阅读说明：本技术 傅里叶变换的lfm-bpsk复合调制雷达信号参数估计方法 (Fourier transform LFM-BPSK composite modulation radar signal parameter estimation method ) 是由 张文旭 范晓蕾 赵忠凯 孙富礼 杜秋影 姚雨双 何俊希 张恒 张春光 李广琦 于 2019-10-15 设计创作，主要内容包括：本发明公开了傅里叶变换的LFM-BPSK复合调制雷达信号参数估计方法,属于雷达信号处理技术领域。首先对LFM-BPSK复合调制信号进行平方处理用于去除相位编码调制,基于插值补偿的优化分数阶傅里叶变换算法对该线性调频信号的起始频率和调频系数进行估计计算,然后重构线性调频信得到基带二相编码信号,最后基于循环谱相关算法提取二相编码信号的码速率。由于采用了插值优化分数阶傅里叶变换算法,提高了对复合信号初始频率和调频斜率的参数估计精度,也间接提高了利用循环谱相关算法对码元速率的估计精度。结合滤波处理和信号重构有效提高了信号参数估计的稳定性。通过参数估计的仿真结果表明在低信噪比下仍具有较高的估计精度和稳定性。(The invention discloses a Fourier transform LFM-BPSK composite modulation radar signal parameter estimation method, and belongs to the technical field of radar signal processing. Firstly, carrying out square processing on an LFM-BPSK composite modulation signal to remove phase coding modulation, carrying out estimation calculation on the initial frequency and the frequency modulation coefficient of the linear frequency modulation signal based on an optimized fractional Fourier transform algorithm of interpolation compensation, then reconstructing the linear frequency modulation signal to obtain a baseband two-phase coding signal, and finally extracting the code rate of the two-phase coding signal based on a cyclic spectrum correlation algorithm. Due to the adoption of the interpolation optimization fractional Fourier transform algorithm, the parameter estimation precision of the initial frequency and the frequency modulation slope of the composite signal is improved, and the estimation precision of the code element rate by using the cyclic spectrum correlation algorithm is also indirectly improved. The stability of signal parameter estimation is effectively improved by combining filtering processing and signal reconstruction. The simulation result of parameter estimation shows that the method still has higher estimation precision and stability under the condition of low signal-to-noise ratio.)

1. The method for estimating the LFM-BPSK composite modulation radar signal parameters through Fourier transform is characterized by mainly comprising the following steps of:

step 1: squaring the LFM-BPSK composite modulation signal to remove phase coding modulation, and converting the original composite modulation signal into a frequency-doubled linear frequency modulation signal;

step 2: estimating the initial frequency and the frequency modulation coefficient of the linear frequency modulation signal by adopting a method from rough estimation to accurate estimation based on an optimized fractional Fourier transform algorithm of interpolation compensation;

and step 3: reconstructing a linear frequency modulation signal by the estimated initial frequency and the frequency modulation coefficient, and carrying out conjugate multiplication on the reconstructed linear frequency modulation signal and the original LFM-BPSK composite modulation signal to obtain a baseband two-phase coding signal;

and 4, step 4: and extracting the code rate of the two-phase coded signal based on a cyclic spectrum correlation algorithm.

2. The method of claim 1, wherein in step 1, the square-multiplied chirp signal is obtained by: the LFM-BPSK signal model can be expressed as:

wherein q (T) is 1, T ∈ [0, T ∈₀]，f₀K is the chirp rate, k is the bandwidth of the signal, B is the bandwidth of the signal, T is NT₀Is the signal time width, q (T) is a rectangular signal, T₀Is the symbol time width, phi₀Is a binary sequence;

firstly, removing phase coding information of an LFM-BPSK composite modulation signal through square processing, wherein an expression after the original signal processing is as follows: x is the number of²(t)＝A²exp{j[4π(f₀t+kt²/2)+2φ(t)]And (2) phi (t) belongs to {0, 2 pi }, squaring the LFM-BPSK composite modulation signal and converting the LFM-BPSK composite modulation signal into a linear frequency modulation signal with noise, wherein the expression of the signal after squaring is as follows:

x²(t)＝A²exp{j[4π(f₀t+kt²/2)]}+N(t)，

wherein N (t) is 2A. exp [ j (2 π f)₀t+πkt²)]·n(t)+n²And (t) is equivalent noise after the LFM-BPSK complex modulation signal is squared.

3. The fourier transformed LFM-BPSK complex modulated radar signal parameter of claim 1The number estimation method is characterized in that the interpolation compensation optimization fractional Fourier transform principle in the step 2 is that the coordinates (α) corresponding to the real peak points₀,u₀) The conditions are satisfied:

the true peak point correspondence values are:

in the formula u₀' represents the coordinates of the quasi-peak point in the fractional order u domain;

the resolution of the discretization u domain causes deviation on the searching of the peak point, and the following can be obtained:

in the formula, α₀' denotes the coordinates of the quasi-peak point in the α domain, α₀、u₀α domain and u domain coordinates representing the true peak point, respectively;

when | A |²/σ_ω ²·|Δl2/π|²＝SNR·4N/π²When > 1:

from α'₀And (3) carrying out interpolation compensation on u by using a function expression of order fractional Fourier transform to obtain more accurate coordinates:

if X₂＞X₁If r is 1, then X₁＞X₂When the ratio of r is-1,

4. the method for estimating the parameters of the Fourier transformed LFM-BPSK complex modulated radar signal as recited in claim 3, wherein the substep of step 2 comprises:

step 2.1: squaring the LFM-BPSK composite modulation signal to obtain a frequency-doubled linear frequency modulation signal;

step 2.2: performing noise reduction processing on the frequency-doubled linear frequency modulation signal by adopting an optimized segmented filtering algorithm;

step 2.3: coarse estimation and accurate estimation are sequentially carried out by adopting fractional Fourier transform algorithm optimized by interpolation to obtain estimation results of initial frequency and frequency modulation slope

Step 2.4: calculating to obtain the initial frequency of the estimated value of the original signal according to the estimation result in the step 3

5. The method for estimating the parameters of the fourier transformed LFM-BPSK complex modulated radar signal according to claim 1, wherein the phase-coded signal in step 3 is obtained by: obtaining an initial frequencyRate of change

In the formula

Assuming that the initial frequency and chirp rate of the signal have higher estimation accuracy, Δ f → 0, Δ k → 0, and s_BThe expression for (t) signal can be written as: s_B(t)＝A·exp[j·θ(t)]+ ω' (t) signal s_B(t) estimating the signal code rate R for the noisy two-phase coded signal by using a cyclic spectrum correlation method_b。

6. The method for estimating the parameters of the Fourier transformed LFM-BPSK complex modulated radar signal as recited in claim 1, wherein the substep of step 4 is:

step 4.1: calculating a signal s_B(t) cyclic spectral correlation function

Step 4.2, searching α as 0 on the (α, f) two-dimensional plane, and obtaining the characteristic spectrum module value

Step 4.3: signal carrier frequency f is obtained from step 4.2_cAt frequency f ═ f_cIn the vicinity of the cycle frequency α being 0, the characteristic spectrum modulus is obtainedRespectively, corresponding to a cyclic frequency of α₁、α₂Then the estimated value of the symbol rate of the signal is: f. of_d＝(|α₁|+|α₂|)/2。

Technical Field

The invention belongs to the technical field of radar signal processing, and particularly relates to a Fourier transform LFM-BPSK composite modulation radar signal parameter estimation method.

Background

The LFM-BPSK composite modulation signal has the advantages of both a linear frequency modulation signal and a phase coding signal, has better low interception performance, and is widely applied to various radars. The waveform is more complex and the spectrum is distributed similarly to a chirp signal but is more oscillating. The composite modulation radar signal is formed by combining a plurality of modulation modes, and can combine the advantages of a plurality of signals and make up the respective defects of the signals. Compared with a single modulation type signal, the composite modulation signal can obtain a larger time-bandwidth product, has better distance resolution and speed resolution, simultaneously improves low interception performance, increases the difficulty of interception, detection and identification of an enemy reconnaissance receiver, and creates a severe challenge for the traditional radar reconnaissance receiver.

The basic idea of the parameter estimation of the complex modulation signal is to perform modulation separation, and convert the complex modulation signal into a single modulation signal, for example, the LFM-BPSK complex modulation signal can be converted into a chirp signal and a bi-phase encoded signal. The LFM-BPSK signal is squared to remove phase coding modulation, the signal is converted into a linear frequency modulation signal, the initial frequency and the frequency modulation coefficient of the LFM signal are estimated by adopting an interpolation optimization fractional Fourier transform method, then the linear frequency modulation signal is reconstructed and is subjected to conjugate multiplication with the original LFM-BPSK composite modulation signal to obtain a baseband BPSK signal, and finally the code rate of the BPSK signal is extracted by adopting a cyclic spectrum correlation technique.

In the aspect of LFM-BPSK composite modulation radar signal parameter estimation, documents 'LFM-BPSK composite modulation signal parameter estimation under pulse noise', 'LFM-BPSK composite modulation signal identification and parameter estimation' and 'LFM-BPSK composite modulation signal identification and parameter estimation' are all parameter estimation for researching the LFM-BPSK composite modulation signal, but the adopted parameter estimation algorithm does not relate to fractional order Fourier transform and cyclic spectrum correlation of interpolation optimization, and is different from the method provided by the invention patent; the document 'research on SAR waveform anti-interference technology based on LFM-PC composite modulation signals' is used for researching the anti-interference problem of composite modulation signals, does not relate to a parameter estimation method, and is different from the patent of the invention; documents LFM signal parameter estimation based on fractional fourier transform and LPI radar signal parameter estimation method research based on FRFT are both researches on fractional fourier transform, but not on parameter estimation of LFM-BPSK complex modulation signals, and a fractional fourier transform algorithm for interpolation optimization is not proposed, which is different from the patent of the present invention; the document LFM-BPSK composite modulation signal parameter estimation based on L-DFT under Alpha stable distributed noise is a research on the parameter estimation problem of composite modulation signal under Alpha stable distributed noise, and the used method is different from the invention patent.

The patent "a method for estimating parameters of phase-coded signals based on undersampling" and "a method and a system for estimating parameters of polynomial phase signals" both study the problem of estimating parameters of phase-coded signals, do not relate to the parameter estimation of complex modulation signals, and are different from the patent of the present invention. Although the patent of 'a linear frequency modulation signal parameter estimation method based on wavelet packet denoising and power spectrum entropy' and 'a DS/FH spread spectrum signal parameter estimation method based on cyclic spectrum theory' are also parameter estimation algorithms for researching signals, the patent does not relate to parameter estimation of LFM-BPSK composite modulation signals, and is different from the patent of the invention.

Disclosure of Invention

The invention aims to provide a Fourier transform LFM-BPSK composite modulation radar signal parameter estimation method which is low in complexity, high in stability and good in effect.

The purpose of the invention is realized by the following technical scheme:

the method for estimating the LFM-BPSK composite modulation radar signal parameters through Fourier transform comprises the following steps:

step 1, performing square processing on an LFM-BPSK composite modulation signal to remove phase coding modulation, and converting an original composite modulation signal into a frequency-doubled linear frequency modulation signal;

step 2, estimating the initial frequency and the frequency modulation coefficient of the linear frequency modulation signal by adopting a method from rough estimation to accurate estimation based on an optimized fractional Fourier transform algorithm of interpolation compensation;

step 3, reconstructing a linear frequency modulation signal by the estimated initial frequency and the frequency modulation coefficient, and carrying out conjugate multiplication on the reconstructed linear frequency modulation signal and the original LFM-BPSK composite modulation signal to obtain a baseband two-phase coding signal;

and 4, extracting the code element rate of the two-phase coded signal based on a cyclic spectrum correlation algorithm.

In step 1, the square frequency-multiplied chirp signal is obtained by the following steps: the LFM-BPSK signal model can be expressed as:

wherein q (T) is 1, T ∈ [0, T ∈₀]，f₀K is the chirp rate, k is the bandwidth of the signal, B is the bandwidth of the signal, T is NT₀Is the signal time width, q (T) is a rectangular signal, T₀Is the symbol time width, phi₀Is a binary sequence;

firstly, removing phase coding information of an LFM-BPSK composite modulation signal through square processing, wherein an expression after the original signal processing is as follows: x is the number of²(t)＝A²exp{j[4π(f₀t+kt²/2)+2φ(t)]And (2) phi (t) belongs to {0, 2 pi }, squaring the LFM-BPSK composite modulation signal and converting the LFM-BPSK composite modulation signal into a linear frequency modulation signal with noise, wherein the expression of the signal after squaring is as follows:

x²(t)＝A²exp{j[4π(f₀t+kt²/2)]}+N(t)，

wherein N (t) is 2A. exp [ j (2 π f)₀t+πkt²)]·n(t)+n²And (t) is equivalent noise after the LFM-BPSK complex modulation signal is squared.

The principle of interpolation compensation optimization fractional Fourier transform in step 2 is that the coordinates (α) corresponding to the real peak points₀,u₀) The conditions are satisfied:

the true peak point correspondence values are:

the resolution in u-domain is Δ l, if the quasi-peak point is kept at the coordinates α in α domain₀If not, the deviation between the quasi-peak point and the real peak point caused by the u-domain discretization is:

u 'in formula'₀Representing the coordinate of the quasi-peak point in a fractional order u domain;

the resolution of the discretization u domain causes deviation on the searching of the peak point, and the following can be obtained:

of formula (II b), α'₀Coordinates representing quasi-peak point in α domain, α₀、u₀α domain and u domain coordinates representing the true peak point, respectively;

when | A |²/σ_ω ²·|Δl2/π|²＝SNR·4N/π²When > 1:

from α'₀Carrying out interpolation compensation on u by using function expression of order fractional Fourier transform to obtainTo the more precise coordinates:

if X₂＞X₁If r is 1, then X₁＞X₂When the ratio of r is-1,

the substep of step 2 is:

step 2.1: squaring the LFM-BPSK composite modulation signal to obtain a frequency-doubled linear frequency modulation signal;

step 2.2: performing noise reduction processing on the frequency-doubled linear frequency modulation signal by adopting an optimized segmented filtering algorithm;

step 2.3: coarse estimation and accurate estimation are sequentially carried out by adopting fractional Fourier transform algorithm optimized by interpolation to obtain estimation results of initial frequency and frequency modulation slope

Step 2.4: calculating to obtain the initial frequency of the estimated value of the original signal according to the estimation result in the step 3And chirp rate

The phase encoding signal obtaining process in step 3 is as follows: obtaining the initial frequency

And chirp rate

After the estimation, the linear frequency modulation signal is repeatedStructure:

the reconstructed signal is multiplied by the LFM-BPSK composite modulation signal in a conjugate mode to obtain a signal s_B(n)：

In the formula

Assuming that the initial frequency and chirp rate of the signal have higher estimation accuracy, Δ f → 0, Δ k → 0, and s_BThe expression for (t) signal can be written as: s_B(t)＝A·exp[j·θ(t)]+ ω' (t) signal s_B(t) estimating the signal code rate R for the noisy two-phase coded signal by using a cyclic spectrum correlation method_b。

The substep of step 4 is:

step 4.1: calculating a signal s_B(t) cyclic spectral correlation function

To obtain

Step 4.2, searching α as 0 on the (α, f) two-dimensional plane, and obtaining the characteristic spectrum module valueCorresponding frequency f_maxThen the estimated value of the carrier frequency of the phase encoded signal is: f. of_c＝f_max；

Step 4.3: signal carrier frequency f is obtained from step 4.2_cAt frequency f ═ f_cIn the vicinity of the cycle frequency α being 0, the characteristic spectrum modulus is obtained

The sub-peak value of (2), the corresponding cycle frequencyIs otherwise α₁、α₂Then the estimated value of the symbol rate of the signal is: f. of_d＝(|α₁|+|α₂|)/2。

The invention has the beneficial effects that:

the composite modulation signal is subjected to filtering pretreatment and signal reconstruction, so that the signal-to-noise ratio of the signal is effectively improved; the parameter estimation algorithm based on interpolation optimization fractional Fourier transform is adopted, so that the accuracy of parameter estimation is effectively improved; the parameter estimation algorithm of the related combination of the fractional Fourier transform and the cyclic spectrum is low in complexity and high in stability.

Drawings

FIG. 1 is a block diagram of the overall implementation of the present solution;

fig. 2 is a time domain waveform diagram and a frequency spectrum diagram of an LFM-BPSK complex modulation signal;

FIG. 3 is a graph of coarse and fine estimation of the fractional Fourier transform of a squared frequency doubled LFM signal;

fig. 4 is a correlation diagram of the reconstructed cyclic spectrum of a BPSK signal;

figure 5 is a graph of NRMSE versus SNR for different LFM-BPSK signal parameter estimates.

Detailed Description

The following further describes embodiments of the present invention with reference to the accompanying drawings:

the method is mainly characterized in that the signals are filtered and preprocessed in a reconstruction mode, and the LFM-BPSK composite modulation signals are subjected to parameter estimation based on an interpolation optimization fractional Fourier transform and a cyclic spectrum correlation algorithm, and the steps of the scheme are shown in figure 1.

(1) The LFM-BPSK signal model can be expressed as:

in the formula (f)₀K is the chirp rate, k is the bandwidth of the signal, B is the bandwidth of the signal, T is NT₀Is the signal time width, q (T) is a rectangular signal, T₀Is the symbol time width, phi₀In a binary sequence, only two values of 0 and pi are possible. LF (Low frequency)The M-BPSK composite signal has both the features of the LFM signal and the BPSK signal, and its time domain waveform diagram and frequency spectrum diagram are shown in fig. 2.

(2) The expression for a noisy chirp signal is:

x(t)＝s(t)+ω(t)＝Aexp(j2πf₀t+jπkt²+jφ₀)+ω(t)

wherein A is the signal amplitude, phi₀For the initial phase of the signal, Δ t is the signal sampling interval, f₀For the signal start frequency, k is the signal chirp rate.

The fractional Fourier transform expression of signal x (t) is:

thus, parameter estimation of a chirp signal can be accomplished using this property, the basic idea is to search for the energy-concentrating peak point | X of the chirp signal in a (α, u) two-dimensional plane_α(u) |, obtaining the peak value coordinateWherein m is a positive integer. The result of the parameter estimation of the chirp rate and the initial frequency is as follows:

in the formula f_sFor sampling frequency, angle [. degree]The argument is taken.

Without prior knowledge, the value range of α is [0, pi ]. the rotation angle interval is set to Δ α according to the actual situation, and the obtained discrete fractional order fourier transform of the corresponding rotation angle α is to perform N-point discrete sampling in the u domain at the interval of 1/Δ l.

The parameter estimation of the chirp signal is to perform peak search on a discretized (α, u) two-dimensional plane, the deviation between the searched peak point and the real peak point is called as a quasi peak point due to the noise and the resolution of the discretized (α, u) plane, and the deviation between the quasi peak point and the real peak point is mainly caused by the discretization of the (α, u) two-dimensional plane because the white noise is uniformly distributed on the (α, u) two-dimensional plane.

Coordinates (α) corresponding to true peak points₀,u₀) The conditions are satisfied:

the true peak point correspondence values are:

the resolution in u-domain is Δ l, if the quasi-peak point is kept at the coordinates α in α domain₀If not, the deviation between the quasi-peak point and the real peak point caused by the u-domain discretization is:

the resolution of the discretized u-field biases the search for the peak point. Due to the discretization of the u-domain, the real peak point u₀Should be at [ (k-1) Δ l/N, (k +1) Δ l/N]Based on the above analysis, α 'is utilized'₀And (4) carrying out interpolation compensation on u by using the function expression of the order fractional Fourier transform to obtain more accurate coordinates.

If it is

Order to

ψ₀＝(u₀-u_k)πΔlcscα′₀，

ψ₁＝(u₀-u_k-1)πΔlcscα′₀，

ψ₂＝(u₀-u_k+1)πΔlcscα′₀。

Then there is

And psi₁＝ψ₀+πcscα′₀，ψ₂＝ψ₀-πcscα′₀，|(u₀-u_k) Pi delta l is less than or equal to pi/2, therefore, phi₀∈[-π/2,0]，ψ₁∈[π/2,π]，ψ₂∈[-3π/2,-π]。

The following can be obtained:

therefore, the coordinates of the more accurate peak point obtained after interpolation compensation in the u domain are:

if X₂＞X₁If r is 1, then X₁＞X₂And r is-1.

Compensated by interpolation

The parameter estimation is carried out, the estimation precision of the initial frequency of the linear frequency modulation signal can be effectively improved, and due to the influence of discretization processing and environmental noise, the estimation deviation of the signal phase information is large. In modern radars, radar signals are high in frequency and large in bandwidth, and generallyThe reason for the deviation is analyzed and found when the search step delta α of α is reduced to 10^-4In the process, the influence caused by the discretization of the α domain is negligible, but the calculated amount is increased rapidly, so that under a proper search step length, interpolation compensation can be performed on the rotation angle α to reduce the deviation between the peak search quasi-peak point and the real peak point and improve the accuracy of signal parameter estimation, if the resolution delta α of the α domain is small enough, the coordinate of the searched quasi-peak point can be infinitely close to the real value, but huge calculation amount can be generated, if the condition that the chirp signal can generate a prominent spectral line in the u domain is ensured, a larger search step length can be set, and the interpolation compensation method can be performed on the rotation angle α to obtain α₀Is accurately estimated

The calculation amount can be effectively reduced.

(3) The bi-phase encoded signal model may be expressed as:

s(t)＝a(t)cos[2πf₀t+φ(t)+φ₀]. Wherein

In the formula { a_nAnd the independent homodistribution sequences are obtained, and the equal probabilities take 1 and-1. The cyclic autocorrelation function is:

wherein the content of the first and second substances,

is the cyclic autocorrelation function of a (t). Get R_s(α, τ) Fourier transforming the argument τ to obtain a cyclic spectral density function of the bi-phase encoded signal s (t):

wherein the cycle of a (t)Ring spectral density function

Comprises the following steps:

where k is an integer, Q (f) is the Fourier transform of q (t), the cyclic spectral density function of the bi-phase encoded signal s (t):

wherein Q (f) is the Fourier transform of the BPSK signal q (T), T_d＝1/f_dIs the symbol time width, f_cFor the signal carrier frequency, k is an integer, f is 0 for the convenience of analysis, and the characteristic spectrum of the modulation signal is obtained

The absolute value is known as:

the carrier frequency, symbol rate and signal amplitude of the two-phase encoded signal determine the absolute value of the cyclic spectrum correlationAnalysis q (f) shows that the amplitude takes a maximum value when the frequency f is 0, and gradually decreases when the frequency f is greater than 0 and f is less than 0. Modulus for signal characteristic spectrum

When k is 0, α is ± 2f_cUnder the conditions of (a) under (b),

maximum value is taken, k is 0, α is + -2 f_c+1/T_dUnder the conditions of (a) under (b),

the second largest value is taken, and the symmetry of the signal cyclic spectrum correlation can be obtained by searching the module value of the characteristic spectrum when α is more than 0

The carrier frequency of the two-phase encoded signal is estimated based on the frequency corresponding to the peak, and the symbol rate of the two-phase encoded signal is estimated based on the frequency corresponding to the peak

The frequency difference between the peak value and the adjacent amplitude secondary peak is realized.

(4) In order to improve the accuracy of the LFM-BPSK complex modulation signal parameter estimation algorithm, the signal needs to be filtered in segments, because the phase encoding signal modulates the phase of the carrier, the instantaneous frequency of the signal generates a sudden change at the jump position of the carrier phase, and if the signal is directly filtered in segments, part of information of the signal may be lost, so the signal is preprocessed first.

Firstly, removing phase coding information of an LFM-BPSK composite modulation signal through square processing, wherein an expression after the original signal processing is as follows: x is the number of²(t)＝A²exp{j[4π(f₀t+kt²/2)+2φ(t)]Where 2 φ (t) is e {0, 2 π }, so that x²(t)＝A²exp{j[4π(f₀t+kt²/2)]}。

After square processing is performed on the LFM-BPSK composite modulation signal, the LFM-BPSK composite modulation signal is converted into a chirp signal with noise, at this time, the initial frequency and the chirp rate of the signal are 2 times of those of the original signal, and the square processing will cause the signal-to-noise ratio of the signal to be reduced. The expression of the squared signal is:

x²(t)＝A²exp{j[4π(f₀t+kt²/2)]formula (i) } + n (t) where n (t) is 2A · exp [ j (2 pi f)₀t+πkt²)]·n(t)+n²And (t) is equivalent noise after the LFM-BPSK complex modulation signal is squared. The output signal-to-noise ratio at this time is:

where SNR is the signal-to-input signal-to-noise ratio. It can be known that the squaring process on the original complex modulation signal results in the reduction of the output signal-to-noise ratio, which will affect the accuracy of signal parameter estimation. And carrying out segmented filtering processing on the signals to improve the precision of parameter estimation. Before windowing the signal frequency domain, roughly estimating the deviation degree between the signal frequency and the quantized frequency, and then enabling the signal frequency to be close to a quantized frequency point through frequency shift. Because the fractional Fourier transform has excellent energy aggregation performance on the linear frequency modulation signal in a fractional domain, and the noise resistance and the anti-interference performance are good, the optimized fractional Fourier transform algorithm is adopted to carry out parameter estimation on the LFM signal obtained after the LFM-BPSK composite modulation signal is squared.

Therefore, the steps of estimating the initial frequency and the chirp rate of the LFM-BPSK complex modulation signal are as follows:

1. and squaring the LFM-BPSK composite modulation signal to obtain a frequency-doubled linear frequency modulation signal.

2. And performing noise reduction on the frequency-doubled linear frequency modulation signal by adopting an optimized segmented filtering algorithm.

3. Then, coarse estimation and accurate estimation are sequentially carried out by adopting an interpolation optimized fractional Fourier transform algorithm to obtain estimation results of initial frequency and frequency modulation slope

4. Since the square frequency multiplication is performed on the original LFM-BPSK composite signal, the estimated initial frequency of the original signal can be obtained by dividing the estimation result of step 3 by 2

And chirp rate

Obtaining the initial frequencyAnd chirp rate

After estimating the value, reconstructing the linear frequency modulation signal:

the reconstructed signal is multiplied by the LFM-BPSK composite modulation signal in a conjugate mode to obtain a signal s_B(n)：

In the formula

Assuming that the initial frequency and chirp rate of the signal have higher estimation accuracy, Δ f → 0, Δ k → 0, and s_BThe expression for (t) signal can be written as: s_B(t)＝A·exp[j·θ(t)]+ω″(t)。

Signal s_B(t) is a noisy two-phase encoded signal, and therefore the signal code rate R can be estimated using cyclic spectrum correlation_b. The specific process is as follows:

1. calculating a signal s_B(t) cyclic spectral correlation function

To obtain

2. When α ═ 0 is searched for on the (α, f) two-dimensional plane, the characteristic spectrum modulus value

Corresponding frequency f_maxThen the estimated value of the carrier frequency of the phase encoded signal is: f. of_c＝f_max；

3. Obtaining the carrier frequency f of the signal from step 2_cAt frequency f ═ f_cIn the vicinity of the cycle frequency α being 0, the characteristic spectrum modulus is obtainedRespectively, corresponding to a cyclic frequency of α₁、α₂Then the estimated value of the symbol rate of the signal is: f. of_d＝(|α₁|+|α₂|)/2。

The scheme is a Fourier transform LFM-BPSK composite modulation radar signal parameter estimation method. Fig. 1 shows an overall implementation block diagram of the present solution. Fig. 2 is a time domain waveform diagram and a frequency spectrum diagram of the LFM-BPSK complex modulation signal. Fig. 3 is a graph of a fractional fourier transform estimate of a squared, multiplied LFM signal. Fig. 4 is a diagram of the estimation of parameters related to the reconstructed cyclic spectrum of the BPSK signal. Fig. 5 is a graph of NRMSE versus SNR for different LFM-BPSK signal parameter estimates. In summary, the results of parameter estimation simulation experiments on different signals under different signal-to-noise ratios show that the LFM-BPSK composite modulation signal parameter estimation method provided by the invention has feasibility and stability.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.