LFM-BPSK signal parameter estimation method based on time-frequency analysis

Abstract

The application discloses a LFM-BPSK signal parameter estimation method based on time-frequency analysis and belongs to the field of radar reconnaissance signal processing. The method comprises the following steps: step 1, using RAT to estimate the frequency modulation slope of the original LFM-BPSK signal with Gaussian white noise; step 2, demodulating the original LFM-BPSK signal by using the frequency modulation slope estimation value obtained in step 1 to obtain a demodulated signal; step 3, calculating the ZAM distribution of the demodulated signal, projecting the ZAM distribution to the time axis and the frequency axis respectively, and estimating the carrier frequency and the sub-pulse width; and step 4, using the estimated carrier frequency and the sub-pulse width to construct a point frequency signal, performing cross-correlation operation on the demodulated signal obtained in step 2, and using a symbol recovery criterion to recover the symbol sequence of the signal phase encoding part. The application improves the performance of LFM-BPSK parameter estimation under low signal-to-noise ratio.

Description

Technical Field

[0001] This invention belongs to the field of radar reconnaissance signal processing, and in particular relates to a method for estimating LFM-BPSK signal parameters based on time-frequency analysis. Background Technology

[0002] Radar signal parameter estimation is a crucial aspect of electronic warfare. To enhance radar survivability on the battlefield, modern radar systems are increasingly employing composite modulation signals. Among these, the Linear Frequency Modulation-Binary Phase Shift Keying (LFM-BPSK) composite modulation signal combines the advantages of both LFM and BPSK signals. It possesses the high ranging accuracy and Doppler insensitivity of LFM signals, along with the high Doppler resolution and velocity accuracy of BPSK signals. Furthermore, this signal exhibits excellent anti-jamming performance and a low probability of intercept, making it widely used in various radar systems. Therefore, efficiently detecting and estimating the parameters of such complex radar modulation signals is of paramount importance, providing a foundation for subsequent countermeasures such as radar jamming.

[0003] Most existing parameter estimation algorithms for LFM-BPSK composite modulation signals first eliminate phase modulation information in the signal through squaring operations, then estimate the starting frequency and modulation slope of the linear frequency modulation (LFM) component, reconstruct the original LFM signal, multiply it by its conjugate to obtain the baseband phase-coded signal, and finally estimate the phase-coded signal separately using cyclic spectrum or phase difference methods. While these algorithms are relatively simple to implement, the use of squaring operations results in a loss of signal-to-noise ratio (SNR), leading to poor parameter estimation performance at low SNR levels and an inability to recover signal symbols. Furthermore, parameter estimation methods based on cyclic spectrum require two-dimensional search, which is computationally intensive and unsuitable for real-time processing. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a time-frequency analysis-based method for estimating LFM-BPSK signal parameters. This method integrates time-frequency analysis methods such as the Radon-Ambiguity Transform (RAT), Zhao-Atlas-Marks (ZAM) distribution, and cross-correlation to propose a new symbol recovery criterion. This overcomes the problems of existing technologies, achieves accurate estimation of the carrier frequency, modulation slope, and symbol parameters of LFM-BPSK signals under low SNR, and can recover symbol sequences with a high success rate, which is of great significance in the field of radar countermeasures.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] The LFM-BPSK signal parameter estimation method based on time-frequency analysis includes the following steps:

[0007] Step 1: Use RAT to estimate the frequency modulation slope of the original LFM-BPSK signal with Gaussian white noise;

[0008] Step 2: Demodulate the original LFM-BPSK signal using the frequency modulation slope estimate obtained in Step 1 to obtain the demodulated signal;

[0009] Step 3: Calculate the ZAM distribution of the demodulated signal and project it onto the time axis and frequency axis respectively to estimate the carrier frequency and subpulse width;

[0010] Step 4: Construct a point frequency signal using the estimated carrier frequency and subpulse width, perform cross-correlation operation with the demodulated signal obtained in Step 2, and use the symbol recovery criterion to recover the symbol sequence of the phase-coded part of the demodulated signal.

[0011] The beneficial effects of this invention are as follows:

[0012] This invention proposes a parameter estimation method for LFM-BPSK signals based on time-frequency analysis. When the signal-to-noise ratio (SNR) is greater than -4dB, the NRMSE for estimating the signal modulation slope, carrier frequency, and subpulse width is less than 0.01. Compared with existing methods, the proposed method has high accuracy in estimating signal parameters and stronger noise resistance. It can also recover the symbol sequence of the signal, and the symbol recovery success rate is greater than or equal to 95% when the SNR is greater than 0dB.

[0013] The signal parameters estimated by this invention can help with radar sorting and jamming in the field of radar countermeasures, and can be used for radar radiation source identification and radar jamming template generation in subsequent processing;

[0014] The LFM-BPSK signal parameter estimation method proposed in this invention uses only one-dimensional peak search in all peak search-related steps, which greatly reduces the amount of computation and is beneficial for engineering implementation. Attached Figure Description

[0015] Figure 1 is a flowchart of the LFM-BPSK signal parameter estimation method based on time-frequency analysis of the present invention;

[0016] Figure 2 shows the time-domain waveform of the LFM-BPSK signal;

[0017] Figure 3(a) is a slice of RAT;

[0018] Figure 3(b) is a magnified view of a portion of the RAT slice;

[0019] Figure 4 shows the time-domain waveform of the demodulated phase-coded signal.

[0020] Figure 5 shows the ZAM distribution of the phase-coded signal;

[0021] Figure 6 is a schematic diagram of the carrier frequency estimation spectrum curve;

[0022] Figure 7 is a schematic diagram of the sub-pulse width estimation curve;

[0023] Figure 8(a) is a schematic diagram of cross-correlation sequences;

[0024] Figure 8(b) is a schematic diagram of the effective data of the cross-correlation sequence;

[0025] Figure 9(a) is a schematic diagram of the envelope under cross-correlation sequences;

[0026] Figure 9(b) is a schematic diagram of the envelope of the cross-correlation sequence after smoothing.

[0027] Figure 10 is a schematic diagram of the recovered symbol sequence;

[0028] Figure 11 is a schematic diagram of the NRMSE parameter as a function of signal-to-noise ratio;

[0029] Figure 12 is a schematic diagram of the symbol sequence recovery success rate as a function of signal-to-noise ratio. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0031] like Figure 1 The flowchart shown below illustrates the LFM-BPSK signal parameter estimation method based on time-frequency analysis, which mainly includes the following steps:

[0032] Step 1: Use RAT to estimate the frequency modulation slope of the original LFM-BPSK signal with Gaussian white noise;

[0033] Step 2: Demodulate the original LFM-BPSK signal using the frequency modulation slope estimate obtained in Step 1 to obtain the demodulated signal;

[0034] Step 3: Calculate the ZAM distribution of the demodulated signal and project it onto the time axis and frequency axis respectively to estimate the carrier frequency and subpulse width;

[0035] Step 4: Construct a point frequency signal using the estimated carrier frequency and subpulse width, perform cross-correlation operation with the demodulated signal obtained in Step 2, and recover the symbol sequence of the signal phase-encoded part using the symbol recovery criterion.

[0036] Furthermore, step 1 includes the following steps:

[0037] Step 1.1, the model of the original LFM-BPSK signal used in this invention is as follows:

[0038] s ( t ) = A ⋅ ∑ n = 1 N rect ( t T )exp[ j ⋅ 2 π ( f 0 t + kt 2 / 2 + φ 0 )]exp( j ⋅ φ n ) q ( t − nT b ) ,

[0039] in, The original LFM-BPSK signal, The signal amplitude, For rectangular window functions, For time vectors, For signal pulse width, It is an imaginary number. The carrier frequency of the signal. This represents the frequency modulation slope of the linear frequency modulation section. For the initial phase, The width of the sub-pulse. The number of code elements For the first The phase of each symbol, with a value of 0 or , It is an exponential function. The duration is equal to the sub-pulse width. The gate function.

[0040] Step 1.2, calculate the ambiguity function of the original LFM-BPSK signal. :

[0041] ,

[0042] in, For time delay, For Doppler frequency shift, superscript This indicates that a conjugate operation is being performed.

[0043] Step 1.3: Perform Radon transform on the ambiguity function of the original LFM-BPSK signal to obtain the RAT slice image:

[0044] ,

[0045] in, For rotation angle, These are the frequency modulation slope values ​​corresponding to different rotation angles. Let RAT(·) be the Radon transform function, and |·| represent the Radon fuzzy transform function of the signal. The above equation shows the characteristic of the amplitude changing with the rotation angle after RAT, and a RAT slice of the signal can be obtained.

[0046] Step 1.4: Set a threshold and search for peak values ​​that exceed the threshold to obtain the angle corresponding to the peak value;

[0047] First, calculate the peak value of the RAT slice of the original LFM-BPSK signal. When there is no noise, the RAT of LFM-BPSK exhibits two peaks with almost identical amplitudes, and the point corresponding to the signal frequency modulation slope is exactly in the middle of the two peaks. However, when there is noise, the amplitude difference between the two peaks is large. In order to allow both peaks to be searched, a threshold is used. Then, the slice angles corresponding to the two peaks exceeding the threshold can be searched. and .

[0048] Step 1.5, adjust the angles of the two slices. and Take the average value to obtain the slice angle corresponding to the frequency modulation slope of the linear frequency modulation part. Substitute Obtain the estimated frequency modulation slope value ,in The sampling frequency is represented by the cot operation, which denotes the complementary angle function of the tangent.

[0049] Furthermore, step 2 includes the following steps:

[0050] Step 2.1, based on the frequency modulation slope estimate obtained in Step 1.5 Construct a baseband linear frequency modulated signal :

[0051] ,

[0052] Step 2.2: Multiply the original LFM-BPSK signal by the conjugate of the constructed baseband linear frequency modulated signal to obtain the demodulated signal. :

[0053] s ^ BPSK = s ( t ) ⋅ s ∗ LFM _ new ( t ) = A ⋅ ∑ n = 1 N rect ( t T )exp[ j ⋅ 2 π ( f 0 t + kt 2 / 2 + φ 0 )]exp( j ⋅ φ n ) q ( t − nT b ) ⋅ rect ( t T )exp( − j π k ^ t 2 ) = A ⋅ rect ( t T )exp( j 2 π f 0 t + j π Δ kt 2 + φ 0 ) ∑ n = 1 N exp( j φ n ) q ( t − nT b ) ,

[0054] Among them, when the frequency modulation slope accuracy is high enough to reach the preset value, the frequency modulation slope estimation error Then the demodulated signal For carrier frequency BPSK signal.

[0055] Furthermore, step 3 includes the following steps:

[0056] Step 3.1, demodulated signal Perform ZAM transformation:

[0057] ZAM s ^ BPSK ( t , f ) = ∫ −∞ +∞ [ h ( τ ) ∫ t − | τ | 2 t + | τ | 2 s ^ BPSK ( x + τ 2 ) s ^ BPSK * ( x − τ 2 ) dx ] ⋅ e − j 2 π f τ d τ ,

[0058] in, For frequency variables, is a window function, and x represents the time variable introduced when calculating the ZAM distribution.

[0059] Step 3.2, transform the time-frequency distribution By selecting the maximum values ​​along each straight line parallel to the time axis and projecting them onto the frequency axis, we obtain the frequency axis projection function. Search for the maximum value to determine the signal carrier frequency. The estimation yields the signal carrier frequency estimate. :

[0060] ,

[0061] ,

[0062] Where max is the function for finding the maximum value. A function that provides the value of the independent variable when a certain function reaches its maximum value.

[0063] Step 3.3, transform the time-frequency distribution Projecting onto the time axis yields the time axis projection function. Then, the minimum value is searched for to estimate the sub-pulse width;

[0064] ,

[0065] in, The function is for finding the minimum value;

[0066] To reduce the impact of noise, the time axis projection function... After projecting the curve onto the time axis and taking the minimum value, a smoothing process is performed, followed by peak search to extract the peak positions that exceed a threshold. , This represents the x-coordinate corresponding to each peak position. The vertical axis represents the value corresponding to each peak, and since the horizontal axis represents the time corresponding to each peak, we obtain the time vector corresponding to each peak. A time difference vector is obtained by calculating the difference between adjacent elements in the time vector. :

[0067] ,

[0068] Let represent the time difference between each adjacent peak, and let i represent the number of peaks found in the search. Then the sub-pulse width... The estimated value Time difference vector The minimum value in.

[0069] Furthermore, step 4 includes the following steps:

[0070] Step 4.1: Use the signal carrier frequency estimate obtained in steps 3.2 and 3.3. Construct a point frequency signal using the pulse width and sub-pulse width. :

[0071] ,

[0072] in, This is the time vector in a point-frequency signal.

[0073] Step 4.2, let the demodulated signal obtained in step 2.2... The point frequency signal obtained in step 4.1 Performing a cross-correlation operation yields a cross-correlation sequence, since the demodulated signal... and point frequency signal The lengths are not equal, causing the demodulated signal to... The length is Point frequency signal The length is When performing cross-correlation, shorter signals are padded with zeros, resulting in a sequence with a length of [missing information] in the first half. Invalid data with a value of 0, therefore the valid portion of the sequence is extracted:

[0074] ,

[0075] ,

[0076] in, For cross-correlation sequences, The effective part of the cross-correlation sequence, It is a cross-correlation function. Cross-correlation sequences The total length.

[0077] Step 4.3: Obtain the lower envelope of the effective portion of the cross-correlation sequence:

[0078] [ up , lo ] = envelope ( yy ) ,

[0079] in, This is the envelope extraction function, which returns... yes The upper envelope, yes The lower envelope.

[0080] Step 4.4, for the effective portion of the cross-correlation sequence Peak search is performed after smoothing the lower envelope;

[0081] When noise is present, the extracted envelope curve will have many "glitches," which will affect subsequent peak search. Therefore, the lower envelope curve is smoothed before peak search. Due to cross-correlation, the time corresponding to the peak obtained by the search needs to be increased by half the sub-pulse width to obtain the actual symbol transition time, resulting in a second time vector. In order to calculate the transition time interval, the initial and end times need to be added to the second time vector to obtain a new time vector. :

[0082] ,

[0083] Where T is the signal pulse width. This represents the x-coordinate of each peak position obtained after the cross-correlation operation.

[0084] Step 4.5, for the new time vector Perform time difference calculations and calculate the number of symbols corresponding to each time difference to obtain the vector corresponding to the number of symbols. :

[0085] ,

[0086] in, This represents the floor function. This represents the number of peaks obtained in step 4.4. Represents the new time vector The number of symbols corresponding to the time difference between adjacent times.

[0087] Step 4.6, based on the above steps, proposes a symbol recovery rule: Let the vector In the vector, odd-numbered positions correspond to the number of 1s, and even-numbered positions correspond to the number of 0s. The numerical values ​​in the vector are replaced with the corresponding number of 1s to obtain the recovered symbol sequence. For example, if the obtained vector... D → = [ 3 , 2 , 1 , 1 ] The symbol sequence obtained according to the symbol recovery rule is: [ 1 , 1 , 1 , 0 , 0 , 1 , 0 ] .

[0088] Example

[0089] To verify the effectiveness of the present invention, two sets of simulations were performed. The main simulation parameters are shown in Table 1. To more intuitively observe the results of each step, the first set of simulations was performed under the ideal condition of no Gaussian noise.

[0090] Table 1

[0091]

[0092] Simulation results are as follows Figures 2 to 10 As shown. The LFM-BPSK signal constructed first is as follows. Figure 2 As shown, the RAT slice obtained after RAT is shown in Figure 3(a), and Figure 3(b) is a magnified view of the local slice. The dashed line represents the set threshold. After searching for the peak, the slice angle corresponding to the frequency modulation slope is obtained, and the estimated value of the frequency modulation slope is obtained by substituting it into the formula. The original signal is demodulated by the linear frequency modulated signal constructed by the frequency modulation slope, and the time-domain waveform of the obtained phase-coded signal is shown in Figure 3(b). Figure 4 As shown. Performing a ZAM transform on the phase-coded signal yields a two-dimensional planar ZAM distribution diagram of the signal, as shown below. Figure 5 As shown. Projecting the ZAM distribution onto the time and frequency axes respectively, the resulting carrier frequency estimation map and subpulse width estimation map are shown below. Figure 6 and Figure 7 As shown in the figure. Next, the baseband signal is constructed using the estimated carrier frequency and subpulse width estimates, and cross-correlation is performed with the original signal to obtain a cross-correlation sequence. The effective data is then extracted, as shown in Figure 8(a), a schematic diagram of the cross-correlation sequence, and Figure 8(b), a schematic diagram of the effective data of the cross-correlation sequence. The lower envelope of the effective cross-correlation data is then extracted and smoothed, as shown in Figure 9(a), a schematic diagram of the lower envelope of the cross-correlation sequence, and Figure 9(b), a schematic diagram of the smoothed lower envelope. Finally, the symbol sequence is recovered using the estimated subpulse width and the proposed symbol recovery criterion. The recovered symbol sequence is shown in the figure. Figure 10 As shown.

[0093] To further verify the noise immunity of the algorithm, Gaussian white noise was added to the signal. Monte Carlo simulations were then performed on the LFM-BPSK signal using the proposed algorithm. The SNR ranges were [-7, 5] dB and [-3, 6] dB, with a step size of 1 dB. 100 Monte Carlo simulations were performed for each SNR. The simulation results are as follows: Figure 11 and Figure 12 As shown, when SNR≥-5dB, the NRMSE of the frequency modulation slope and carrier frequency is less than 0.01; when SNR≥-4dB, the NRMSE of the subpulse width is less than 0.01; and when SNR>-1dB, the success rate of symbol recovery is greater than or equal to 90%.

[0094] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for estimating LFM-BPSK signal parameters based on time-frequency analysis, characterized in that, Includes the following steps: Step 1: Use RAT to estimate the frequency modulation slope of the original LFM-BPSK signal with Gaussian white noise; Step 2: Demodulate the original LFM-BPSK signal using the frequency modulation slope estimate obtained in Step 1 to obtain the demodulated signal; Step 3: Calculate the ZAM distribution of the demodulated signal and project it onto the time axis and frequency axis respectively to estimate the carrier frequency and subpulse width; Step 4: Construct a point frequency signal using the estimated carrier frequency and subpulse width, perform cross-correlation operation with the demodulated signal obtained in Step 2, and use the symbol recovery criterion to recover the symbol sequence of the phase-coded part of the demodulated signal.

2. The method for estimating LFM-BPSK signal parameters based on time-frequency analysis according to claim 1, characterized in that, Step 1 includes: Step 1.1: Construct the model of the original LFM-BPSK signal as follows: ， in, The original LFM-BPSK signal, The signal amplitude, For rectangular window functions, For time vectors, For signal pulse width, It is an imaginary number. For signal carrier frequency, This represents the frequency modulation slope of the linear frequency modulation section. For the initial phase, The width of the sub-pulse. The number of code elements For the first The phase of each symbol, with a value of 0 or , It is an exponential function. The duration is equal to the sub-pulse width. The gate function; Step 1.2: Calculate the ambiguity function of the original LFM-BPSK signal. : ， in, For time delay, For Doppler frequency shift, superscript This indicates a conjugate operation; Step 1.3: Perform Radon transform on the ambiguity function of the original LFM-BPSK signal to obtain the RAT slice image: ， in, For rotation angle, These are the frequency modulation slope values ​​corresponding to different rotation angles. RAT(·) represents the Radon transform function, RAT(·) represents the Radon fuzzy transform function of the signal, and |·| represents the modulus operation. Step 1.4: Calculate the RAT slice peak value of the original LFM-BPSK signal. Set threshold And search for values ​​exceeding that threshold. The two peaks are used to obtain the slice angles corresponding to the two peaks. and ; Step 1.5: Adjust the angles of the two slices. and Take the average value to obtain the frequency modulation slope of the linear frequency modulation part. Corresponding slice angle Substitute Obtain the estimated frequency modulation slope value ,in Where cot represents the sampling frequency, and cot denotes the tangent-coordinate function operation.

3. The method for estimating LFM-BPSK signal parameters based on time-frequency analysis according to claim 2, characterized in that, Step 2 includes: Step 2.1: Based on the frequency modulation slope estimate obtained in Step 1.5 Constructing a baseband linear frequency modulated signal : ， Step 2.2: Convert the original LFM-BPSK signal With the constructed baseband linear frequency modulated signal The demodulated signal is obtained by multiplying the conjugates. ; ， Among them, when the frequency modulation slope accuracy reaches the preset value, the frequency modulation slope estimation error At this time, the demodulated signal The carrier frequency is the signal carrier frequency. BPSK signal.

4. The method for estimating LFM-BPSK signal parameters based on time-frequency analysis according to claim 3, characterized in that, Step 3 includes: Step 3.1: Demodulate the signal Perform ZAM transformation; ， in, For frequency variables, The function is a window function, and x represents the time variable introduced when calculating the ZAM distribution; Step 3.2: Transform the time-frequency distribution By selecting the maximum values ​​along each straight line parallel to the time axis and projecting them onto the frequency axis, we obtain the frequency axis projection function. Search for the maximum value to determine the signal carrier frequency. The estimation yields the signal carrier frequency estimate. : ， ， Where max is the function for finding the maximum value. A function that provides the value of the independent variable when a certain function reaches its maximum value; Step 3.3: Transform the time-frequency distribution Projecting onto the time axis yields the time axis projection function. Then, the minimum value is searched for to estimate the sub-pulse width: ， in, The function is for finding the minimum value; Projection function of time axis After projecting onto the time axis and taking the minimum value, the resulting curve is smoothed and then peak search is performed to extract peaks exceeding a threshold. peak position , This represents the x-coordinate corresponding to each peak position. Representing the ordinate of each peak position, we obtain the time vector corresponding to each peak position. Calculate the time vector The time difference vector is obtained by finding the difference between adjacent elements. : ， The time differences between adjacent peak positions are represented by , i represents the number of peaks found in the search, and the sub-pulse width is . The estimated value Time difference vector The minimum value in.

5. The method for estimating LFM-BPSK signal parameters based on time-frequency analysis according to claim 4, characterized in that, Step 4 includes: Step 4.1: Use the signal carrier frequency estimate obtained in steps 3.2 and 3.

3. Sub-pulse width The estimated value Constructing point frequency signals ,in Point frequency signal The time vector in; Step 4.2, set the demodulated signal The length is Point frequency signal The length is The demodulated signal With point frequency signal Perform cross-correlation to obtain a cross-correlation sequence, and extract the effective portion of the cross-correlation sequence: ， ， in, For cross-correlation sequences, The effective part of the cross-correlation sequence, It is a cross-correlation function. Cross-correlation sequences The total length; Step 4.3: Obtain the lower envelope of the effective portion of the cross-correlation sequence: ， in, For envelope extraction function, It is the effective part of the cross-correlation sequence. The upper envelope, It is the effective part of the cross-correlation sequence. The lower envelope; Step 4.4: Analyze the effective portion of the cross-correlation sequence. lower envelope After smoothing, peak search is performed to obtain a new time vector. : ， in, This represents the x-coordinate of each peak position obtained after the cross-correlation operation; Step 4.5: For the new time vector Perform time difference calculations and calculate the number of symbols corresponding to each time difference to obtain the vector corresponding to the number of symbols. : ， in, This represents the floor function. This represents the number of peaks obtained in step 4.

4. Represents the new time vector The number of code elements corresponding to the time difference between adjacent time intervals; Step 4.6: Propose symbol recovery rules: Let the vector corresponding to the number of symbols... In the middle, odd-numbered positions correspond to the number of code symbols 1, and even-numbered positions correspond to the number of code symbols 0. The vector corresponding to the number of code symbols is then... The numerical values ​​are replaced with the corresponding number of code elements to obtain the recovered code element sequence.

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