Multi-channel asynchronous sampling and parameter estimation method for ultra-wideband linear frequency modulation signals

Abstract

A multi-channel asynchronous sampling and parameter estimation method for ultra-wideband linear frequency modulation (LFM) signals achieves low-speed sampling and high-precision parameter measurement of LFM signals. The sampling framework incorporates three asynchronous sub-Nyquist sampling channels. To address frequency aliasing, two algorithms for estimating the frequency modulation coefficient K and clock interleaving parameters in undersampling environments are proposed. This method can recover signal parameters with a small number of samples even in highly noisy environments with extremely wide signal durations. Simulation results demonstrate that compared to other methods, the proposed method achieves higher reconstruction accuracy and noise robustness.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and in particular relates to a multi-channel asynchronous sampling and parameter estimation method for ultra-wideband linear frequency modulation signals. Background Art

[0002] Ultra-wideband linear frequency modulation (LFM) signals are widely used in radar, sonar, wireless communications, electronic reconnaissance, and many other engineering applications. LFM pulse signals are a common form of LFM signal in many practical applications due to the requirements for distance detection and practical power limitations. By measuring and estimating the pulse position and modulation parameters of LFM signals, we can determine target range and the frequency modulation of radar signals. Therefore, LFM signal sampling and parameter estimation are important tasks in many engineering applications.

[0003] Numerous methods for sampling and estimating LFM signals have been proposed. The Maximum Likelihood (ML) algorithm can effectively estimate the FM coefficient and frequency, but it is computationally complex due to its involvement in grid search and multidimensional integration. Jensen et al. proposed a fast ML estimation algorithm, but it still requires a grid method and recursive updates. Guner et al. proposed a WHT system for implementing an FPGA. Bai et al. proposed a new FM coefficient estimation algorithm based on the Multiple Discrete Polynomial Phase Transform (MDPT) and weighted combination, but this method requires a large number of iterations. The Fractional Fourier Transform (FRFT), also a classic algorithm for measuring LFM signal parameters, requires a two-dimensional search and, consequently, requires processing a large amount of data. However, all of these methods are based on the Nyquist sampling theorem, which requires a sampling rate of at least twice the signal bandwidth. For ultra-wideband LFM signals, these systems face a common problem, namely, not only a very high sampling rate is required, but also complex processing is required to complete parameter estimation. Therefore, the measurement of ultra-wideband LFM signals requires a high sampling rate and heavy processing work.

[0004] Research on sub-Nyquist sampling and parameter estimation of ultra-wideband (LFM) signals has become a hot topic in the field of signal processing. However, these methods are generally subject to two challenges: First, in ultra-wideband scenarios, the sampling data is massive and computationally intensive. Direct sub-Nyquist sampling of LFM signals can lead to frequency aliasing due to the periodicity of trigonometric functions. Second, existing methods suffer from low detection efficiency and parameter estimation accuracy at low signal-to-noise ratios. Therefore, sub-Nyquist sampling and parameter estimation of ultra-wideband (UWB) linear frequency modulation (LFM) signals are critical issues that require urgent resolution. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this paper proposes a multi-channel asynchronous sampling and parameter estimation method for measuring the parameters of ultra-wideband linear frequency modulation (LFM) signals. This method, consisting of three asynchronous sub-Nyquist sampling channels, addresses the frequency aliasing problem caused by sub-Nyquist sampling of LFM signals through feedback regulation and signal delay, achieving low-rate sampling and high-precision parameter measurement of ultra-wideband LFM signals.

[0006] The technical solution adopted by the present invention to solve its technical problem is:

[0007] A method for multi-channel asynchronous sampling and parameter estimation of ultra-wideband linear frequency modulation signals, comprising the following steps:

[0008] In step 1, the ultra-wideband LFM signal to be measured enters the power divider for splitting. The mathematical model of the ultra-wideband LFM signal is as follows:

[0009]

[0010] Among them, t∈(0,T] represents the simulation time variable, T∈C is the duration of the signal, A(A≠0,A∈R) is the amplitude parameter of the LFM signal, and f c is the carrier frequency of the LFM signal, 0≤f c <f max , f max is the maximum frequency limit, K is the frequency modulation coefficient, B is the bandwidth. The power divider is controlled to split the ultra-wideband linear frequency modulation signal x(t) into two channels: a main sampling channel and a feedback sampling channel. The main sampling channel uses a low-speed analog-to-digital converter (ADC) to perform sub-Nyquist sampling on the split signal. The feedback sampling channel mixes the input signal with the feedback information of the main sampling channel and then performs sub-Nyquist sampling before splitting it into two asynchronous channels.

[0011] Step 2: The main sampling channel performs sub-Nyquist sampling on the shunt signal and uses a low-speed analog-to-digital converter ADC to uniformly sample the signal with a sampling rate of f s (f s <B, B is the bandwidth of the signal), then the sampling value is expressed as:

[0012]

[0013] Among them, n (n∈1,2,...N) represents the sampling point sequence, N is an integer, which represents the number of signal sampling samples, T s =1 / f s represents the sampling interval;

[0014] Step 3: Use the K parameter estimation algorithm to estimate the frequency modulation coefficient K parameter from the samples x[n] collected from the main channel; the process is described as follows:

[0015] Step 3.1, obtain three consecutive samples x[n], x[n+1], x[n+2] (n∈{1,2,3...,N}), respectively:

[0016]

[0017] Step 3.2: Eliminate the carrier frequency component. Divide the second sample by the first sample to obtain the sample:

[0018]

[0019] Divide the third sample by the second sample to get the sample:

[0020]

[0021] Then divide the sample X2 by the sample X1 to get the sample:

[0022]

[0023] In order to increase the robustness of the algorithm under noisy conditions, N-3 groups of samples are cross-divided to obtain the sample average:

[0024]

[0025] Step 3.3, calculate the frequency modulation coefficient K by taking the sample average value Y ver The frequency modulation coefficient K is obtained by using the principal value of the argument:

[0026]

[0027] Here, angle(·) represents the principal value of the argument of the complex number (·).

[0028] Step 4: Feedback sampling channel mixing operation, input the frequency modulation coefficient K value obtained from the main sampling channel into the feedback signal generator to generate an analog frequency modulation signal:

[0029]

[0030] Where t∈(0,T] represents the analog time variable and T∈C is the duration of the signal. The FM signal p(t) is then mixed with the input signal x(t) to obtain the mixed signal:

[0031]

[0032] Step 5: Asynchronous delayed sampling. In the feedback sampling channel, the mixing signal y(t) is split into two asynchronous delayed sampling channels: the first channel is f s (f s The sampling rate of <B) is uniformly sampled, and the collected samples are:

[0033]

[0034] Among them, the parameter U = e j2πfc / fs The second channel also processes the signal y(t) with f s (f s <B) sampling rate, but the sampling start time is delayed by T relative to the first channel e The amount of time, where the time delay is required to be less than or equal to the Nyquist sampling interval, that is, T e ≤1 / f max , assuming that the sample obtained by sampling the second channel is represented by y e [n′], where n′ (n′∈1,2,...N′) represents the sampling point sequence, and N′ is an integer representing the number of samples of this signal;

[0035] Step 6: Use spectrum estimation algorithm to solve the amplitude parameter A. Estimating the amplitude parameter A and parameter U from the sample y[n] is a typical spectrum estimation problem. At this time, spectrum estimation methods can be used to solve it, such as the zeroing filter method. However, due to the periodicity of trigonometric functions, it is difficult to estimate the carrier frequency parameter f from the parameter U. c Frequency aliasing problems may occur, making the estimated carrier frequency parameter f c Error occurs when the system sampling rate can meet the requirements of Nyquist sampling theorem, that is, f s >f max (f max is the maximum frequency), the frequency parameter f c The solution is unique and is calculated as:

[0036]

[0037] Among them, 0≤∠(·)<π represents the principal value of the complex number (·). However, when the system sampling rate cannot meet the requirements of the Nyquist sampling theorem, that is, f s <f max When the frequency parameter f c There will be multiple possible solutions:

[0038]

[0039] in, is the minimum possible solution that satisfies formula (13), Indicates the degree of deviation of other possible solutions. Since there are infinite values of m, the corresponding frequency parameter f c There are infinite solutions to this problem, which is called the "frequency aliasing" problem;

[0040] Step 7: Use the time-interleaved algorithm to solve the carrier frequency parameter f c Due to the existence of the "frequency aliasing" problem, the delayed sampling channel is used to collect samples for joint estimation to obtain the optimal carrier frequency parameter fc to solve the frequency aliasing problem and find the correct m value; in order to solve the frequency aliasing problem, an auxiliary sampling channel (delayed sampling channel) is added. The function of the auxiliary sampling channel is to find the correct frequency parameter from all possible solutions, that is, to obtain the correct frequency parameter from all possible solutions through the delayed sampling value y e [n′] determines the value of m, thereby finding the frequency parameter f c The exact solution of .

[0041] Furthermore, the steps of step seven are as follows:

[0042] Step 7.1: The sampling time of the auxiliary sampling channel differs from that of the main sampling channel by a time delay T e , the sampling rate is f s , then the delayed sampling value y e [n′] is expressed as follows:

[0043]

[0044] Among them, n′(n′∈1,2,...N′) represents the sampling point sequence, N′ is an integer, which represents the number of sampling samples of this signal. is a known quantity, is an unknown quantity. In order to solve for m, we need to first find the value of b and write the above formula as y e [n′]=a n′ b;

[0045] Step 7.2: Since the signal model is a single harmonic, only the first sample (n'=1) needs to be taken, where b=y e / an′ , then according to Find the value of m;

[0046] Step 7.3, taking into account the frequency parameter f c Satisfy 0≤f c <f max , frequency parameter f c The minimum possible solution satisfy Combined with formula (13), we have:

[0047]

[0048] Simplifying the above relationship, we can get 0≤mf s <f max , therefore, when the delay T e satisfy When 0≤2πmf s T e <2π, then has a unique solution:

[0049]

[0050] Among them, ∠(·) represents the main value of the argument of (·), 0≤∠(·)<2π, similarly, when the delay T e satisfy When -2π<2πmf s T e ≤0, then There is a unique solution:

[0051]

[0052] In short, when the delay T e satisfy When , m can be uniquely determined:

[0053]

[0054] After obtaining m, the frequency parameter is determined as

[0055] The method of the present invention mainly includes a three-way asynchronous sub-Nyquist sampling channel, and proposes two parameter estimation algorithms, namely the K parameter estimation algorithm and the time interleaving algorithm, to obtain the frequency modulation coefficient K, amplitude value A and carrier frequency f of the ultra-wideband LFM signal to be measured. c , realizing low-speed sampling and high-precision parameter measurement of ultra-wideband LFM signals.

[0056] The beneficial effects of the present invention are mainly manifested in: realizing low-rate sampling and high-precision parameter measurement of ultra-wideband LFM signals, and having high reconstruction accuracy and robustness to noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a flow chart of a multi-channel asynchronous sampling and parameter estimation method for ultra-wideband linear frequency modulation signals.

[0058] Figure 2 It is a comparison chart of parameter A recovery performance when the signal-to-noise ratio increases.

[0059] Figure 3 is the parameter f when the signal-to-noise ratio increases c Recovery performance comparison chart.

[0060] Figure 4 It is a comparison chart of the recovery performance of parameter K when the signal-to-noise ratio increases. DETAILED DESCRIPTION

[0061] The present invention will be further described below with reference to the accompanying drawings.

[0062] Reference Figures 1 to 4 , a multi-channel asynchronous sampling and parameter estimation method for ultra-wideband linear frequency modulation signals, comprising the following steps:

[0063] In step 1, the ultra-wideband LFM signal to be measured enters the power divider for splitting. The mathematical model of the ultra-wideband LFM signal is as follows:

[0064]

[0065] Among them, t∈(0,T] represents the simulation time variable, T∈C is the duration of the signal, A(A≠0,A∈R) is the amplitude parameter of the LFM signal, and f c is the carrier frequency of the LFM signal, 0≤f c <f max , f max is the maximum frequency limit, K is the frequency modulation coefficient, B is the bandwidth. The power divider is controlled to split the ultra-wideband linear frequency modulation signal x(t) into two channels: a main sampling channel and a feedback sampling channel. The main sampling channel uses a low-speed analog-to-digital converter (ADC) to perform sub-Nyquist sampling on the split signal. The feedback sampling channel mixes the input signal with the feedback information of the main sampling channel and then performs sub-Nyquist sampling before splitting it into two asynchronous channels.

[0066] Step 2: The main sampling channel performs sub-Nyquist sampling on the shunt signal and uses a low-speed analog-to-digital converter ADC to uniformly sample the signal with a sampling rate of f s (f s<B, B is the bandwidth of the signal), then the sampling value is expressed as:

[0067]

[0068] Among them, n (n∈1,2,...N) represents the sampling point sequence, N is an integer, which represents the number of signal sampling samples, T s =1 / f s represents the sampling interval;

[0069] Step 3: Use the K parameter estimation algorithm to estimate the frequency modulation coefficient K parameter from the samples x[n] collected from the main channel; the process is described as follows:

[0070] Step 3.1, obtain three consecutive samples x[n], x[n+1], x[n+2] (n∈{1,2,3...,N}), respectively:

[0071]

[0072] Step 3.2: Eliminate the carrier frequency component. Divide the second sample by the first sample to obtain the sample:

[0073]

[0074] Divide the third sample by the second sample to get the sample:

[0075]

[0076] Then divide the sample X2 by the sample X1 to get the sample:

[0077]

[0078] In order to increase the robustness of the algorithm under noisy conditions, N-3 groups of samples are cross-divided to obtain the sample average:

[0079]

[0080] Step 3.3, calculate the frequency modulation coefficient K by taking the sample average value Y ver The frequency modulation coefficient K is obtained by using the principal value of the argument:

[0081]

[0082] Here, angle(·) represents the principal value of the argument of the complex number (·).

[0083] Step 4: Feedback sampling channel mixing operation, input the frequency modulation coefficient K value obtained from the main sampling channel into the feedback signal generator to generate an analog frequency modulation signal:

[0084]

[0085] Where t∈(0,T] represents the analog time variable and T∈C is the duration of the signal. The FM signal p(t) is then mixed with the input signal x(t) to obtain the mixed signal:

[0086]

[0087] Step 5: Asynchronous delayed sampling. In the feedback sampling channel, the mixing signal y(t) is split into two asynchronous delayed sampling channels: the first channel is f s (f s The sampling rate of <B) is uniformly sampled, and the collected samples are:

[0088]

[0089] Among them, the parameter U = e j2πfc / fs The second channel also processes the signal y(t) with f s (f s <B) sampling rate, but the sampling start time is delayed by T relative to the first channel e The amount of time, where the time delay is required to be less than or equal to the Nyquist sampling interval, that is, T e ≤1 / f max Assume that the sample obtained by sampling the second channel is represented by y e [n′], where n′ (n′∈1,2,...N′) represents the sampling point sequence, and N′ is an integer representing the number of samples of this signal.

[0090] Step 6: Use spectrum estimation algorithm to solve the amplitude parameter A. Estimating the amplitude parameter A and parameter U from the sample y[n] is a typical spectrum estimation problem. At this time, spectrum estimation methods can be used to solve it, such as the zeroing filter method. However, due to the periodicity of trigonometric functions, it is difficult to estimate the carrier frequency parameter f from the parameter U. c Frequency aliasing problems may occur, making the estimated carrier frequency parameter f c Error occurs when the system sampling rate can meet the requirements of Nyquist sampling theorem, that is, f s >f max (f max is the maximum frequency), the frequency parameter f c The solution is unique and is calculated as:

[0091]

[0092] Among them, 0≤∠(·)<π represents the principal value of the complex number (·). However, when the system sampling rate cannot meet the requirements of the Nyquist sampling theorem, that is, f s <fmax When the frequency parameter f c There will be multiple possible solutions:

[0093]

[0094] in, is the minimum possible solution that satisfies formula (13), Indicates the degree of deviation of other possible solutions. Since there are infinite values of m, the corresponding frequency parameter f c There are infinite solutions to this problem, which is called the "frequency aliasing" problem;

[0095] Step 7: Use the time-interleaved algorithm to solve the carrier frequency parameter f c Due to the existence of the "frequency aliasing" problem, the delayed sampling channel is used to collect samples for joint estimation to obtain the optimal carrier frequency parameter fc to solve the frequency aliasing problem and find the correct m value; in order to solve the frequency aliasing problem, an auxiliary sampling channel (delayed sampling channel) is added. The function of the auxiliary sampling channel is to find the correct frequency parameter from all possible solutions, that is, to obtain the correct frequency parameter from all possible solutions through the delayed sampling value y e [n′] determines the value of m, thereby finding the frequency parameter f c The exact solution of ; the steps are as follows:

[0096] Step 7.1: The sampling time of the auxiliary sampling channel differs from that of the main sampling channel by a time delay T e , the sampling rate is f s , then the delayed sampling value y e [n′] is expressed as follows:

[0097]

[0098] Among them, n′(n′∈1,2,...N′) represents the sampling point sequence, N′ is an integer, which represents the number of sampling samples of this signal. is a known quantity, is an unknown quantity. In order to solve for m, we need to first find the value of b and write the above formula as y e [n′]=a n′ b;

[0099] Step 7.2: Since the signal model is a single harmonic, only the first sample (n'=1) needs to be taken, where b=y e / a n′ , then according to Find the value of m;

[0100] Step 7.3, taking into account the frequency parameter f c Satisfy 0≤f c <f max, frequency parameter f c The minimum possible solution satisfy Combined with formula (13), we have:

[0101]

[0102] Simplifying the above relationship, we can get 0≤mf s <f max , therefore, when the delay T e satisfy When 0≤2πmf s T e <2π, then has a unique solution:

[0103]

[0104] Among them, ∠(·) represents the main value of the argument of (·), 0≤∠(·)<2π, similarly, when the delay T e satisfy When -2π<2πmf s T e ≤0, then There is a unique solution:

[0105]

[0106] In short, when the delay T e satisfy When , m can be uniquely determined:

[0107]

[0108] After obtaining m, the frequency parameter is determined as

[0109] Experimental comparison: In the first experiment, we verified that the method of the present invention can reconstruct the original signal with a small amount of calculation under noise-free conditions. In this experiment, we set the signal duration T = 0.1μs, amplitude A = 1.2, carrier frequency f c =450Mhz, the frequency modulation coefficient is K=5e16, and the recovery results in the absence of noise are shown in Table 1. As can be seen from the table, the method of the present invention can accurately recover the parameters of the original signal.

[0110] parameter Original value Estimated value A 1.2 1.2 <![CDATA[f c ]]> 450Mhz 450Mhz K 5e16 5e16

[0111] Table 1

[0112] In the second experiment, the reconstruction performance of the proposed method in the presence of noise was verified. In this experiment, the classical fractional Fourier transform (FRFT) algorithm was selected as a comparative experiment, and the parameters were set as signal duration T = 0.1 μs, amplitude A = 1.2, carrier frequency f c =450Mhz, the frequency modulation coefficient is K=2.5e16, and then Gaussian noise is added to the LFM signal to be measured. The signal-to-noise ratio (SNR) of this noise is defined as follows:

[0113]

[0114] Among them, P signal and P noise Represent the power of the signal and noise, respectively. The SNR value range is [0, 60]dB. In a noisy environment, the normalized mean squared error (NMSE) is used as the evaluation metric. For ease of comparison, its logarithmic form is used. Assuming that the experiment is repeated Num times, the NMSE of the frequency parameter can be calculated as:

[0115]

[0116] l k is the true value of the measured parameter, Represented as the parameter l in the i-th experiment k The experiment was conducted 1000 times in total, and the experimental results are shown in the figure below. Under the condition of low signal-to-noise ratio, this scheme still has good reconstruction performance. As the SNR increases, the method of the present invention has higher accuracy. The experimental results show that under the condition of low sampling rate that meets the sub-Nyquist sampling rate, the traditional FRFT algorithm will lose its effect in the environment of low signal-to-noise ratio and ultra-wideband signal model. The method of the present invention has higher accuracy and better anti-interference performance than the FRFT algorithm.

[0117] The embodiments of this specification are merely examples of implementations of the invention and are provided for illustrative purposes only. The scope of protection of the present invention should not be considered limited to the specific embodiments described in these embodiments. The scope of protection of the present invention also extends to equivalent technical means that can be conceived by a person of ordinary skill in the art based on the invention.

Claims

1. A method for multi-channel asynchronous sampling and parameter estimation of ultra-wideband linear frequency modulation signals, characterized in that: The method comprises the following steps: In step 1, the ultra-wideband LFM signal to be measured enters the power divider for splitting. The mathematical model of the ultra-wideband LFM signal is as follows: （1） in, represents the simulation time variable, is the duration of the signal, A is the amplitude parameter of the LFM signal, , , f c is the carrier frequency of the LFM signal, , f max is the maximum frequency limit, K is the frequency modulation coefficient, , B The power divider is controlled to split the ultra-wideband linear frequency modulation signal x(t) into two channels: a main sampling channel and a feedback sampling channel. The main sampling channel uses a low-speed analog-to-digital converter (ADC) to perform sub-Nyquist sampling on the shunted signal. The feedback sampling channel mixes the input signal with the feedback information of the main sampling channel and then performs sub-Nyquist sampling before splitting it into two asynchronous channels. Step 2: The main sampling channel performs sub-Nyquist sampling on the shunt signal and uses a low-speed analog-to-digital converter ADC to uniformly sample the signal with a sampling rate of f s , f s ＜B , B is the bandwidth of the signal, then the sampling value is expressed as: （2） in, n represents the sampling point sequence, , N is an integer, indicating the number of signal sampling samples. represents the sampling interval; Step three, use K The parameter estimation algorithm estimates the frequency modulation coefficient parameters from the samples x[n] collected by the main channel; the process is described as follows: Step 3.1, obtain three consecutive samples x[n], x[n+1], x[n+2], , respectively: (3) Step 3.2: Eliminate the carrier frequency component and divide the second sample obtained by the first sample to obtain the sample: (4) Divide the third sample by the second sample to get the sample: (5) Then the sample X 2 with sample X Divide by 1 to get the sample: (6) In order to increase the robustness of the algorithm under noisy conditions, we use N - Cross-divide the 3 groups of samples to get the sample average: (7) Step 3.3, calculate the frequency modulation coefficient K , by finding the sample mean Y ver The frequency modulation coefficient is obtained by taking the principal value of the argument K : (8) in, Indicates plural The principal value of the argument; Step 4: Feedback sampling channel mixing operation, the frequency modulation coefficient obtained by the main sampling channel K The value is input into the feedback signal generator to generate an analog FM signal: (9) in, represents the simulation time variable, is the duration of the signal, and then the FM signal p(t) is mixed with the input signal x(t) to obtain the mixed signal: （10） Step 5: Asynchronous delayed sampling. In the feedback sampling channel, the mixing signal y(t) is split into two asynchronous delayed sampling channels: the first channel is f s The sampling rate is uniformly sampled, f s < B , the samples collected are: （11） Among them, the parameters The second channel also processes the signal y(t) with f s Sampling is performed at a sampling rate of f s < B , but the sampling start time is delayed relative to the first channel T e The amount of time, where the time delay is required to be less than or equal to the Nyquist sampling interval, that is , assuming that the sample obtained by sampling the second channel is expressed as ,in: n’ represents the sampling point sequence, , N’ is an integer, indicating the number of samples of this signal; Step 6: Use spectrum estimation algorithm to solve amplitude parameters A , from the sample y [n] Calculate the amplitude parameters A and parameters U A typical spectrum estimation problem can be solved by spectrum estimation method. However, due to the periodicity of trigonometric function, the parameters U Estimated carrier frequency parameters f c Frequency aliasing problems may occur, making it difficult to estimate carrier frequency parameters f c Error occurs. When the system sampling rate can meet the requirements of Nyquist sampling theorem, that is, f s > f max hour, f max is the maximum frequency, frequency parameter f c The solution is unique and is calculated as: （12） in, Indicates plural However, when the system sampling rate cannot meet the requirements of Nyquist sampling theorem, that is, f s < f max When the frequency aliasing problem occurs, the frequency parameter f c There will be multiple possible solutions: （13） in, is the minimum possible solution that satisfies formula (13), Indicates the degree of deviation of other possible solutions, since m There are infinite values, and the corresponding frequency parameters f c There are infinite solutions to this problem, which is called the "frequency aliasing" problem; Step 7: Use time-interleaved algorithm to solve the carrier frequency parameters f c Due to the existence of the "frequency aliasing" problem, the optimal carrier frequency parameters are obtained by collecting samples through the delayed sampling channel and performing joint estimation. f c To solve the frequency aliasing problem, find the correct m In order to solve the frequency aliasing problem, an auxiliary sampling channel is added, namely the delayed sampling channel. The function of the auxiliary sampling channel is to find the correct frequency parameter from all possible solutions, that is, to delay the sampling value. Sure m The value of , thus finding the frequency parameter f c The exact solution of .

2. The method for multi-channel asynchronous sampling and parameter estimation of ultra-wideband linear frequency modulation signals according to claim 1, wherein: The steps of step seven are as follows: Step 7.1: The sampling time of the auxiliary sampling channel differs from that of the main sampling channel by a time delay. T e , the sampling rate is f s , then the delayed sampling value It is expressed as follows: （14） in, n’ represents the sampling point sequence, , N’ is an integer, indicating the number of samples of this signal. is a known quantity, is an unknown quantity, in order to solve m , you need to first obtain b The value of , the above formula can be written as ; Step 7.2: Since the signal model is a single harmonic, only the first sample needs to be taken, where , then according to Find m The value of Step 7.3, taking into account the frequency parameter f c Satisfy 0≤ f c ≤ f max , frequency parameter f c The minimum possible solution satisfy , combined with formula (13), we have: （15） Simplifying the above relationship, we get 0≤ mf s ≤ f max , so when the delay T e satisfy Sometimes, there are ,So has a unique solution: （16） in, express The principal value of the argument, , similarly, when the delay T e satisfy Sometimes, there are ,So There is a unique solution: （17） In short, when the delay T e satisfy hour, m Can be uniquely determined: （18） In seeking m After that, the frequency parameter is determined as .

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