CN118300937A - Method for estimating packing rate of super Nyquist system capable of resisting frequency offset and phase noise - Google Patents
Method for estimating packing rate of super Nyquist system capable of resisting frequency offset and phase noise Download PDFInfo
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Abstract
本发明公开了一种可抗频偏和相噪的超奈奎斯特系统打包率估计方法，包括：基于超奈奎斯特系统及传输帧，构建以仿真传输帧处理及传输过程的传输仿真模型；获取若干个假定下采样因子，将假定下采样因子分别输入传输仿真模型，得到下采样符号，基于下采样符号得到若干个下采样后的导频块，对若干个下采样后的导频块及传输导频块进行非相干相关差分后验累加处理，生成若干个判决值；提取数值最大的判决值对应的假定下采样因子，根据提取的假定下采样因子，得到超奈奎斯特系统对应的打包率。通过上述技术方案，本发明可以有效抵抗频偏和相噪，提高超奈奎斯特系统的打包率估计精度。
The present invention discloses a method for estimating the packing rate of a super-Nyquist system that can resist 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 packing rate estimation accuracy of the super-Nyquist system.
Description
Technical Field
The invention relates to the technical field of communication, in particular to a method for estimating the packing rate of a super Nyquist system, which can resist frequency offset and phase noise.
Background
With the urgent need for high-rate, high-quality communication services, communication systems with higher spectral efficiency and large capacity are becoming urgent. Therefore, the super nyquist system, as a physical layer technology, can improve capacity and spectrum efficiency without requiring additional bandwidth and antennas, thereby gaining attention in the field of communication. However, the nyquist criterion is violated, so that the super-nyquist system introduces intersymbol interference. This naturally led to a study of both aspects of the super nyquist system.
On the one hand, the signal detection algorithm is a necessary means for ensuring the reliability of the super Nyquist system. The signal detection algorithm in the super Nyquist system mainly comprises Bahl-Cocke-Jerinek-Raviv (BCJR), iterative interference cancellation, equalization and precoding. By inserting a cyclic suffix into each transmitted symbol block, shinya Sugiura converts an intersymbol interference matrix caused by the super nyquist system into a cyclic matrix, and a frequency domain equalization algorithm is proposed. The pre-coding algorithm pre-processes the mapped symbols by using intersymbol interference matrix decomposition, and performs corresponding decoding at the receiving end to recover the transmitted symbols. All signal detection algorithms for the super nyquist system, except the time domain equalization algorithm, assume that the packing rate is precisely known at the receiver and transmitter by a control frame or preset method.
On the other hand, intersymbol interference caused by the super nyquist is regarded as artificial noise, and physical layer security is realized by using the super nyquist system. The university of adult electronics Wang Jianquan in its published paper "Filter Hopping Based Faster-Than-Nyquist Signaling for Physical Layer Security"(IEEE Wireless Communications Letters,2018,894-897) considers the time-dependent change of the pulse shaping filter in the transmitter in the super nyquist system. The filter hopping pattern is pre-shared between the transmitter and the legitimate receiver. On this basis, the university of adult electronics Yuan Li proposes a variable packing rate based super nyquist system scheme for physical layer security in its published paper "AVariable Symbol Duration Based FTN Signaling Scheme for PLS"(International Conferenceon Wireless Communications and Signal Processing,2019,1-5), in which the information rates of the cooperative and non-cooperative links are derived. Furthermore, shinya Sugiura in its published paper "Secrecy performance of eigendecomposition-based super nyquist signaling and NOFDM in Quasi-static fading channels"(IEEE Transactions on Wireless Communications,2021,5872-5882) proposes to extend the privacy rate and privacy break probability of a fading eavesdropping channel to a feature decomposition-based super nyquist of a quasi-static frequency flat rayleigh fading channel. These studies are based on the assumption that the packing-rate pattern between the receiver and the transmitter has been determined or synchronized when the super nyquist system is established.
In view of the above considerations, a packing-fraction estimation method for a super nyquist system is essential for achieving the full potential of the super nyquist system. Furthermore, since most frequency offset estimation algorithms are semi-blind and use pilot blocks after downsampling, they require an accurate packing rate. Therefore, it is desirable to perform packet rate estimation and resist frequency offset before frequency offset estimation. Based on deep learning, the university of western electronics Song Peiyang presents a blind packing rate estimation for the super nyquist system in its published 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 use in the super nyquist system. Therefore, for the super Nyquist system, a packing rate estimation method capable of resisting frequency offset and phase noise is important.
Disclosure of Invention
In order to solve the problems in the prior art, the invention aims to provide a method for estimating the packing rate of a super Nyquist system, which can resist frequency offset and phase noise, so as to resist the frequency offset and the phase noise and improve the estimation precision of the packing rate of the super Nyquist system.
In order to achieve the above purpose, the present invention provides a method for estimating the packing rate of a super nyquist system, which can resist frequency offset and phase noise, comprising the following steps:
Based on a super Nyquist system and a transmission frame, constructing a transmission simulation model for simulating a transmission process of the transmission frame, wherein the transmission frame is constructed based on a transmission pilot block;
acquiring a plurality of assumed downsampling factors, respectively inputting the assumed downsampling factors into the transmission simulation model to obtain downsampling symbols, obtaining a plurality of downsampled pilot blocks based on the downsampling symbols, and performing incoherent correlation differential posterior accumulation processing on the plurality of downsampled pilot blocks and the transmission pilot blocks to generate a plurality of decision values;
And extracting an 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.
Optionally, the transmission simulation model is:
Where y k represents the kth downsampled symbol, E s is the average power of the framed signal, 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, The downsampling factor is assumed to be not larger than an upsampling parameter Q of the root-raised cosine shaping pulse, T is a symbol period of the root-raised cosine shaping pulse, Q is an upsampling parameter of the root-raised cosine shaping pulse, j is an imaginary unit, gamma (k) is frequency offset and phase noise after downsampling, and eta k represents colored noise.
Optionally, the construction process of the transmission frame includes:
And obtaining a mapped symbol transmitted by the super Nyquist system, and inserting a transmission pilot block into the mapped symbol to generate a transmission frame.
Optionally, the process for constructing the transmission simulation model includes:
and carrying out simulation construction on the basis of the transmission process of the transmission frame of the super Nyquist system, wherein the transmission process of the transmission frame comprises the following steps: up-sampling and baseband shaping are carried out on the transmission frame, and a transmitting signal is generated;
Adding frequency offset, phase noise and noise to the transmitting signal based on the sequentially performed frequency offset adding phase noise and channel transmission to obtain a receiving signal;
And adjusting the received signal based on the matched filtering and the downsampling which are sequentially carried out, and generating downsampled symbols.
Optionally, the generating a simulation process corresponding to the transmission signal includes:
Where s (T) represents a transmission signal, E s is an average power of a signal in a transmission frame, N is a symbol length in the transmission frame, b n represents an nth symbol in a corresponding transmission frame, N is a symbol index in the transmission frame, c (T) is a root-raised cosine shaped pulse of unit energy corresponding to time T, and T is a symbol period of the root-raised cosine shaped pulse.
Optionally, the obtaining a simulation process corresponding to the received signal includes:
Wherein s (t) represents a transmitting signal, r (t) represents a receiving signal, and Δf is a frequency offset; And n (t) are phase noise and additive white gaussian noise, respectively, j represents an imaginary unit, and t represents time.
Optionally, the generating process of the decision value includes:
Where Λ represents a decision value corresponding to an assumed downsampling factor, For the i symbol of the k pilot block after downsampling, p i is the i symbol of the transmission pilot block, l is the time span, i represents the symbol index in the pilot block, and superscript "×" represents the matrix conjugate.
Optionally, the acquiring process of the packing rate corresponding to the super nyquist system includes:
where τ is the packing fraction, And (3) representing an assumed downsampling factor corresponding to the decision value with the largest value, wherein Q is an upsampling parameter of the root raised cosine shaping pulse.
Compared with the prior art, the invention has the following advantages and technical effects:
The invention discloses the following technical effects: the invention provides a method for estimating the packing rate of a super Nyquist system, which can resist frequency offset and phase noise by utilizing a super Nyquist transmission system based on pilot frequency, and the problem of estimating the packing rate is converted into the problem of estimating a downsampling factor. In addition, in order to combat frequency offset, the invention introduces a non-coherent correlation differential posterior accumulation algorithm into the packing rate estimation, overcomes phase rotation and phase noise, improves the packing rate estimation precision of a super Nyquist system, and ensures the safe and reliable realization of signal detection and physical layer.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application. In the drawings:
Fig. 1 is a diagram of a pilot-based super nyquist transmission system of the present invention;
FIG. 2 is a framing process of the super Nyquist system;
FIG. 3 is a flow chart of an implementation of the method for estimating the packing rate of the super Nyquist system with resistance to frequency offset and phase noise of the present invention;
FIG. 4 is a diagram of simulation results of performing 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 the phase noise is present, and the normalized frequency offset is 0.2 and the phase noise is present in the embodiment of the present invention;
Fig. 5 is a diagram of simulation results of packet rate estimation performed in the presence of frequency offset and phase noise and random and uniform distribution of packet rate according to an embodiment of the present invention.
Detailed Description
It should be noted that, without conflict, the embodiments of the present application and features of the embodiments may be combined with each other. The application will be described in detail below with reference to the drawings in connection with embodiments.
It should be noted that the steps illustrated in the flowcharts of the figures may be performed in a computer system such as a set of computer executable instructions, and that although a logical order is illustrated in the flowcharts, in some cases the steps illustrated or described may be performed in an order other than that illustrated herein.
In order to solve the problems in the prior art, the invention aims to provide a method for estimating the packing rate of a super Nyquist system, which can resist frequency offset and phase noise, so as to resist the frequency offset and the phase noise and improve the estimation precision of the packing rate of the super Nyquist system.
In order to achieve the technical purpose, the invention provides the following scheme: the invention provides a method for estimating the packing rate of a super Nyquist system, which can resist frequency offset and phase noise, and comprises the following steps: constructing a pilot-based super Nyquist transmission frame; for a random super Nyquist system, simulating a transmission process of a transmission frame, and constructing a transmission simulation model based on the simulation, wherein the transmission process of the transmission frame comprises the following steps: the transmission frame is subjected to up-sampling and baseband forming to obtain a transmission signal, and the transmission signal is transmitted; the transmitting signal is subjected to frequency offset, phase noise and channel addition to simulate the transmission process of the transmitting signal, so as to obtain a receiving signal; performing matched filtering on the received signal; downsampling the matched and filtered received signal by adopting an assumed downsampling factor; generating downsampling symbols corresponding to different assumed downsampling factors by using a transmission simulation model, and extracting a downsampled pilot block from the downsampling symbols; performing incoherent correlation differential posterior accumulation operation on the transmission pilot frequency block and the pilot frequency block after downsampling to obtain a judgment value corresponding to the assumed downsampling factor; iterating the downsampling operation and the decision value computing operation; and finding out an assumed downsampling factor corresponding to the decision value with the maximum correlation, and calculating the packing rate of the super Nyquist system.
As some embodiments, the mapped symbols are inserted into pilot blocks to form a pilot-based super nyquist transmission frame, and the kth transmission frame is:
wherein b k has a length of B k, k represents the index of the transmission frame, and thenAnd each represents a mapped symbol block.
As some embodiments, a simulation process for generating a transmission signal in a transmission process is as follows, up-sampling and baseband shaping are performed on a transmission frame, and the transmission signal is obtained:
Where s (T) represents a transmission signal, E s is an average power of a signal in a transmission frame, N is a symbol length in the transmission frame, b n represents an nth symbol in a corresponding transmission frame, N is an index of a symbol in the transmission frame, c (T) is a root-raised cosine shaped pulse of unit energy corresponding to time T, and T is a symbol period of the root-raised cosine shaped pulse.
As some embodiments, a simulation process for generating a received signal in a transmission process is as follows, and a transmitted signal is subjected to frequency offset, phase noise and channel addition to obtain the received signal:
Wherein s (t) represents a transmitting signal, r (t) represents a receiving signal, and Δf is a frequency offset; and n (t) are phase noise and additive white gaussian noise, respectively.
As some embodiments, the received signal is matched filtered.
As some embodiments, a simulation process is generated for downsampled symbols in a transmission process that ultimately generates a transmission simulation model with the output of downsampled symbols having the packing rate and the assumed downsampling factor as variables, when the assumed downsampling factor does not exceed the upsampling parameters of the root-raised cosine shaped pulse, i.eThen the downsampled received signal is downsampled using the hypothesized downsampling factor to obtain downsampled symbols:
Where y k represents the kth downsampled symbol, E s is the average power of the framed signal, 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, The downsampling factor is assumed, the value of the downsampling factor is not larger than the upsampling parameter Q of the root raised cosine shaping pulse, T is the symbol period of the root raised cosine shaping pulse, Q is the upsampling parameter of the root raised cosine shaping pulse, e is a natural constant, the superscript j is an imaginary unit,Representing the frequency offset and phase noise after downsampling, η k represents colored noise.
Extracting the relative position symbol in the downsampled symbol, and further obtaining a downsampled pilot block:
Wherein, For the kth downsampled pilot block,Representing the ith symbol in the kth downsampled pilot block.
Performing incoherent correlation differential posterior accumulation operation on the transmission pilot block p= [ p 0,p1,p2,…,pL-1) and the pilot block after downsampling to obtain a decision value corresponding to the assumed downsampling factor:
Where Λ represents a decision value corresponding to an assumed downsampling factor, For the i symbol of the kth pilot block after downsampling, p i is the i symbol of the transmission pilot block, l is the time span, i represents the symbol index in the pilot block, and superscript "×" represents the matrix conjugate.
And selecting the numerical value of a plurality of downsampling factors in a certain range, inputting the numerical value of the downsampling factors into the downsampling factor generation model according to each selected downsampling factor, sequentially performing downsampling pilot frequency block operation and accumulation algorithm operation, generating different judgment values according to different downsampling factors, storing the judgment values generated by different downsampling factors, selecting the downsampling factor corresponding to the judgment value with the largest numerical value from the judgment values as the most suitable downsampling factor, calculating the packing rate by using the most suitable downsampling factor, thus obtaining the estimated packing rate, and stopping iteration.
In order to expand the searching range, the numerical value of the downsampling factor is continuously adjusted through iterative updating in a certain range, for example, a downsampling factor is generated for the first time, then a downsampling symbol is generated through a downsampling factor generation model by using the downsampling factor, a downsampled pilot block is extracted from the downsampled symbol, then the downsampled pilot block and a transmission pilot are subjected to related operation to obtain a judgment value, and the judgment value is stored; then, performing a second iteration to generate a downsampling factor, performing the downsampling, pilot frequency block and correlation operation once again to obtain a decision value, and storing the decision value; and carrying out the third iteration to obtain a decision value, taking the process as an example, and continuously iterating until the downsampling factor generated by the iteration is greater than the upsampling parameter of the root raised cosine shaping pulse, and stopping the iteration. At this time, all the stored decision values are compared, the decision factor with the largest value, namely the decision factor with the largest correlation, is selected, then the downsampling factor corresponding to the largest decision value is used as the most suitable downsampling factor, and the packing rate is calculated by using the most suitable downsampling factor.
The numerical value of the downsampling factor is continuously adjusted through iterative updating, based on each downsampling factor after adjustment in the iterative updating process, the downsampling factor generated by iteration is input into a downsampling symbol generation model to be simulated, a downsampling pilot block is extracted from each downsampling symbol obtained through simulation, and relevant operation is carried out on the downsampling pilot block and the transmission pilot block to obtain a judgment factor, and the judgment value is stored. And sequentially iterating the steps of generating the downsampling factor, obtaining the downsampled pilot frequency block, the correlation operation and the storage operation until the downsampling factor is larger than the upsampling parameter of the root raised cosine shaping pulse, and stopping the iteration.
In the iterative updating process of the downsampling factors, the numerical value of the downsampling factors of the last iteration is increased by a fixed step length to perform iterative updating, wherein the initial value of the initial downsampling factors and the fixed step length are set according to the upsampling parameters of the root raised cosine shaping pulse.
As some embodiments, finding out the assumed downsampling factor corresponding to the decision value with the largest value, namely the largest correlation, and calculating the packing rate of the super nyquist system:
where τ is the packing fraction, Is the hypothesized downsampling factor corresponding to the most relevant decision value.
The invention discloses the following technical effects: the invention provides a method for estimating the packing rate of a super Nyquist system, which can resist frequency offset and phase noise by utilizing a super Nyquist transmission system based on pilot frequency, and the problem of estimating the packing rate is converted into the problem of estimating a downsampling factor. In addition, in order to combat frequency offset, the invention introduces a non-coherent correlation differential posterior accumulation algorithm into the packing rate estimation, overcomes phase rotation and phase noise, improves the packing rate estimation precision of a super Nyquist system, and ensures the safe and reliable realization of signal detection and physical layer.
The foregoing will be described in detail with reference to the accompanying drawings.
Aiming at the defects of the prior art, the invention provides a method for estimating the packing rate of a super Nyquist system, which can resist frequency deviation and phase noise, so as to resist the frequency deviation and improve the packing rate estimation precision of the super Nyquist system.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
The invention relates to a super Nyquist transmission system based on pilot frequency by utilizing frequency offset construction, which is adopted by referring to fig. 1-2, and mainly comprises a data source module, a constellation mapping module, a framing module, an up-sampling module, a baseband forming module, a frequency offset module, a phase noise module, a channel module, a matched filtering module and a packing rate estimation module, wherein:
The data source module generates bit data required to be transmitted by the system and transmits the bit data to the constellation mapping module;
the constellation mapping module maps the bit data into symbols according to constellation mapping rules and transmits the mapped symbols to the framing module;
The framing module is used for inserting a known transmission pilot frequency block into each mapped symbol block, forming a transmission frame so as to construct the transmission frame based on the transmission pilot frequency block and the mapped symbols, and transmitting the transmission frame to the up-sampling module;
The up-sampling module performs zero value interpolation on the transmission frame to perform up-sampling on the transmission frame and transmits the transmission frame subjected to zero value interpolation to the baseband shaping module;
the baseband forming module is used for performing super Nyquist forming on the up-sampled transmission frame to perform baseband forming on the transmission frame, transmitting the transmission frame after the baseband forming, namely a transmission signal, and transmitting the transmission frame to the frequency offset module;
the frequency offset module is used for carrying out frequency offset on the transmission frame after the baseband shaping and transmitting the transmission frame after the offset to the phase noise module;
The phase noise module adds phase noise to the transmission frame subjected to frequency offset and transmits the transmission frame added with the phase noise to the channel module;
the channel module is used for adding Gaussian white noise to the transmission frame added with the phase noise and transmitting the transmission frame added with the Gaussian white noise to the matched filtering module;
the matched filtering module carries out matched filtering on a transmission frame, namely a received signal, after Gaussian white noise is added, and transmits the received signal to the packing rate estimation module;
The packing rate estimation module adopts different assumed downsampling factors to downsample the transmission frames after matching and filtering to obtain a downsampled pilot block, and performs incoherent correlation differential posterior accumulation operation on the transmission pilot block and the downsampled pilot block to obtain a judgment value corresponding to the assumed downsampling factors; iterative downsampling operation and decision value calculation operation, find out the correspondent assumption downsampling factor of decision value with maximum relativity; and calculating the packing rate of the super Nyquist system.
Referring to fig. 3, the steps of the present invention for packet rate estimation using the above-mentioned nyquist system are as follows:
Step 1, inserting a pilot block into the mapped symbol to form a super Nyquist transmission frame based on pilot, wherein the kth transmission frame is:
wherein b k has a length of B k first L symbols constitute a transmission pilot block, laterAnd each represents a mapped symbol block.
Step 2, the simulation process of the generation of the transmitting signal in the transmission process is as follows, up-sampling and baseband shaping are carried out on the transmission frame, and the transmitting signal is obtained:
Where s (T) represents a transmission signal, E s is an average power of a signal in a transmission frame, N is a symbol length in the transmission frame, b n represents an nth symbol in a corresponding transmission frame, N is an index of the transmission frame, c (T) is a root-raised cosine shaped pulse of unit energy corresponding to time T, and T is a symbol period of the root-raised cosine shaped pulse.
Step 3, the simulation process of receiving signal generation in the transmission process is as follows, the transmitting signal passes through frequency offset, phase noise and channel, and the receiving signal is obtained:
Wherein s (t) represents a transmitting signal, r (t) represents a receiving signal, and Δf is a frequency offset; and n (t) are phase noise and additive white gaussian noise, respectively.
And step 4, performing matched filtering on the received signal.
Step 5, generating a simulation process for the downsampled symbols in the transmission process, wherein the process finally generates a transmission simulation model taking the downsampled symbols with the packing rate and the assumed downsampling factor as variables as output, when the assumed downsampling factor is not more than the upsampling parameters of the root raised cosine shaped pulse, namelyThen the downsampled received signal is downsampled using the hypothesized downsampling factor to obtain downsampled symbols:
Where y k represents the kth downsampled symbol, τ is the packing fraction, 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, Representing an assumed downsampling factor whose value is not greater than the upsampling parameter Q of the root-raised cosine shaped pulse, T being the symbol period of the root-raised cosine shaped pulse, Q being the upsampling parameter of the root-raised cosine shaped pulse,Representing the frequency offset and phase noise after downsampling, η k represents colored noise. And further obtaining a pilot frequency block after downsampling:
Wherein, For the kth downsampled pilot block,Representing the ith symbol in the kth downsampled pilot block.
Performing incoherent correlation differential posterior accumulation operation on the transmission pilot block p= [ p 0,p1,p2,…,pL-1) and the pilot block after downsampling to obtain a decision value corresponding to the assumed downsampling factor:
Where Λ represents a decision value corresponding to an assumed downsampling factor, For the i symbol of the kth pilot block after downsampling, p i is the i symbol of the transmission pilot block and l is the time span.
And selecting the numerical values of a plurality of downsampling factors in a certain range, inputting the numerical values into the downsampling factor generation model under the condition that simulation parameters corresponding to the super Nyquist system and transmission frames are determined for each downsampling factor, sequentially performing downsampling pilot frequency block operation and accumulation algorithm operation, generating different judgment values for different downsampling factors, storing the judgment values generated by different downsampling factors, and stopping iteration.
Meanwhile, in order to expand the searching range, the numerical value of the downsampling factors is continuously adjusted through iterative updating in a certain range, based on each downsampling factor after adjustment in the iterative updating process, under the condition that simulation parameters corresponding to the ultranyquist system and transmission frames are determined, the downsampling factors are input into a downsampling symbol generation model to simulate, downsampling pilot blocks are extracted from downsampling symbols corresponding to the downsampling factors, the downsampling pilot block operation and related operation are sequentially iterated, decision values corresponding to different downsampling factors generated in the iterating process are stored until the downsampling factors are larger than the upsampling parameters of the root raised cosine shaping pulse, and iteration is stopped.
In the iterative updating process of the downsampling factors, the numerical value of the downsampling factors of the last iteration is increased to perform iterative updating, wherein the initial value and the fixed step length of the initial downsampling factors are set according to the upsampling parameters of the raised cosine shaping pulse, the initial value of the initial downsampling factors is smaller than the upsampling parameters of the raised cosine shaping pulse, and the fixed step length is set to be 1.
Step 6, finding out the assumed downsampling factor corresponding to the decision value with the largest value, namely the largest correlation, and calculating the packing rate of the super Nyquist system:
where τ is the packing fraction, Is the hypothesized downsampling factor corresponding to the most relevant decision value.
In this embodiment, the effect of this embodiment is further described in connection with a simulation experiment;
1. Simulation conditions
The simulation experiments of this example were performed under MATLAB 2022B software. In the simulation experiment of this embodiment, BPSK is used as the modulation method of the pilot block, and the length of a single pilot block is 32, and the frequency offset is normalized.
The roll-off factor of the root raised cosine filter and the matched filter is set to 0.3.
Phase noise is set to be randomly distributed between 0 and 2 pi, but the transformation is quite slow.
2. Simulation content and result analysis
Under the condition, taking the packing rate fixed, the normalized frequency offset being 0 and the phase noise being 0, the normalized frequency offset being 0.1 and the phase noise being 0.2 and the normalized frequency offset being the phase noise being 0.2 into consideration, the invention and the coherent correlation algorithm are used for respectively estimating the super Nyquist packing rate, and the result is shown in figure 4.
Simulation 2, under the above conditions, when the frequency offset and the phase noise are considered to exist and the packing rate is randomly and uniformly distributed in [0.6,0.7,0.8,0.9,1], the super Nyquist packing rate estimation is respectively carried out by using the method and the coherent correlation algorithm, and the result is shown in figure 5.
The horizontal axis in fig. 4 and 5 represents the bit signal-to-noise ratio of the nyquist system in dB (decibel) and the vertical axis represents the false alarm probability PFA (Probability ofFalseAlarm).
As can be seen from fig. 4, in the absence of frequency offset, the false alarm probability of the coherent correlation algorithm is lower than that of the present invention under the same bit signal to noise ratio. However, when the frequency deviation exists, the false alarm probability of the coherent correlation algorithm is not reduced along with the increase of the bit signal to noise ratio, and the false alarm probability of the invention is obviously lower than that of the coherent correlation algorithm. In addition, under the same frequency offset degree, the false alarm probability of the invention is the lowest when the packing rate is 1, and the false alarm probability of the invention is the highest when the packing rate is 0.6. As can be seen from fig. 5, when the packing rate is uniformly distributed at random, the packing rate estimation performance of both algorithms decreases with increasing frequency offset. But compared with a coherent correlation algorithm, the method can effectively relieve the influence of frequency offset and phase noise. The method has the effects of resisting frequency deviation and phase noise, improves the packing rate estimation precision of the super Nyquist system, and can realize a reliable super Nyquist transmission system.
The present application is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present application are intended to be included in the scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.
Claims (8)
1. The method for estimating the packing rate of the super Nyquist system capable of resisting frequency offset and phase noise is characterized by comprising the following steps of:
Based on a super Nyquist system and a transmission frame, constructing a transmission simulation model for simulating a transmission process of the transmission frame, wherein the transmission frame is constructed based on a transmission pilot block;
acquiring a plurality of assumed downsampling factors, respectively inputting the assumed downsampling factors into the transmission simulation model to obtain downsampling symbols, obtaining a plurality of downsampled pilot blocks based on the downsampling symbols, and performing incoherent correlation differential posterior accumulation processing on the plurality of downsampled pilot blocks and the transmission pilot blocks to generate a plurality of decision values;
And extracting an 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.
2. The method of claim 1, wherein the step of determining the position of the substrate comprises,
The transmission simulation model is as follows:
Where y k represents the kth downsampled symbol, E s is the average power of the framed signal, 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, The downsampling factor is assumed to be not larger than an upsampling parameter Q of the root-raised cosine shaping pulse, T is a symbol period of the root-raised cosine shaping pulse, Q is an upsampling parameter of the root-raised cosine shaping pulse, j is an imaginary unit, gamma (k) is frequency offset and phase noise after downsampling, and eta k represents colored noise.
3. The method of claim 1, wherein the step of determining the position of the substrate comprises,
The construction process of the transmission frame comprises the following steps:
And obtaining a mapped symbol transmitted by the super Nyquist system, and inserting a transmission pilot block into the mapped symbol to generate a transmission frame.
4. The method of claim 1, wherein the step of determining the position of the substrate comprises,
The construction process of the transmission simulation model comprises the following steps:
and carrying out simulation construction on the basis of the transmission process of the transmission frame of the super Nyquist system, wherein the transmission process of the transmission frame comprises the following steps: up-sampling and baseband shaping are carried out on the transmission frame, and a transmitting signal is generated;
Adding frequency offset, phase noise and noise to the transmitting signal based on the sequentially performed frequency offset adding phase noise and channel transmission to obtain a receiving signal;
And adjusting the received signal based on the matched filtering and the downsampling which are sequentially carried out, and generating downsampled symbols.
5. The method of claim 4, wherein the step of determining the position of the first electrode is performed,
The simulation process corresponding to the transmitting signal comprises the following steps:
Where s (T) represents a transmission signal, E s is an average power of a signal in a transmission frame, N is a symbol length in the transmission frame, b n represents an nth symbol in a corresponding transmission frame, N is a symbol index in the transmission frame, c (T) is a root-raised cosine shaped pulse of unit energy corresponding to time T, and T is a symbol period of the root-raised cosine shaped pulse.
6. The method of claim 4, wherein the step of determining the position of the first electrode is performed,
The simulation process for obtaining the received signal comprises the following steps:
Wherein s (t) represents a transmitting signal, r (t) represents a receiving signal, and Δf is a frequency offset; And n (t) are phase noise and additive white gaussian noise, respectively, j represents an imaginary unit, and t represents time.
7. The method of claim 1, wherein the step of determining the position of the substrate comprises,
The generation process of the decision value comprises the following steps:
Where Λ represents a decision value corresponding to an assumed downsampling factor, For the i symbol of the k pilot block after downsampling, p i is the i symbol of the transmission pilot block, l is the time span, i represents the symbol index in the pilot block, and superscript "×" represents the matrix conjugate.
8. The method of claim 1, wherein the step of determining the position of the substrate comprises,
The process for acquiring the packing rate corresponding to the super Nyquist system comprises the following steps:
where τ is the packing fraction, And (3) representing an assumed downsampling factor corresponding to the decision value with the largest value, wherein Q is an upsampling parameter of the root raised cosine shaping pulse.
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