Fast high-resolution coherent integration method for random pulse-to-pulse agile radar

Abstract

The present invention provides a rapid high-resolution coherent accumulation method for random pulse-to-pulse agile radar, belonging to the field of radar signal processing, comprising: performing matched filtering on an echo signal; performing fast-time FFT processing on the matched-filtered echo signal to convert it from the fast-time time domain to the frequency domain, thereby obtaining a frequency-domain echo signal; combining KT and NUFFT techniques to scale the phase of the frequency-domain echo signal using joint truncated Sinc interpolation to obtain an interpolated corrected frequency-domain signal; performing fast-time I FFT processing on the interpolated corrected frequency-domain signal to convert it from the fast-time frequency domain to the time domain, thereby obtaining a corrected time-domain signal; performing high-resolution phase compensation on the corrected time-domain signal according to a fast-time compensation term, and performing slow-time FFT processing on the compensated signal to complete coherent accumulation. The present invention can realize the accumulation of random pulse-to-pulse agile signals, significantly improving computational efficiency while achieving high resolution using the agile bandwidth.

Description

Technical Field

[0001] The present invention belongs to the field of radar signal processing, and in particular relates to a fast high-resolution coherent accumulation method for a random pulse-to-pulse agile radar. Background Art

[0002] In today's high-tech military and civilian sectors, the performance and capabilities of radar systems have become key factors in measuring advanced reconnaissance capabilities. Random pulse-to-pulse agility signals have become a key means of improving radar performance. Their carrier frequency and repetition rate vary according to a specific strategy. This variation effectively reduces signal loss caused by ground clutter, electronic interference, and multipath effects, while enhancing the radar's ability to counter electronic countermeasures. This significantly improves the radar's adaptability and detection performance in complex environments and against low-observable targets.

[0003] There are two main existing random pulse-to-pulse agility signal coherent accumulation technologies, namely search compensation and interpolation correction.

[0004] The Radon Fourier Transform (RFT) technique based on search compensation achieves relatively ideal accumulation results by dividing the target motion parameters into a grid and performing point-by-point traversal compensation. Although this technique achieves good results, it has a high computational complexity, which is not conducive to real-time target detection applications.

[0005] The interpolation-based correction techniques, KT (Keystone Transform) and NUFFT (Non-Uniform Fast Fourier Transform), respectively correct for carrier frequency agility and repetition frequency agility to achieve accumulation. Interpolation-based correction techniques do not require search and have lower computational complexity than RFT, making them suitable for unknown target detection. However, correction sacrifices agility bandwidth, resulting in lower resolution. Furthermore, NUFFT is difficult to implement in engineering, and its computational complexity still needs to be optimized.

[0006] Therefore, how to reduce the computational complexity of coherent integration technology as much as possible while ensuring resolution and accumulation performance has become a technical problem that needs to be solved urgently in the industry. Summary of the Invention

[0007] The purpose of the present invention is to propose a fast high-resolution coherent accumulation method for random pulse-to-pulse agile radar, which can realize the accumulation of random pulse-to-pulse agile signals and significantly improve the computational efficiency while achieving high resolution by utilizing the agile bandwidth.

[0008] The present invention is achieved through the following technical solutions:

[0009] A rapid high-resolution coherent accumulation method for random pulse-to-pulse agile radar includes the following steps:

[0010] Step S1, performing matched filtering on the echo signal;

[0011] Step S2, performing fast time FFT processing on the echo signal processed in step S1 to convert it from the fast time domain to the frequency domain to obtain a frequency domain echo signal;

[0012] Step S3: Combining KT and NUFFT techniques, using joint truncated Sinc interpolation to scale the phase of the frequency domain echo signal to obtain an interpolated corrected frequency domain signal;

[0013] Step S4, performing fast-time IFFT processing on the interpolated corrected frequency domain signal obtained in step S3 to convert it from the fast-time frequency domain to the time domain to obtain a corrected time domain signal;

[0014] Step S5: Perform high-resolution phase compensation on the corrected time domain signal obtained in step S4 according to the fast-time constructed compensation term, and perform slow-time FFT processing on the compensated signal to complete coherent accumulation.

[0015] Furthermore, in step S1, the echo signal after matched filtering is expressed as in, is the slow time variable, T a For PRI agility sequence, r T for the center PRI q The cycle agility range obeys uniform distribution, that is, T a ~U[T r -T q / 2,T r +T q / 2], L is the number of uniform motion targets, is a trigonometric function, τ l =2(R l -v l t n ) / c is the time delay, R l and v l is the distance and speed of the lth target, F a is the carrier frequency agility sequence, which is in B with f0 as the center frequency f The bandwidth agility range obeys uniform distribution, that is, F a ~U[f0-B f / 2,f0+B f / 2], t is the fast time variable, T p is the pulse width, n is the pulse number, A l is the echo amplitude of the lth target, and c is the speed of light.

[0016] Furthermore, in step S2, the frequency domain echo signal is represented as in,

[0017] Furthermore, in step S3, the phase of the frequency domain echo signal is scaled to obtain Then the interpolation-corrected frequency domain signal reconstructed after Sinc interpolation is in, is the interpolation kernel, T r is a uniform slow time series with a sampling interval.

[0018] Furthermore, in step S4, the corrected time domain signal is expressed as

[0019] Furthermore, in step S5, the phase compensation is performed on the corrected time domain signal to obtain The compensated signal is processed by slow time FFT to accumulate the signal Among them, F(t,f d ) is the phase compensation term after FFT processing, δ(·) is the impulse response function,

[0020] Furthermore, in step S3, the Sinc interpolation process specifically includes:

[0021] Step S31: Select the (i, j)th data unit, take the (i, j)th data unit as the center, select a data unit of length P in the slow time dimension, and construct a corresponding Sinc interpolation kernel;

[0022] Step S32: determine whether i>P / 2 holds. If so, proceed to step S33. Otherwise, fill the blank data cells with zeros, set the interpolation kernel weights at the corresponding positions to 0, and proceed to step S34.

[0023] Step S33, determine whether i>NP / 2 holds. If so, fill the blank data cells with zeros, set the interpolation kernel weight of the corresponding position to 0, and proceed to step S34. Otherwise, proceed to step S34;

[0024] Step S34: Perform P-point multiplications on the data unit of length P and the interpolation kernel of corresponding length P, and sum them up to output a reconstructed (i, j)th data unit; perform P-point multiplications on the data unit of length P and the interpolation kernel, and sum them up to output a reconstructed (i, j)th data unit;

[0025] Step S35: Determine whether the traversal reaches the last data unit. If so, end the process. Otherwise, set i=i+1, j=j+1 and proceed to step S31.

[0026] Where i and j are integers, N is the number of slow-time sampling points, and P is the number of interpolation points.

[0027] Furthermore, in step S5, the phase compensation term F(t,f d ) in the fast time dimension appears as a special envelope, and its expression is The distance resolution after compensation is

[0028] The present invention has the following beneficial effects:

[0029] 1. The present invention first performs matched filtering on the echo signal, then performs fast time FFT processing on the processed echo signal to transform it from the fast time domain to the frequency domain to obtain the frequency domain echo signal, then combines KT and NUFFT technology, uses joint truncated Sinc interpolation to scale the phase of the frequency domain echo signal to obtain the interpolation correction frequency domain signal, then performs fast time IFFT processing on the interpolation correction frequency domain signal to transform it from the fast time frequency domain to the time domain to obtain the correction time domain signal, and finally constructs the compensation term according to the fast time to compensate the signal obtained in step S4. The corrected time domain signal is subjected to high-resolution phase compensation, and the compensated signal is subjected to slow-time FFT processing to complete coherent accumulation. In the process of accumulating random pulse-to-pulse agile signals, the use of joint truncated Sinc interpolation can significantly reduce the interpolation complexity, thereby achieving a significant reduction in the amount of calculation while ensuring data accuracy and significantly improving computational efficiency. The compensation term constructed by the present invention appears as a special envelope in the fast time dimension, and its period shows periodic changes in the fast time. Therefore, the distance resolution after compensation makes full use of the agile bandwidth to achieve high resolution in the distance dimension. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The present invention will be described in further detail below with reference to the accompanying drawings.

[0031] Figure 1 Flowchart of the present invention.

[0032] Figure 2 Schematic diagram of the carrier frequency and repetition frequency agile sequence generated by the present invention.

[0033] Figure 3 This is a top view of the target original echo signal envelope generated by the present invention.

[0034] Figure 4 This is a top view of the echo signal envelope after matched filtering of the present invention.

[0035] Figure 5 This is a specific flow chart of the Sinc interpolation process of the present invention.

[0036] Figure 6 This is a top view of the envelope of the time domain signal corrected by the present invention.

[0037] Figure 7 The present invention is |E[F(t,f d )]|'s envelope changes.

[0038] Figure 8 This is the accumulated range-Doppler map of the present invention. DETAILED DESCRIPTION

[0039] like Figure 1 As shown in FIG, a fast high-resolution coherent accumulation method for random pulse-to-pulse agile radar includes the following steps:

[0040] Step S1, performing matched filtering on the echo signal;

[0041] Specifically, a single-frequency pulse is used as the transmitting signal, F a is the carrier frequency agility sequence, which is in B with f0 as the center frequency f The bandwidth agility range obeys uniform distribution, that is, F a ~U[f0-B f / 2,f0+B f / 2];t n is the slow time variable, T a is the PRI (pulse repetition interval, i.e. (1 / repetition frequency)) agile sequence, which is T r T is the central period q The cycle agility range obeys uniform distribution, that is, T a ~U[T r -T q / 2,T r +T q / 2].

[0042] In this embodiment, a three-target scenario is used as an example for technical simulation. A 13th Gen Intel(R) Core(TM) i9-13900HX 2.20GHz processor, 16G RAM, and MATLAB 2023a under Windows 11 system are used for simulation.

[0043] The radar parameters are set as shown in Table 1:

[0044] Table 1

[0045] parameter Numerical <![CDATA[Radar center frequency f0]]> 12GHz <![CDATA[Carrier frequency agile bandwidth B f > 100MHz <![CDATA[Central period T r > 2.5μs <![CDATA[PRI agility range T q > 1μs <![CDATA[Pulse width T p > 100ns <![CDATA[Sampling rate f s > 200MHz Pulse accumulation number N 256 Signal-to-noise ratio (SNR) -5dB

[0046] The target parameters are shown in Table 2:

[0047] Table 2

[0048] parameter Goal 1 Goal 2 Goal 3 distance 200m 240m 243m speed 5000m / s 5500m / s 5500m / s

[0049] like Figure 2FIG. 1 is a schematic diagram of a carrier frequency agile sequence and a repetition frequency agile sequence generated in this embodiment.

[0050] Assuming there are L uniformly moving targets, the echo signal after matched filtering is expressed as is a trigonometric function, τ l =2(R l -v l t n ) / c is the time delay, R l and v l is the distance and speed of the lth target, and the time delay is substituted into the above echo signal expression to obtain t is the fast time variable, T p is the pulse width, n is the pulse number, A l is the echo amplitude of the lth target, and c is the speed of light. In this embodiment, the number of pulse width sampling points is 20, and the signal gain after matched filtering is 26.02dB. The generated target original echo signal envelope is shown in the top view. Figure 3 As shown, the top view of the echo signal envelope after matched filtering is as follows Figure 4 shown.

[0051] Step S2: Perform fast time FFT processing on the echo signal processed in step S1 to convert it from the fast time domain to the frequency domain to obtain a frequency domain echo signal, so as to facilitate subsequent interpolation correction processing in the frequency domain. The frequency domain echo signal is represented as Among them, sinc 2 (·) is the square of the sinc function, From the frequency domain echo signal expression, we can see that v l The coupling with f in the fast time frequency domain leads to the time domain envelope range migration, F a and t n The phase jitter caused by this makes it impossible to effectively accumulate the signal.

[0052] Step S3: Combine KT and NUFFT technology and use joint truncated Sinc interpolation to scale the phase of the frequency domain echo signal. in T r is a uniform slow time series with a sampling interval, we get Then the interpolation-corrected frequency domain signal reconstructed after Sinc interpolation is

[0053] In the prior art, KT and NUFFT are used for interpolation correction respectively. The main implementation of KT is Sinc interpolation, and its interpolation kernel is η n =f0 / (f+F a (n))t nNUFFT is a fast algorithm based on the improvement of NUDFT. The NUDFT transform can be derived as follows:

[0054] For the discrete sampling signal s(t,t n ), and its frequency domain signal S(t,f d ) is observed, the signal is equivalent to a band-limited signal, which can be expressed as Among them, f dc is the Doppler center frequency. When there is no ambiguity, f dc = 0, when there is fuzziness and the fuzzy number is K, f dc =K·PRF. According to NUDFT transformation, the signal accumulation process can be transformed into

[0055] At this time, by performing inverse Fourier transform on both sides of the equation, we can get in, T r is a uniform slow time series with a sampling interval, T r =1 / PRF.

[0056] Therefore, the NUDFT accumulation process is equivalent to Sinc interpolation and FFT transformation. It can be found that since both the KT implementation method and the NUDFT are Sinc interpolation, the interpolation kernel of KT and NUDFT can be combined to perform a joint Sinc interpolation operation on the original signal to achieve computational optimization.

[0057] At the same time, according to the characteristics of the Sinc function, since the function value approaches 0 the farther away from the main lobe, the weighted value of the sampling point farther away from the interpolation point is closer to 0. This means that the convolution kernel can be truncated without excessive loss of accuracy. Therefore, in practical applications, convolution operations are generally performed only on sampling points near the interpolation point.

[0058] Specifically, in this embodiment, Figure 5 As shown in Figure 2, the Sinc interpolation process specifically includes:

[0059] Step S31: Select the (i, j)th data unit, take the (i, j)th data unit as the center, select a data unit of length P in the slow time dimension, and construct a corresponding Sinc interpolation kernel;

[0060] Step S32: determine whether i>P / 2 holds. If so, proceed to step S33. Otherwise, fill the blank data cells with zeros, set the interpolation kernel weights at the corresponding positions to 0, and proceed to step S34.

[0061] Step S33, determine whether i>NP / 2 holds. If so, fill the blank data cells with zeros, set the interpolation kernel weight of the corresponding position to 0, and proceed to step S34. Otherwise, proceed to step S34;

[0062] Step S34: perform P point multiplications on the data unit of length P and the interpolation kernel of corresponding length P, and sum them up to output the reconstructed (i, j)th data unit;

[0063] Step S35: Determine whether the traversal has reached the last data unit. If so, end. Otherwise, set i=i+1, j=j+1 and enter step S31, where i and j are integers, N is the number of slow time sampling points, and P is the number of interpolation points.

[0064] Assuming that the number of fast time sampling points is M and the number of slow time sampling points is N, the interpolation calculation complexity of the existing technology is 2MN 2 The computational complexity of this method is MNP, significantly reducing the required computational effort while ensuring data accuracy. In this embodiment, an interpolation kernel with eight points was used, and eight-point interpolation was performed on each point in the two-dimensional matrix, resulting in 1,187,840 calculations. This operation effectively corrected the range migration and slow-time phase jitter caused by agility.

[0065] Step S4: Perform fast time IFFT processing on the interpolated corrected frequency domain signal obtained in step S3 to convert it from the fast time frequency domain to the time domain to obtain a corrected time domain signal, which is expressed as The signal envelope top view is as follows Figure 6 As shown;

[0066] Step S5: construct a phase compensation term according to the fast time t to perform high-resolution phase compensation on the corrected time domain signal obtained in step S4 to obtain The compensated signal is processed by slow time FFT to accumulate the signal Among them, F(t,f d ) is the phase compensation term after FFT processing, δ(·) is the impulse response function, It can be seen that both distance and Doppler information can be accumulated at the correct position, and due to F a (n) is evenly distributed in the slow time dimension, and the compensation term F(t,f d )'s envelope behaves like a Sinc function, with a resolution of c / (2B f ), specifically:

[0067] The phase compensation term F(t,f d ) in the fast time dimension appears as a special envelope, and its expression is

[0068] In order to obtain statistically significant cumulative results, F(t,f d ) can be expressed as The E=[F(t,f d )] appears as an impulse function in the Doppler dimension and shows periodic changes in the fast time dimension, such as Figure 7 The figure shows |E[F(t,f d )]|, |E[F(t,f d )]|=0, then t=k / B f +2R l / c, k=0,±1,±2,..., from this we can know that its period T=Δt=1 / B f , substitute the conclusion into It can be deduced that the distance resolution after compensation is It can be seen that the agile bandwidth B is fully utilized f , achieving high resolution in the distance dimension.

[0069] For a 256-point FFT, the ideal gain after accumulation is 48.16 dB. Therefore, from the original echo to the end of coherent accumulation, the theoretical signal gain should be 74.18 dB. Figure 8 The accumulated range-Doppler diagram is shown. Three targets can be clearly distinguished from the diagram. Their accumulated gains are 71.53dB, 69.18dB, and 69.25dB, respectively. The average loss is 2.86dB, and the total processing time is 0.4294 seconds.

[0070] The above description is merely a preferred embodiment of the present invention and therefore cannot be used to limit the scope of the present invention. In other words, equivalent changes and modifications made according to the scope of the patent application and the contents of the specification should still fall within the scope of the patent of the present invention.

Claims

1. A rapid high-resolution coherent integration method for random pulse-to-pulse agile radar, characterized by: The steps include: Step S1, performing matched filtering on the echo signal; Step S2, performing fast time FFT processing on the echo signal processed in step S1 to convert it from the fast time domain to the frequency domain to obtain a frequency domain echo signal; Step S3: Combining KT and NUFFT techniques, using joint truncated Sinc interpolation to scale the phase of the frequency domain echo signal to obtain an interpolated corrected frequency domain signal; Step S4, performing fast-time IFFT processing on the interpolated corrected frequency domain signal obtained in step S3 to convert it from the fast-time frequency domain to the time domain to obtain a corrected time domain signal; Step S5: Perform high-resolution phase compensation on the corrected time domain signal obtained in step S4 according to the fast-time constructed compensation term, and perform slow-time FFT processing on the compensated signal to complete coherent accumulation.

2. The rapid high-resolution coherent integration method for random pulse agile radar according to claim 1, characterized in that: In step S1, the echo signal after matched filtering is expressed as in, is the slow time variable, T a For PRI agility sequence, r T for the center PRI q The cycle agility range obeys uniform distribution, that is, T a ~U[T r -T q / 2,T r +T q / 2], L is the number of uniform motion targets, is a trigonometric function, τ l =2(R l -v l t n ) / c is the time delay, R l and v l is the distance and speed of the lth target, F a is the carrier frequency agility sequence, which is in B with f0 as the center frequency f The bandwidth agility range obeys uniform distribution, that is, F a ~U[f0-B f / 2,f0+B f / 2], t is the fast time variable, T p is the pulse width, n is the pulse number, A l is the echo amplitude of the lth target, and c is the speed of light.

3. The rapid high-resolution coherent integration method for random pulse agile radar according to claim 2, characterized in that: In step S2, the frequency domain echo signal is represented as in, 4. The rapid high-resolution coherent integration method for random pulse agility radar according to claim 3, characterized in that: In step S3, the phase of the frequency domain echo signal is scaled to obtain Then the interpolation-corrected frequency domain signal reconstructed after Sinc interpolation is in, is the interpolation kernel, T r is a uniform slow time series with a sampling interval.

5. The rapid high-resolution coherent integration method for random pulse agility radar according to claim 4, characterized in that: In step S4, the corrected time domain signal is expressed as 6. The rapid high-resolution coherent integration method for random pulse agile radar according to claim 5, characterized in that: In step S5, the phase compensation is performed on the corrected time domain signal to obtain The compensated signal is processed by slow time FFT to accumulate the signal Among them, F(t,f d ) is the phase compensation term after FFT processing, δ(·) is the impulse response function, 7. The rapid high-resolution coherent integration method for random pulse agile radar according to claim 3, characterized in that: In step S3, the Sinc interpolation process specifically includes: Step S31: Select the (i, j)th data unit, take the (i, j)th data unit as the center, select a data unit of length P in the slow time dimension, and construct a corresponding Sinc interpolation kernel; Step S32: determine whether i>P / 2 holds. If so, proceed to step S33. Otherwise, fill the blank data cells with zeros, set the interpolation kernel weights at the corresponding positions to 0, and proceed to step S34. Step S33, determine whether i>NP / 2 holds. If so, fill the blank data cells with zeros, set the interpolation kernel weight of the corresponding position to 0, and proceed to step S34. Otherwise, proceed to step S34; Step S34: perform P point multiplications on the data unit of length P and the interpolation kernel of corresponding length P, and sum them up to output the reconstructed (i, j)th data unit; Step S35: Determine whether the traversal reaches the last data unit. If so, end the process. Otherwise, set i=i+1, j=j+1 and proceed to step S31. Where i and j are integers, N is the number of slow-time sampling points, and P is the number of interpolation points.

8. The rapid high-resolution coherent integration method for random pulse agile radar according to claim 3, characterized in that: In step S5, the phase compensation term F(t,f d ) in the fast time dimension appears as a special envelope, and its expression is The distance resolution after compensation is

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