LFM signal parameter estimation method based on matched Fourier transform and box dimension

Abstract

The invention relates to the field of radar signal processing, in particular to an LFM signal parameter estimation method based on matched Fourier transform and box dimension, and mainly solves the problems that an existing LFM signal parameter estimation method of a radar interception receiver is high in complexity and poor in estimation performance under the low signal-to-noise ratio. According to the method, for received radar echoes, firstly, a matching Fourier transform primary function is constructed by adopting a hierarchical iteration method, and matching Fourier transform is carried out; then carrying out normalization processing on the converted frequency spectrum; then calculating box dimensions of the normalized frequency spectrum under different transformation bases, taking the transformation base corresponding to the minimum box dimension as a matching base function of the LFM signal, and obtaining an estimated value of the frequency modulation slope of the LFM signal through the transformation base; on the basis of frequency modulation slope estimation, the center frequency of the LFM signal can be obtained through one-time Fourier transform.

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal processing. Background Art

[0002] Linear Frequency Modulation (LFM) has been widely used in radar, communication and other fields because of its large time-bandwidth product. In the process of radar passive detection, friend-or-foe identification and communication, the effective estimation of the frequency modulation slope and center frequency of LFM signals under low signal-to-noise ratio is a major difficulty. The traditional Fourier transform cannot directly obtain the instantaneous frequency information of the signal. Although the short-time Fourier transform can reflect the time-frequency characteristics of the signal to a certain extent, its time-frequency resolution is limited by the length of the slice window. As a nonlinear transform, the Wigner-Ville transform will have serious cross-term interference under the condition of multi-component LFM signals. In recent years, fractional Fourier transform, as an emerging time-frequency analysis tool, has been widely used in parameter estimation of LFM signals. However, in the parameter estimation process, peak search needs to be performed in the two-dimensional fractional Fourier transform domain.

[0003] Chen Yanli et al. specifically disclosed a method for estimating LFM signal parameters based on fractional Fourier transform in their patent publication number CN105783974B, entitled "A method and system for detecting and estimating parameters of linear frequency modulation signals". This method calculates the fractional Fourier spectrum of the LFM signal at different rotation angles, then performs peak search in the two-dimensional directions of angle and frequency, and calculates the frequency modulation slope of the LFM signal through the corresponding coordinates of the peak point. The disadvantage of this method is that under the same parameter estimation accuracy, more fractional Fourier transforms are required, and a maximum value search is required on a two-dimensional plane, which greatly increases the amount of calculation.

[0004] Cao Weihao et al. proposed a method for estimating the parameters of linear frequency modulation signals based on short-time fractional Fourier transform and variable weight fitting in their paper "Linear frequency modulation signal parameter estimation based on interpolated short-time fractional Fourier transform and variable weight fitting. Acta Armamentarii, 2020, 41(1):86-94". This method estimates the instantaneous frequency of the LFM signal in each slice and fits the linear variation law of the instantaneous frequency in different slices to achieve the purpose of estimating the parameters of the LFM signal. The disadvantage of this method is that the instantaneous frequency of LFM is estimated by the maximum frequency in the time domain signal slice, which is easily affected by the slice width and noise power. The error of the LFM signal parameter estimation is large. At the same time, the two-dimensional time-frequency transform also has the problem of large computational complexity. Summary of the invention

[0005] In view of the problems that the existing LFM signal parameter estimation methods have high complexity and poor estimation performance under low signal-to-noise ratio, the present invention proposes a LFM signal parameter estimation method based on matching Fourier transform and box dimension, adopts a hierarchical iterative method to construct matching Fourier transform basis functions, which can greatly reduce the amount of calculation and improve the parameter estimation accuracy of the LFM signal. On this basis, the box dimension method is used to describe the spectrum of LFM under different matching Fourier transform basis functions, and the matching Fourier transform basis function corresponding to the minimum box dimension is used to estimate the frequency modulation rate of the LFM signal, and the algorithm of the traditional two-dimensional plane peak search is reduced to a one-dimensional plane search, which can further reduce the number of searches. On the basis of the estimation of the frequency modulation slope of the LFM signal, the corresponding matching Fourier transform basis function is constructed, and the center frequency of the LFM signal can be estimated by a single Fourier transform.

[0006] In order to achieve the above technical objectives, the present invention proposes a method for estimating LFM signal parameters based on matching Fourier transform and box dimension, the implementation process of which includes:

[0007] Step 1: For the discrete LFM signal s(n) received by the radar, construct the matching Fourier transform basis function h(n) in the search range p∈(0,2) by hierarchical iteration, make a rough estimate of the frequency modulation slope of the LFM signal, and set the search step size M is a positive integer, the search value is (0:Δp:2), the matching Fourier transform is calculated for each search value, the transformed spectrum is S(k), the spectrum is normalized, the normalized result is S1(k), the box dimension D corresponding to the normalized spectrum S1(k) is calculated b , the search value corresponding to the minimum box dimension is recorded as p′, and the rough estimate of the frequency modulation slope of the LFM signal is

[0008]

[0009] Step 2: Construct a precise search range of the LFM signal according to the search value p′ corresponding to the rough estimate of the LFM signal frequency modulation slope. The precise search range is set to [p′-Δp, p′+Δp], and the search step length Δp′ is set to Calculate the matching Fourier transform under each search value, normalize it, calculate the box dimension of the normalized spectrum, and record the search value corresponding to the minimum box dimension as Estimation of the frequency modulation slope of the LFM signal

[0010] Step 3: Determine whether the search step length Δp′ is less than the set fine search step length threshold T h , T h ∈(0,0.2], if it is less than T h , then the estimated value That is, the accurate estimate of the frequency modulation slope μ of the LFM signal. Otherwise, according to the search value And the search step length Δp′ constructs a further fine search range The search step size is set to Through multiple iterations, until the search step size is less than T h until;

[0011] Step 4: Based on the estimation of the frequency modulation slope of the LFM signal, use the estimated value Construct a matching Fourier transform basis and perform matching Fourier transform. The abscissa f0′ corresponding to the maximum value of the spectrum is the estimated value of the center frequency f0 of the LFM signal.

[0012] Furthermore, the discrete LFM signal in step 1 Where exp represents the exponential calculation with the natural constant e as the base, j represents the symbol of the imaginary unit, T s represents the time domain sampling interval, N represents the discrete signal length, n∈(0,1,…,N-1), f0 represents the LFM signal center frequency, μ=B / T represents the LFM signal frequency modulation slope, B is the LFM signal bandwidth, T is the LFM signal pulse width, and the sampling rate fs=1 / T s And fs≥2B.

[0013] Furthermore, the matching Fourier transform basis function constructed in step 1 is h(n)=exp[jπ(nT s ) 2 cotα], cot is the cotangent operation.

[0014] Furthermore, in step 1, the Fourier transform spectrum is matched

[0015] Furthermore, in step 1, the Fourier transform normalized spectrum is matched

[0016] Furthermore, the box dimension calculation in step 1 further includes:

[0017] Step 1-1: For the normalized spectrum sampling interval q = 1 / N, calculate the intermediate variable

[0018]

[0019] Step 1-2: Box Dimension D b =-lnZ(q) / lnq.

[0020] Furthermore, in step 2, the LFM signal is used to accurately estimate the value The constructed matching Fourier transform basis function is

[0021]

[0022] Compared with the prior art, the present invention has the following significant advantages: 1) The LFM signal parameter estimation method based on matching Fourier transform and box dimension proposed in the present invention adopts a hierarchical iterative method to construct matching Fourier transform basis functions, which can greatly reduce the amount of calculation and improve the parameter estimation accuracy of the LFM signal; 2) The box dimension method is used to describe the frequency spectrum of LFM under different matching Fourier transform basis functions, and the frequency modulation rate of the LFM signal is estimated by the matching Fourier transform basis function corresponding to the minimum box dimension, and the traditional two-dimensional plane peak search algorithm is reduced to a one-dimensional plane search, which can further reduce the number of peak searches; 3) Based on the estimation of the frequency modulation slope of the LFM signal, the corresponding matching Fourier transform basis function is constructed, and the center frequency of the LFM signal can be estimated by a single Fourier transform. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Flow chart for implementing the present invention. DETAILED DESCRIPTION

[0024] The implementation process of the present invention is described in detail below.

[0025] Taking a shore-based passive sea detection radar as an example, the radar echo data received in a certain detection area of ​​the radar within a period of time is r(t)=s(t)+n(t), where s(t) is a discrete LFM signal and n(t) is the radar receiver noise. In order to estimate the frequency modulation slope of the LFM signal, the specific implementation steps are as follows:

[0026] Step 1: Make a rough estimate of the frequency modulation slope of the LFM signal within the search range p∈(0,2). First, use a larger search step size M is set to 100, the search value is set to (0:0.02:2), and the Fourier transform basis function h(n) = exp[jπ(nT s ) 2 cotα], cot is the cotangent operation. Calculate the matching Fourier transform under each search value The transformed spectrum is S(k), and the spectrum is normalized. The normalized result is When q = 1 / N, calculate the intermediate variable Then the box dimension D corresponding to the normalized spectrum S1(k) is b = -lnZ(q) / lnq, the search value corresponding to the minimum box dimension is recorded as p′, the rough estimate of the frequency modulation slope of the LFM signal

[0027] Step 2: Construct the LFM signal fine search range according to the search value p′ corresponding to the rough estimate of the LFM signal frequency modulation slope. The fine search range is set to [p′-Δp, p′+Δp]. Here, the search step Δp′ becomes 0.0002. Calculate the matching Fourier transform under each search value and normalize it. Calculate the box dimension of the normalized spectrum. The search value corresponding to the minimum box dimension is recorded as Estimation of the frequency modulation slope of the LFM signal

[0028] Step 3: Determine whether the search step length Δp′ is less than the set fine search step length threshold T h , T h Set to 0.001. If it is less than T h , then the estimated value That is, the accurate estimate of the frequency modulation slope μ of the LFM signal. Otherwise, according to the search value And the search step length Δp′ constructs a further fine search range The search step size is set to Continue iterating according to step 2 until the search step size is less than T h So far, the final estimated value That is the precise estimate of the frequency modulation slope μ of the LFM signal.

[0029] Step 4: Based on the estimation of the frequency modulation slope of the LFM signal, use the estimated value Construct a matching Fourier transform basis and perform a matching Fourier transform. At this time, the matching Fourier transform is The matching Fourier transform result is approximately when When the maximum value is taken, f=f0, then the abscissa f0′ corresponding to the maximum value of the normalized spectrum is the estimated value of the center frequency f0 of the LFM signal.

Claims

1. A method for estimating LFM signal parameters based on matching Fourier transform and box dimension, characterized in that: Step 1: For the discrete LFM signal s(n) received by the radar, construct the matching Fourier transform basis function h(n) in the search range p∈(0,2) by hierarchical iteration, make a rough estimate of the frequency modulation slope of the LFM signal, and set the search step size M is a positive integer, the search value is (0:Δp:2), the matching Fourier transform is calculated for each search value, the transformed spectrum is S(k), the spectrum is normalized, the normalized result is S1(k), the box dimension D corresponding to the normalized spectrum S1(k) is calculated b , the search value corresponding to the minimum box dimension is recorded as p′, and the rough estimate of the frequency modulation slope of the LFM signal is Step 2: Construct a precise search range of the LFM signal according to the search value p′ corresponding to the rough estimate of the LFM signal frequency modulation slope. The precise search range is set to [p′-Δp, p′+Δp], and the search step length Δp′ is set to Calculate the matching Fourier transform under each search value, normalize it, calculate the box dimension of the normalized spectrum, and record the search value corresponding to the minimum box dimension as Estimation of the frequency modulation slope of the LFM signal Step 3: Determine whether the search step length Δp′ is less than the set fine search step length threshold T h , T h ∈(0,0.2), if it is less than T h , then the estimated value That is, the accurate estimate of the frequency modulation slope μ of the LFM signal. Otherwise, according to the search value And the search step length Δp′ constructs a further fine search range The search step size is set to Through multiple iterations, until the search step size is less than T h until; Step 4: Based on the estimation of the frequency modulation slope of the LFM signal, use the estimated value Construct a matching Fourier transform basis and perform matching Fourier transform. The abscissa f0′ corresponding to the maximum value of the spectrum is the estimated value of the center frequency f0 of the LFM signal.

2. The method for estimating LFM signal parameters based on matched Fourier transform and box dimension according to claim 1, characterized in that: In step 1, the LFM signal is discretized Where exp represents the exponential calculation with the natural constant e as the base, T s represents the time domain sampling interval, N represents the discrete signal length, n∈(0,1,…,N-1), f0 represents the LFM signal center frequency, μ=B / T represents the LFM signal frequency modulation slope, B is the LFM signal bandwidth, T is the LFM signal pulse width, and the sampling rate fs=1 / T s And fs≥2B.

3. The method for estimating LFM signal parameters based on matched Fourier transform and box dimension according to claim 1, characterized in that: The matching Fourier transform basis function constructed in step 1 is h(n)=exp[jπ(nT s ) 2 cotα], p∈(0,2), cot is the cotangent operation.

4. The method for estimating LFM signal parameters based on matched Fourier transform and box dimension according to claim 1, characterized in that: In step 1, the Fourier transform spectrum is matched 5. The method for estimating LFM signal parameters based on matched Fourier transform and box dimension according to claim 1, characterized in that: In step 1, the Fourier transform normalized spectrum is matched 6. The method for estimating LFM signal parameters based on matched Fourier transform and box dimension according to claim 1, characterized in that: The box dimension calculation in step 1 also includes: Step 1-1: For the normalized spectrum sampling interval q=1 / N, calculate the intermediate variable: Step 1-2: Box Dimension D b =-lnZ(q) / lnq.

7. The method for estimating LFM signal parameters based on matched Fourier transform and box dimension according to claim 1, characterized in that: In step 2, the LFM signal is used to accurately estimate the value The constructed matching Fourier transform basis function is

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