Joint estimation method and system for time-frequency overlapped multi-signal time domain parameters under non-Gaussian noise

Abstract

The invention belongs to the technical field of communication, and particularly relates to a time-frequency overlapping multi-signal time domain parameter joint estimation method and system under non-Gaussian noise, and the joint estimation is carried out on signal amplitude and time delay through the position and peak value of a discrete spectral line; carrying out spectrum peak position search by adopting a PSO algorithm of a dynamic inertia weight coefficient; deducing the Cramer-Rao bound of time-frequency overlapping multi-signal amplitude-time delay joint estimation under alpha stable distribution noise to carry out effectiveness evaluation; parameter estimation can be carried out on the time-frequency overlapping multi-signal amplitude-time delay joint estimation task based on the cyclic correlation entropy spectrum by using the method provided by the invention; by using the PSO algorithm of the dynamic inertia weight coefficient, the global and local search capability can be enhanced, the situation of local optimum is not easily caused, the effectiveness of the MCRB to parameter estimation is corrected for evaluation, and the performance of the method can be comprehensively and accurately judged; the method has better performance and wider universality.

Description

Technical Field

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

[0002] The amplitude and delay of a signal are two key parameters affecting the signal transmission quality of a communication system. Accurately estimating the signal amplitude can achieve effective control of the power of the communication transmission system. At the same time, accurately estimating the signal delay is beneficial for the receiving end to improve the accuracy of positioning and synchronization and reduce the impact of channel fading and delay on the communication system. Due to the influence of factors such as noise interference and channel fading, the intensity of the signal will change significantly during the communication transmission process, resulting in more challenging amplitude estimation of the received signal. As an important aspect of signal feature parameter extraction, delay estimation has wide application value in many fields such as communication system synchronization and positioning, and radar system target tracking.

[0003] For traditional single-signal amplitude estimation, Jain et al. proposed a method for estimating the amplitude of periodic signals based on interpolated fast Fourier transform, which has good estimation performance under high signal-to-noise ratio conditions (Jain V K, Collins W L, Davis D C. High-accuracy analog measurements via interpolated FFT[J]. IEEE Transactions on Instrumentation and Measurement, 1979, 28(2): 113-122.). Angrisani et al. proposed a method for estimating the amplitude of sine signals by combining the numerical differentiation theorem and the central Lagrange interpolation theorem, but this method is only applicable to sine signals with amplitudes within a certain range (Angrisani L, Napolitano A, Vadursi M. True-power measurement in digital communicationsystems affected by in-channel interference[J]. IEEE Transactions onInstrumentation andMeasurement, 2009, 58(12): 3985-3994.). Liu et al. proposed a method for estimating the amplitude of hybrid MSK signals based on the max-min idea for the amplitude estimation problem in non-cooperative communication flat fading channels, but the estimation performance of this method degrades severely when the signal-to-noise ratio is less than 10 dB, and this method is only applicable to two-path MSK hybrid signals and has limitations in the case of multi-path hybrid signals (Liu M, Yu S, Chen Y, et al. Blindparameter estimation for co-channel digital communication signals[J]. WirelessNetworks, 2023: 1-11.).Based on the cyclostationary characteristics of digital modulation signals, Knapp et al. utilized the spectral line information of the cyclic spectrum to achieve the amplitude estimation of time-frequency overlapping multi-signals. Experimental simulations demonstrated that this method has high estimation accuracy when the power of each signal component in time-frequency overlapping multi-signals is relatively low, and can still achieve effective estimation in a low signal-to-noise ratio environment. However, this method is no longer applicable in the case of non-Gaussian noise (Knapp C, Carter G. The generalized correlation method for estimation of time delay[J]. IEEE transactions on acoustics, speech, and signal processing, 1976, 24(4): 320-327.).

[0004] In recent years, scholars at home and abroad have proposed many time delay estimation methods. In order to break through the limitations of traditional adaptive time delay estimation methods under non-Gaussian noise, Wong et al. combined the P-norm with a generalized weighting function and proposed a generalized weighted adaptive time delay estimation method based on the minimum average P-norm, which solved the time delay estimation problem under non-Gaussian noise (Wong K M, et al. Design of optimum signals for the simultaneous estimation of time delay and Doppler shift[J]. IEEE transactions on signal processing, 1993, 41(6):2141-2154.). In response to the problem that the performance of traditional time delay estimation methods is poor under low signal-to-noise ratio, Wan et al. estimated the time delay through the discrete Fourier transform of time delay search. The simulation results show that this method has high estimation accuracy under a certain bandwidth limit (Wan Y, Liu A, Hu Q, et al. Multiband delay estimation for localization using a two-stage global estimation scheme[J]. IEEE Transactions on Wireless Communications, 2023.). Xu et al. combined the least squares method and the particle swarm algorithm to estimate the signal time delay and further improved the estimation accuracy using multi-band gain (Xu H, Ding F, Champagne B. Joint parameter and time-delay estimation for a class of nonlinear time-series models[J]. IEEE Signal Processing Letters, 2022, 29:947-951.). Chen et al. proposed a time delay estimation method based on weighted correlation entropy spectral density. The simulation results show that this method can achieve accurate estimation under both Gaussian noise and impulse noise with low signal-to-noise ratio.The above method is only applicable to the time delay estimation of a single signal and is no longer applicable to time-frequency overlapping multi-signals. Therefore, scholars have carried out further research on the time delay estimation problem of time-frequency overlapping multi-signals (Chen S H, Tu S L, Wan J, et al. A sequential Monte Carlo method for blind signal separation using the difference of time delays[C] / / TENCON 2007-2007 IEEE Region 10 Conference. IEEE, 2007:1-4.). Li et al. combined Bayesian inference with parameter estimation theory for the problem of blind parameter estimation in a single channel of a digital communication system and proposed a new time delay estimation method for time-frequency overlapping signals. This method can achieve the simultaneous estimation of two signals in a single channel, but it is easily affected by the carrier frequency offset of the signal (Li T, Hu R, Zhang Z, et al. A time delay estimation method of LFM hybrid signals based on hough transform[C] / / 2021 IEEE 5th Advanced Information Technology, Electronic and Automation Control Conference (IAEAC). IEEE, 2021, 5:1457-1460.).

[0005] Through the above analysis, the problems and defects of the existing technologies are as follows:

[0006] (1) The existing signal amplitude-time delay joint estimation methods cannot distinguish multiple signal components when time-frequency overlapping occurs, and most methods are only applicable to Gaussian noise. The estimation performance of signal amplitude and time delay seriously degrades in non-Gaussian noise fading channels.

[0007] (2) The existing methods for evaluating the performance of joint estimation results lack overall consideration and have poor system stability. Summary of the Invention

[0008] 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 multiple signals with time-frequency overlap under non-Gaussian noise; jointly estimate the signal amplitude and delay through the position and peak value of discrete spectral lines, use the PSO algorithm with dynamic inertia weight coefficient to search for the spectral peak position, and derive the Cramer-Rao bound for joint amplitude-delay estimation of multiple signals with time-frequency overlap under alpha-stable distribution noise for effectiveness evaluation, thereby improving the convergence speed and estimation performance.

[0009] To achieve the above purpose, the technical solution adopted by the present invention is as follows: A method for jointly estimating time-domain parameters of multiple signals with time-frequency overlap under non-Gaussian noise jointly estimates the signal amplitude and delay through the position and peak value of discrete spectral lines; uses the PSO algorithm with dynamic inertia weight coefficient to search for the spectral peak position; and derives the Cramer-Rao bound for joint amplitude-delay estimation of multiple signals with time-frequency overlap under alpha-stable distribution noise for effectiveness evaluation.

[0010] A method for jointly estimating time-domain parameters of multiple signals with time-frequency overlap under non-Gaussian noise is characterized by specifically including the following steps:

[0011] Step 1, jointly estimate the signal amplitude and delay through the position and peak value of discrete spectral lines;

[0012] Step 2, search for the spectral peak position in Step 1 using the PSO algorithm with dynamic inertia weight coefficient;

[0013] Step 3, perform effectiveness evaluation on the joint estimation result processed in Step 2 using the Cramer-Rao bound for joint amplitude-delay estimation of multiple signals with time-frequency overlap under alpha-stable distribution noise.

[0014] In the above Step 1, the process of jointly estimating the signal amplitude and delay through the position and peak value of discrete spectral lines is as follows:

[0015] Let a second-order cyclostationary random process {x(t); t ∈ (-∞, +∞)}, and its autocorrelation entropy function is defined as:

[0016] V x (t, τ) = E[κ σ (x(t) - x * (t + τ))]

[0017] where E[·] is the mathematical expectation, and κ σ (·) is the Gaussian kernel function, also called the Gaussian probability density function, and is defined in the following form:

[0018]

[0019] where σ is the kernel length of the Gaussian kernel function.

[0020] At any time t, take 2N + 1 points with an interval of T (i.e., the sampling period is T 0 = T s = T 0 ) of the second-order cyclostationary random process to perform time averaging on the autocorrelation function, then the autocorrelation function can be expressed as:

[0021]

[0022] where, is the duration of the signal x(t), N is the length of the data sequence, and T 0 is the sampling period.

[0023] Let N tend to infinity, that is:

[0024]

[0025] where ε is the cyclic frequency.

[0026] Perform Fourier transform on the cyclic correlation entropy function of the signal x(t), and its cyclic correlation entropy spectrum can be obtained. Its expression is:

[0027]

[0028] For the convenience of derivation, perform Taylor series expansion on the definition of the autocorrelation entropy function. Since the main characteristics of the cyclic correlation entropy are concentrated in its second-order statistics, the first two terms of the Taylor series expansion are taken for analysis, that is:

[0029]

[0030] and substitute it into the cyclic correlation entropy function to obtain

[0031]

[0032] where, is the cyclic autocorrelation function of the second-order stationary random process x(t).

[0033] and substitute it into the Fourier transform of the cyclic correlation entropy function to obtain

[0034]

[0035] where, is the cyclic spectrum of the second-order stationary random process x(t), is the cyclic autocorrelation function when the cyclic frequency is 0, and δ(f) is the impulse function.

[0036] S11. Joint estimation of time-domain parameters of multiple signals with time-frequency overlap under non-Gaussian noise for amplitude and time delay τ 0 for estimation;

[0037] S11.1. Take the cross-section of the cyclic correlation entropy spectrum at the spectral frequency f = 0 for analysis;

[0038] S11.2. Search for spectral peaks in the range near 2f c -B < ε < 2f c +B in the cross-section at the spectral frequency f = 0;

[0039] S11.3. Obtain the spectral peak value of the cyclic correlation entropy spectrum in the cross-section at the spectral frequency f = 0

[0040] S11.4. Substitute into the cyclic correlation entropy function to obtain the expression for estimating the amplitude of the time-frequency overlapping signal:

[0041]

[0042] S12.1. Take the cross-section of the cyclic correlation entropy spectrum at the spectral frequency f = f c for analysis; for analysis;

[0043] S12.2. Search for spectral peaks in the range near 1 / T c in the cross-section at the spectral frequency f = f b -B < ε < 1 / T b +B;

[0044] S12.3. Obtain the spectral peak value of the cyclic correlation entropy spectrum in the cross-section at the spectral frequency f = f c ;

[0045] S12.4. Substitute into the estimated value expression to calculate the initial time delay information τ 0 , and its estimated value expression is:

[0046]

[0047] In the second step described above, the PSO algorithm with a dynamic inertia weight coefficient is used to search for the spectral peak position. The specific process is as follows:

[0048] S21. Search for the spectral peak position based on the PSO algorithm with a dynamic inertia weight coefficient;

[0049] S22. Input the objective function, randomly initialize the particle swarm, set the maximum number of iterations to iter max , and set the velocity and position of the i-th particle to be and

[0050] S22. Calculate the fitness value of each particle;

[0051] S23. Update the velocity and position of each particle. The update expressions are:

[0052]

[0053] where t is the current iteration number, d is the dimension of the current search space, and are the velocity and position of the particle respectively. is the local optimal value of the particle, is the global optimal value of the particle swarm, and are two random numbers in the d-th dimension, whose range is within the interval [0, 1]. c 1 and c 2 are learning factors, which are used to adjust the influence of the particle's own experience and the overall experience of the particle swarm during the particle movement respectively. Their values are usually set as c 1 = c 2 = 2. ω is the inertia weight coefficient. A dynamic inertia weight coefficient is adopted, such as a linearly decreasing inertia weight coefficient. The linearly decreasing inertia weight coefficient in the t-th iteration can be expressed as:

[0054]

[0055] where ω ini is the initial value of the inertia weight coefficient, generally set as ω ini = 0.9; ω end is the termination value of the inertia weight coefficient when iterating to the maximum number of evolutionary generations, generally set as ω end = 0.4; iter max is the maximum number of iterations;

[0056] S24. Update the pbest of the particle and the gbest of the particle swarm;

[0057] S25. If the iteration number is equal to iter max , then output the global optimal value gbest of the particle swarm, that is, the spectral peak position;

[0058] S26. If the iteration number is not equal to iter max , then go to step S22;

[0059] S27. The global optimal solution obtained after the algorithm program is iterated for iter max times is the spectral peak position used for subsequent signal amplitude and time delay estimation.

[0060] In the third step, the effectiveness of the joint estimation result processed in the second step is evaluated using the Cramer-Rao bound of the amplitude-delay joint estimation of time-frequency overlapping multi-signals under alpha-stable distribution noise. The specific process is as follows:

[0061] Assume that the received time-frequency overlapping signal is interfered by alpha-stable distribution noise. Then, the mathematical model of the time-frequency overlapping received signal containing M signal components can be expressed as:

[0062]

[0063] Among them, the m-th signal component of the time-frequency overlapping signal can be expressed as:

[0064]

[0065] Among them, A m , f cm , τ m , T bm are respectively 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, 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, ω(t) is the alpha-stable distribution noise that is uncorrelated with each component of the transmitted signal. Since the probability density function of the alpha-stable distribution noise does not have a clear 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:

[0066]

[0067] Among them, γ and δ are respectively the scale parameter and the position parameter.

[0068] If the parameter vector to be estimated is expressed as λ = (λ 1 , λ 2 ... λ N ), Τ , then the probability density function of the received signal can be expressed as:

[0069]

[0070] Among them, K is the observation time, is the vector expression of the transmitted symbol.

[0071] For the convenience of solving, taking the logarithm on both sides of the probability density function of the received signal gives:

[0072]

[0073] Taking the partial derivative of the parameter to be estimated of the time-frequency overlapping signal, we can obtain:

[0074]

[0075] The element value F in the Fisher information matrix F ij (i, j = 1, 2,..., N) is expressed as:

[0076]

[0077] When the number of signal components is 2, the joint estimation vector λ of amplitude and time delay can be expressed as:

[0078] λ = (A 1 , τ 1 , A 2 , τ 2 ) Τ

[0079] Since the signal components of the time-frequency overlapping signal are uncorrelated with each other, when i = j, can be expressed as:

[0080]

[0081] When i ≠ j, can be expressed as:

[0082]

[0083] Therefore, the Fisher information matrix F can be expressed as:

[0084]

[0085] Among them,

[0086] By performing the inverse transformation, the modified Cramer-Rao bound of the amplitude and time-delay joint estimation vector λ = (A 1 , τ 1 , A 2 , τ 2 ) Τ is:

[0087]

[0088] Another object of the present invention is to provide a system for a method of jointly estimating time-domain parameters of time-frequency overlapping multi-signals under non-Gaussian noise, including:

[0089] The cyclic correlation entropy spectrum module is used to jointly estimate the signal amplitude and delay of time-frequency overlapping multi-signals in step one by using an amplitude-time delay joint estimation method based on cyclic correlation entropy spectrum;

[0090] The spectral peak search module is used to search for the spectral peak position by using the PSO algorithm with dynamic inertia weight coefficient in step two;

[0091] The efficiency evaluation module is used to evaluate the effectiveness of the joint estimation result by using the Cramer-Rao bound of amplitude-time delay joint estimation of time-frequency overlapping multi-signals under alpha-stable distribution noise in step three.

[0092] Combined with the above technical solutions, the advantages and positive effects of the present invention are as follows:

[0093] First, the present invention uses a method for jointly estimating time-domain parameters of time-frequency overlapping multi-signals under non-Gaussian noise, jointly estimating the signal amplitude and delay through the position and peak value of discrete spectral lines; using the PSO algorithm with dynamic inertia weight coefficient to search for the spectral peak position; deriving the Cramer-Rao bound of amplitude-time delay joint estimation of time-frequency overlapping multi-signals under alpha-stable distribution noise to evaluate the effectiveness; this invention fills the gap in this field.

[0094] Using the amplitude-time delay joint estimation method of time-frequency overlapping multi-signals based on cyclic correlation entropy can effectively distinguish time-frequency overlapping signals containing multiple signal components, and jointly estimate the signal amplitude and delay through the position and peak value of discrete spectral lines.

[0095] The proposed PSO algorithm with dynamic inertia weight coefficient for spectral peak position search can enhance the global and local search capabilities and is not easily trapped in the local optimum.

[0096] The proposed modified MCRB for evaluating the effectiveness of parameter estimation can comprehensively and accurately judge the performance of the method of the present invention.

[0097] The research of the present invention should focus on developing signal parameter estimation algorithms with faster convergence speed, better estimation performance, and more thorough suppression of non-Gaussian noise; the present invention explores the use of the PSO particle swarm algorithm technology with dynamic inertia weight coefficient, which can jointly estimate the amplitude and delay of time-frequency overlapping multi-signals; the present invention proposes a modified MCRB to evaluate the effectiveness of parameter estimation, which can comprehensively and accurately judge the performance of the method of the present invention.

[0098] In summary, compared with the prior art, the present invention explores the spectral peak search problem of the dynamic inertia weight PSO algorithm, emphasizing the importance of solving the spectral peak search problem of the PSO algorithm for the parameter estimation method of time-frequency overlapping multi-signals; any amplitude-delay joint estimation task involving time-frequency overlapping multi-signals can use the present invention for estimation; the use of the PSO search algorithm with a dynamic inertia weight coefficient further improves the speed and accuracy of spectral peak search; the present invention has better performance and wider generality.

[0099] Second, the processing of time-frequency overlapping multi-signals in the current non-Gaussian noise environment faces the problem of insufficient accuracy in signal amplitude and delay estimation. Especially in the scenario of complex noise interference and multi-signal overlap, traditional methods often have difficulty effectively distinguishing the characteristics of each signal. In addition, the existing technology has low search efficiency for the spectral peak position and is prone to falling into local optima, resulting in slow algorithm convergence speed and unstable estimation results. These problems limit the high-precision processing requirements for multi-signals in fields such as radar and communication.

[0100] The present invention significantly improves the efficiency and accuracy of spectral peak position search through the particle swarm optimization (PSO) algorithm with a dynamic inertia weight coefficient. At the same time, by combining cyclic correlation entropy with the characteristics of non-Gaussian noise distribution, a new method for joint estimation of signal amplitude and delay is proposed, greatly improving the estimation accuracy. In addition, the alpha-stable distribution model is used to calculate the Cramer-Rao bound to theoretically verify the effectiveness of the estimation method, thus providing a reliable guarantee for high-precision parameter estimation in complex signal environments.

[0101] The technical solution of the present invention has broad industrial application potential and is particularly suitable for scenarios such as radar signal processing, wireless communication demodulation, and multi-signal feature extraction. In these fields, the present invention significantly improves the signal detection ability and anti-noise performance of the system, and solves the problems of false detection and missed detection that are prone to occur in the traditional method in the non-Gaussian noise environment. At the same time, by optimizing the algorithm, the calculation time and resource consumption are reduced, providing an efficient solution for real-time signal processing in complex environments, and having significant economic value and technological driving force.

[0102] Third, the traditional parameter estimation method for time-frequency overlapping multi-signals shows problems of poor adaptability and low accuracy in the non-Gaussian noise environment. Especially the signal amplitude and delay estimation in the complex noise background are easily interfered, resulting in unstable results. In addition, existing spectral peak search algorithms such as the static PSO algorithm have low efficiency in the multi-dimensional search space and are prone to falling into local optima, unable to meet the requirements of high-dimensional parameter estimation tasks for accuracy and efficiency. These problems seriously restrict the application of multi-signal parameter estimation technology in practical scenarios such as radar and communication.

[0103] The present invention improves the spectral peak search efficiency and accuracy through a PSO algorithm with a dynamic inertia weight coefficient, realizes fast global optimization in a complex search space, and significantly enhances the algorithm convergence speed. Meanwhile, a cyclic correlation entropy model and an alpha-stable distribution are introduced to optimize specifically for a non-Gaussian noise environment, ensuring higher robustness and accuracy in the joint estimation of signal amplitude and time delay under a strong noise background. In addition, the effectiveness of the estimation result is verified by deriving and correcting the Cramer-Rao bound, providing a theoretical guarantee for the algorithm.

[0104] The algorithms and mathematical models of the present invention effectively solve the bottleneck problem of multi-signal time-frequency overlap processing in a non-Gaussian noise environment, and have strong adaptability and high efficiency. Its application scenarios are extensive, including radar signal detection, wireless communication system demodulation, electronic countermeasure, and multi-sensor data fusion and other fields. This technical solution not only improves the performance of the signal processing system, but also reduces the computational complexity, meets the real-time requirements, and provides an advanced solution for high-precision and noise-resistant parameter estimation in a multi-signal environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Figure 1 is a flowchart of a method, system, medium, and device for jointly estimating time-domain parameters of multi-signal time-frequency overlap under non-Gaussian noise provided by an embodiment of the present invention.

[0106] Figure 2 is a schematic structural diagram of a system for jointly estimating amplitude-time delay of multi-signal time-frequency overlap based on cyclic correlation entropy spectrum provided by an embodiment of the present invention;

[0107] Figure 2 In the figure: 1. Cyclic correlation entropy spectrum module; 2. Spectral peak search module; 3. Efficiency evaluation module.

[0108] Figure 3 is a schematic diagram of the simulation experiment results of the comparison of the PSO algorithm search performance of the system for jointly estimating amplitude-time delay of multi-signal time-frequency overlap based on cyclic correlation entropy spectrum provided by an embodiment of the present invention under different generalized signal-to-noise ratios.

[0109] Figure 4 is a schematic diagram of the simulation experiment results of the comparison of the estimation performance of amplitude and time delay of the system for jointly estimating amplitude-time delay of multi-signal time-frequency overlap based on cyclic correlation entropy spectrum provided by an embodiment of the present invention under different power ratios.

[0110] Figure 5 is a schematic diagram of the simulation experiment results of the comparison of the estimation performance of amplitude and time delay of the system for jointly estimating amplitude-time delay of multi-signal time-frequency overlap based on cyclic correlation entropy spectrum provided by an embodiment of the present invention under different sampling data lengths.

[0111] Figure 6It is a schematic diagram of the simulation experimental results of comparing the estimation performance of amplitude and time delay under different spectral overlap degrees of the amplitude-time delay joint estimation system for time-frequency overlapping multi-signals based on cyclic correlation entropy spectrum provided by the embodiments of the present invention.

[0112] Figure 7 It is a schematic diagram of the simulation experimental results of comparing the estimation performance of amplitude and time delay of different methods of the amplitude-time delay joint estimation system for time-frequency overlapping multi-signals based on cyclic correlation entropy spectrum provided by the embodiments of the present invention. Specific embodiments

[0113] In order to make the objectives, technical solutions and advantages of the present invention clearer, 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.

[0114] Application Embodiment 1: Radar signal processing

[0115] In the radar target detection in complex environments, signals are often interfered by non-Gaussian noises (such as clutter noise and external interference). The method of the present invention can effectively improve the resolution and accuracy of target signals by jointly estimating the amplitude and time delay parameters of time-frequency overlapping radar signals under non-Gaussian noise backgrounds.

[0116] Actual application scenario: Multiple radar transmitters work simultaneously, and signals are superimposed at the receiving end and interfered by environmental noises. By using this method, the spectral peak position is optimized through the PSO algorithm with dynamic inertia weight, the effective signal features are extracted, and the target distance and speed are estimated.

[0117] Expected effect: Improve the detection accuracy of multi-target radar signals, reduce the false detection rate and missed detection rate caused by noises, and provide more reliable data support for real-time radar monitoring and navigation.

[0118] Application Embodiment 2: Signal demodulation of wireless communication systems

[0119] In wireless communication systems, especially in environments with tight spectral resources, time-frequency overlapping phenomena frequently occur for multiple signals, and they are also affected by non-Gaussian distributed noises. The method of the present invention can be used for the joint estimation of the amplitude and time delay of wireless signals to optimize the demodulation performance of communication systems.

[0120] Actual application scenario: In cellular communication, multiple users share spectral resources. The signals at the receiving end are time-frequency overlapping and the noises have the characteristics of alpha-stable distribution. This method estimates the time-domain parameters of signals through cyclic correlation entropy and the PSO algorithm, so as to realize the separation and recovery of multi-user signals.

[0121] Expected effect: Improve the demodulation ability of the communication system, increase the channel utilization rate in a multi-user sharing environment, reduce the system bit error rate, and provide technical support for 5G and future 6G communication networks.

[0122] 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 under non-Gaussian noise. The present invention will be described in detail below with reference to the accompanying drawings.

[0123] Those of ordinary skill in the art in the industry can also implement the method, system, medium and device for jointly estimating time-domain parameters of time-frequency overlapping multi-signals under non-Gaussian noise provided by the present invention by using other steps. Figure 1 The method, system, medium and device for jointly estimating time-domain parameters of time-frequency overlapping multi-signals under non-Gaussian noise provided by the present invention are only a specific embodiment.

[0124] As Figure 1 shown, the amplitude-delay joint estimation of time-frequency overlapping multi-signals based on cyclic correlation entropy spectrum provided by the embodiment of the present invention is specifically as follows:

[0125] Step 1: Jointly estimate the signal amplitude and delay through the position and peak of the discrete spectral line. The specific process is as follows:

[0126] Let a second-order cyclostationary random process {x(t); t ∈ (-∞, +∞)}, and its autocorrelation entropy function is defined as:

[0127] V x (t, τ) = E[κ σ (x(t) - x * (t + τ))]

[0128] where E[·] is the mathematical expectation, and κ σ (·) is the Gaussian kernel function, also called the Gaussian probability density function, and is defined in the following form:

[0129]

[0130] where σ is the kernel length of the Gaussian kernel function.

[0131] For any time t, take 2N + 1 points of the second-order cyclostationary random process with an interval of T 0 (i.e., the sampling period is T s = T 0 ) to perform time averaging on the autocorrelation function. Then the autocorrelation function can be expressed as:

[0132]

[0133] where is the duration of the signal x(t), N is the length of the data sequence, and T 0 is the sampling period.

[0134] Let N approach infinity, that is:

[0135]

[0136] where ε is the cyclic frequency.

[0137] For the cyclic correlation entropy function of the signal x(t) Performing a Fourier transform, its cyclic correlation entropy spectrum can be obtained Its expression is:

[0138]

[0139] For the convenience of derivation, the definition of the autocorrelation entropy function is expanded by Taylor series. Since the main characteristics of the cyclic correlation entropy are concentrated in its second-order statistics, the first two terms of the Taylor series expansion are taken for analysis, that is:

[0140]

[0141] And substituting it into the cyclic correlation entropy function, we can get

[0142]

[0143] where is the cyclic autocorrelation function of the second-order stationary random process x(t).

[0144] And substituting it into the Fourier transform of the cyclic correlation entropy function, we can get

[0145]

[0146] where is the cyclic spectrum of the second-order stationary random process x(t), is the cyclic autocorrelation function when the cyclic frequency is 0, and δ(f) is the impulse function.

[0147] S11. The method for jointly estimating the time-domain parameters of multiple signals with time-frequency overlap under non-Gaussian noise estimates the amplitude and the time delay τ 0 ;

[0148] S11.1. Take the cross-section of the cyclic correlation entropy spectrum at the spectral frequency f = 0 for analysis;

[0149] S11.2. Search for the spectral peaks in the range near 2f c -B < ε < 2f c +B in the cross-section of the spectral frequency f = 0;

[0150] S11.3. Obtain the spectral peak value of the cyclic correlation entropy spectrum at the spectral frequency f = 0 cross-section

[0151] S11.4. Substitute into the cyclic correlation entropy function to obtain the expression for estimating the amplitude of the time-frequency overlapping signal:

[0152]

[0153] S12.1. Take the cross-section of the cyclic correlation entropy spectrum at the spectral frequency f = f c for analysis; Perform analysis;

[0154] S12.2. Search for the spectral peak within the range near 1 / T c - B < ε < 1 / T b - B < ε < 1 / T b + B in the cross-section at the spectral frequency f = f

[0155] S12.3. Obtain the spectral peak value of the cyclic correlation entropy spectrum at the spectral frequency f = f c cross-section

[0156] S12.4. Substitute into the estimation value expression to calculate the initial time delay information The expression for its estimated value is:

[0157]

[0158] In step two, the PSO algorithm with a dynamic inertia weight coefficient is used to search for the spectral peak position. The specific process is as follows:

[0159] S21. Search for the spectral peak position based on the PSO algorithm with a dynamic inertia weight coefficient;

[0160] S22. Input the objective function, randomly initialize the particle swarm, and set the maximum number of iterations to Let the th particle's velocity and position be set to and

[0161] S22. Calculate the fitness value of each particle;

[0162] S23. Update the velocity and position of each particle. The update expressions are:

[0163]

[0164] Among them, is the current iteration number, is the dimension of the current search space, and The velocity and position of individual particles. Is the local optimum value of the particle, Is the global optimum value of the particle swarm, And Are respectively the Two random numbers in the dimension, whose range is within Interval, And Are learning factors, which are respectively used to adjust the influence of the experience of the particle itself and the experience of the whole particle swarm during the particle movement. Their values are usually set to Is the inertia weight coefficient. A dynamic inertia weight coefficient is adopted, such as a linearly decreasing inertia weight coefficient. In the The linearly decreasing inertia weight coefficient in the i-th iteration can be expressed as:

[0165]

[0166] Among them, Is the initial value of the inertia weight coefficient, generally set to Is the termination value of the inertia weight coefficient when it iterates to the maximum number of evolutionary generations, generally set to Is the maximum number of iterations;

[0167] S24. Update the Of the particle and the

[0168] S25. If the number of iterations is equal to Then output the global optimum value of the particle swarm That is, the spectral peak position;

[0169] S26. If the number of iterations is not equal to Then enter step S22;

[0170] S27. The global optimum solution obtained after the algorithm program has been Iterations is the spectral peak position used for subsequent signal amplitude and delay estimation.

[0171] In step three, the effectiveness of the joint estimation result processed in step two is evaluated using the Cramer-Rao bound for joint amplitude-delay estimation of time-frequency overlapping multiple signals under alpha-stable distribution noise. The specific process is as follows:

[0172] Assume that the received time-frequency overlapping signal is interfered by alpha-stable distribution noise. Then the mathematical model of the time-frequency overlapping received signal containing Signal components can be expressed as:

[0173]

[0174] Among them, the th signal component of the time-frequency overlapping signal can be expressed as:

[0175]

[0176] Among them, are respectively the th signal component's amplitude, carrier frequency, time delay, and symbol period (the reciprocal of which is the symbol rate ), is the initial phase, is an independent and identically distributed data symbol sequence, is the length of the data sequence transmitted by the th signal component, is the shaping function, is the overall gain of the multipath fading channel of is the alpha-stable distribution noise that is uncorrelated with each component of the transmitted signal. Since the probability density function of the alpha-stable distribution noise does not have an explicit closed expression, the characteristic parameter is taken, that is, the noise distribution is approximated by the Cauchy distribution, and its probability function can be described as:

[0177]

[0178] Among them, and are respectively the scale parameter and the location parameter.

[0179] If the vector of parameters to be estimated is expressed as then the probability density function of the received signal can be expressed as:

[0180]

[0181] Among them, is the observation time, is the vector expression of the transmitted symbol.

[0182] For the convenience of solution, taking the logarithm of both sides of the probability density function of the received signal gives:

[0183]

[0184] Taking the partial derivative with respect to the parameters to be estimated of its time-frequency overlapping signal gives:

[0185]

[0186] The elements in the Fisher information matrix are expressed as:

[0187]

[0188] When the number of signal components is 2, the joint estimation vector of amplitude and time delay can be expressed as:

[0189]

[0190] Since the signal components of the time-frequency overlapping signals are uncorrelated with each other, when time, can be expressed as:

[0191]

[0192] When time, can be expressed as:

[0193]

[0194] Therefore, the Fisher information matrix can be expressed as:

[0195]

[0196] where

[0197] By performing an inverse transformation, the modified Cramer-Rao bound of the joint estimation vector of amplitude and time delay is:

[0198]

[0199] As Figure 2 shown, the time-frequency overlapping multi-signal amplitude-time delay joint estimation system based on cyclic correlation entropy spectrum provided by the embodiments of the present invention includes:

[0200] A cyclic correlation entropy spectrum module 1, configured to perform joint estimation of signal amplitude and time delay on time-frequency overlapping multi-signals by using a method for joint estimation of amplitude and time delay based on cyclic correlation entropy spectrum in step one;

[0201] A spectral peak search module 2, configured to search for the spectral peak position by using a PSO algorithm with a dynamic inertia weight coefficient in step two;

[0202] An efficiency evaluation module 3, configured to evaluate the effectiveness of the joint estimation result by using the Cramer-Rao bound of the amplitude-time delay joint estimation of time-frequency overlapping multi-signals under alpha-stable distribution noise in step three.

[0203] The parameter estimation method provided by the present invention can be used for joint estimation of the amplitude and time delay of time-frequency overlapping multi-signals based on cyclic correlation entropy spectrum.

[0204] The technical effects of the present invention will be described in detail below in combination with simulation experiments.

[0205] To evaluate the performance of the present invention, simulation verification is carried out. In the simulation experiment, a time-frequency overlapping multi-signal amplitude-delay joint estimation system based on cyclic correlation entropy spectrum is considered. The specific parameters set in the simulation experiment are as follows: The types of time-frequency overlapping signal components used in the simulation are BPSK, QPSK, and 16QAM digital modulation signals respectively; 500 Monte Carlo simulations are carried out for each experiment; The performance evaluation criterion of the parameter estimation method is the normalized root mean square error, that is, NRMSE; The background noise uses alpha-stable distribution noise. Since the alpha-stable distribution model does not have a finite second moment, therefore, the scale parameter of the noise based on alpha-stable distribution and the variance of the signal Redefine the traditional signal-to-noise ratio as the Generalized Signal-to-Noise Ratio (GSNR), which can be expressed as:

[0206]

[0207] To further verify the spectrum peak search performance of the algorithm, the search accuracy of the algorithm at different generalized signal-to-noise ratios is evaluated by changing the generalized signal-to-noise ratio. Among them, the search accuracy is defined as:

[0208]

[0209] Among them, is the number of accurate searches, is the number of simulation experiments.

[0210] Set the symbol rates of the two signal components in the time-frequency overlapping signal to be and The carrier frequencies are respectively and The sampling frequency is The generalized signal-to-noise ratio varies between -10 dB and 15 dB, and the change step is 5 dB. The power ratios of the main signal component to the auxiliary signal component are 1:1, 1:2, and 1:4 respectively; The length of the sampled data varies between 2000 and 7000, and the change step is 1000.

[0211] Define the spectrum overlap degree of the time-frequency overlapping multi-signal as:

[0212]

[0213] Among them, is the spectrum width of the first signal component, is the spectral width of the second signal component, is the spectral width of the overlapping part of the two signals.

[0214] The spectral overlap degrees are 0%, 20%, 40%, 60%, 80%, and 100%, that is, the carrier frequencies of the two signal components are respectively and and and and and and

[0215] Figure 3 shows the comparison of search performances under different generalized signal-to-noise ratios. From Figure 3 it can be seen that the search accuracy increases with the increase of the generalized signal-to-noise ratio. When the generalized signal-to-noise ratio is greater than 0 dB, the search accuracy of this algorithm stabilizes above 90%. When the generalized signal-to-noise ratio is 15 dB, the search accuracy is close to 100%. Therefore, this algorithm has good search performance and can be used to implement the spectral peak search of the cyclic correlation entropy spectrum. Figure 4 shows the comparison of the success rates of frequency modulation slope estimation by different methods. Figure 4 shows the comparison of the estimation performances of amplitude and time delay under different power ratios. From Figure 4 (a) it can be seen that when the power ratio of the main signal component to the auxiliary signal component is 1:1, the amplitude estimation performance based on the cyclic correlation entropy spectrum is the best. When the power ratio is 1:4, the amplitude estimation performance is the worst. When the generalized signal-to-noise ratio is 5 dB, its NRMSE is As the power ratio decreases, the amplitude estimation performance deteriorates. This is because when the power ratio is low, the power of the auxiliary signal component is large, resulting in the power of the main signal component being easily interfered by the spectral leakage and noise of the auxiliary signal component, thus generating a large estimation error. From Figure 4 (b) it can be seen that when the power ratios are 1:1 and 1:2, the estimation performances are good and relatively close. When the generalized signal-to-noise ratio is 5 dB, its NRMSE is When the power ratio is 1:4, the estimation performance is slightly worse, but the gap is not obvious. Therefore, although the time delay estimation performance is also affected by the power ratio, compared with the amplitude estimation, this influence is smaller because the time delay estimation only needs to accurately find the spectral line position without obtaining the exact spectral peak value, and the change of the power ratio has less interference on the spectral line position and spectral line interval, so the estimation performance changes less significantly compared with the amplitude estimation. Figure 5 shows the comparison of the estimation performances of amplitude and time delay under different sampling data lengths. From Figure 5It can be seen that as the length of the sampled data increases, the NRMSEs of the amplitude estimation and time-delay estimation for multi-signals with time-frequency overlap both gradually decrease. This is because the cyclic correlation entropy spectrum has an asymptotic cyclostationary property. When the length of the sampled data is less than 5000, the performance of the amplitude estimation and time-delay estimation deteriorates severely. This is because when the length of the sampled data is too low, the resolution of the cyclic correlation entropy spectrum decreases, resulting in a significant decline in the performance of the amplitude-time delay joint estimation method based on spectral line features. When the length of the sampled data is greater than 5000, the estimation performance of this method tends to be stable, that is, the spectral resolution approaches saturation, and the NRMSEs of the amplitude and time-delay estimations are respectively stable at and or so. Therefore, appropriately increasing the length of the sampled data can effectively improve the performance of the amplitude-time delay joint estimation method based on the cyclic correlation entropy spectrum. Figure 6 shows the comparison of the estimation performance of the amplitude and time-delay under different spectral overlap degrees. From Figure 6 it can be seen that the higher the spectral overlap degree, the greater the estimation errors of the amplitude and time-delay. This is because the increase in the spectral overlap degree makes the spectral line intervals become more dense. If the resolution accuracy is insufficient, it will cause the overlap of spectral lines, thus deteriorating the estimation performance. However, on the premise of meeting a certain resolution accuracy and the length of the sampled data sequence, as long as the symbol rates of each signal component are different and there is no integer multiple relationship, it is still possible to accurately estimate the amplitude and time-delay of the time-frequency overlap signals. Therefore, the simulation results show that this method is less affected by the spectral overlap degree and has strong stability. Figure 7 shows the comparison of the amplitude and time-delay estimation performance of different methods. From Figure 7 it can be seen that the amplitude and time-delay estimation performances of the method proposed in the present invention and the cyclic spectrum method both improve with the increase of the generalized signal-to-noise ratio. However, the estimation performance of the method proposed in the present invention is better than that of the cyclic spectrum method. When the generalized signal-to-noise ratio is greater than or equal to 0 dB, the method proposed in the present invention has good estimation performance. When the generalized signal-to-noise ratio is greater than or equal to 5 dB, the NRMSE of the time-delay estimation is less than or equal to and the estimation performance is close to its MCRB. When the generalized signal-to-noise ratio is greater than or equal to 10 dB, the NRMSE of the amplitude estimation is less than or equal to and the estimation performance is close to its MCRB, which proves the effectiveness of the method proposed in the present invention for amplitude and time-delay estimations.

[0216] 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 a suitable 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, for example, such code is 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.

[0217] 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 modification, equivalent replacement, and improvement made within the spirit and principle of the present invention by those skilled in the art within the technical scope disclosed by 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 multi-signals with time-frequency overlap under non-Gaussian noise, characterized in that: The method includes: Based on the position and peak value of the discrete spectral lines, the amplitude and delay of the signal are jointly estimated; The particle swarm optimization (PSO) algorithm with dynamic inertia weight coefficient is used to search for the peak position; Calculate the joint estimation correction value of signal amplitude and delay, and verify the validity of the joint estimation result; In a non-Gaussian noise environment, the accuracy of the joint estimate is evaluated by deriving a modified Cramer-Rao bound.

2. The method for joint estimation of time domain parameters of time-frequency overlapping multi-signals under non-Gaussian noise as claimed in claim 1, characterized in that: The signal amplitude and delay are estimated by cyclic correlation entropy spectrum, including the following steps: In a fixed frequency cross section, the local maximum of the cyclic correlation entropy spectrum is extracted by analyzing the peak position of the spectrum. Substitute the extracted local maximum into the correlation entropy function to calculate the estimated value of the amplitude; An estimate of the initial delay is determined based on an expression derived from the cyclic correlation entropy function.

3. The method for joint estimation of time domain parameters of time-frequency overlapping multi-signals under non-Gaussian noise as claimed in claim 1, characterized in that: The particle swarm optimization algorithm uses a dynamic inertia weight coefficient to optimize the search for the spectral peak position, including: Initialize the velocity and position of the particle swarm; According to the historical optimal solution and global optimal solution of the individual particle swarm, the movement direction of each particle is dynamically adjusted; Use a linearly decreasing inertia weight coefficient to control the particle velocity update in each iteration; After reaching the maximum number of iterations, the global optimal solution of the particle swarm is output as the optimal estimate of the spectral peak position.

4. The method for joint estimation of time domain parameters of time-frequency overlapping multi-signals under non-Gaussian noise according to claim 1, characterized in that: Based on the mathematical model of the signal, a modified Cramer-Rao bound for joint estimation is constructed, including: The joint distribution density of the amplitude, delay and other parameters of the expression signal; Take partial derivatives of the logarithmic function of the joint distribution density and construct the Fisher information matrix; The Fisher information matrix is ​​inversely transformed to obtain a revised lower bound for the joint estimation of amplitude and delay.

5. The method for joint estimation of time domain parameters of time-frequency overlapping multi-signals under non-Gaussian noise according to claim 1, characterized in that: The modified Cramer-Rao bound is calculated in a non-Gaussian noise environment, using an approximate description of the alpha stable distribution, specifically including: Construct a noisy model based on the multipath fading characteristics of the signal; Express the noise distribution through an approximate probability density function; Constraints are imposed on the joint estimation parameters of the signals, and their theoretical lower bounds are derived.

6. The method for joint estimation of time domain parameters of time-frequency overlapping multi-signals under non-Gaussian noise according to claim 1, characterized in that: Dynamic weights and multi-dimensional optimization strategies are used to iteratively correct the amplitude and delay of the signal, including: Iteratively update the amplitude parameter of the signal according to the initial estimate; Substitute the corrected amplitude parameter into the delay model to update the delay estimate; The robustness and accuracy of the estimate are evaluated after each revision until the preset conditions are met.

7. A system for joint estimation of time domain parameters of multi-signals with time-frequency overlap under non-Gaussian noise, characterized in that: The system includes: A signal acquisition module, used to acquire a received signal containing multiple signals with time-frequency overlap; The feature extraction module is used to perform cyclic correlation entropy analysis on the received signal, extract the spectral line position and peak value, and calculate the initial estimation value of the signal amplitude and delay; The optimization search module is connected with the feature extraction module, and uses the particle swarm optimization algorithm with dynamic inertia weight coefficient to perform a global search for the spectrum peak position and output the optimal spectrum peak position; The validity verification module is connected with the optimization search module, calculates the joint estimation value of signal amplitude and delay based on the alpha stable distribution model, and evaluates the estimation result through the modified Cramer-Rao bound; The result output module is connected with the validity verification module and is used to output the optimized signal amplitude and delay joint estimation result.

8. The system of claim 1, wherein: The signal acquisition module comprises: A signal input unit, used for receiving a noisy signal; The preprocessing unit performs filtering, noise reduction and normalization on the received signal to extract the input data required for the cyclic correlation entropy spectrum.

9. The system according to claim 1, characterized in that The feature extraction module further comprises: A spectrum frequency section analysis unit, used for searching for a local maximum value within a fixed spectrum frequency section and extracting a spectrum peak value; The preliminary estimation unit calculates the initial estimation values ​​of the signal amplitude and delay according to the extracted spectrum peak value, and passes them to the optimization search module.

10. The system according to claim 1, wherein: The optimization search module includes: Initialization unit, used to randomly generate the initial velocity and position of the particle swarm; Dynamic weight update unit, which adjusts the particle movement speed through the linearly decreasing inertia weight coefficient to control the convergence rate of the particle swarm; The global optimal solution calculation unit is used to iteratively update the particle swarm position and calculate the global optimal spectrum peak position as an input parameter for subsequent joint estimation.

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