A method for estimating parameters of LFM signal based on matching Fourier transform and box dimension

Abstract

The present application relates to the field of radar signal processing, in particular to a LFM signal parameter estimation method based on matched Fourier transform and box dimension, mainly solving the problems of high complexity and poor estimation performance under low signal-to-noise ratio of the existing LFM signal parameter estimation method of radar intercept receiver. For the received radar echo, firstly, a hierarchical iteration method is adopted to construct a matched Fourier transform basis function and perform matched Fourier transform; then the transformed spectrum is normalized; then the box dimension of the normalized spectrum under different transform bases is calculated, the transform base corresponding to the minimum box dimension is taken as the matched basis function of the LFM signal, and the estimation value of the frequency modulation slope of the LFM signal can be obtained through the transform base; on the basis of the frequency modulation slope estimation, the center frequency of the LFM signal can be obtained through one Fourier transform.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radar signal processing. BACKGROUND

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

[0003] Yanli Chen et al. in their publication CN105783974B, entitled "A linear frequency modulation signal detection, parameter estimation method and system" specifically discloses a LFM signal parameter estimation method based on fractional Fourier transform. The method calculates the fractional Fourier spectrum of LFM signal under different rotation angles, then carries out peak value search in the two-dimensional direction of angle and frequency, and calculates the frequency modulation slope of LFM signal through the coordinates corresponding to the peak points. The deficiency of this method is that more times of fractional Fourier transform are needed under the same parameter estimation accuracy, and maximum value search needs to be carried out in the two-dimensional plane, which greatly increases the amount of calculation.

[0004] Wei-hao Cao et al. in their published paper "Linear frequency modulation signal parameter estimation based on interpolation short-time fractional Fourier transform-variable weight fitting. Ordnance Industry Academy, 2020, 41(1): 86-94" propose a linear frequency modulation signal parameter estimation method based on short-time fractional Fourier transform-variable weight fitting. The method estimates the instantaneous frequency of LFM signal in each slice, fits the linear variation law of instantaneous frequency in different slices, and achieves the purpose of estimating LFM signal parameters. The deficiency of this method is that the maximum frequency in the time domain signal slice is used to estimate the instantaneous frequency of LFM, which is easily affected by the slice width and noise power, and the LFM signal parameter estimation error is large. At the same time, the two-dimensional time-frequency transform also has the problem of large amount of calculation. SUMMARY

[0005] In view of the problems of high complexity and poor estimation performance under low signal-to-noise ratio of the existing LFM signal parameter estimation method, the application provides an LFM signal parameter estimation method based on matched Fourier transform and box dimension, a hierarchical iterative method is adopted to construct a matched Fourier transform base function, the operation amount is greatly reduced, and the parameter estimation precision of the LFM signal is improved, on this basis, a box dimension method is adopted to describe the spectrum of the LFM under different matched Fourier transform base functions, the frequency modulation rate of the LFM signal is estimated through the matched Fourier transform base function corresponding to the minimum box dimension, the search times are further reduced by reducing the two-dimensional plane peak search algorithm to one-dimensional plane search.

[0006] In order to achieve the above technical purpose, the application provides an LFM signal parameter estimation method based on matched Fourier transform and box dimension, and the implementation process comprises the following steps:

[0007] Step 1: a discrete LFM signal s(n) received by a radar is constructed in a hierarchical iterative method in a search range p e (0, 2) to construct a matched Fourier transform base function h(n), the frequency modulation rate of the LFM signal is coarsely estimated, and the search step is set as M is a positive integer, the search value is (0: Δp: 2), the matched Fourier transform under each search value is calculated, the spectrum after the transformation is S(k), the spectrum is normalized, the normalized processing result is S1(k), and 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 coarse estimation value of the frequency modulation rate of the LFM signal is

[0008]

[0009] Step 2: the search range of the LFM signal is constructed according to the search value p' corresponding to the coarse estimation value of the frequency modulation rate of the LFM signal, the fine search range is set as [p'- Δp, p'+ Δp], and the search step Δp' is set as The matched Fourier transform under each search value is calculated, and the normalized processing is performed, the box dimension of the normalized spectrum is calculated, and the search value corresponding to the minimum box dimension is recorded as The estimation value of the frequency modulation rate of the LFM signal is

[0010] Step 3: whether the search step Δp' is smaller than the set fine search step threshold T is judged h , T h e (0, 0.2], if smaller than T h , the estimation value That is, the precise estimate of the LFM signal modulation slope μ; otherwise, the search value is used. Construct a further refined search range using the search step size Δp′. 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 LFM signal frequency modulation slope estimation, use the estimated value... Construct a matched Fourier transform basis and perform a matched Fourier transform. The x-coordinate f0′ corresponding to the maximum spectral value is the estimated value of the center frequency f0 of the LFM signal.

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

[0013] Furthermore, the matched 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 matched Fourier transform normalized spectrum...

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

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

[0018]

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

[0020] Furthermore, in step 2, the LFM signal is used to precisely estimate the value. The constructed matched Fourier transform basis functions are

[0021]

[0022] Compared with the prior art, the present application has the following advantages: 1) the LFM signal parameter estimation method based on the matched Fourier transform and the box dimension proposed by the present application can improve the parameter estimation precision of the LFM signal while greatly reducing the operation amount by adopting the hierarchical iteration method to construct the matched Fourier transform base function; 2) the box dimension method is adopted to describe the spectrum of the LFM in different matched Fourier transform base functions, and the frequency modulation rate of the LFM signal is estimated by the matched Fourier transform base function corresponding to the minimum box dimension, so that the two-dimensional plane peak search algorithm is reduced to one-dimensional plane search, and the peak search times can be further reduced; 3) on the basis of the frequency modulation rate estimation of the LFM signal, the corresponding matched Fourier transform base function is constructed, and the center frequency of the LFM signal can be estimated by one Fourier transform. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 The flowchart of the present application is shown. DETAILED DESCRIPTION

[0024] The implementation process of the present application is described in detail as follows.

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

[0026] Step 1: the frequency modulation rate of the LFM signal is coarsely estimated in the search range p ∈ (0, 2), and a larger search step size is first taken M is set to 100, the search value is set to (0:0.02:2), the matched Fourier transform base function h(n) = exp[jπ(nT s ) 2 cotα], cot is the cotangent operation. The matched Fourier transform S(k) is calculated under each search value. The spectrum after the matched Fourier transform is S(k), and the normalized processing result is When q = 1 / N, the intermediate variable is calculated. The box dimension D b of the normalized spectrum S1(k) is -lnZ(q) / lnq, the search value corresponding to the minimum box dimension is recorded as p', and the coarse estimation value of the frequency modulation rate of the LFM signal is

[0027] Step 2: Construct the fine search range of LFM signal according to the search value p' corresponding to the coarse estimate of the frequency modulation slope of LFM signal, the fine search range is set as [p'-Δp, p'+Δp], here the search step Δp' is changed to 0.0002, calculate the matching Fourier transform under each search value, and normalize the processing, calculate the box dimension of the normalized spectrum, and record the search value corresponding to the minimum box dimension as The estimate of the frequency modulation slope of LFM signal

[0028] Step 3: Determine whether the search step Δp' is less than the set fine search step threshold T h , T h is set to 0.001, if it is less than T h , then the estimate is the fine estimate of the frequency modulation slope μ of LFM signal, otherwise, construct a further fine search range according to the search value and the search step Δp', the search step is set as Continue iteration according to the method of step 2 until the search step is less than T h , the final estimate is the fine estimate of the frequency modulation slope μ of LFM signal.

[0029] Step 4: On the basis of the estimate of the frequency modulation slope of LFM signal, construct the matching Fourier transform basis using the estimate , and perform the matching Fourier transform, at this time the matching Fourier transform is The result of the matching Fourier transform is approximately When takes the maximum value, f=f0, then the abscissa f0' corresponding to the maximum value of the normalized spectrum is the estimate of the center frequency f0 of LFM signal.

Claims

1. A method for LFM signal parameter estimation based on matched Fourier transform and box dimension, characterized in that: Step 1: constructing the matching Fourier transform base function h(n) in a hierarchical iterative method in the search range p∈(0,2) for the discrete LFM signal s(n) received by the radar, coarsely estimating the frequency modulation slope of the LFM signal, and setting the search step M is a positive integer, the search value is (0:Δp:2), the matching Fourier transform under each search value is calculated, 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', the coarsely estimated value of the frequency modulation slope of the LFM signal is Step 2: Construct the fine search range of LFM signal according to the search value p' corresponding to the coarse estimation value of the frequency modulation slope of the LFM signal, and set the fine search range as [p'-Ap, p'+Ap], and set the search step Ap' as Calculate the matching Fourier transform under each search value, and normalize the processing, calculate the box dimension of the normalized spectrum, and record the search value corresponding to the minimum box dimension as The estimation value of the frequency modulation slope of the LFM signal Step 3: Determine whether the search step size Δp′ is less than the set fine search step size threshold T. h T h ∈(0,0.2), if less than T h Then the estimated value That is, the precise estimate of the LFM signal modulation slope μ; otherwise, the search value is used. Construct a further refined search range using the search step size Δp′. 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, the estimated value The matching Fourier transform base is constructed, and the matching Fourier transform is performed. 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 LFM signal parameter estimation method based on matching Fourier transform and box dimension according to claim 1, characterized in that: the discrete LFM signal in step 1 where exp denotes the exponential calculation with the natural constant e, T s denotes the time domain sampling interval, N denotes the length of the discrete signal, n ∈ (0, 1, …, N-1), f0denotes the center frequency of the LFM signal, μ = B / T denotes the frequency modulation slope of the LFM signal, B is the bandwidth of the LFM signal, T is the pulse width of the LFM signal, and the sampling rate fs = 1 / T s and fs≥ 2B.

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

4. The LFM signal parameter estimation method based on matching Fourier transform and box dimension according to claim 2, characterized in that: The step 1 matched Fourier transform spectrum 5. The LFM signal parameter estimation method based on matching Fourier transform and box dimension according to claim 1, characterized in that: The step 1 matched Fourier transform normalized spectrum 6. The LFM signal parameter estimation method based on matching Fourier transform and box dimension according to claim 2, characterized in that, The box dimension calculation in step 1 further comprises: Step 1-1: For the normalized spectrum sampling interval q = 1 / N, calculate the intermediate variable: Steps 1-2: Box dimension D b = -ln Z(q) / ln q.

7. The LFM signal parameter estimation method based on matching Fourier transform and box dimension according to claim 2, characterized in that: The step 2 utilizes the LFM signal to refine the value The constructed matched Fourier transform basis function is

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