A method for estimating LFM pulse signal parameters under aliasing conditions

Abstract

This invention discloses a method for estimating LFM pulse signal parameters under aliasing conditions, applied in the field of radar technology. Addressing the problem of aliasing in the time-frequency domain of direct-arrival wave signals from multiple external radiation sources with similar parameters, this invention utilizes fractional Fourier transform to accumulate energy in the direct-arrival wave signal. Based on the analytical expression of the peak-to-peak linear frequency modulated (LFM) pulse signal obtained after accumulation and its fractional Fourier transform, a multi-channel signal is constructed. Finally, using the constructed multi-channel signal, the LFM pulse signal is de-aliased in the fractional Fourier transform domain through blind source separation, ultimately improving the signal-to-noise ratio and separating different pulse signals with similar parameters, thereby achieving accurate parameter estimation. The process of this invention can be implemented using the fast fractional Fourier transform method, which is beneficial for engineering implementation.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and specifically relates to a radar pulse signal parameter estimation technique. Background Technology

[0002] The continuous advancement of military electronics technology has driven the development of passive detection. Passive radar achieves target detection by estimating the parameters of direct-wave radar signals from non-cooperative external radiation sources, and linear frequency modulated (LFM) signals are widely used in various types of radiation sources due to their low interception characteristics. Therefore, accurate parameter estimation of direct-wave LFM signals is a crucial step in passive radar detection.

[0003] However, with the increasing complexity of the electromagnetic environment and the growing density of radiation sources on the battlefield, passive radar reference antennas may receive multiple pulse signals with similar parameters, leading to aliasing between these signals across multiple domains. Furthermore, the received direct wave signal often originates from the sidelobes of the radiation source, resulting in a low signal-to-noise ratio (SNR). For passive detection in situations with dense radiation sources, it is necessary to achieve pulse signal dealiasing under low SNR conditions to ensure accurate pulse parameter estimation.

[0004] Currently, parameter estimation methods for linear frequency modulated (LFM) pulse signals include those based on the short-time Fourier transform (ST-FT) and the Wigner distribution (WD). Specifically, these methods obtain the time-frequency response curves of the signal sequence through time-frequency analysis and estimate the signal parameters through curve identification and fitting. However, these methods struggle to handle direct-wave signals containing multiple pulses. The generalized Radon-Fourier transform (GRFT) estimates signal parameters through multi-dimensional parameter search, but this method requires a high signal-to-noise ratio. The fractional Fourier transform (FrFT) exhibits good energy concentration for LFM signals; therefore, the short-time fractional Fourier transform (ST-FrFT) and fractional Fourier filtering are widely used for parameter estimation of LFM pulse signals. When there are pulses with similar parameters in the signal, causing aliasing between the pulses, the parameter estimation performance of the above method will decrease. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a method for estimating the parameters of an LFM (Linear Frequency Modulation) pulse signal under aliasing conditions. This method can remove aliasing between pulses and achieve accurate estimation of the parameters of a linear frequency modulated pulse signal even under low signal-to-noise ratio conditions.

[0006] The technical solution adopted in this invention is: a method for estimating LFM pulse signal parameters under aliasing conditions, comprising:

[0007] S1. For multiple linear frequency modulated pulse external radiation sources, receive their direct wave signals;

[0008] S2. Perform fractional Fourier transform on the received direct wave signal to obtain the position of the peak value in the fractional Fourier transform domain.

[0009] S3. Based on the position of the signal in the fractional Fourier transform domain, construct a new channel signal according to the analytical expression of the fractional Fourier transform.

[0010] S4. Process the multi-channel signal constructed within the passband by blind source separation to obtain the separated channel signal; calculate the negative entropy of the separated channel signal, and determine that the signal corresponding to the channel with the largest negative entropy is the form of the dealiased signal in the fractional Fourier transform domain.

[0011] S5. The signal after blind source separation and dealiasing is transformed to the time domain through fractional Fourier inverse transform, and the transformed signal in the time domain is subjected to threshold detection to extract the pulse segment.

[0012] S6. For the truncated signal, calculate its pulse width, and calculate its frequency modulation slope and center frequency through fractional Fourier transform, thereby completing the accurate estimation of the pulse signal parameters.

[0013] Step S3 specifically involves: first, estimating the peak position in the fractional Fourier transform domain; then, calculating the analytical expression of the peak corresponding to each pulse at the same fractional Fourier transform order, thereby constructing a multi-channel signal; and constructing a fractional Fourier bandpass filter centered on the peak position to perform fractional Fourier filtering on the multi-channel signal.

[0014] The beneficial effects of this invention are as follows: This invention provides a method for estimating the parameters of linear frequency modulated (LFM) pulse signals under multi-domain aliasing conditions. Addressing the problem of aliasing in the time-frequency domain caused by similar parameters of direct-arrival (DA) signals from multiple external radiation sources, this invention utilizes fractional Fourier transform (FFT) to accumulate energy in the direct-arrival (DA) signals. Based on the analytical expression of the accumulated peak-to-frequency (CFM) LFM pulse signal after FFT, a multi-channel signal is constructed. Finally, using the constructed multi-channel signal, the LFM pulse signal is de-aliased in the FFT domain through blind source separation, ultimately improving the signal-to-noise ratio (SNR) and separating different pulse signals with similar parameters, thereby achieving accurate parameter estimation. The process of this invention can be implemented using the fast fractional Fourier transform (FFT) method, which is beneficial for engineering implementation. Attached Figure Description

[0015] Figure 1 This is a flowchart of an embodiment of the present invention.

[0016] Figure 2 This is a time-domain diagram of receiving a low signal-to-noise ratio pulse signal in an embodiment of the present invention.

[0017] Figure 3 This is a pulse time-domain diagram after dealiasing in an embodiment of the present invention. Detailed Implementation

[0018] This invention primarily utilizes the scientific computing software Matlab R2021a for simulation experiments to verify its correctness. The embodiments of this invention are further described below with reference to the accompanying drawings.

[0019] Please see Figure 1 The present invention proposes a method for estimating the parameters of a linear frequency modulated pulse signal under multi-domain aliasing conditions, which is implemented through the following steps:

[0020] Step 1: For multiple linear frequency modulated pulse external radiation sources, receive their direct wave signals.

[0021] In this embodiment, the receiver receives the direct wave signal from the external radiation source as follows: Where N s This indicates the number of pulses in the received direct wave signal. τ i A i T pi f i and k i These represent time delay, pulse amplitude, pulse width, center frequency, and frequency modulation slope, respectively. n(t) represents Gaussian white noise, and t represents time.

[0022] In this embodiment, the system parameters used are as follows: the number of received linear frequency modulated pulses is 2, where the center frequency of pulse 1 is 505.9MHz, the signal bandwidth is 1MHz, and the pulse width is 100us (corresponding to a frequency modulation slope of 1×1). 10 The pulse frequency is Hz / s, and the arrival time is 0.33ms; the center frequency of pulse 2 is 506.1MHz, the signal bandwidth is 2MHz, and the pulse width is 150us (corresponding to a frequency modulation slope of 1.33×1). 10 The receiver has a sampling frequency of 30MHz, a digital down-conversion reference frequency of 500MHz, and a signal-to-noise ratio of 0dB. The arrival time is 0.35ms.

[0023] Step 2: Perform fractional Fourier transform on the received direct wave signal to obtain the position of the transformed peak in the fractional Fourier transform domain.

[0024] In this embodiment, a fractional Fourier transform is performed on the signal s(t), and the search range p of the transform order p is... min Take 0, p max Set the value to 2, and set Δp to 0.01; the transformed signal is Peak points (p) corresponding to the i-th pulse signal and the j-th pulse signal are obtained through peak detection. i ,u i ) and (p j ,u j ).

[0025]

[0026] in, u represents the coordinates in the fractional Fourier transform domain.

[0027] Step 3: Based on the position of the signal in the fractional Fourier transform domain, construct a new channel signal according to the analytical expression of the fractional Fourier transform. First, estimate the peak position in the fractional Fourier transform domain, and then calculate the analytical expression of the peak corresponding to each pulse on the same fractional Fourier transform order to construct a multi-channel signal. Construct a fractional Fourier bandpass filter centered on the peak position to perform fractional Fourier filtering on the signal.

[0028] In this embodiment, for the peak point (p) after the fractional Fourier transform corresponding to the j-th pulse... j ,u j ), construct signal Perform a fractional-order inverse Fourier transform on it. Subsequently, regarding S f21 (u) Perform fractional Fourier filtering to obtain Where rect(·) represents the rectangular window function, Pf This represents the width of the fractional Fourier bandpass filter.

[0029] Step 4: The multi-channel signal constructed within the passband is processed by blind source separation to solve the problem of uncertainty in the amplitude and initial phase of the channel signal constructed by analytical expression; the separated channel signal is determined by negative entropy, and the signal corresponding to the channel with the largest negative entropy is the form of the de-aliased signal in the fractional Fourier transform domain.

[0030] In this embodiment, step 4 includes the following process:

[0031] First, transform the signal s(t) to order p. i The fractional Fourier transform yields the signal. right Perform fractional Fourier filtering to obtain the signal Signal y ji (u) and Written in matrix form:

[0032]

[0033] Then, based on S, a separation matrix W is constructed using the Fast Independent Component Analysis (Fast-ICA) method to perform blind source separation on signal S, resulting in the two separated signals:

[0034]

[0035] Finally, using the negative entropy G(|y(u)| 2 The determination is made based on the channel signal y corresponding to the maximum negative entropy. i (u) is the result of the fractional Fourier transform of the i-th pulse after dealiasing, where G(x) = xexp(-x 2 / 2).

[0036] Step 5: The signal after blind source separation, dealiasing, and fractional Fourier bandpass filtering is transformed to the time domain by inverse fractional Fourier transform, and threshold detection is performed on the signal to extract the pulse segment.

[0037] In this embodiment, the signal y obtained in step 4 i (u) Perform a fractional-order inverse Fourier transform to obtain the time-domain signal s corresponding to pulse i. i (t); By detecting the rising edge toa1 and falling edge toa2 of the threshold energy detection pulse, the pulse width pw = toa2 - toa1 of the signal is estimated, and the pulse is extracted to obtain a pulse signal with a duty cycle of 100%.

[0038] Step 6: Calculate the pulse width of the truncated signal, and calculate its frequency modulation slope and center frequency through fractional Fourier transform, thereby completing the accurate estimation of the pulse signal parameters.

[0039] In this embodiment, a fractional Fourier transform is performed on the extracted pulse signal with a 100% duty cycle, and the peak point (P) is obtained. i U i The frequency modulation slope of the pulse signal is determined based on the peak position. and center frequency Perform parameter estimation:

[0040]

[0041] To illustrate the effectiveness of this method, Table 1 presents the parameter results obtained using the method of this invention, while Tables 2 and 3 present the parameter estimation results of short-time fractional Fourier transform and fractional Fourier filtering in traditional methods. Compared with the parameter estimation results obtained by this invention, existing methods cannot effectively solve the problem of aliasing between pulses, which leads to a decrease in parameter estimation performance.

[0042] Table 1. Parameter estimation results of the method proposed in the embodiments of the present invention.

[0043] Center frequency (MHz) Frequency modulation slope (Hz / s) Pulse width (µs) True value 505.9 <![CDATA[1×1 10 ]]> 100 estimated value 505.904 <![CDATA[9.96×1 9 ]]> 99.56

[0044] Table 2. Parameter estimation results based on short-time fractional Fourier transform.

[0045] Center frequency (MHz) Frequency modulation slope (Hz / s) Pulse width (µs) True value 505.9 <![CDATA[1×1 10 ]]> 100 estimated value 510.12 <![CDATA[9.96×1 9 ]]> 141.56

[0046] Table 3. Parameter estimation results based on fractional Fourier filtering

[0047] Center frequency (MHz) Frequency modulation slope (Hz / s) Pulse width (µs) True value 505.9 <![CDATA[1×1 10 ]]> 100 estimated value 511.58 <![CDATA[9.96×1 9 ]]> 142.73

[0048] like Figure 2 As shown, the time-domain plot of the received signal is given. It can be seen that under low signal-to-noise ratio conditions, the signal is completely submerged in noise, such as... Figure 3 As shown, the signal with a high signal-to-noise ratio is obtained after filtering and dealiasing the signal using the method proposed in this invention.

[0049] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A method for estimating LFM pulse signal parameters under aliasing conditions, characterized in that, include: S1. For multiple linear frequency modulated pulse external radiation sources, receive their direct wave signals; S2. Perform fractional Fourier transform on the received direct wave signal to obtain the position of the peak value in the fractional Fourier transform domain. S3. Based on the position of the signal in the fractional Fourier transform domain, construct a new channel signal according to the analytical expression of the fractional Fourier transform. S4. Process the multi-channel signal obtained in step S3 through blind source separation to obtain the separated channel signal; calculate the negative entropy of the separated channel signal, and determine that the signal corresponding to the channel with the largest negative entropy is the form of the dealiased signal in the fractional Fourier transform domain; Step S4 is specifically as follows: The signal processed in step S3 is recorded as follows: ; The direct wave signal from the external radiation source received in step S1 The order of the transformation is The fractional Fourier transform yields the signal. ; right Perform fractional Fourier filtering to obtain the signal ; Signal and Written in matrix form: ； Constructing a separation matrix using the Fast Independent Component Analysis (Fast-ICA) method For signal Blind source separation is performed to obtain two separate signals; Calculate the negative entropy of each of the two separated signals. The channel signal with the maximum negative entropy is the result of the i-th pulse after dealiasing, after undergoing a fractional Fourier transform. ; S5. The signal after blind source separation and dealiasing is transformed to the time domain through fractional Fourier inverse transform, and the transformed signal in the time domain is subjected to threshold detection to extract the pulse segment. S6. For the truncated signal, calculate its pulse width, and calculate its frequency modulation slope and center frequency through fractional Fourier transform, thereby completing the accurate estimation of the pulse signal parameters.

2. The method for estimating LFM pulse signal parameters under aliasing conditions according to claim 1, characterized in that, The direct wave signal from the external radiation source received in step S1 is represented as follows: ； in, This indicates the number of pulses in the received direct wave signal. , Indicates time delay. Indicates pulse amplitude. Indicates the pulse width. Indicates the center frequency. This indicates the frequency modulation slope.

3. The method for estimating LFM pulse signal parameters under aliasing conditions according to claim 2, characterized in that, The position of the peak value of the i-th pulse signal after transformation in step S2 in the fractional Fourier transform domain is represented as follows: , This represents the transform order corresponding to the peak value of the i-th pulse signal. This represents the transform domain coordinates corresponding to the peak value of the i-th pulse signal in the fractional Fourier transform domain.

4. The method for estimating LFM pulse signal parameters under aliasing conditions according to claim 3, characterized in that, The specific implementation process of step S3 is as follows: First, based on the peak position of the fractional Fourier transform domain obtained in step S2, the analytical expression of the peak corresponding to each pulse on the same fractional Fourier transform order is calculated, thereby constructing a multi-channel signal; then, a fractional Fourier bandpass filter centered on the peak position is constructed to perform fractional Fourier filtering on the multi-channel signal; thus obtaining the multi-channel signal constructed within the passband.

5. The method for estimating LFM pulse signal parameters under aliasing conditions according to claim 4, characterized in that, Step S5 is specifically implemented as follows: For the signal... Perform a fractional-order inverse Fourier transform to obtain the time-domain signal corresponding to pulse i. ; The rising edge of the pulse is detected by threshold energy. and falling edge The pulse width of the signal is estimated. The pulse is extracted to obtain a pulse signal with a duty cycle of 100%.

6. The method for estimating LFM pulse signal parameters under aliasing conditions according to claim 5, characterized in that, The specific implementation process of step S6 is as follows: perform a fractional Fourier transform on the extracted pulse signal with a duty cycle of 100%, and obtain the peak point position. The frequency modulation slope of the pulse signal is determined based on the peak position. and center frequency Perform parameter estimation: 。

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