A method for estimating packing rate of super-Nyquist systems that is resistant to frequency offset and phase noise

Abstract

The present invention discloses a method for estimating the packing rate of a super-Nyquist system that is resistant to frequency offset and phase noise, comprising: constructing a transmission simulation model for simulating transmission frame processing and transmission process based on a super-Nyquist system and a transmission frame; obtaining a number of assumed downsampling factors, inputting the assumed downsampling factors into the transmission simulation model respectively, obtaining downsampling symbols, obtaining a number of downsampled pilot blocks based on the downsampled symbols, performing non-coherent correlation differential a posteriori accumulation processing on the several downsampled pilot blocks and the transmission pilot blocks, and generating a number of decision values; extracting the assumed downsampling factor corresponding to the decision value with the largest value, and obtaining the packing rate corresponding to the super-Nyquist system according to the extracted assumed downsampling factor. Through the above technical scheme, the present invention can effectively resist frequency offset and phase noise, and improve the estimation accuracy of the packing rate of the super-Nyquist system.

Description

Technical Field

[0001] The present invention relates to the field of communication technology, and in particular to a super-Nyquist system packing rate estimation method capable of resisting frequency offset and phase noise. 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] 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 makes it unsuitable for super-Nyquist systems. Therefore, for super-Nyquist systems, a packing rate estimation method that is resistant to frequency offset and phase noise 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 super-Nyquist system packing rate estimation method that is resistant to frequency offset and phase noise, so as to resist frequency offset 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 method for estimating the packing rate of a super-Nyquist system that is resistant to frequency offset and phase noise, comprising the following steps:

[0008] Based on a super-Nyquist system and a transmission frame, a transmission simulation model is constructed to simulate a transmission process of the transmission frame, wherein the transmission frame is constructed based on a transmission pilot block;

[0009] Acquire a plurality of assumed downsampling factors, input the assumed downsampling factors into the transmission simulation model respectively, obtain downsampling symbols, obtain a plurality of downsampled pilot blocks based on the downsampled symbols, perform non-coherent correlation differential a posteriori accumulation processing on the plurality of downsampled pilot blocks and the transmission pilot blocks, and generate a plurality of decision values;

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

[0011] Optionally, the transmission simulation model is:

[0012]

[0013] Among them, y k represents the kth down-sampled symbol, E s is the average power of the signal after framing, b n represents the nth symbol in the corresponding transmission frame, n is the symbol index in the transmission frame, N is the symbol length in the transmission frame, k is the index of the transmission frame, 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, represents the assumed downsampling factor, whose value is not greater than the upsampling parameter Q of the root raised cosine shaped pulse, T is the symbol period of the root raised cosine shaped pulse, Q is the upsampling parameter of the root raised cosine shaped pulse, j represents the imaginary unit, γ(k) represents the frequency deviation and phase noise after downsampling, η k Represents colored noise.

[0014] Optionally, the construction process of the transmission frame includes:

[0015] Mapped symbols transmitted by a super-Nyquist system are acquired, and transmission pilot blocks are inserted into the mapped symbols to generate transmission frames.

[0016] Optionally, the construction process of the transmission simulation model includes:

[0017] The transmission simulation model is constructed by simulating the transmission frame transmission process of the super-Nyquist system, wherein the transmission frame transmission process includes: up-sampling and baseband shaping the transmission frame to generate a transmission signal;

[0018] Based on the sequential addition of frequency offset phase noise and channel transmission, frequency offset, phase noise and noise are added to the transmission signal to obtain a received signal;

[0019] Based on the matched filtering and down-sampling performed in sequence, the received signal is adjusted to generate down-sampled symbols.

[0020] Optionally, the simulation process corresponding to generating the transmission signal includes:

[0021]

[0022] 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 represents the nth symbol in the corresponding transmission frame, n is the symbol index 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.

[0023] Optionally, obtaining a simulation process corresponding to the received signal includes:

[0024]

[0025] Where s(t) represents the transmitted signal, r(t) represents the received signal, and Δf is the frequency deviation; and n(t) are phase noise and additive white Gaussian noise respectively, j represents the imaginary unit, and t represents time.

[0026] Optionally, the process of generating the judgment value includes:

[0027]

[0028] Among them, Λ represents the decision value corresponding to an assumed downsampling factor, 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 index in the pilot block, and the superscript “*” represents matrix conjugation.

[0029] Optionally, the process of obtaining the packing rate corresponding to the super-Nyquist system includes:

[0030]

[0031] Among them, τ is the packing rate, It represents the assumed downsampling factor corresponding to the decision value with the largest value, and Q is the upsampling parameter of the root raised cosine shaped pulse.

[0032] Compared with the prior art, the present invention has the following advantages and technical effects:

[0033] The present invention discloses the following technical effects: using a pilot-based super-Nyquist transmission system, the present invention proposes a super-Nyquist system packing rate estimation method that is resistant to frequency offset and phase noise, and the packing rate estimation problem is converted into a downsampling factor estimation problem. In addition, in order to combat frequency offset, the present invention introduces a non-coherent correlation differential 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

[0034] 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:

[0035] Figure 1 A super-Nyquist transmission system based on pilot of the present invention;

[0036] Figure 2 The framing process for the super-Nyquist system;

[0037] Figure 3 The present invention is a flow chart of the method for estimating the packing rate of a super-Nyquist system that is resistant to frequency offset and phase noise;

[0038] Figure 4 It is a simulation result diagram of the packing rate estimation when the packing rate is fixed and the normalized frequency offset is 0 and the phase noise is 0, the normalized frequency offset is 0.1 and there is phase noise, and the normalized frequency offset is 0.2 and there is phase noise according to an embodiment of the present invention;

[0039] Figure 5 This is a diagram of simulation results of estimating the packing rate when there is frequency offset and phase noise and the packing rate is randomly and evenly distributed according to an embodiment of the present invention. DETAILED DESCRIPTION

[0040] 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.

[0041] 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.

[0042] In order to solve the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a super-Nyquist system packing rate estimation method that is resistant to frequency offset and phase noise, so as to resist frequency offset and phase noise and improve the estimation accuracy of the super-Nyquist system packing rate.

[0043] To achieve the above technical objectives, the present invention provides the following solutions: The present invention provides a method for estimating the packing rate of a super-Nyquist system that is resistant to frequency offset and phase noise, comprising: constructing a super-Nyquist transmission frame based on a pilot; simulating the transmission process of the transmission frame for a random super-Nyquist system, and building a transmission simulation model based on this, wherein the transmission process of the transmission frame comprises: obtaining a transmission signal after upsampling and baseband shaping of the transmission frame, and transmitting the transmission signal; obtaining a received signal after adding frequency offset, phase noise and channel to the transmission signal to simulate the transmission process of the transmission signal; performing matched filtering on the received signal; downsampling the received signal after matched filtering using an assumed downsampling factor; using the transmission simulation model to generate downsampling symbols corresponding to different assumed downsampling factors, and extracting the downsampled pilot blocks from the downsampling symbols; performing a non-coherent correlation differential a posteriori accumulation operation on the transmission pilot block and the downsampled pilot block to obtain a decision value corresponding to the assumed downsampling factor; iterating the downsampling operation and the decision value calculation operation; finding the assumed downsampling factor corresponding to the decision value with the largest correlation, and calculating the packing rate of the super-Nyquist system.

[0044] As some embodiments, a pilot block is inserted into the mapped symbol to form a pilot-based super-Nyquist transmission frame, and the kth transmission frame is:

[0045]

[0046] Among them, b k The length is b k The first L symbols of the transmission pilot block, k represents the index of the transmission frame, and the following represents the mapped symbol block.

[0047] As some embodiments, the simulation process for generating a transmission signal during transmission is as follows: upsampling and baseband shaping are performed on the transmission frame to obtain a transmission signal:

[0048]

[0049] 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 represents the nth symbol in the corresponding transmission frame, n is the index of the symbol 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.

[0050] As some embodiments, the simulation process for generating a received signal during transmission is as follows: the transmitted signal is added with frequency offset, phase noise and channel to obtain a received signal:

[0051]

[0052] Where s(t) represents the transmitted signal, r(t) represents the received signal, and Δf is the frequency deviation; and n(t) are phase noise and additive white Gaussian noise, respectively.

[0053] As some embodiments, matched filtering is performed on the received signal.

[0054] As some embodiments, a simulation process for down-sampling symbols in a transmission process is generated, which ultimately generates a transmission simulation model with down-sampling symbols having a packing rate and an assumed down-sampling factor as variables as output. When the assumed down-sampling factor does not exceed the up-sampling parameter of the root raised cosine shaped pulse, that is, Then use the assumed downsampling factor to downsample the received signal after matched filtering to obtain the downsampled symbols:

[0055]

[0056] Among them, y krepresents the kth down-sampled symbol, E s is the average power of the signal after framing, b n represents the nth symbol in the corresponding transmission frame, n is the symbol index in the transmission frame, k is the index of the transmission frame, 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, represents the assumed downsampling factor, whose value is not greater than the upsampling parameter Q of the root raised cosine shaped pulse, T is the symbol period of the root raised cosine shaped pulse, Q is the upsampling parameter of the root raised cosine shaped pulse, e represents a natural constant, and the superscript j is an imaginary unit. represents the frequency deviation and phase noise after downsampling, η k Represents colored noise.

[0057] The symbols at the relative positions in the above downsampled symbols are extracted to obtain the downsampled pilot blocks:

[0058]

[0059] in, is the kth down-sampled pilot block, represents the i-th symbol in the k-th downsampled pilot block.

[0060] For the transmission pilot block p = [p 0 ,p 1 ,p 2 ,…,p L-1 ] performs a non-coherent correlation differential a posteriori accumulation operation with the downsampled pilot block to obtain a decision value corresponding to the assumed downsampling factor:

[0061]

[0062] Among them, Λ represents the decision value corresponding to an assumed downsampling factor, 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 index in the pilot block, and the superscript “*” represents matrix conjugation.

[0063] Within a certain range, select several values ​​of downsampling factors, input each selected downsampling factor into the downsampling factor generation model, and perform downsampling pilot block operations and accumulation algorithm operations in turn, and generate different decision values ​​for different downsampling factors. The decision values ​​generated by different downsampling factors are stored, and the downsampling factor corresponding to the largest decision value is selected from these decision values ​​as the most appropriate downsampling factor. The packing rate is calculated using this most appropriate downsampling factor, thereby obtaining the estimated packing rate, and the iteration stops.

[0064] 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, for example, the first iteration generates a downsampling factor, and then the downsampling factor is used to generate downsampling symbols through the downsampling factor generation model, and the downsampled pilot block is extracted from the downsampling symbol, and then the downsampling pilot block and the transmission pilot are correlated to obtain a decision value, which is stored; then the second iteration generates a downsampling factor, and the above downsampling, pilot block, and related operations are performed again, and another decision value is obtained, which is stored; the third iteration will obtain another decision value. Taking the above process as an example, after continuous iteration, until the downsampling factor generated by the iteration is greater than the upsampling parameter of the root raised cosine shaped pulse, the iteration stops. At this time, all the stored decision values ​​are compared, and the decision value with the largest value, that is, the decision factor with the largest correlation, is selected, and then the downsampling factor corresponding to the largest decision value is used as the most appropriate downsampling factor, and the packaging rate is calculated using this most appropriate downsampling factor.

[0065] The value of the downsampling factor is continuously adjusted through iterative updating, and based on each downsampling factor adjusted in the iterative updating process, the iteratively generated downsampling factor is input into the downsampling symbol generation model for simulation, and the downsampling pilot block is extracted from each downsampling symbol obtained by simulation, and the downsampling pilot block and the transmission pilot block are subjected to correlation operations to obtain the decision factor, and the decision value is stored. The generation of the downsampling factor, the acquisition of the downsampling pilot block, the correlation operation and the storage operation are iterated in sequence until the downsampling factor is greater than the upsampling parameter of the root raised cosine shaped pulse, and the iteration stops.

[0066] During the iterative update 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.

[0067] As some embodiments, find out the assumed downsampling factor corresponding to the decision value with the largest value, that is, the largest correlation, and calculate the packing rate of the super-Nyquist system:

[0068]

[0069] Among them, τ is the packing rate, is the assumed downsampling factor corresponding to the decision value with the largest correlation.

[0070] The present invention discloses the following technical effects: using a pilot-based super-Nyquist transmission system, the present invention proposes a super-Nyquist system packing rate estimation method that is resistant to frequency offset and phase noise, and the packing rate estimation problem is converted into a downsampling factor estimation problem. In addition, in order to combat frequency offset, the present invention introduces a non-coherent correlation differential 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.

[0071] The above contents will be described in detail later in conjunction with the relevant drawings.

[0072] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and to propose a method for estimating the packing rate of a super-Nyquist system that is resistant to frequency offset and phase noise, so as to combat frequency offset and improve the estimation accuracy of the packing rate of the super-Nyquist system.

[0073] 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.

[0074] Reference Figure 1-2 The pilot-based super-Nyquist transmission system constructed by using 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:

[0075] The data source module generates the bit data required to be transmitted by the system and passes the bit data to the constellation mapping module;

[0076] A constellation mapping module maps bit data into symbols according to the constellation mapping rules and passes the mapped symbols to the framing module;

[0077] 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;

[0078] 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;

[0079] 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 frequency deviation module;

[0080] 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;

[0081] 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;

[0082] 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;

[0083] A matched filtering module performs matched filtering on the transmission frame after adding Gaussian white noise, that is, the received signal, and transmits the received signal to the packing rate estimation module;

[0084] The packing rate estimation module uses different assumed downsampling factors to downsample the transmission frame after matched filtering to obtain the downsampled pilot block, and performs non-coherent correlation differential posterior accumulation operation on the transmission pilot block and the downsampled pilot block to obtain the decision value corresponding to the assumed downsampling factor; iterates the downsampling operation and the decision value calculation operation to find the assumed downsampling factor corresponding to the decision value with the largest correlation; and calculates the packing rate of the super-Nyquist system.

[0085] Reference Figure 3 The steps of using the super-Nyquist system to estimate the packing rate in the present invention are as follows:

[0086] Step 1: insert pilot blocks into the mapped symbols to form a pilot-based super-Nyquist transmission frame. Then the kth transmission frame is:

[0087]

[0088] Among them, b k The length is b k The first L symbols of the transmission pilot block, represents the mapped symbol block.

[0089] Step 2, the simulation process for the generation of the transmission signal during the transmission process is as follows: the transmission frame is upsampled and baseband shaped to obtain the transmission signal:

[0090]

[0091] 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 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.

[0092] Step 3, the simulation process for generating the received signal during the transmission process is as follows. The transmitted signal undergoes frequency deviation, phase noise and channel to obtain the received signal:

[0093]

[0094] Where s(t) represents the transmitted signal, r(t) represents the received signal, and Δf is the frequency deviation; and n(t) are phase noise and additive white Gaussian noise, respectively.

[0095] Step 4: Perform matched filtering on the received signal.

[0096] Step 5, a simulation process is generated for the down-sampling symbols in the transmission process, which finally generates a transmission simulation model with down-sampling symbols with the packing rate and the assumed down-sampling factor as variables as output. When the assumed down-sampling factor does not exceed the up-sampling parameter of the root raised cosine shaped pulse, that is, Then use the assumed downsampling factor to downsample the received signal after matched filtering to obtain the downsampled symbols:

[0097]

[0098] Among them, y k represents the kth downsampled symbol, τ is the packing rate, E s is the average power of the framed signal, n is the symbol index, g(t) represents the impulse response of the super-Nyquist system transfer function, M represents the upsampling multiple of the super-Nyquist system, represents the assumed downsampling factor, whose value is not greater than the upsampling parameter Q of the root raised cosine shaped pulse, 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 frequency deviation and phase noise after downsampling, η k Represents colored noise. Then we get the downsampled pilot block:

[0099]

[0100] in, is the kth down-sampled pilot block, represents the i-th symbol in the k-th downsampled pilot block.

[0101] For the transmission pilot block p = [p 0 ,p 1 ,p 2 ,…,p L-1 ] performs a non-coherent correlation differential a posteriori accumulation operation with the downsampled pilot block to obtain a decision value corresponding to the assumed downsampling factor:

[0102]

[0103] Among them, Λ represents the decision value corresponding to an assumed downsampling factor, 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.

[0104] Within a certain range, several values ​​of downsampling factors are selected. For each selected downsampling factor, when the simulation parameters and transmission frame corresponding to the super-Nyquist system are determined, it is 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.

[0105] 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, when the simulation parameters and transmission frame corresponding to the super-Nyquist system are determined, 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.

[0106] 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 raised cosine shaped pulse, the initial value of the initial downsampling factor is less than the upsampling parameters of the raised cosine shaped pulse, and the fixed step size is set to 1.

[0107] Step 6, find the assumed downsampling factor corresponding to the decision value with the largest value, that is, the largest correlation, and calculate the packing rate of the super-Nyquist system:

[0108]

[0109] Among them, τ is the packing rate, is the assumed downsampling factor corresponding to the decision value with the largest correlation.

[0110] In this embodiment, the effect of this embodiment is further explained in combination with simulation experiments;

[0111] 1. Simulation conditions

[0112] 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.

[0113] Set the roll-off factor of the root raised cosine filter and the matched filter to 0.3.

[0114] Sets the phase noise to be randomly distributed between 0 and 2π, but changes quite slowly.

[0115] 2. Simulation content and result analysis

[0116] Simulation 1, under the above conditions, considering the packing rate is fixed and the normalized frequency offset is 0 and the phase noise is 0, the normalized frequency offset is 0.1 and there is phase noise, and the normalized frequency offset is 0.2 and there is phase noise, the present invention and the coherent correlation algorithm are used to estimate the super-Nyquist packing rate, respectively, and the results are as follows: Figure 4 .

[0117] 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 present invention and the coherent correlation algorithm are used to perform super-Nyquist packing rate estimation respectively, and the results are as follows: Figure 5 .

[0118] 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 false alarm probability PFA (Probability of False Alarm).

[0119] from Figure 4 It can be seen that when there is no frequency deviation, at the same bit signal-to-noise ratio, the false alarm probability of the coherent correlation algorithm is lower than that of the present invention. However, when there is frequency deviation, the false alarm probability of the coherent correlation algorithm no longer decreases with the increase of the bit signal-to-noise ratio, and the false alarm probability of the present invention is significantly lower than that of the coherent correlation algorithm. In addition, at the same frequency deviation level, the false alarm probability of the present invention is the lowest when the packing rate is 1, and the false alarm probability of the present invention is the highest when the packing rate is 0.6. From Figure 5 It can be seen that when the packing rate is randomly and uniformly distributed, as the frequency offset increases, the packing rate estimation performance of the two algorithms decreases. However, compared with the coherent correlation algorithm, the present invention can effectively alleviate the influence of frequency offset and phase noise. This shows that the present invention has the effect of resisting frequency offset and phase noise, improves the packing rate estimation accuracy of the super-Nyquist system, and can realize a reliable super-Nyquist transmission system.

[0120] 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 method for estimating the packing rate of a super-Nyquist system that is resistant to frequency offset and phase noise, characterized in that: The following steps are involved: Based on a super-Nyquist system and a transmission frame, a transmission simulation model is constructed to simulate a transmission process of the transmission frame, wherein the transmission frame is constructed based on a transmission pilot block; Acquire a plurality of assumed downsampling factors, input the assumed downsampling factors into the transmission simulation model respectively, obtain downsampling symbols, obtain a plurality of downsampled pilot blocks based on the downsampled symbols, perform non-coherent correlation differential a posteriori accumulation processing on the plurality of downsampled pilot blocks and the transmission pilot blocks, and generate a plurality of decision values; Extracting an assumed downsampling factor corresponding to the decision value with the largest value, and obtaining a packing rate corresponding to the super-Nyquist system according to the extracted assumed downsampling factor; Based on the super-Nyquist system and the transmission frame, the process of constructing a transmission simulation model for simulating the transmission process of the transmission frame includes: The mapped symbols transmitted by the super-Nyquist system are obtained, and pilot blocks are inserted into the mapped symbols to form a pilot-based super-Nyquist transmission frame; the transmission frame is up-sampled and baseband-shaped to obtain the transmission signal: 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 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 transmit signal is transmitted; the transmit signal is subjected to adding frequency deviation, phase noise and channel to simulate the transmission process of the transmit signal to obtain the receive signal: s(t) represents the transmitted signal, r(t) represents the received signal, and Δf is the frequency deviation; and n(t) are phase noise and additive white Gaussian noise, respectively; Performing matched filtering on the received signal; The process of obtaining a plurality of assumed downsampling factors and inputting the assumed downsampling factors into the transmission simulation model respectively to obtain downsampling symbols includes: Use the transmission simulation model to generate downsampled symbols for different assumed downsampling factors: Among them, y k represents the kth down-sampled symbol, E s is the average power of the signal after framing, b n represents the nth symbol in the corresponding transmission frame, n is the symbol index in the transmission frame, N is the symbol length in the transmission frame, k is the index of the transmission frame, 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, represents the assumed downsampling factor, whose value is not greater than the upsampling parameter Q of the root raised cosine shaped pulse, T is the symbol period of the root raised cosine shaped pulse, Q is the upsampling parameter of the root raised cosine shaped pulse, j represents the imaginary unit, γ(k) represents the frequency deviation and phase noise after downsampling, η k represents colored noise; The process of obtaining a plurality of downsampled pilot blocks based on the downsampled symbols, performing non-coherent correlation differential a posteriori accumulation processing on the plurality of downsampled pilot blocks and the transmission pilot blocks, and generating a plurality of decision values ​​includes: The symbols at the relative position in the downsampled symbols are extracted to obtain the downsampled pilot blocks: in, is the kth down-sampled pilot block, represents the i-th symbol in the k-th downsampled pilot block; for the transmission pilot block p = [p0, p1, p2, ..., p L-1 ] performs a non-coherent correlation differential a posteriori accumulation operation with the downsampled pilot block to obtain a decision value corresponding to the assumed downsampling factor: Among them, Λ represents the decision value corresponding to an assumed downsampling factor, 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 index in the pilot block, and the superscript "*" represents matrix conjugation; The process of extracting the assumed downsampling factor corresponding to the decision value with the largest value and obtaining the packing rate corresponding to the super-Nyquist system according to the extracted assumed downsampling factor includes: Iterate downsampling operation and decision value calculation operation; find out the assumed downsampling factor corresponding to the decision value with the largest correlation, input it into the above-mentioned downsampling factor generation model, and perform downsampling pilot block operation and accumulation algorithm operation in sequence, and generate different decision values ​​for different downsampling factors, store the decision values ​​generated by different downsampling factors, select the downsampling factor corresponding to the decision value with the largest value as the most appropriate downsampling factor among these decision values, use this most appropriate downsampling factor to calculate the packing rate, thereby obtaining the estimated packing rate, and the iteration stops; calculate the packing rate of the super-Nyquist system: Among them, τ is the packing rate, is the assumed downsampling factor corresponding to the decision value with the largest correlation.

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