Joint estimation method and system for time-frequency overlapping multi-signal time domain parameters

Abstract

The invention relates to the technical field of signal processing, in particular to a joint estimation method and system for time domain parameters of multiple time-frequency overlapped signals, and the method comprises the steps: obtaining a generalized cyclic correlation entropy spectrum of the multiple time-frequency overlapped signals, reconstructing the generalized cyclic correlation entropy spectrum through a compressed sampling matching pursuit algorithm, removing redundant information, and improving the definition and resolution of the spectrum; the speed and precision of spectrum peak searching are improved through an improved grey wolf optimization algorithm, spectrum peak searching is carried out on generalized cyclic correlation entropy spectrum projection, and therefore joint estimation of the carrier frequency and the code element rate is achieved. According to the method, joint estimation and correction of the Cramer-Rao bound in the alpha stable distribution noise environment is deduced, and the method is used for evaluating the effectiveness of the method. When the method is used for reconstructing the entropy spectrum, the influence of impulse noise can be suppressed, so that the reconstructed entropy spectrum is sharper and more gathered; the method has low calculation complexity and higher estimation precision, is suitable for efficient joint estimation of multi-signal time domain parameters, and meets the multi-signal processing requirement in a complex environment.

Description

Technical Field

[0001] The present invention belongs to the field of communication technologies, and particularly relates to a method, a system, a device and a medium for jointly estimating time-domain parameters of multiple signals with time-frequency overlap. Background Art

[0002] In practical applications, there are often multiple signals overlapping in the same time and the same frequency band, that is, multiple signals with time-frequency overlap. However, in actual communication, a non-cooperative communication mode is often adopted. In order to achieve blind processing of communication signals in the non-cooperative communication mode, it is necessary to accurately estimate the carrier frequency and symbol rate of the received multiple signals with time-frequency overlap. Therefore, the problem of estimating the carrier frequency and symbol rate of multiple signals with time-frequency overlap has become a key problem that needs to be solved urgently at present. At the same time, signals in communication transmission are extremely vulnerable to various noises, especially non-Gaussian noises with pulse characteristics, such as burst noises and atmospheric noises, etc., which have a serious impact on the estimation of the carrier frequency and symbol rate. Therefore, due to the influence of non-Gaussian noise fading channels and time-frequency overlap of multiple signal components, the joint estimation of the carrier frequency-symbol rate of the received multiple signals with time-frequency overlap is extremely challenging.

[0003] The carrier frequency is an important parameter for signal synchronization, positioning, demodulation, and recovery. Therefore, accurate and effective estimation of it is crucial. Traditional single-signal carrier frequency estimation methods have been relatively mature. In recent years, scholars at home and abroad have focused their research on the carrier frequency estimation of multi-signals with time-frequency overlap in a single channel and have achieved certain research results in this field. Yu et al. (YU Z, SHI Y Q, SU W. A blind carrier frequency estimation algorithm for digitally modulated signals [C] / / IEEE MILCOM 2004. Military Communications Conference, 2004. IEEE, 2004, 1: 48-53.) addressed the problem of carrier frequency estimation for single-tone digital modulation signals in an automatic modulation recognition environment. Without prior knowledge of the symbol rate, shaping pulse, and modulation type of the transmitted signal in the automatic modulation recognition receiver, they proposed a carrier frequency estimation method based on the autocorrelation phase information of the received signal and improved the accuracy of carrier frequency estimation through an iterative mechanism. Jiang et al. (JIANG S, FU N, WEI Z, et al. Joint spectrum, carrier, and DOA estimation with beamforming MWC sampling system [J]. IEEE Transactions on Instrumentation and Measurement, 2022, 71: 1-15.) proposed a new beamforming modulation broadband converter system for carrier frequency estimation and verified the effectiveness and robustness of the proposed method through experimental simulations. Zhu (ZHU Bo. Research on parameter analysis and implementation of multi-channel time-frequency overlapping signals based on wavelet [D]. Chengdu: University of Electronic Science and Technology of China, 2010.) addressed the problem of time-frequency overlap of multiple signals in a single channel and proposed a carrier frequency estimation method based on the energy center of gravity. However, this method performs poorly in the case of low signal-to-noise ratio.

[0004] Symbol rate estimation, also known as baud rate estimation, plays a crucial role in aspects such as signal synchronization, demodulation, filtering, and frequency correction in digital communication systems. Accurately and effectively estimating the symbol rate of a signal can improve the reliability and stability of the communication system. The methods for estimating the symbol rate of a single signal have been relatively mature, such as the nonlinear transformation method, zero-crossing detection method, phase difference method, and wavelet transform method (CHAN Y T, PLEWS J W, HO K C. Symbol rate estimation by the wavelet transform[C] / / 1997 IEEE International Symposium on Circuits and Systems(ISCAS). IEEE, 1997, 1:177-180.)(SAWAI R, HARADA H, SHIRAI H, et al. General-purpose symbol rate and symbol timing estimation method by using multi-resolution analysis based on wavelet transform for multimode software radio[C] / / Gateway to 21st Century Communications Village. VTC 1999-Fall. IEEE VTS 50th Vehicular Technology Conference(Cat.No.99CH36324). IEEE, 1999, 4:2128-2132.)(XU J, ZHANG Y, JIANG H. Symbol rate estimation based on wavelet transform[C] / / 2012 8th International Conference on Wireless Communications, Networking and Mobile Computing. IEEE, 2012:1-4.) and so on.Xu et al. (XU H, ZHOU Y, HUANG Z. Blind roll-off factor and symbol rate estimation using IFFT and least squares estimator[C] / / 2007 International Conference on Wireless Communications, Networking and Mobile Computing. IEEE, 2007:1052-1055.) proposed a symbol rate estimation method based on the inverse Fourier transform and least squares estimation, and proved the effectiveness of this method for symbol rate estimation of linearly digitally modulated signals. Yang et al. (YANG C, LIU X, GUAN Y L, et al. Blind symbol-rate estimation for short and bursty communications[J]. IEEE Transactions on Vehicular Technology, 2022, 71(11):12392-12396.) proposed a cyclic stationary method based on bias cancellation for the symbol rate estimation problem in asynchronous burst communication systems to improve the accuracy of peak detection in the cyclic stationary method.

[0005] The above are all estimation methods for single parameters. However, in practical applications, due to insufficient prior knowledge, joint estimation of carrier frequency and symbol rate is often required. Huang et al. (Huang Chunlin, Liu Zheng, Jiang Wenli, etc. Estimation of chip width, carrier frequency, and amplitude of spread-spectrum direct-sequence signals based on cyclic spectral envelope [J]. Acta Electronica Sinica, 2002, (09): 1353-1356.) utilized the second-order cyclic stationary characteristics of spread-spectrum direct-sequence signals and proposed a joint estimation method for symbol rate, carrier frequency, and amplitude of spread-spectrum direct-sequence signals based on cyclic spectral envelope. However, this method has a high computational complexity, low estimation accuracy at low signal-to-noise ratios, and is only applicable to Gaussian background noise. Zhang et al. (ZHANG Z, LI L, et al. Carrier frequency and chip rate estimation based on cyclic spectral density of MPSK signals [C] / / 2004 International Conference on Communications, Circuits and Systems (Cat. No. 04EX914). IEEE, 2004, 2: 859-862.) proposed a joint estimation method for carrier frequency-symbol rate of MPSK modulated signals based on cyclic stationary characteristics, and this method still has high estimation accuracy under low signal-to-noise ratio conditions.

[0006] Through the above analysis, the problems and defects existing in the existing technologies are as follows:

[0007] (1) Most of the existing joint estimation technologies for carrier frequency-symbol rate can only be realized under specific prerequisite requirements or at relatively high signal-to-noise ratios. Otherwise, the performance of the joint estimation technology for carrier frequency-symbol rate will decline significantly.

[0008] (2) The existing joint estimation technologies for carrier frequency-symbol rate have a high computational complexity, and most of the existing technologies are carried out under the assumption environment of Gaussian background noise. The joint estimation technology for carrier frequency-symbol rate of time-frequency overlapping multi-signals in non-Gaussian noise fading channels still needs to be further studied. Summary of the Invention

[0009] To overcome the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a method, system, medium and device for jointly estimating time-domain parameters of time-frequency overlapping multi-signals; obtain the generalized cyclic correlation entropy spectrum of the signals, reconstruct the generalized cyclic correlation entropy spectrum by using the Compressive Sampling Matching Pursuit (CoSaMP) algorithm, improve the spectrum peak search method by using the Grey Wolf Optimization (GWO) algorithm and perform spectrum peak search on the projection of the generalized cyclic correlation entropy spectrum, jointly estimate the carrier frequency-symbol rate through spectrum peak search, and derive the modified Cramér-Rao bound for the joint estimation of the carrier frequency-symbol rate of time-frequency overlapping multi-signals under alpha-stable distribution noise, reducing the computational complexity and improving the estimation performance.

[0010] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0011] A method for jointly estimating time-domain parameters of time-frequency overlapping multi-signals, obtaining the generalized cyclic correlation entropy spectrum of the signals; reconstructing the generalized cyclic correlation entropy spectrum by using the CoSaMP algorithm; improving the spectrum peak search method by using the GWO algorithm and performing spectrum peak search on the projection of the generalized cyclic correlation entropy spectrum; jointly estimating the carrier frequency-symbol rate through spectrum peak search; and deriving the modified Cramér-Rao bound for the joint estimation of the carrier frequency-symbol rate of time-frequency overlapping multi-signals under alpha-stable distribution noise.

[0012] A method for jointly estimating time-domain parameters of time-frequency overlapping multi-signals specifically includes the following steps:

[0013] Step 1, obtaining the generalized cyclic correlation entropy spectrum of the signals;

[0014] Step 2, reconstructing the generalized cyclic correlation entropy spectrum obtained after the processing in Step 1 by using the CoSaMP algorithm;

[0015] Step 3, improving the spectrum peak search method by using the GWO algorithm and performing spectrum peak search on the projection of the reconstructed generalized cyclic correlation entropy spectrum obtained after the processing in Step 2;

[0016] Step 4, jointly estimating the carrier frequency-symbol rate through the spectrum peak search performed in Step 3;

[0017] Step 5, deriving the modified Cramér-Rao bound for the joint estimation of the carrier frequency-symbol rate of time-frequency overlapping multi-signals under alpha-stable distribution noise.

[0018] In the said Step 1, the specific process of obtaining the generalized cyclic correlation entropy spectrum of the signals is as follows:

[0019] The mathematical model of time-frequency overlapping multi-signals under a non-Gaussian noise fading channel can be described in the following form:

[0020]

[0021] Among them, the i-th signal component A i , f ci , τ i , T bi are respectively the amplitude, carrier frequency, initial time delay and symbol period of the i-th signal component (the reciprocal of which is the symbol rate f bi ), a i (k) is a sequence of independent and identically distributed random data symbols, K i is the length of the transmitted data sequence, θ is the initial phase, q(t) is the shaping function, L is the number of paths of the multipath fading channel, h l (t) is the amplitude attenuation factor of the l-th path, ω(t) is a non-Gaussian noise uncorrelated with each component of the transmitted signal, and N represents the number of signals.

[0022] In an actual communication system, there are many noises with pulse characteristics, such as burst noise, radio frequency noise, atmospheric noise, lightning interference, etc. Such noises often do not follow a Gaussian distribution and are therefore collectively referred to as non-Gaussian noises. Currently, three distribution models are often used for modeling non-Gaussian noises, namely Gaussian mixture distribution, alpha-stable distribution and generalized Gaussian distribution.

[0023] The present invention uses the alpha-stable distribution to simulate non-Gaussian noises in an actual communication system. Since there is no probability density function expression that can accurately describe the alpha-stable distribution, it can only be represented by the Fourier transform of its probability density function, that is, the characteristic function of the alpha-stable distribution:

[0024]

[0025] Among them, sgn(·) is the sign function, α is the characteristic exponent, β is the symmetry parameter, γ is the scale parameter, and δ is the location parameter.

[0026] Let a second-order cyclostationary random process, and its generalized autocorrelation entropy function can be defined as:

[0027]

[0028] Among them, E[·] is the mathematical expectation, G μν (·) is the generalized Gaussian kernel function, also called the generalized Gaussian probability density function, and is defined in the following form:

[0029]

[0030] Among them, Γ(·) is the gamma function, μ ∈ (0, +∞) is the shape parameter, ν ∈ (0, +∞) is the scale parameter, and λ = ν -μis the kernel parameter, and μ / 2νΓ(1 / μ) is the normalization constant.

[0031] The generalized cyclic correlation entropy function can be written in the following form:

[0032]

[0033] where ε = m / T 0 is the cyclic frequency. Since the generalized cyclic correlation entropy and the generalized cyclic correlation entropy spectrum form a Fourier transform pair, therefore, taking the Fourier transform of the generalized cyclic correlation entropy of the signal x(t), the generalized cyclic correlation entropy spectrum can be obtained. Its expression is:

[0034]

[0035] In the second step, the CoSaMP algorithm is used to reconstruct the generalized cyclic correlation entropy spectrum. The specific process is as follows:

[0036] In the following steps, t represents the number of iterations, J t represents the index of the atoms selected in the iteration, Δ t represents the set of indices, A t represents the set of atoms corresponding to the indices in Δ t , a i represents the i-th column of the observation matrix, v represents the correlation degree between the atoms and the residuals, ∪ represents the union of two sets, and abs[·] represents the absolute value function.

[0037] S21. Input the observation vector y = Φu, the observation matrix Φ (random Gaussian matrix), the sparsity K, and the maximum number of iterations iter max , where u is the column vector of the discrete generalized cyclic correlation entropy spectrum function. The discrete generalized cyclic correlation entropy spectrum function can be expressed in matrix form:

[0038]

[0039] where, u n (n = 1, 2,..., N) are the respective column vectors of the discrete generalized cyclic correlation entropy spectrum function;

[0040] S22. Initialize, the number of iterations t = 1, the initial residual r 0 = y, the initial index set

[0041] S23. Calculate the correlation degree, the correlation matrix v = abs[Φ T r t-1 , sort each column of the correlation matrix v from largest to smallest, and select the indices i of the first 2K items corresponding to the observation matrix to form the set Jt-1 ;

[0042] S24. Update the candidate atom library, Δ t = Δ t-1 ∪ J t-1 , A t = A t-1 ∪ a i (for all i ∈ J t-1 );

[0043] S25. Solve y = A t u t , that is

[0044] S26. Delete atoms, select the top K terms with the largest absolute values from and denote them as the corresponding atom set A t denoted as A tK , and the corresponding index set Δ t denoted as Δ tK , update Δ t = Δ tK ;

[0045] S27. Calculate and update the residual

[0046] S28. Result judgment, if t > iter max or the residual r t = 0, then stop the iteration, otherwise, return to step 2 for the next iteration;

[0047] S29. Reconstruct the generalized cyclic correlation entropy spectrum function from the set of estimated values of the discrete generalized cyclic correlation entropy spectrum function column vectors , and after reconstruction, it can be expressed as:

[0048]

[0049] In the third step above, the GWO algorithm is used to improve the spectral peak search method and perform spectral peak search on the generalized cyclic correlation entropy spectrum projection. The specific process is as follows:

[0050] S31. Calculate the cross-sectional expression of the generalized cyclic correlation entropy spectrum function and construct the fitness function;

[0051] S32. Initialize the gray wolf population parameters and the maximum number of iterations iter max。The basic idea of the GWO algorithm is to continuously adjust the position of each grey wolf by simulating the cooperation and competition among grey wolves of different ranks in a grey wolf group, making them move in the best direction to find the global optimal solution. In this algorithm, each grey wolf represents a potential solution, and the fitness of the grey wolf (i.e., the quality of the solution) determines its status in the group. According to the status in the group from high to low, they are named α, β, δ, and ω in turn. The calculation process of the GWO algorithm mainly includes the following three steps:

[0052] Step 1: Hunting prey. At the beginning of the algorithm, all grey wolf individuals randomly initialize their positions, which represent potential solutions in the search space. Each grey wolf will adjust according to its own position and the position of the prey, trying to approach the position of the prey and hunt the prey. This process can be described by the following expression:

[0053]

[0054] where t is the current iteration number, and are the position vectors of the grey wolf and the prey in the current iteration respectively, is the distance between the grey wolf individual and the prey, is the coefficient vector. Adjusting and updating it can make the grey wolf individual approach the best position of the prey as much as possible. The calculation formula is as follows:

[0055]

[0056] where, is a group of random vectors with modulus values in the range of [0, 1], is the convergence factor, which is set as a linear function in this algorithm. The calculation formula is as follows:

[0057]

[0058] where iter max represents the maximum number of iterations.

[0059] Step 2: Hunting the prey. Hunting the prey is usually commanded by the α wolf. The β wolf and the δ wolf participate in the hunting under the leadership of the α wolf. Calculate the distance between them and the prey according to the current positions of the α, β, and δ wolves. This process can be expressed in the following form:

[0060]

[0061] where, and respectively represent the distances between the α, β, and δ wolves (the three wolves with the best fitness values) and the prey, and respectively represent the current positions of α, β, and δ wolves, represents the position of the current gray wolf individual, and are coefficient vectors respectively. The position of the gray wolf individual is updated under the leadership of α, β, and δ wolves, and its moving direction is expressed in the following form:

[0062]

[0063] where, and are coefficient vectors respectively.

[0064] Step 3: Attack the prey. After completing the hunting operation, the wolf pack starts to attack the prey, that is, by changing the convergence factor to simulate the attack process of the wolf pack, and the coefficient vector also changes accordingly. When , continue to expand the global search range of the wolf pack until the prey is found. When , the wolf pack launches an attack, that is, finds the local optimal value;

[0065] S33. Calculate the fitness of each gray wolf and determine α, β, and δ wolves;

[0066] S34. Update the positions of the gray wolves and the coefficient vectors, and let the leading wolf lead the wolf pack to pursue and attack;

[0067] S35. Calculate the fitness of each gray wolf, and update the fitness and positions of α, β, and δ wolves;

[0068] S36. Judge whether the number of iterations is equal to iter max , if it is equal, output the position of the optimal wolf, otherwise return to the above S32;

[0069] According to the above steps, the global optimal solution obtained after iter max iterations is the spectral peak position used for subsequent signal carrier frequency and symbol rate estimation.

[0070] In the fourth step, the carrier frequency-symbol rate is jointly estimated through spectral peak search. The specific process is as follows:

[0071] S41. Calculate the generalized cyclic correlation entropy spectrum of the received signal according to the first step

[0072] S42. Obtain the projection of the generalized cyclic correlation entropy spectrum on the cyclic frequency axis;

[0073] S43. In 2f c - B < ε < 2f cPerform a spectral peak search on the spectral projection within the range of +B to obtain an estimated value of the carrier frequency where B represents the bandwidth;

[0074] S44. Calculate the generalized cyclic correlation entropy spectrum of the zero-intermediate frequency output signal to obtain its projection on the cyclic frequency axis;

[0075] S45. In the range of 1 / T b -B < ε < 1 / T b +B, perform a spectral peak search on the spectral projection to obtain an estimated value of the symbol rate

[0076] S46. Repeat steps 1 to 5 to obtain the carrier frequency and symbol rate of each signal component of the time-frequency overlapping multi-signals respectively.

[0077] In step 5, the modified Cramer-Rao bound for the joint estimation of the carrier frequency-symbol rate of the time-frequency overlapping multi-signals under alpha-stable distributed noise is derived. The specific process is as follows:

[0078] Assume that the received time-frequency overlapping signal is interfered by alpha-stable distributed noise. Then the mathematical model of the time-frequency overlapping received signal containing M signal components can be expressed as:

[0079]

[0080] where the m-th signal component of the time-frequency overlapping signal can be expressed as:

[0081]

[0082] where A m , f cm , τ m , T bm are the amplitude, carrier frequency, time delay, and symbol period (the reciprocal of which is the symbol rate f bm ) of the m-th signal component respectively, is the initial phase, a m (k) is an independent and identically distributed data symbol sequence, K m is the length of the data sequence transmitted by the m-th signal component, q(t) is the shaping function, h l is the overall gain of the multipath fading channel, and ω(t) is the alpha-stable distributed noise that is uncorrelated with each component of the transmitted signal. Since the probability density function of the alpha-stable distributed noise has no explicit closed expression, the characteristic parameter α = 1 is taken, that is, the noise distribution is approximated by the Cauchy distribution, and its probability function can be described as:

[0083]

[0084] Among them, γ and δ are the scale parameter and the position parameter respectively.

[0085] If the parameter vector to be estimated is expressed as λ = (λ 1 , λ 2 ..., λ N ), Τ , then the element value F ij (i, j = 1, 2,..., N) in the corresponding Fisher information matrix F can be expressed as:

[0086]

[0087] When the number of signal components is 2, the joint estimation vector λ of the carrier frequency and the symbol rate can be expressed as λ = (f c1 , f b1 , f c2 , f b2 ). Τ .

[0088] Since the signal components of the time-frequency overlapping signal are mutually uncorrelated, when i = j, it can be expressed as:

[0089]

[0090]

[0091] When i ≠ j, it can be expressed as:

[0092]

[0093] Therefore, the Fisher information matrix F can be expressed as:

[0094]

[0095] Among them,

[0096] By performing the inverse transformation on the above formula, the modified Cramer-Rao lower bound of the joint estimation vector λ = (f c1 , f b1 , f c2 , f b2 ) Τ is:

[0097]

[0098] The present invention also provides a system for a method of jointly estimating time-domain parameters of time-frequency overlapping multi-signals, including:

[0099] A generalized cyclic correlation entropy spectrum module, used to obtain the generalized cyclic correlation entropy spectrum of the signal in step 1;

[0100] A generalized cyclic correlation entropy spectrum reconstruction module, used to reconstruct the generalized cyclic correlation entropy spectrum using the CoSaMP algorithm in step 2;

[0101] A spectrum peak search module, used to improve the spectrum peak search method by using the GWO algorithm in step 3 and perform spectrum peak search on the generalized cyclic correlation entropy spectrum projection;

[0102] A carrier frequency-symbol rate joint estimation module, used for jointly estimating the carrier frequency-symbol rate by spectrum peak search in step 4;

[0103] The modified Cramer-Rao bound derivation module is used to derive the modified Cramer-Rao bound for the joint estimation of carrier frequency-symbol rate of time-frequency overlapping multi-signals under alpha stable distribution noise in step five.

[0104] The present invention also provides a device for a method for jointly estimating time domain parameters of time-frequency overlapping multi-signals, comprising: a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the method for jointly estimating time domain parameters of time-frequency overlapping multi-signals can be implemented as described in any one of steps one to five.

[0105] The present invention also provides a computer storage medium for receiving a program input by a user. When the computer program stored in the storage medium is executed by a processor, it can perform a joint estimation of the carrier frequency-symbol rate of time-frequency overlapping multi-signals based on the joint estimation method of time domain parameters of time-frequency overlapping multi-signals described in any one of steps one to five.

[0106] In combination with the above technical solutions, the advantages and positive effects of the present invention are as follows:

[0107] The present invention utilizes the CoSaMP algorithm to reconstruct the generalized cyclic correlation entropy spectrum; adopts the GWO algorithm to improve the spectrum peak search method; and derives the modified Cramer-Rao bound for the joint estimation of carrier frequency-symbol rate of time-frequency overlapping multi-signals under alpha stable distribution noise; the invention fills the gap in this field.

[0108] The CoSaMP algorithm used can reconstruct the generalized cyclic correlation entropy spectrum, eliminate some redundant information of the generalized cyclic correlation entropy spectrum, suppress the wild points caused by impulse noise, make the reconstructed generalized cyclic correlation entropy spectrum sharper and clearer than the original spectrum, and improve the spectral resolution and spectral peak aggregation.

[0109] The adopted GWO algorithm can improve the spectrum peak search method and increase the speed and accuracy of spectrum peak search.

[0110] The proposed modified Cramer-Rao bound for joint estimation of carrier frequency and symbol rate of time-frequency overlapping multi-signals under alpha-stable distribution noise can accurately evaluate the effectiveness of the joint estimation method of carrier frequency and symbol rate.

[0111] The research of this invention should focus on developing a joint estimation algorithm for carrier frequency and symbol rate of time-frequency overlapping multi-signals with better estimation performance, lower computational complexity, and better non-Gaussian noise suppression effect; this invention explores the use of compressive sensing technology and swarm optimization algorithm, which can jointly estimate the carrier frequency and symbol rate of time-frequency overlapping multi-signals.

[0112] In summary, compared with the prior art, the research of this invention explores the problem of reconstructing the generalized cyclic correlation entropy spectrum using the CoSaMP algorithm, and emphasizes the importance of solving the problem of reconstructing the generalized cyclic correlation entropy spectrum using the CoSaMP algorithm in the joint estimation method of time-domain parameters of time-frequency overlapping multi-signals; any task involving joint estimation of carrier frequency and symbol rate of time-frequency overlapping multi-signals can use this invention for joint estimation; reconstructing the generalized cyclic correlation entropy spectrum using the CoSaMP algorithm can suppress the outliers caused by impulse noise, making the reconstructed generalized cyclic correlation entropy spectrum sharper and clearer than the original spectrum, improving the spectral resolution and spectral peak aggregation, and the derivation of the joint estimation modified Cramer-Rao bound can accurately evaluate the effectiveness of the joint estimation method; this invention has lower computational complexity and better estimation performance. Brief Description of the Drawings

[0113] Figure 1 It is a flowchart of a joint estimation method, system, medium, and device for time-domain parameters of time-frequency overlapping multi-signals provided by an embodiment of the present invention.

[0114] Figure 2 It is a schematic structural diagram of a joint estimation system for carrier frequency and symbol rate of time-frequency overlapping multi-signals provided by an embodiment of the present invention;

[0115] Figure 2 In it: 1. Generalized cyclic correlation entropy spectrum module; 2. Generalized cyclic correlation entropy spectrum reconstruction module; 3. Spectral peak search module; 4. Carrier frequency-symbol rate joint estimation module; 5. Modified Cramer-Rao bound derivation module.

[0116] Figure 3 It is a schematic diagram of the simulation experiment results of comparing the carrier frequency and symbol rate estimation performances of different methods of a joint estimation system for carrier frequency and symbol rate of time-frequency overlapping multi-signals provided by an embodiment of the present invention.

[0117] Figure 4 It is a schematic diagram of the simulation experiment results of the carrier frequency and symbol rate estimation performances at different characteristic exponents of a joint estimation system for carrier frequency and symbol rate of time-frequency overlapping multi-signals provided by an embodiment of the present invention. Detailed implementation manners

[0118] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0119] In view of the problems existing in the prior art, the present invention provides a method, system, medium and device for jointly estimating time-domain parameters of time-frequency overlapping multi-signals. The present invention will be described in detail below in conjunction with the accompanying drawings.

[0120] The method for jointly estimating time-domain parameters of time-frequency overlapping multi-signals provided by the present invention includes the following steps:

[0121] Obtain the generalized cyclic correlation entropy spectrum of time-frequency overlapping multi-signals;

[0122] Reconstruct the generalized cyclic correlation entropy spectrum by using the Compressive Sampling Matching Pursuit (CoSaMP) algorithm;

[0123] Improve the spectrum peak search method by using the Grey Wolf Optimization (GWO) algorithm, and perform spectrum peak search on the projection of the reconstructed generalized cyclic correlation entropy spectrum;

[0124] Jointly estimate the carrier frequency and symbol rate through spectrum peak search;

[0125] Deduce the modified Cramer-Rao bound for the joint estimation of the carrier frequency and symbol rate of time-frequency overlapping multi-signals under alpha-stable distribution noise.

[0126] The process of obtaining the generalized cyclic correlation entropy spectrum includes: modeling the mathematical model of the received signal based on alpha-stable distribution noise, and using Fourier transform to convert the generalized cyclic correlation entropy of the signal to generate the generalized cyclic correlation entropy spectrum.

[0127] The process of reconstructing the generalized cyclic correlation entropy spectrum by using the CoSaMP algorithm includes:

[0128] Initialize the observation vector, observation matrix, sparsity and maximum number of iterations;

[0129] Iteratively select atoms and calculate the residual through correlation sorting and candidate atom library update;

[0130] Reconstruct the generalized cyclic correlation entropy spectrum according to the iterative result.

[0131] The process of performing spectrum peak search on the projection of the generalized cyclic correlation entropy spectrum by using the GWO algorithm includes:

[0132] Initialize the grey wolf population parameters and the maximum number of iterations;

[0133] Determine the optimal position through the calculation of the fitness function;

[0134] Update the position according to the leading wolf's guidance and optimize the fitness, and finally output the global optimal solution.

[0135] During the spectral peak search process, combined with the projection result of the generalized cyclic correlation entropy spectrum, search for the carrier frequency and symbol rate respectively within specific frequency ranges, and output the corresponding estimated values.

[0136] During the derivation of the modified Cramer-Rao bound, based on the Fisher information matrix, perform an inverse transformation calculation on the joint estimation vector of the carrier frequency and symbol rate to obtain the expression of the modified Cramer-Rao bound.

[0137] Time-frequency overlapping multi-signals are modeled as a mathematical expression in an alpha-stable distribution noise environment. By analyzing the input signals, their time-frequency characteristics are extracted. Use the Fourier transform to calculate the generalized cyclic correlation entropy spectrum of the signals. The entropy spectrum describes the correlation characteristics of the signals in the cyclic frequency domain, and can reveal the basic structure and characteristics of the time-frequency overlapping signals, providing a basis for subsequent processing.

[0138] To improve the resolution of the entropy spectrum and suppress noise interference, the compressive sampling matching pursuit (CoSaMP) algorithm is used to reconstruct the generalized cyclic correlation entropy spectrum. Through iterative optimization, calculate the correlation between the entropy spectrum and the residual, select the optimal sparse atoms and update the residual, and finally obtain the reconstructed entropy spectrum. This process removes redundant information, improves the sharpness and aggregation of the spectrum, and makes the time-frequency characteristics clearer.

[0139] Based on the entropy spectrum reconstruction, use the grey wolf optimization (GWO) algorithm to improve the spectral peak search method, and determine the global optimal solution through the fitness function. The specific steps include initializing the grey wolf population, calculating the fitness value, updating the grey wolf position, and determining the optimal position guided by the leading wolf. Perform spectral peak search in the projection of the reconstructed entropy spectrum to extract the estimated values of the carrier frequency and symbol rate, and complete the joint parameter estimation.

[0140] To verify the effectiveness and estimation performance of the algorithm, the modified Cramer-Rao bound in an alpha-stable distribution noise environment is derived. Based on the signal parameter vector and its Fisher information matrix, calculate the lower bound of the joint estimation of the carrier frequency and symbol rate. The calculation results of the modified Cramer-Rao bound show that this method has high estimation accuracy and computational stability in complex noise environments.

[0141] Ordinary technicians in the industry can also adopt other steps to implement the method, system, medium, and device for jointly estimating time-domain parameters of time-frequency overlapping multi-signals provided by the present invention. Figure 1 The method, system, medium, and device for jointly estimating time-domain parameters of time-frequency overlapping multi-signals provided by the present invention is only a specific embodiment.

[0142] Example 1: Joint Estimation of Parameters of Time-Frequency Overlapped Communication Signals

[0143] In a certain wireless communication system, multiple user signals overlap in the time-frequency domain and are interfered by bursty non-Gaussian noise (such as lightning interference). The method of the present invention is used to jointly estimate the carrier frequency and symbol rate of these signals:

[0144] 1) Acquisition of Generalized Cyclic Correlation Entropy Spectrum: Construct a mathematical model of the communication signal and calculate the generalized cyclic correlation entropy spectrum of the signal using Fourier transform.

[0145] 2) Entropy Spectrum Reconstruction: The CoSaMP algorithm is used to remove redundant information in the entropy spectrum, generate a high-resolution entropy spectrum, and improve the separation ability of overlapping signals.

[0146] 3) Spectrum Peak Search: The improved GWO algorithm is used to perform spectrum peak search in the entropy spectrum projection to quickly and accurately find the peak positions of the carrier frequency and symbol rate.

[0147] 4) Joint Estimation Verification: Derive the modified Cramer-Rao bound under alpha-stable distribution noise to prove the accuracy of the estimation method. After verification, the method in this example can effectively separate signals of different users and accurately estimate their time-domain parameters.

[0148] Example 2: Radar Signal Processing under Impulse Noise Interference

[0149] In a high-resolution radar system, the received echo signal may be affected by time-frequency overlapped target signals and impulse noise at the same time. To accurately extract the target motion parameters, the method of the present invention is used to process the radar echo signal:

[0150] 1) Entropy Spectrum Extraction: Use the generalized cyclic correlation entropy function to analyze the echo signal, calculate its entropy spectrum, and extract the frequency-domain information reflecting the target parameter characteristics.

[0151] 2) Spectrum Reconstruction: The CoSaMP algorithm is used to reconstruct the entropy spectrum, eliminate the outliers in the spectrum caused by impulse noise, enhance the sharpness of the spectrum peak, and improve the recognition of target signals.

[0152] 3) Target Parameter Estimation: Perform spectrum peak search on the entropy spectrum through the improved GWO algorithm to determine the Doppler frequency and symbol rate of the target, and obtain the joint estimated value of the target motion parameters.

[0153] 4) Performance Evaluation: Use the modified Cramer-Rao bound to verify the estimation accuracy of the method in a strong noise environment. The results show that the system can achieve high-precision target parameter extraction under impulse noise interference.

[0154] AsFigure 1 As shown in the figure, the method for jointly estimating time-domain parameters of time-frequency overlapping multi-signals provided by the embodiment of the present invention specifically includes the following steps:

[0155] Step 1: Obtain the generalized cyclic correlation entropy spectrum of the signal. The specific process is as follows:

[0156] The mathematical model of time-frequency overlapping multi-signals in a non-Gaussian noise fading channel can be described in the following form:

[0157]

[0158] Among them, the i-th signal component A i , f ci , τ i , T bi are respectively the amplitude, carrier frequency, initial delay and symbol period of the i-th signal component (the reciprocal of which is the symbol rate f bi ), a i (k) is an independent and identically distributed random data symbol sequence, K i is the length of the transmitted data sequence, θ is the initial phase, q(t) is the shaping function, L is the number of paths of the multipath fading channel, h l (t) is the amplitude attenuation factor of the l-th path, ω(t) is non-Gaussian noise that is uncorrelated with each component of the transmitted signal, and N represents the number of signals.

[0159] In an actual communication system, there are many noises with pulse characteristics, such as burst noise, radio frequency noise, atmospheric noise, lightning interference, etc. Such noises often do not follow a Gaussian distribution, so they are collectively referred to as non-Gaussian noises. Currently, three distribution models are often used for modeling non-Gaussian noises, namely Gaussian mixture distribution, alpha-stable distribution and generalized Gaussian distribution.

[0160] The present invention uses the alpha-stable distribution to simulate non-Gaussian noises in an actual communication system. Since there is no probability density function expression that can accurately describe the alpha-stable distribution, it can only be represented by the Fourier transform of its probability density function, that is, the characteristic function of the alpha-stable distribution:

[0161]

[0162] Among them, sgn(·) is the sign function, α is the characteristic exponent, β is the symmetry parameter, γ is the scale parameter, and δ is the position parameter.

[0163] Let a second-order cyclostationary random process, and its generalized autocorrelation entropy function can be defined as:

[0164]

[0165] Among them, E[·] is the mathematical expectation, and G μν (·) is the generalized Gaussian kernel function, also known as the generalized Gaussian probability density function, which is defined in the following form:

[0166]

[0167] where Γ(·) is the gamma function, μ ∈ (0, +∞) is the shape parameter, ν ∈ (0, +∞) is the scale parameter, λ = ν -μ is the kernel parameter, and μ / 2νΓ(1 / μ) is the normalization constant.

[0168] The generalized cyclic correlation entropy function can be written in the following form:

[0169]

[0170] where ε = m / T 0 is the cyclic frequency. Since the generalized cyclic correlation entropy and the generalized cyclic correlation entropy spectrum form a pair of Fourier transform pairs, therefore, taking the Fourier transform of the generalized cyclic correlation entropy of the signal x(t), the generalized cyclic correlation entropy spectrum can be obtained. Its expression is:

[0171]

[0172] Step 2, use the CoSaMP algorithm to reconstruct the generalized cyclic correlation entropy spectrum. The specific process is as follows:

[0173] In the following steps, t represents the number of iterations, J t represents the index of the atoms selected in the iteration, Δ t represents the set of indices, A t represents the set of atoms corresponding to the indices in Δ t , a i represents the i-th column of the observation matrix, v represents the correlation degree between the atom and the residual, ∪ represents the union of two sets, and abs[·] represents the absolute value function.

[0174] S21. Input the observation vector y = Φu, the observation matrix Φ (random Gaussian matrix), the sparsity K, and the maximum number of iterations iter max , where u is the column vector of the discrete generalized cyclic correlation entropy spectrum function. The discrete generalized cyclic correlation entropy spectrum function can be expressed in matrix form:

[0175]

[0176] where u n (n = 1, 2,..., N) are the respective column vectors of the discrete generalized cyclic correlation entropy spectrum function;

[0177] S22. Initialization, the iteration number \(t = 1\), the initial residual \(r\) 0 = \(y\), the initial index set

[0178] S23. Relevance calculation, the correlation matrix \(v=\vert\varPhi\) T \(r\) t-1 \(\vert\), sort each column of the correlation matrix \(v\) from large to small, and select the indices \(i\) of the first \(2K\) items corresponding to the observation matrix to form the set \(J\) t-1 ;

[0179] S24. Update the candidate atom library, \(\Delta\) t = \(\Delta\) t-1 \(\cup J\) t-1 , \(A\) t = \(A\) t-1 \(\cup a\) i (for all \(i\in J\) t-1 );

[0180] S25. Solve \(y = A\) t \(u\) t , that is

[0181] S26. Delete atoms, select the first \(K\) items with the largest absolute values from and record them as The corresponding atom set \(A\) t is recorded as \(A\) tK , and the corresponding index set \(\Delta\) t is recorded as \(\Delta\) tK , update \(\Delta\) t = \(\Delta\) tK ;

[0182] S27. Calculate and update the residual,

[0183] S28. Result determination, if \(t>iter\) max or the residual \(r\) t = 0, then stop the iteration, otherwise, return to step 2 for the next iteration;

[0184] S29. Reconstruct the generalized cyclic correlation entropy spectrum function from the set of estimated values of the discrete generalized cyclic correlation entropy spectrum function column vectors It can be expressed after reconstruction as:

[0185]

[0186] Step 3. Use the GWO algorithm to improve the spectral peak search method and project the generalized cyclic correlation entropy spectrum into S31. Calculate the cross-sectional expression of the generalized cyclic correlation entropy spectrum function and construct the fitness function;

[0187] S32. Initialize the parameters of the gray wolf population and the maximum number of iterations iter max . The basic idea of the GWO algorithm is to simulate the cooperation and competition among gray wolves of different ranks in the gray wolf population, continuously adjust the positions of each gray wolf, and let them move in the best direction to find the global optimal solution. In this algorithm, each gray wolf represents a potential solution, and the fitness of the gray wolf (i.e., the quality of the solution) determines its status in the population. According to the status of the gray wolf in the population from high to low, they are named α, β, δ, and ω in turn. The calculation process of the GWO algorithm mainly includes the following three steps:

[0188] Step 1: Surround the prey. At the beginning of the algorithm, all gray wolf individuals randomly initialize their positions, which represent potential solutions in the search space. Each gray wolf will adjust according to its own position and the position of the prey, try to approach the position of the prey and surround the prey. This process can be described by the following expressions:

[0189]

[0190] where t is the current iteration number, and are the position vectors of the gray wolf and the prey in the current iteration respectively, is the distance between the gray wolf individual and the prey, is the coefficient vector. Adjusting and updating it can make the gray wolf individual approach the best position of the prey as much as possible. The calculation formula is as follows:

[0191]

[0192] where, is a group of random vectors with modulus values in the range of [0, 1], is the convergence factor, which is set as a linear function in this algorithm. The calculation formula is as follows:

[0193]

[0194] where iter max represents the maximum number of iterations.

[0195] Step 2: Hunt the prey. Hunting the prey is usually commanded by the α wolf, and the β wolf and the δ wolf participate in the hunt under the leadership of the α wolf. Calculate the distance between them and the prey according to the current positions of the α, β, and δ wolves. This process can be expressed in the following form:

[0196]

[0197] where, $d_{\alpha}$, $d_{\beta}$, and $d_{\delta}$ represent the distances between the $\alpha$, $\beta$, and $\delta$ wolves (the three wolves with the best fitness values) and the prey, respectively. and $\overrightarrow{D_{\alpha}}$, $\overrightarrow{D_{\beta}}$, and $\overrightarrow{D_{\delta}}$ represent the current positions of the $\alpha$, $\beta$, and $\delta$ wolves, respectively. $\overrightarrow{D}$ represents the position of the current gray wolf individual. and $\overrightarrow{A}$ and $\overrightarrow{C}$ are coefficient vectors, respectively. The position of the gray wolf individual is updated under the leadership of the $\alpha$, $\beta$, and $\delta$ wolves, and its movement direction is expressed in the following form:

[0198]

[0199] where and $\overrightarrow{A}$ and $\overrightarrow{C}$ are coefficient vectors, respectively.

[0200] Step 3: Attack the prey. After completing the hunting operation, the wolf pack starts to attack the prey, that is, the attack process of the wolf pack is simulated by the change of the convergence factor $\lambda$, and the coefficient vector $\overrightarrow{C}$ also changes accordingly. When $\lambda \gt 0.5$, the global search range of the wolf pack is continuously expanded until the prey is found. When $\lambda \leq 0.5$, the wolf pack launches an attack, that is, the local optimal value is found;

[0201] S33. Calculate the fitness of each gray wolf and determine the $\alpha$, $\beta$, and $\delta$ wolves;

[0202] S34. Update the positions of the gray wolves and the coefficient vectors, and the leading wolves guide the wolf pack to pursue and attack;

[0203] S35. Calculate the fitness of each gray wolf and update the fitness and positions of the $\alpha$, $\beta$, and $\delta$ wolves;

[0204] S36. Determine whether the number of iterations is equal to iter max , if it is equal, output the position of the optimal wolf, otherwise return to the above S32;

[0205] According to the above steps, the global optimal solution obtained after iter max iterations of the algorithm is the spectral peak position used for subsequent signal carrier frequency and symbol rate estimation.

[0206] Step 4: Jointly estimate the carrier frequency-symbol rate through spectral peak search. The specific process is as follows:

[0207] S41. Calculate the generalized cyclic correlation entropy spectrum of the received signal according to the above Step 1

[0208] S42. Obtain the projection of the generalized cyclic correlation entropy spectrum on the cyclic frequency axis;

[0209] S43. At 2fc -B < ε < 2f c Perform a spectral peak search on the spectral projection within the range of +B to obtain an estimated value of the carrier frequency where B represents the bandwidth;

[0210] S44. Calculate the generalized cyclic correlation entropy spectrum of the zero-intermediate frequency output signal to obtain its projection on the cyclic frequency axis;

[0211] S45. In the range of 1 / T b -B < ε < 1 / T b +B, perform a spectral peak search on the spectral projection to obtain an estimated value of the symbol rate

[0212] S46. Repeat steps 1 to 5 to obtain the carrier frequency and symbol rate of each signal component of the time-frequency overlapping multi-signals respectively.

[0213] In step 5, the modified Cramer-Rao bound for the joint estimation of the carrier frequency-symbol rate of the time-frequency overlapping multi-signals under alpha-stable distributed noise is derived. The specific process is as follows:

[0214] Assume that the received time-frequency overlapping signal is interfered by alpha-stable distributed noise. Then the mathematical model of the time-frequency overlapping received signal containing M signal components can be expressed as:

[0215]

[0216] where the m-th signal component of the time-frequency overlapping signal can be expressed as:

[0217]

[0218] where A m , f cm , τ m , T bm are the amplitude, carrier frequency, time delay, and symbol period (the reciprocal of which is the symbol rate f bm ) of the m-th signal component respectively, is the initial phase, a m (k) is an independent and identically distributed data symbol sequence, K m is the length of the data sequence transmitted by the m-th signal component, q(t) is the shaping function, h l is the overall gain of the multipath fading channel, and ω(t) is the alpha-stable distributed noise that is uncorrelated with each component of the transmitted signal. Since the probability density function of the alpha-stable distributed noise does not have an explicit closed expression, the characteristic parameter α = 1 is taken, that is, the noise distribution is approximated by the Cauchy distribution, and its probability function can be described as:

[0219]

[0220] Among them, γ and δ are the scale parameter and the position parameter respectively.

[0221] If the parameter vector to be estimated is expressed as λ = (λ 1 , λ 2 ..., λ N ), Τ , then the element value F ij (i, j = 1, 2,..., N) in the corresponding Fisher information matrix F can be expressed as:

[0222]

[0223] When the number of signal components is 2, the joint estimation vector λ of the carrier frequency and the symbol rate can be expressed as λ = (f c1 , f b1 , f c2 , f b2 ). Τ .

[0224] Since the signal components of the time-frequency overlapping signal are uncorrelated with each other, when i = j, can be expressed as:

[0225]

[0226] When i ≠ j, can be expressed as:

[0227]

[0228] Therefore, the Fisher information matrix F can be expressed as:

[0229]

[0230] Among them,

[0231] By performing the inverse transformation on the above formula, the modified Cramer-Rao bound of the joint estimation vector λ = (f c1 , f b1 , f c2 , f b2 ) Τ is:

[0232]

[0233]

[0234] Such as Figure 2As shown in the figure, the time-frequency overlapping multi-signal carrier frequency-symbol rate joint estimation system provided by the embodiment of the present invention includes:

[0235] A generalized cyclic correlation entropy spectrum module for obtaining the generalized cyclic correlation entropy spectrum of a signal.

[0236] A generalized cyclic correlation entropy spectrum reconstruction module for reconstructing the generalized cyclic correlation entropy spectrum using the CoSaMP algorithm.

[0237] A spectral peak search module for improving the spectral peak search method using the GWO algorithm and performing spectral peak search on the projection of the generalized cyclic correlation entropy spectrum.

[0238] A carrier frequency-symbol rate joint estimation module for jointly estimating the carrier frequency-symbol rate through spectral peak search.

[0239] A modified Cramer-Rao bound derivation module for deriving the modified Cramer-Rao bound for the joint estimation of the carrier frequency-symbol rate of time-frequency overlapping multi-signals under alpha-stable distribution noise.

[0240] The joint estimation method provided by the present invention can be used for jointly estimating the carrier frequency-symbol rate of time-frequency overlapping multi-signals.

[0241] The technical effects of the present invention will be described in detail below in combination with simulation experiments.

[0242] To evaluate the performance of the present invention, simulation verification is carried out. In the simulation experiment, a series of simulation experiments are carried out using the MATLAB software platform, and the results are analyzed. Each experiment is carried out with 500 Monte Carlo simulations. The performance evaluation criterion for the parameter joint estimation method is the normalized root mean square error, that is, NRMSE, and the background noise uses alpha-stable distribution noise.

[0243] Since the alpha-stable distribution model does not have a finite second moment, therefore, based on the scale parameter γ of the alpha-stable distribution noise and the variance of the signal The traditional signal-to-noise ratio is redefined as the generalized signal-to-noise ratio (GSNR), which can be expressed as:

[0244]

[0245] The signals used in the simulation are time-frequency overlapping signals composed of two binary phase shift keying (BPSK) signal components. The symbol rates of the two signal components in the time-frequency overlapping signal are set to f b1 = 800 Baud and f b2 = 1000 Baud, the carrier frequencies are f c1 = 3580 Hz and f c2 = 4000 Hz, and the sampling frequency is fs = 16000 Hz, Figure 3 The simulated generalized signal-to-noise ratio of Figure 3 varies between -10 dB and 15 dB, with a step size of 5 dB. Figure 4 The simulated generalized signal-to-noise ratio of Figure 4 is 8 dB, and the characteristic exponent of the alpha-stable distribution noise varies between 1 and 2, with a step size of 0.2.

[0246] Figure 3 shows the comparison of the carrier frequency and symbol rate estimation performances of different methods. From Figure 3 it can be seen that as the generalized signal-to-noise ratio increases, the performances of both the parameter estimation method based on the generalized cyclic correlation entropy spectrum (GCCES) and the parameter estimation method based on CoSaMP-GCCES proposed in the present invention are improved. When the generalized signal-to-noise ratio is greater than 10 dB, the estimation performances of the two methods are relatively close, and the performance of the CoSaMP-GCCES method proposed in the present invention is slightly better than that of the traditional GCCES method; when the generalized signal-to-noise ratio is less than 10 dB, the advantage of the method proposed in the present invention is more obvious, which proves that the CoSaMP reconstruction method can effectively suppress the influence caused by non-Gaussian noise. When the generalized signal-to-noise ratio is greater than or equal to 5 dB, the performance of the method proposed in the present invention is relatively close to the modified Cramer-Rao bound (MCRB) corresponding to the carrier frequency and symbol rate, verifying the effectiveness of this method. Figure 4 shows the estimation performances of the carrier frequency and symbol rate at different characteristic exponents. From Figure 4 it can be seen that as the characteristic exponent increases from 1 to 2, that is, the pulse intensity of the alpha-stable distribution noise gradually weakens, the estimation performance of the symbol rate gradually improves. When the characteristic exponent is less than 1.4, the estimation error of the symbol rate is relatively large, because when the characteristic exponent is close to 1, the pulse spikes of the alpha-stable distribution noise are more obvious, while the spectral line amplitude corresponding to the symbol rate estimation is relatively small and is easily affected by the pulse spikes, resulting in the deterioration of its estimation performance; when the characteristic exponent is greater than or equal to 1.4, the pulse spike characteristics of the alpha-stable distribution noise gradually weaken, and the NRMSE of the symbol rate estimation can reach 2×10 -3 , and the estimation performance is relatively stable. Moreover, the spectral line amplitude corresponding to the carrier frequency estimation in this method is much larger than that of the symbol rate estimation and is not easily affected by this pulse spike characteristic. Therefore, the estimation performance of the carrier frequency is relatively stable within the range of α ∈ (1, 2). Therefore, the estimation performance of the joint estimation method proposed in the present invention is better than that of the existing methods, and the simulation experiments verify the effectiveness of the joint estimation method proposed in the present invention.

[0247] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated designed hardware. Those of ordinary skill in the art can understand that the above devices and methods can be implemented using computer-executable instructions and / or included in processor control code, such as provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and their modules of the present invention can be implemented by hardware circuits of programmable hardware devices such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, or can be implemented by a combination of the above hardware circuits and software such as firmware.

[0248] As described above, the above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims

1. A method for joint estimation of time domain parameters of time-frequency overlapping multi-signals, characterized in that: The following steps are involved: S1, obtain the generalized cyclic correlation entropy spectrum of multiple signals with overlapping time and frequency; S2, reconstruct the generalized cyclic correlation entropy spectrum using the compressed sampling matching pursuit (CoSaMP) algorithm; S3, the Grey Wolf Optimization (GWO) algorithm is used to improve the spectrum peak search method, and the spectrum peak search is performed on the reconstructed generalized cyclic correlation entropy spectrum projection; S4, jointly estimate the carrier frequency and symbol rate by spectrum peak search; S5, derive the modified Cramer-Rao bound for the joint estimation of carrier frequency and symbol rate of time-frequency overlapping multi-signals in the presence of alpha-stable distributed noise.

2. The method for joint estimation of time domain parameters of time-frequency overlapping multi-signals as claimed in claim 1, characterized in that: The process of obtaining the generalized cyclic correlation entropy spectrum includes: modeling a mathematical model of a received signal based on alpha stable distribution noise, transforming the generalized cyclic correlation entropy of the signal by Fourier transform, and generating a generalized cyclic correlation entropy spectrum.

3. The method for joint estimation of time domain parameters of time-frequency overlapping multi-signals as claimed in claim 1, characterized in that: The process of reconstructing the generalized cyclic correlation entropy spectrum using the CoSaMP algorithm includes: Initialize the observation vector, observation matrix, sparsity and maximum number of iterations; Through relevance sorting and candidate atom library updating, atoms are iteratively selected and residuals are calculated; The generalized cyclic correlation entropy spectrum is reconstructed according to the iterative results.

4. The method for joint estimation of time domain parameters of time-frequency overlapping multi-signals as claimed in claim 1, characterized in that: The process of using the GWO algorithm to search for spectrum peaks on the generalized cyclic correlation entropy spectrum projection comprises: Initialize the gray wolf population parameters and the maximum number of iterations; Determine the best position through fitness function calculation; According to the guidance of the leader, the position is updated and the fitness is optimized, and finally the global optimal solution is output.

5. The method for joint estimation of time domain parameters of time-frequency overlapping multi-signals as claimed in claim 1, characterized in that: In the spectrum peak search process, the carrier frequency and the symbol rate are searched within a specific frequency range in combination with the projection result of the generalized cyclic correlation entropy spectrum, and the corresponding estimated values ​​are output.

6. The method for joint estimation of time domain parameters of time-frequency overlapping multi-signals as claimed in claim 1, characterized in that: In the derivation process of the modified Cramer-Rao bound, an inverse transformation calculation is performed on the joint estimation vector of the carrier frequency and the symbol rate based on the Fisher information matrix to obtain an expression of the modified Cramer-Rao bound.

7. A system for jointly estimating time domain parameters of time-frequency overlapped multi-signals for implementing the method for jointly estimating time domain parameters of time-frequency overlapped multi-signals according to any one of claims 1 to 6, characterized in that: The time-domain parameter joint estimation system for time-frequency overlapping multi-signal comprises: Generalized cyclic correlation entropy spectrum module, used to obtain the generalized cyclic correlation entropy spectrum of multiple signals with time-frequency overlap; A generalized cyclic correlation entropy spectrum reconstruction module is used to reconstruct the generalized cyclic correlation entropy spectrum using a compressed sampling matching pursuit (CoSaMP) algorithm; A spectrum peak search module is used to perform spectrum peak search on the reconstructed generalized cyclic correlation entropy spectrum projection using the Grey Wolf Optimization (GWO) algorithm; A joint estimation module, used for jointly estimating the carrier frequency and the symbol rate by spectrum peak search; The modified Cramer-Rao bound derivation module is used to derive the modified Cramer-Rao bound for the joint estimation of carrier frequency and symbol rate in alpha stable distribution noise.

8. The time-domain parameter joint estimation system for time-frequency overlapping multi-signals according to claim 7, characterized in that: The generalized cyclic correlation entropy spectrum module includes: A unit for constructing a mathematical model of time-frequency overlapping signals in an alpha stable distribution noise environment; Unit for converting the generalized cyclic correlation entropy of a signal into a generalized cyclic correlation entropy spectrum by Fourier transform.

9. The time-domain parameter joint estimation system for time-frequency overlapping multi-signals according to claim 7, characterized in that: The generalized cyclic correlation entropy spectrum reconstruction module includes: Units for initializing observation vectors, observation matrices, and sparsity; Unit for selecting atoms and reconstructing the generalized cyclic correlation entropy spectrum by iterative correlation ranking and residual calculation.

10. The time-domain parameter joint estimation system for time-frequency overlapping multi-signals according to claim 7, characterized in that: The spectrum peak search module comprises: Unit for initializing gray wolf population parameters and maximum number of iterations; A unit used to calculate the fitness function, update the position of the gray wolf, and output the global optimal solution of the spectrum peak search.

Images