol period of the root raised cosine shaped pulse, Q is the upsampling parameter of the root raised cosine shaped pulse, represents the assumed downsampling factor, is the colored noise after downsampling, The process of coherently correlating the down-sampled pilot and the transmission pilot includes: in, represents the i-th symbol of the k-th pilot after downsampling, p i is the i-th symbol of the transmission pilot, L represents the length of the transmission pilot, and i represents the symbol number in the transmission pilot; The generation process of the packing rate of the super-Nyquist system includes: Where τ is the packing rate, Q is the upsampling parameter of the root raised cosine shaped pulse, is the assumed downsampling factor corresponding to the maximum decision value.

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