Joint estimation method of time and frequency difference between multi-antenna signals in distributed systems

Abstract

The embodiments of the present application relate to the field of communication technology, and in particular to a method for jointly estimating time and frequency differences between multi-antenna signals in a distributed system. The method comprises: optimizing and solving a variational mode decomposition algorithm using a QPSO algorithm to obtain an optimal solution for the number of decomposition layers and an optimal solution for a penalty factor; performing variational mode decomposition on a received signal based on the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor to obtain multiple IMF components; calculating the variance contribution rate of each IMF component respectively, and filtering out IMF components whose variance contribution rate is less than a first preset threshold; performing wavelet threshold processing on each retained IMF component; performing signal reconstruction based on each IMF component after wavelet threshold processing, calculating the conjugate ambiguity function of the reconstructed received signal, and performing peak detection on the conjugate ambiguity function to estimate the time delay difference and frequency difference between multi-antenna signals in the distributed system. The method can achieve high-precision joint estimation of time and frequency differences.

Description

Technical Field

[0001] The embodiments of the present application relate to the field of communication technology, and in particular to a method for jointly estimating time and frequency differences between multi-antenna signals in a distributed system. Background Art

[0002] The antenna arrays of each receiving device within a distributed system are randomly arranged and irregularly shaped. Antenna types, orientations, and receiver channel characteristics vary, and Doppler shift affects the center frequency fluctuations of the received signal. Consequently, significant arrival time and frequency differences can occur between different array elements within a distributed system. Estimating and compensating for these differences is crucial and challenging for achieving effective synthesis.

[0003] Currently, research teams at home and abroad have proposed several methods for estimating and compensating for delay and frequency differences between signals. One approach involves separately estimating and compensating for delay and frequency differences. Traditional delay estimation methods include: delay estimation based on blind separation techniques, variable-step-size LMS algorithms, generalized quadratic cross-correlation algorithms based on sparse Fourier transforms, and minimum mean square delay estimation algorithms. For frequency estimation and compensation, a common approach is to approximate a single-tone sinusoidal signal using conjugate point products. In this case, the sinusoidal signal frequency is the frequency difference between the two signals, which is then converted into a frequency estimation problem for the single-tone sinusoidal signal. Traditional frequency estimation methods include: sinusoidal signal frequency estimation algorithms based on interpolation between fast Fourier transforms and discrete-time Fourier transforms, FFT frequency offset estimation algorithms based on interpolation and binary search, improved Rife algorithms, and fine frequency offset estimation algorithms based on reference signal construction and binary search. However, all of these methods rely on independent parameter estimation and compensation, which can incur additional algorithmic overhead due to parameter decoupling and even negatively impact parameter estimation performance.

[0004] Another estimation method is the joint estimation of time-frequency differences (TFDs) based on the dual relationship between arrival time difference and frequency difference. The mutual ambiguity function, a classic algorithm used in time-frequency analysis, is able to achieve accurate estimations while maintaining computational complexity under conditions of high signal-to-noise ratio and high sampling rate. However, because this method performs a grid search in parameter space, it can only obtain estimates for integer multiples of the sampling interval. Other methods include methods using the maximum likelihood joint estimation model based on importance sampling, joint estimation algorithms for time-frequency differences for sparse signals in the frequency domain, improved maximum likelihood joint estimation models based on the Markov chain Monte Carlo method, and joint estimation algorithms for time-frequency differences based on fractional low-order cyclostationarity.

[0005] The above-mentioned time-frequency difference estimation methods are mostly simulated and designed under non-correlated noise. However, the actual communication environment is very complex nowadays and is affected by correlated noise. The use of the above-mentioned methods may lead to inaccurate estimation results.

[0006] Through the above analysis, the time difference and frequency difference estimation methods currently proposed still have the following defects.

[0007] First, most of the current distributed signal parameter difference estimation technologies focus on independent estimation of time difference and frequency difference, which does not fully utilize the characteristics of collaborative reception of distributed systems, nor does it fully utilize the time-frequency duality relationship between received signals.

[0008] Second, most of the current methods for estimating parameter differences between distributed signals consider the influence of uncorrelated noise, and lack research on the joint estimation of time-frequency differences under the influence of uncorrelated noise. Summary of the Invention

[0009] To solve the above technical problems, an embodiment of the present application proposes a method for jointly estimating the time difference and frequency difference between multi-antenna signals in a distributed system, which can effectively avoid the problem of under-decomposition or over-decomposition of the signal during variational mode decomposition, and can effectively avoid the false filtering of useful signals, and has a good denoising effect, thereby realizing high-precision joint estimation of time difference and frequency difference.

[0010] To achieve the above-mentioned objectives, an embodiment of the present application provides a method for jointly estimating the time difference and frequency difference between multi-antenna signals in a distributed system, the method comprising the following steps: optimizing and solving the variational mode decomposition algorithm using the QPSO algorithm to obtain the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor, performing variational mode decomposition on the received signal based on the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor to obtain multiple IMF components; calculating the variance contribution rate of each IMF component respectively, and filtering out the IMF components whose variance contribution rate is less than a first preset threshold; performing wavelet threshold processing on the retained IMF components; performing signal reconstruction based on the IMF components after wavelet threshold processing, calculating the conjugate ambiguity function of the reconstructed received signal, and performing peak detection on the conjugate ambiguity function to estimate the time delay difference and frequency difference between the multi-antenna signals in the distributed system.

[0011] To achieve the above-mentioned objectives, an embodiment of the present application also provides a system for jointly estimating time difference and frequency difference between multi-antenna signals in a distributed system, the system comprising: an IMF component acquisition module, configured to optimize and solve the variational mode decomposition algorithm using a QPSO algorithm, obtain the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor, and perform variational mode decomposition on the received signal based on the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor to obtain multiple IMF components; an IMF component filtering module, configured to respectively calculate the variance contribution rate of each IMF component and filter out the IMF components whose variance contribution rate is less than a first preset threshold; a wavelet threshold processing module, configured to perform wavelet threshold processing on the retained IMF components; a joint time difference and frequency difference estimation module, configured to perform signal reconstruction based on the IMF components after wavelet threshold processing, calculate the conjugate ambiguity function of the reconstructed received signal, and perform peak detection on the calculated conjugate ambiguity function to estimate the time delay difference and frequency difference between the multi-antenna signals in the distributed system.

[0012] To achieve the above-mentioned purpose, an embodiment of the present application also provides an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute a method for jointly estimating time and frequency differences between multiple antenna signals in a distributed system as described above.

[0013] To achieve the above-mentioned purpose, an embodiment of the present application further provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it can implement a method for jointly estimating time and frequency differences between multi-antenna signals in a distributed system as described above.

[0014] In some optional embodiments, before using the QPSO algorithm to optimize and solve the variational mode decomposition algorithm, the method further includes:

[0015] Obtain two received signals and establish a signal model for the two received signals. There is both a time delay difference and a frequency difference between the two received signals. The established signal model is expressed by the formula:

[0016] ;

[0017] in, Indicates the first channel receiving signal, Indicates the second channel receiving signal, Indicates the amplitude attenuation of the first received signal during the propagation process, Indicates the amplitude attenuation of the second-channel received signal during the propagation process. Represents the useful signal radiated by the radiation source, Indicates the time delay of the first received signal transmission, Indicates the time delay of the second receiving signal transmission, represents the additive Gaussian noise added to the first received signal. represents the additive Gaussian noise added to the second received signal;

[0018] The first receiving signal As a reference signal, the signal model is simplified. The simplified signal model is expressed by the formula:

[0019] ;

[0020] / ;

[0021] ;

[0022] in, is the attenuation coefficient ratio, is the delay difference between the two received signals to be determined, is the frequency difference between the two received signals to be determined.

[0023] In some optional embodiments, after simplifying the signal model, the method further includes:

[0024] The fitness function is designed to be the ratio of the envelope entropy and the kurtosis value;

[0025] The calculation formula of envelope entropy is:

[0026] ;

[0027] ;

[0028] in, represents the envelope entropy, is the total number of IMF components obtained by variational mode decomposition, represents the first The envelope signal of the IMF components after Hilbert demodulation;

[0029] The calculation formula of the kurtosis value is:

[0030] ;

[0031] in, represents the kurtosis value, represents the total number of discrete points in the discrete sequence, Indicates the first discrete sequence of time domain waveforms The vibration amplitude corresponding to the discrete points is Represents the average amplitude of a discrete sequence.

[0032] In some optional embodiments, the QPSO algorithm is used to optimize and solve the variational mode decomposition algorithm to obtain the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor. Based on the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor, variational mode decomposition is performed on the received signal to obtain multiple IMF components, which is achieved by the following steps:

[0033] S11, decomposition layer and penalty factor As an optimization variable, and set the number of decomposition levels Search range and penalty factor Search scope;

[0034] S12, set population size and spatial search dimensions , initialize the population particles and set the number of iterations at this time to ;

[0035] S13, based on the designed fitness function, calculate the current fitness value of the particle. If the current fitness value is better than the fitness value of the previous iteration, the current position of the particle is used as the individual optimal position of the particle. Otherwise, the individual optimal position of the particle is not updated. The update of the individual optimal position is achieved by the following formula:

[0036] ;

[0037] in, for The random numbers between and obey the normal distribution, Indicates the The particle in The optimal position of the individual after the update at the iteration, Indicates the The particle in The optimal position of the individual before the update at the iteration, represents the global optimal position;

[0038] S14, comparing the fitness values ​​of all particles in the population with the global optimal position respectively. If the fitness value of a particle is better than the fitness value of the global optimal position, the individual optimal position of the example whose fitness value is better than the fitness value of the global optimal position is taken as the global optimal position;

[0039] S15, calculate the average optimal position of the particle swarm, the average optimal position of the particle swarm is calculated by the following formula:

[0040] ;

[0041] in, represents the average optimal position of the particle swarm;

[0042] S16, calculating the potential well center of the non-optimal particle for each dimension of the particle, and calculating the position of a random point;

[0043] S17, update the particle position, calculate the new position of the particle in each dimensional space, the new position of the particle in each dimensional space is calculated by the following formula;

[0044] ;

[0045] ;

[0046] in, is the contraction-expansion coefficient, and is the shrinkage expansion coefficient parameter, is the maximum number of iterations, Indicates the The particle in The new position determined at the completion of the iteration, Indicates the The particle in The new position determined at the completion of the iteration;

[0047] S18, update the number of iterations plus one, repeat S13 to S17, if the fitness decreases, update the number of decomposition layers and penalty factor , until the maximum number of iterations is reached , output The global optimal value obtained after iterations is taken as the number of decomposition layers The optimal solution and penalty factor The optimal solution of

[0048] S19, based on the number of decomposition levels The optimal solution and penalty factor The optimal solution of is used to perform variational mode decomposition on the received signal and obtain multiple IMF components.

[0049] In some optional embodiments, the variance contribution rate of each IMF component is calculated separately, which is achieved by the following formula:

[0050] ;

[0051] in, It represents the total number of IMF components obtained by performing variational mode decomposition on the received signal. Indicates the IMF components, Indicates the The variance contribution rate of each IMF component.

[0052] In some optional embodiments, wavelet threshold processing is performed on each retained IMF component, including:

[0053] Select appropriate wavelet basis to analyze each IMF component Layer wavelet decomposition;

[0054] Adaptive wavelet threshold function processing is performed on each scale to estimate the wavelet coefficients;

[0055] The estimated wavelet coefficients are reconstructed and denoised to obtain the IMF components after wavelet threshold processing, i.e. the denoised IMF components;

[0056] The expression of the adaptive wavelet threshold function is as follows:

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] in, represents the wavelet threshold function, represents the adaptive threshold, represents the noise variance, Indicates the signal length, Indicates the The wavelet decomposition threshold of the layer, Indicates the The correlation strength between the layer wavelet decomposition coefficients and the original signal coefficients, Represents the original signal data, Indicates the The signal data after layer wavelet decomposition, Indicates the calculation of covariance, Indicates the calculation of variance.

[0062] In some optional embodiments, a conjugate ambiguity function of the reconstructed received signal is calculated, and peak detection is performed on the conjugate ambiguity function to estimate the time delay difference and frequency difference between the multi-antenna signals in the distributed system, which is achieved by the following formula:

[0063] ;

[0064] ;

[0065] in, Represents the reconstructed first received signal, Represents the reconstructed second-channel received signal, represents the conjugate ambiguity function of the reconstructed two-way received signal, It represents the estimated time delay difference and frequency difference between multi-antenna signals in the distributed system.

[0066] The embodiments of the present application provide a method for jointly estimating time and frequency differences between multi-antenna signals in a distributed system, which has the following technical effects.

[0067] First, the QPSO algorithm was used to optimize the variational mode decomposition algorithm, and the optimal solutions for the number of decomposition layers and the penalty factor were obtained. The received signal was subjected to variational mode decomposition using the obtained optimal solution, thereby obtaining multiple IMF components. The variance contribution rate of each IMF component was calculated, and the IMF components with too small variance contribution rate were filtered out, which was able to transmit the characteristics of the original signal with less information loss. The remaining IMF components were subjected to wavelet threshold processing, which included selecting wavelet functions for wavelet decomposition and adaptive threshold denoising. The signal was reconstructed, the conjugate fuzzy function of the reconstructed signal was calculated, and the time delay difference and frequency difference between the signals were estimated through peak detection, filling the gap in this field.

[0068] Second, the ratio of envelope entropy and kurtosis value is selected as the fitness function. By searching for the global minimum fitness value, the optimal combination of decomposition layers and penalty factors is quickly and accurately determined and used for variational mode decomposition. This can effectively avoid under-decomposition or over-decomposition of the signal during variational mode decomposition.

[0069] Third, an adaptive wavelet threshold function is designed in the wavelet denoising process. On this basis, in order to more accurately select the threshold to adapt to the characteristics of the noise coefficient change, a new threshold that changes with the number of decomposition layers is further proposed. It can adaptively select the appropriate threshold according to the correlation coefficient between the data after each layer of decomposition and the original data, which is in line with the characteristic of small modulus value of noise signal under high-level decomposition, effectively avoiding the false filtering of useful signals and achieving better denoising effect.

[0070] In summary, this application proposes a method for joint estimation of time and frequency differences between multi-antenna signals in a distributed system. This method emphasizes the importance of resolving the parameter acquisition problem of the variational mode decomposition algorithm using quantum particle swarm optimization (QPSO) in the joint estimation algorithm for time and frequency differences. This method can be used for any joint estimation task involving QPSO optimization under the influence of correlated noise. This method has good denoising effects and universal applicability, enabling high-precision joint estimation of time and frequency differences. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the related technologies, the following is a brief introduction to the drawings required for use in the embodiments of the present application or the description of the related technologies. Obviously, the following drawings are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. The drawings described here are only used to explain the present application and are not used to limit the present application.

[0072] Figure 1 This is a flow chart of a method for jointly estimating time and frequency differences between multi-antenna signals in a distributed system, proposed in one embodiment of the present application;

[0073] Figure 2 A diagram comparing the root mean square error of delay difference estimation between a method for jointly estimating time and frequency differences between multi-antenna signals in a distributed system and a traditional method for jointly estimating time and frequency differences, provided in one embodiment of the present application;

[0074] Figure 3 A diagram comparing the root mean square error of frequency difference estimation between a method for jointly estimating time and frequency differences between multi-antenna signals in a distributed system and a traditional method for jointly estimating time and frequency differences, provided in one embodiment of the present application;

[0075] Figure 4 1 is a structural diagram of a system for jointly estimating time and frequency differences between multi-antenna signals in a distributed system provided in another embodiment of the present application;

[0076] Figure 5 It is a structural diagram of an electronic device provided in another embodiment of the present application. DETAILED DESCRIPTION

[0077] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, each embodiment of the present application will be described in detail below with reference to the accompanying drawings. Those skilled in the art will appreciate that in each embodiment of the present application, many technical details are provided to enable the reader to better understand the present application. However, even without these technical details and various changes and modifications based on the following embodiments, the technical solutions claimed in the present application can be implemented. The division of the following embodiments is for convenience of description and should not constitute any limitation on the specific implementation of the present application. The various embodiments can be combined with each other and referenced to each other under the premise of no contradiction.

[0078] An embodiment of the present application proposes a method for jointly estimating the time difference and frequency difference between multiple antenna signals in a distributed system, which is applied to an electronic device, wherein the electronic device can be a terminal or a server. This embodiment and the following embodiments are all described using the server as an example. The implementation details of the method for jointly estimating the time difference and frequency difference between multiple antenna signals in a distributed system proposed in this embodiment are specifically described below. The following content is only the implementation details provided for easy understanding and is not necessary for implementing this solution.

[0079] The specific process of the method for jointly estimating the time and frequency differences between multi-antenna signals in a distributed system proposed in this embodiment can be as follows: Figure 1 Shown, including:

[0080] S1, the QPSO algorithm is used to optimize and solve the variational mode decomposition algorithm to obtain the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor. Based on the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor, the received signal is subjected to variational mode decomposition to obtain multiple IMF components.

[0081] In specific implementations, after acquiring the received signal, the server uses the QPSO algorithm to optimize the variational mode decomposition algorithm, obtaining the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor. Based on these optimal solutions, the received signal is subjected to variational mode decomposition, resulting in multiple IMF components. The QPSO algorithm can quickly and accurately determine the optimal combination of decomposition layers and penalty factors, thereby performing optimal variational mode decomposition.

[0082] In one example, the server considers the situation where there is both a time delay difference and a frequency difference between two received signals, and establishes a signal model for the two received signals. The established signal model is expressed by the formula:

[0083] ;

[0084] in, Indicates the first channel receiving signal, Indicates the second channel receiving signal, Indicates the amplitude attenuation of the first received signal during the propagation process, Indicates the amplitude attenuation of the second-channel received signal during the propagation process. Represents the useful signal radiated by the radiation source, Indicates the time delay of the first receiving signal transmission, Indicates the time delay of the second receiving signal transmission, , used to represent the observation space, represents the additive Gaussian noise added to the first received signal. Represents the additive Gaussian noise added to the second received signal. and The power is and . and It can be relevant or irrelevant.

[0085] Furthermore, the first receiving signal As a reference signal, the established signal model is simplified. The simplified signal model can be expressed by the formula:

[0086] ;

[0087] / ;

[0088] ;

[0089] in, is the attenuation coefficient ratio, is the delay difference between the two received signals to be determined, is the frequency difference between the two received signals to be determined. In the subsequent joint estimation of time difference and frequency difference, it is only necessary to estimate The value and The value of .

[0090] In one example, a fitness function needs to be set in the QPSO algorithm, and the server designs the fitness function as a ratio of envelope entropy to kurtosis value.

[0091] In one example, the envelope entropy is calculated as:

[0092] ;

[0093] ;

[0094] in, represents the envelope entropy, is the total number of IMF components obtained by variational mode decomposition, represents the first The envelope signal of the IMF components after Hilbert demodulation.

[0095] In one example, the kurtosis value is calculated as:

[0096] ;

[0097] in, represents the kurtosis value, represents the total number of discrete points in the discrete sequence, Indicates the first discrete sequence of time domain waveforms The vibration amplitude corresponding to the discrete points is Represents the average amplitude of a discrete sequence.

[0098] In one example, after completing the construction of the signal model and the design of the fitness function, the QPSO algorithm can be used to optimize the variational mode decomposition algorithm. Based on time cost considerations, the server sets the number of decomposition layers. The search scope is , and set the penalty factor The search scope is .

[0099] The server uses the QPSO algorithm to optimize the variational mode decomposition algorithm and obtain the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor. Based on the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor, the received signal is subjected to variational mode decomposition to obtain multiple IMF components. This is achieved through the following steps:

[0100] S11, decomposition layer and penalty factor As an optimization variable, and set the number of decomposition levels Search range and penalty factor Search scope.

[0101] S12, set population size and spatial search dimensions , initialize the population particles and set the number of iterations at this time to .

[0102] S13, based on the designed fitness function, calculate the current fitness value of the particle. If the current fitness value is better than the fitness value of the previous iteration, the current position of the particle is used as the individual optimal position of the particle. Otherwise, the individual optimal position of the particle is not updated. The update of the individual optimal position is achieved by the following formula:

[0103] ;

[0104] in, for The random numbers between and obey the normal distribution, Indicates the The particle in The optimal position of the individual after the update at the iteration, Indicates the The particle in The optimal position of the individual before the update at the iteration, represents the global optimal position.

[0105] S14, comparing the fitness values ​​of all particles in the population with the global optimal position respectively. If the fitness value of a particle is better than the fitness value of the global optimal position, the individual optimal position of the example whose fitness value is better than the fitness value of the global optimal position is taken as the global optimal position.

[0106] S15, calculate the average optimal position of the particle swarm, the average optimal position of the particle swarm is calculated by the following formula:

[0107] ;

[0108] in, represents the average optimal position of the particle swarm.

[0109] S16, calculating the potential well center of the non-optimal particle for each dimension of the particle, and calculating the position of a random point.

[0110] S17, update the particle position, calculate the new position of the particle in each dimensional space, the new position of the particle in each dimensional space is calculated by the following formula;

[0111] ;

[0112] ;

[0113] in, is the contraction-expansion coefficient, and is the shrinkage expansion coefficient parameter, is the maximum number of iterations, Indicates the The particle in The new position determined at the completion of the iteration, Indicates the The particle in The new position is determined at the end of the iteration. When Will take ,when When Will take .

[0114] S18, update the number of iterations plus one, repeat S13 to S17, if the fitness decreases, update the number of decomposition layers and penalty factor , until the maximum number of iterations is reached , output The global optimal value obtained after iterations is taken as the number of decomposition layers The optimal solution and penalty factor The optimal solution of .

[0115] S19, based on the number of decomposition levels The optimal solution and penalty factor The optimal solution of is used to perform variational mode decomposition on the received signal and obtain multiple IMF components.

[0116] Server based on decomposition layer The optimal solution and penalty factor The optimal solution of the received signal is used to perform variational mode decomposition on the received signal, which can decompose the received signal into IMF components.

[0117] S2, respectively calculating the variance contribution rate of each IMF component, and filtering out the IMF components whose variance contribution rate is less than a first preset threshold.

[0118] In the specific implementation, the server completes the variational mode decomposition of the received signal and obtains After the IMF components are obtained, the variance contribution rate of each IMF component can be calculated respectively, and the IMF components with variance contribution rates less than a first preset threshold are filtered out. The first preset threshold can be set by those skilled in the art according to actual needs.

[0119] In one example, the server calculates the variance contribution rate of each IMF component separately, which can be achieved by the following formula:

[0120] ;

[0121] in, It represents the total number of IMF components obtained by performing variational mode decomposition on the received signal. Indicates the IMF components, Indicates the The variance contribution rate of each IMF component.

[0122] In one example, the first preset threshold is set to 0.01, and the server The IMF components of the image are filtered out, and the retained (remaining) IMF components are denoised.

[0123] S3, performing wavelet threshold processing on each retained IMF component.

[0124] In a specific implementation, the wavelet threshold processing process is the denoising process. The server performs wavelet threshold processing on each retained IMF component in turn to obtain each IMF component after wavelet threshold processing, that is, each IMF component after denoising.

[0125] In one example, the server first needs to select a suitable wavelet basis to perform Layer wavelet decomposition is performed, and then adaptive wavelet threshold function processing is performed on each scale to estimate the wavelet coefficients. Finally, the estimated wavelet coefficients are reconstructed and denoised to obtain the IMF components after wavelet threshold processing, that is, the denoised IMF components.

[0126] In one example, the adaptive wavelet threshold function is expressed as follows:

[0127] ;

[0128] ;

[0129] ;

[0130] ;

[0131] in, represents the wavelet threshold function, represents the adaptive threshold, The selection is crucial. represents the noise variance, , is the calculated median of the original signal, Indicates the signal length, Indicates the The wavelet decomposition threshold of the layer, It is a monotonically decreasing function. The larger the number of decomposition layers, The smaller the value of Indicates the The correlation strength between the layer wavelet decomposition coefficient and the original signal coefficient, assuming Represents the original signal data, Indicates the The signal data after layer wavelet decomposition, Indicates the calculation of covariance, Indicates the calculation of variance, .

[0132] S4, performing signal reconstruction based on each IMF component after wavelet threshold processing, calculating the conjugate ambiguity function of the reconstructed received signal, and performing peak detection on the conjugate ambiguity function to estimate the time delay difference and frequency difference between the multi-antenna signals of the distributed system.

[0133] In the specific implementation, after the server obtains the IMF components after wavelet threshold processing, it can reconstruct the signal based on the IMF components after wavelet threshold processing, calculate the conjugate ambiguity function of the reconstructed received signal, and perform peak detection on the conjugate ambiguity function to estimate the delay difference and frequency difference between the multi-antenna signals of the distributed system.

[0134] In one example, the server calculates the conjugate ambiguity function of the reconstructed received signal and performs peak detection on the conjugate ambiguity function to estimate the time delay difference and frequency difference between the multi-antenna signals in the distributed system. This is achieved using the following formula:

[0135] ;

[0136] ;

[0137] in, Represents the reconstructed first received signal, Represents the reconstructed second-channel received signal, represents the conjugate ambiguity function of the reconstructed two-way received signal, It represents the estimated time delay difference and frequency difference between multi-antenna signals in the distributed system.

[0138] This embodiment proposes a method for jointly estimating time and frequency differences between multi-antenna signals in a distributed system, which has the following technical effects.

[0139] First, the QPSO algorithm was used to optimize the variational mode decomposition algorithm, and the optimal solutions for the number of decomposition layers and the penalty factor were obtained. The received signal was subjected to variational mode decomposition using the obtained optimal solution, thereby obtaining multiple IMF components. The variance contribution rate of each IMF component was calculated, and the IMF components with too small variance contribution rate were filtered out, which was able to transmit the characteristics of the original signal with less information loss. The remaining IMF components were subjected to wavelet threshold processing, which included selecting wavelet functions for wavelet decomposition and adaptive threshold denoising. The signal was reconstructed, the conjugate fuzzy function of the reconstructed signal was calculated, and the time delay difference and frequency difference between the signals were estimated through peak detection, filling the gap in this field.

[0140] Second, the ratio of envelope entropy and kurtosis value is selected as the fitness function. By searching for the global minimum fitness value, the optimal combination of decomposition layers and penalty factors is quickly and accurately determined and used for variational mode decomposition. This can effectively avoid under-decomposition or over-decomposition of the signal during variational mode decomposition.

[0141] Third, an adaptive wavelet threshold function is designed in the wavelet denoising process. On this basis, in order to more accurately select the threshold to adapt to the characteristics of the noise coefficient change, a new threshold that changes with the number of decomposition layers is further proposed. It can adaptively select the appropriate threshold according to the correlation coefficient between the data after each layer of decomposition and the original data, which is in line with the characteristic of small modulus value of noise signal under high-level decomposition, effectively avoiding the false filtering of useful signals and achieving better denoising effect.

[0142] In summary, this application proposes a method for joint estimation of time and frequency differences between multi-antenna signals in a distributed system. This method emphasizes the importance of resolving the parameter acquisition problem of the variational mode decomposition algorithm using quantum particle swarm optimization (QPSO) in the joint estimation algorithm for time and frequency differences. This method can be used for any joint estimation task involving QPSO optimization under the influence of correlated noise. This method has good denoising effects and universal applicability, enabling high-precision joint estimation of time and frequency differences.

[0143] The steps of the various methods described above are divided for clarity of description only. They can be combined into a single step, or some steps can be broken down into multiple steps. As long as they share the same logical relationships, they are all within the scope of protection of this application. Adding minor modifications or introducing minor design changes to the algorithm or process, but not changing the core design of the algorithm or process, is also within the scope of protection of this application.

[0144] In one embodiment, in order to evaluate the performance of the proposed method for joint estimation of time and frequency differences between multiple antenna signals in a distributed system (hereinafter referred to as the method), we conducted relevant simulation experiments. In the simulation experiments, the specific parameters set are as follows: Matlab software is used to simulate the BPSK signal, the carrier frequency for , sampling rate for , attenuation coefficient Set to 1 to set the delay difference between signals for , set the frequency difference At 5kHz, the additional noise of the signal and The signal-to-noise ratio (SNR) range of the signal is set to -15dB to 5dB. 1000 Monte Carlo simulations are performed for each experiment to verify the proposed method and compare its performance with that of the traditional joint estimation method.

[0145] The root mean square error of the delay difference estimation of this method is compared with the traditional time-frequency difference joint estimation method (such as the second-order mutual fuzzy algorithm and the fourth-order cumulant algorithm). Figure 2 As shown, the root mean square error of the frequency difference estimation is Figure 3 As shown in the figure, this method is feasible and can handle the delay and frequency difference estimation problems in the presence of correlated noise. Under the same simulation conditions, this method achieves a smaller root mean square error than several other methods, resulting in better estimation performance. Therefore, this method outperforms traditional methods, and simulation experiments validate its creativity.

[0146] Another embodiment of the present application proposes a system for jointly estimating the time difference and frequency difference between multiple antenna signals in a distributed system. The details of the system for jointly estimating the time difference and frequency difference between multiple antenna signals in a distributed system proposed in this embodiment are described in detail below. The following content is only the implementation details provided for easy understanding and is not necessary for implementing this example.

[0147] Figure 4 This is a structural diagram of a system for jointly estimating time and frequency differences between multi-antenna signals in a distributed system proposed in this embodiment. The system includes: an IMF component acquisition module M1, an IMF component filtering module M2, a wavelet threshold processing module M3 and a joint time and frequency difference estimation module M4.

[0148] The IMF component acquisition module M1 is used to optimize and solve the variational mode decomposition algorithm using the QPSO algorithm to obtain the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor. Based on the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor, the received signal is subjected to variational mode decomposition to obtain multiple IMF components.

[0149] The IMF component filtering module M2 is used to calculate the variance contribution rate of each IMF component respectively, and filter out the IMF components whose variance contribution rate is less than a first preset threshold.

[0150] The wavelet threshold processing module M3 is used to perform wavelet threshold processing on each retained IMF component.

[0151] The time difference and frequency difference joint estimation module M4 is used to reconstruct the signal based on the IMF components after wavelet threshold processing, calculate the conjugate ambiguity function of the reconstructed received signal, and perform peak detection on the calculated conjugate ambiguity function to estimate the time delay difference and frequency difference between the multi-antenna signals of the distributed system.

[0152] It is not difficult to find that this embodiment is a system embodiment corresponding to the above-mentioned method embodiment, and this embodiment can be implemented in conjunction with the above-mentioned method embodiment. The relevant technical details and technical effects mentioned in the above-mentioned embodiments are still valid in this embodiment, and to reduce repetition, they are not repeated here. Accordingly, the relevant technical details mentioned in this embodiment can also be applied to the above-mentioned embodiments.

[0153] It is worth mentioning that all modules involved in this embodiment are logical modules. In actual applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. In addition, to highlight the innovation of this application, this embodiment does not include units that are not closely related to solving the technical problem proposed by this application. However, this does not mean that other units do not exist in this embodiment.

[0154] Another embodiment of the present application provides an electronic device. The specific structure of the electronic device can be as follows: Figure 5 As shown, it includes: at least one processor C1; and a memory C2 communicatively connected to the at least one processor C1; wherein the memory C2 stores instructions that can be executed by the at least one processor C1, and the instructions are executed by the at least one processor C1 so that the at least one processor C1 can execute a method for jointly estimating time and frequency differences between multiple antenna signals in a distributed system as described in the above-mentioned method embodiments.

[0155] The memory and processor are connected using a bus, which includes any number of interconnected buses and bridges. The bus connects various circuits of one or more processors and memories. The bus can also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits. These are all well known in the art and therefore will not be described further in this article. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single component or multiple components, such as multiple receivers and transmitters, providing a unit for communicating with various other devices on a transmission medium. Data processed by the processor is transmitted on a wireless medium via an antenna. Furthermore, the antenna also receives data and transmits it to the processor.

[0156] The processor is responsible for managing the bus and general processing, and can also provide various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory can be used to store data used by the processor when performing operations.

[0157] Another embodiment of the present application proposes a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it can implement a method for jointly estimating time and frequency differences between multiple antenna signals in a distributed system as described in the above method embodiments.

[0158] That is, those skilled in the art will understand that all or part of the steps in the above-described method embodiments can be implemented by instructing the relevant hardware through a program. The program is stored in a storage medium and includes a number of instructions for causing a device (such as a microcontroller, chip, etc.) or processor to execute all or part of the steps in the method embodiments described herein. Storage media include various media capable of storing program code, such as USB flash drives, mobile hard drives, read-only memories, random access memories, magnetic disks, or optical disks.

[0159] Those skilled in the art will appreciate that the above embodiments are specific embodiments for implementing the present application, and that in actual applications, various modifications may be made to the embodiments in form and detail without departing from the spirit and scope of the present application. Those skilled in the art will appreciate that improvements and modifications may be made without departing from the principles of the present application, and such improvements and modifications are also considered to be within the scope of protection of the present application.

Claims

1. A method for jointly estimating time and frequency differences between multi-antenna signals in a distributed system, characterized in that: The method comprises: The QPSO algorithm is used to optimize the variational mode decomposition algorithm to obtain the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor. Based on the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor, the received signal is subjected to variational mode decomposition to obtain multiple IMF components. Calculating the variance contribution rate of each IMF component respectively, and filtering out the IMF components whose variance contribution rate is less than a first preset threshold; Perform wavelet threshold processing on each retained IMF component; Signal reconstruction is performed based on each IMF component after wavelet threshold processing. The conjugate ambiguity function of the reconstructed received signal is calculated, and the peak value of the conjugate ambiguity function is detected to estimate the time delay difference and frequency difference between the multi-antenna signals in the distributed system. The QPSO algorithm is used to optimize and solve the variational mode decomposition algorithm to obtain the optimal solution of the decomposition layer number and the optimal solution of the penalty factor. Based on the optimal solution of the decomposition layer number and the optimal solution of the penalty factor, the received signal is subjected to variational mode decomposition to obtain multiple IMF components. This is achieved by the following steps: S11, decomposition layer and penalty factor As an optimization variable, and set the number of decomposition levels Search range and penalty factor Search scope; S12, set population size and spatial search dimensions , initialize the population particles and set the number of iterations at this time to ; S13, based on the designed fitness function, calculate the current fitness value of the particle. If the current fitness value is better than the fitness value of the previous iteration, the current position of the particle is used as the individual optimal position of the particle. Otherwise, the individual optimal position of the particle is not updated. The update of the individual optimal position is achieved by the following formula: ； in, for The random numbers between and obey the normal distribution, Indicates the The particle in The optimal position of the individual after the update at the iteration, Indicates the The particle in The optimal position of the individual before the update at the iteration, represents the global optimal position; S14, comparing the fitness values ​​of all particles in the population with the global optimal position respectively. If the fitness value of a particle is better than the fitness value of the global optimal position, the individual optimal position of the example whose fitness value is better than the fitness value of the global optimal position is taken as the global optimal position; S15, calculate the average optimal position of the particle swarm. The average optimal position of the particle swarm is calculated by the following formula: ； in, represents the average optimal position of the particle swarm; S16, calculating the potential well center of the non-optimal particle for each dimension of the particle, and calculating the position of a random point; S17, update the particle position, calculate the new position of the particle in each dimensional space, the new position of the particle in each dimensional space is calculated by the following formula; ； ； in, is the contraction-expansion coefficient, and is the shrinkage expansion coefficient parameter, is the maximum number of iterations, Indicates the The particle in The new position determined at the completion of the iteration, Indicates the The particle in The new position determined at the completion of the iteration; S18, update the number of iterations plus one, repeat S13 to S17, if the fitness decreases, update the number of decomposition layers and penalty factor , until the maximum number of iterations is reached , output The global optimal value obtained after iterations is taken as the number of decomposition layers The optimal solution and penalty factor The optimal solution of S19, based on the number of decomposition levels The optimal solution and penalty factor The optimal solution of is used to perform variational mode decomposition on the received signal and obtain multiple IMF components.

2. The method for jointly estimating time and frequency differences between multi-antenna signals in a distributed system according to claim 1, characterized in that: Before using the QPSO algorithm to optimize and solve the variational mode decomposition algorithm, the method further includes: Obtain two received signals and establish a signal model for the two received signals. There is both a time delay difference and a frequency difference between the two received signals. The established signal model is expressed by the formula: ； in, Indicates the first channel receiving signal, Indicates the second channel receiving signal, Indicates the amplitude attenuation of the first received signal during the propagation process, Indicates the amplitude attenuation of the second-channel received signal during the propagation process. Represents the useful signal radiated by the radiation source, Indicates the time delay of the first receiving signal transmission, Indicates the time delay of the second receiving signal transmission, represents the additive Gaussian noise added to the first received signal. represents the additive Gaussian noise added to the second received signal; The first receiving signal As a reference signal, the signal model is simplified. The simplified signal model is expressed by the formula: ； / ； ； in, is the attenuation coefficient ratio, is the delay difference between the two received signals to be determined, is the frequency difference between the two received signals to be determined.

3. The method for jointly estimating time and frequency differences between multi-antenna signals in a distributed system according to claim 2, characterized in that: After simplifying the signal model, the method further includes: The fitness function is designed to be the ratio of the envelope entropy and the kurtosis value; The calculation formula of envelope entropy is: ； ； in, represents the envelope entropy, is the total number of IMF components obtained by variational mode decomposition, represents the first The envelope signal of the IMF components after Hilbert demodulation; The calculation formula of the kurtosis value is: ； in, represents the kurtosis value, represents the total number of discrete points in the discrete sequence, Indicates the first discrete sequence of time domain waveforms The vibration amplitude corresponding to the discrete points is Represents the average amplitude of a discrete sequence.

4. The method for jointly estimating time and frequency differences between multi-antenna signals in a distributed system according to claim 1, characterized in that: The variance contribution rate of each IMF component is calculated separately, which is achieved through the following formula: ； in, It represents the total number of IMF components obtained by performing variational mode decomposition on the received signal. Indicates the IMF components, Indicates the The variance contribution rate of each IMF component.

5. The method for jointly estimating time and frequency differences between multi-antenna signals in a distributed system according to claim 4, characterized in that: Perform wavelet threshold processing on each retained IMF component, including: Select appropriate wavelet basis to analyze each IMF component Layer wavelet decomposition; Adaptive wavelet threshold function processing is performed on each scale to estimate the wavelet coefficients; The estimated wavelet coefficients are reconstructed and denoised to obtain the IMF components after wavelet threshold processing, i.e. the denoised IMF components; The expression of the adaptive wavelet threshold function is as follows: ； ； ； ； in, represents the wavelet threshold function, represents the adaptive threshold, represents the noise variance, Indicates the signal length, Indicates the The wavelet decomposition threshold of the layer, Indicates the The correlation strength between the layer wavelet decomposition coefficients and the original signal coefficients, Represents the original signal data, Indicates the The signal data after layer wavelet decomposition, Indicates the calculation of covariance, Indicates the calculation of variance.

6. The method for jointly estimating time and frequency differences between multi-antenna signals in a distributed system according to claim 5, characterized in that: The conjugate ambiguity function of the reconstructed received signal is calculated and peak detection is performed on the conjugate ambiguity function to estimate the time delay difference and frequency difference between the multi-antenna signals in the distributed system. This is achieved using the following formula: ； ； in, Represents the reconstructed first received signal, Represents the reconstructed second-channel received signal, represents the conjugate ambiguity function of the reconstructed two-way received signal, It represents the estimated time delay difference and frequency difference between multi-antenna signals in the distributed system.

7. A system for jointly estimating time and frequency differences between multi-antenna signals in a distributed system, characterized in that: The system comprises: The IMF component acquisition module is used to optimize and solve the variational mode decomposition algorithm using the QPSO algorithm to obtain the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor. Based on the optimal solution for the number of decomposition layers and the optimal solution for the penalty factor, the received signal is subjected to variational mode decomposition to obtain multiple IMF components. An IMF component filtering module is used to calculate the variance contribution rate of each IMF component respectively, and filter out the IMF component whose variance contribution rate is less than a first preset threshold; A wavelet threshold processing module is used to perform wavelet threshold processing on each retained IMF component; The time difference and frequency difference joint estimation module is used to reconstruct the signal based on each IMF component after wavelet threshold processing, calculate the conjugate ambiguity function of the reconstructed received signal, and perform peak detection on the calculated conjugate ambiguity function to estimate the time delay difference and frequency difference between the multi-antenna signals in the distributed system; The QPSO algorithm is used to optimize and solve the variational mode decomposition algorithm to obtain the optimal solution of the decomposition layer number and the optimal solution of the penalty factor. Based on the optimal solution of the decomposition layer number and the optimal solution of the penalty factor, the received signal is subjected to variational mode decomposition to obtain multiple IMF components. This is achieved by the following steps: S11, decomposition layer and penalty factor As an optimization variable, and set the number of decomposition levels Search range and penalty factor Search scope; S12, set population size and spatial search dimensions , initialize the population particles and set the number of iterations at this time to ; S13, based on the designed fitness function, calculate the current fitness value of the particle. If the current fitness value is better than the fitness value of the previous iteration, the current position of the particle is used as the individual optimal position of the particle. Otherwise, the individual optimal position of the particle is not updated. The update of the individual optimal position is achieved by the following formula: ； in, for The random numbers between and obey the normal distribution, Indicates the The particle in The optimal position of the individual after the update at the iteration, Indicates the The particle in The optimal position of the individual before the update at the iteration, represents the global optimal position; S14, comparing the fitness values ​​of all particles in the population with the global optimal position respectively. If the fitness value of a particle is better than the fitness value of the global optimal position, the individual optimal position of the example whose fitness value is better than the fitness value of the global optimal position is taken as the global optimal position; S15, calculate the average optimal position of the particle swarm. The average optimal position of the particle swarm is calculated by the following formula: ； in, represents the average optimal position of the particle swarm; S16, calculating the potential well center of the non-optimal particle for each dimension of the particle, and calculating the position of a random point; S17, update the particle position, calculate the new position of the particle in each dimensional space, the new position of the particle in each dimensional space is calculated by the following formula; ； ； in, is the contraction-expansion coefficient, and is the shrinkage expansion coefficient parameter, is the maximum number of iterations, Indicates the The particle in The new position determined at the completion of the iteration, Indicates the The particle in The new position determined at the completion of the iteration; S18, update the number of iterations plus one, repeat S13 to S17, if the fitness decreases, update the number of decomposition layers and penalty factor , until the maximum number of iterations is reached , output The global optimal value obtained after iterations is taken as the number of decomposition layers The optimal solution and penalty factor The optimal solution of S19, based on the number of decomposition levels The optimal solution and penalty factor The optimal solution of is used to perform variational mode decomposition on the received signal and obtain multiple IMF components.

8. An electronic device, characterized in that: include: at least one processor; as well as, a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute a method for jointly estimating time and frequency differences between multi-antenna signals in a distributed system as described in any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, it can implement a method for jointly estimating time and frequency differences between multi-antenna signals in a distributed system according to any one of claims 1 to 6.

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