CN104765033B - Method using distance side lobe in cross-correlation function suppression step frequency imaging - Google Patents

Abstract

The invention provides a kind of method that utilization cross-correlation function suppresses distance side lobe in step frequency imaging, by obtaining the cross-correlation function with certain altitude, and suppress jointly to synthesize the distance side lobe of correlation function using cross-correlation function and auto-correlation function, the echo of collection difference LFM pulse, time delay between LFM pulse echo is removed, and the echo of all LFM pulses is superimposed, matched filtering, Wave beam forming is carried out to the echo after superposition and extracts intensity, obtain the picture of target.The method that invention is proposed can effectively reduce the distance side lobe of composite signal.

Description

Method for inhibiting range sidelobe in step frequency imaging by utilizing cross-correlation function

Technical Field

The present invention relates to an array imaging method.

Background

In array imaging technologies such as sonar, radar, and medicine, in order to improve the range resolution of an imaging system, a large bandwidth of a transmission signal needs to be used. But large bandwidth signals can result in instantaneous bandwidth increase at the transmitting and receiving ends of the imaging system, thereby increasing system hardware cost. To overcome this drawback, a step-and-frequency system (Gill G, Detection of words embedded in a recording using frequency step wave form, Proceedings of the1994International Symposium on Noise and recording project in a radio and imaging sensor, Kawasaki, Japan,1994:115. Liu shohong, Signal analysis and processing of a high-range resolution imaging radar, the Master thesis of the university of Western electronics technology, 2006) may use multiple small-bandwidth signals to synthesize a signal with a large bandwidth, increasing the range resolution without increasing the instantaneous bandwidth of the imaging system.

In the processing process, the existing step frequency imaging method considers the cross-correlation function as a kind of interference. In order to suppress cross-correlation interference, the frequency bands of a plurality of transmission pulses in a step frequency system are separated from each other, and thus the range side lobe of the composite signal tends to be high. To suppress the range side lobe, Levanon et al used frequency domain weighting (N.Levanon, "Stepped-frequency pulse-train radial signal," IEE Proc. -radial Source & Navigation, vol.194, No.6, pp.297-309, Dec.2002) and range grating lobe zeroing (N.Levanon, E.Mozeson, "NullifyingACF gradingloops in Stepped-frequency trains," IEEE pulse, "Transactionson Aero-space and Electronic System, vol.39, No.2, pp.694-703, Apr.2003) to obtain lower range side lobe. These methods tend to cause the distance main lobe of the composite signal to widen, resulting in a decrease in distance resolution. Furthermore, these methods simply synthesize the autocorrelation function (or self-ambiguity function), neglecting the effect of the cross-correlation function and suppressing it as interference.

Disclosure of Invention

In order to suppress high-distance side lobes of a synthesized correlation function in a step frequency imaging system, the invention provides a method for shaping the synthesized correlation function by using a cross-correlation function and an autocorrelation function together and obtaining low-distance side lobes. In order to utilize the cross-correlation function rather than suppress it, the present invention designs a set of chirp (LFM) pulses as the transmit signal for a stepped frequency system. By setting the frequency bands of adjacent LFM pulses to be overlapped and setting the frequency modulation directions to be opposite, the invention obtains a cross-correlation function (the cross-correlation peak value is larger than 0.1 time of the autocorrelation peak value) which is higher than that of the traditional method, and reserves and utilizes the cross-correlation peak value as a useful component, and finally achieves the purpose of depressing the distance side lobe of the synthesized correlation function by optimizing the pulse signal parameters.

The technical scheme adopted by the invention for solving the technical problem comprises the following steps:

1) setting array parameters, wherein a transmitting array adopts an array system of a step frequency system, and a single transmitting array element is positioned on a coordinate origin; the receiving array is an N-element ULA, the ULA represents a uniform linear array, and the array element interval is d; using a two-dimensional coordinate system, the coordinates of a transmitting array element are (0,0), the coordinates of an nth receiving array element are { [ N-1- (N-1)/2] d,0}, and N is 1,2, … …, N;

2) designing a group of LFM pulses, wherein the number M of the pulses is more than or equal to 2, the frequency bands of adjacent pulses are overlapped, the frequency modulation directions of the adjacent pulses are opposite, and the mth LFM pulse is set as s_m(t)，

Wherein t represents time, f_m＝f₀-D_m(B₀+ Δ B)/2 is the center frequency of the mth LFM pulse, Δ B is the coincidence bandwidth, which is negative, f₀In the whole frequency bandHeart frequency, B₀Is the bandwidth of a single LFM pulse, T₀Is the pulse width, D, of a single LFM pulse_mFor the FM direction control parameters, when the m-th LFM pulse is up-modulated, D_m1, when the m-th LFM pulse is down-modulated, D_m＝-1，m＝1,2,…,M；

Superposing the autocorrelation function and the cross-correlation function of all LFM pulses to obtain the correlation function of the synthesized signalWherein R is_m,m(t) is the autocorrelation function of the mth LFM pulse, R_m,i(t) is a cross-correlation function between the mth LFM pulse and the other LFM pulses;

shaping the synthesized correlation function by utilizing the cross-correlation function and the autocorrelation function together, and obtaining a low-range side lobe while obtaining an expected range main lobe, namely the peak value of the range side lobe is less than or equal to 0.1 time of the peak value of the main lobe;

3) transmitting the M LFM pulses designed in the step 2) by using the array in the step 1) according to the time interval delta T, and collecting echoes, wherein the echo on the nth receiving array element is x_n(t)，

Wherein σ_pThe scattering intensity of the P-th scattering point is represented by P1, 2, …, and P is the number of scattering points,is the time delay from a single transmit array element to the p-th scattering point,is the time delay from the p-th scattering point to the n-th receiving array element, Δ T represents the time interval between adjacent LFM pulses at the time of transmission, z_n(t) represents a noise term;

4)after obtaining the echo, carrying out time delay correction and time domain superposition on the echoes of different LFM pulses to obtain the echo of the signalMatched filtering is carried out on the echo by copying M LFM pulses to obtain MN matched filtering outputs, and the mth matched filter processes the nth echo to obtain an output y_m,n(t)＝x_n(t)*h_m(t) wherein h_m(t)＝[s_m(T₀-t)]^cIs an impulse response function of the mth matched filter]^cRepresenting conjugation;

assuming that the transmitted signal is uncorrelated with noise, then

And performing beam forming processing on the MN matched filter outputs to obtain different beam outputs so as to obtain a two-dimensional or three-dimensional image of the target.

The invention has the beneficial effects that: the invention adopts a group of LFM pulse signals, and utilizes the cross-correlation function and the autocorrelation function between the LFM pulse signals to restrain the range side lobe of a synthesized signal. To achieve this, the present invention sets the frequency bands of adjacent LFM pulses to overlap each other while the frequency modulation directions are opposite. These parameter combinations are optimized to find the parameter combination corresponding to the lowest range side lobe.

The basic principle of the method is derived theoretically, the implementation scheme is verified by computer numerical simulation, and the result shows that the method provided by the invention can effectively reduce the distance side lobe of the synthesized signal.

Drawings

FIG. 1 is a schematic illustration of an array used in the present invention (exemplified by an array used for two-dimensional imaging);

fig. 2 is a diagram showing the signal design result when M is 2, wherein (a) is a diagram showing the relationship between the peak of the autocorrelation function of the synthesized signal and the coincidence frequency bandwidth Δ B; (b) is a schematic diagram of the designed autocorrelation function and cross-correlation function of 2 LFM signals; (c) a schematic diagram of the correlation function of the synthesized signal;

FIG. 3 is a main flow chart of the steps involved in the present invention;

FIG. 4 is a flow chart of processing echoes by a receiving end to obtain imaging results;

fig. 5 is a schematic diagram of imaging results when M is 2, where (a) is an angle and distance two-dimensional imaging map, and (b) is a distance dimensional slice schematic diagram.

Detailed Description

The present invention will be further described with reference to the following drawings and examples, which include, but are not limited to, the following examples.

The main contents of the invention are:

1. contrary to the conventional approach that considers the cross-correlation function to be detrimental and to be suppressed, the present invention considers that the cross-correlation function can be exploited. The invention obtains the cross-correlation function with a certain height (the cross-correlation peak value is larger than 0.1 time of the self-correlation peak value), and uses the cross-correlation function and the self-correlation function to jointly inhibit the distance side lobe of the synthesized correlation function. Specifically, a group of FM pulses is designed as a transmission signal, and the frequency bands of adjacent pulse signals are set to overlap each other, while the frequency modulation directions are set to be opposite (in a conventional step frequency system, the frequency bands are required to be separated from each other). Before signal transmission, a correlation function of a signal synthesized by the group of OFDM-LFM pulses is considered, signal parameters are optimized, so that a cross-correlation function between adjacent pulses is in a higher level (the cross-correlation peak value is more than or equal to 0.1 time of the self-correlation peak value) (in a traditional step frequency system, the lower the cross-correlation is, the better the cross-correlation is, the cross-correlation function is required to have a certain height), and the cross-correlation function and the self-correlation function are utilized to jointly restrain distance side lobes of the synthesized correlation function.

2. The echo of different LFM pulses is collected, the time delay between LFM pulse echoes is removed, and the echoes of all LFM pulses are superposed (in the traditional step frequency imaging system, the echoes of different pulses are required to be separated from each other, so that the cross-correlation interference can be avoided). And performing matched filtering, beam forming and intensity extraction on the superposed echoes to obtain an image of the target.

3. The imaging results obtained with the method of the present invention are given by computer simulation. The imaging result verifies the effectiveness of the range sidelobe suppression method provided by the invention.

Technical scheme of the invention

The technical scheme adopted by the invention for solving the existing problems can be divided into the following 4 steps:

1) and setting array parameters. The transmitting array is the same as the array system of the traditional step frequency system. The single transmitting array element is positioned on the origin of coordinates, and the receiving array is an N-element Uniform Linear Array (ULA).

2) A group of LFM pulses with lower synthetic range sidelobe is designed (the range sidelobe peak value is less than or equal to 0.1 time of the main lobe peak value, and the number M of the pulses is more than or equal to 2). In the set of LFM pulses, the frequency bands of adjacent pulses are set to coincide while the frequency modulation directions of adjacent pulses are set to be opposite. Therefore, a high cross-correlation function (the peak value of the cross-correlation function is more than or equal to 0.1 time of the peak value of the autocorrelation function) is obtained, the cross-correlation function and the autocorrelation function are used for shaping the synthesized correlation function together, and a desired distance main lobe is obtained and simultaneously a low distance side lobe (the peak value of the distance side lobe is less than or equal to 0.1 time of the peak value of the main lobe) is obtained by optimizing the signal pulse width, the signal bandwidth and the frequency band interval.

3) And (3) transmitting the M LFM pulses designed in the step 2) according to the time interval sequence of delta T by using the array in the step 1), and collecting echoes.

4) And carrying out time delay correction, time domain superposition, matched filtering, beam forming and intensity extraction processing on the echoes of different LFM pulses to obtain an imaging result. After the echoes are collected, the echoes corresponding to different LFM pulses are aligned and overlapped on a time domain, the time delay delta T between the LFM pulses is removed, and time delay correction is carried out (in the traditional method, the time delay delta T introduced between the transmitted pulses is used for ensuring that the echoes between the pulses do not generate cross-correlation interference). And (3) performing matched filtering processing on the superposed echoes by using the copies of the M LFM pulses designed in the step 2), and performing beam forming on the matched filtering processing to obtain a final imaging result.

The specific content related to the step 1) is as follows:

the single transmitting array element is positioned at the origin of coordinates, the receiving array is an N-element ULA, and the array element interval is d. Using a two-dimensional coordinate system, the coordinates of the transmitting array element are (0,0) meters, and the coordinates of the N (N-1, 2, … …, N) -th receiving array element are { [ N-1- (N-1)/2] d,0} meters. The imaging array and its two-dimensional coordinate system are shown in fig. 1, where the triangle "Δ" represents the transmit array element and the circle "o" represents the receive array element.

The specific content related to the step 2) is as follows:

a group of LFM pulses are used as a transmitting signal of a stepping frequency imaging system, and the number of the pulses meets the condition that M is more than or equal to 2. The frequency bands of adjacent LFM pulses are overlapped, and the frequency modulation directions of LFM pulse signals with overlapped frequency bands are opposite, so that a cross-correlation function with a certain height (the cross-correlation peak is more than or equal to 0.1 times of the autocorrelation peak) is obtained. And superposing the autocorrelation functions and the cross-correlation functions of all LFM pulses to obtain the correlation function of the synthesized signal. Let the mth (M ═ 1,2, …, M) LFM pulse, s_m(t) is expressed as:

wherein t represents time, f_m＝f₀-D_m(B₀+ Δ B)/2 is the center frequency of the mth LFM pulse, Δ B is the coincidence bandwidth, which is negative, f₀Is the center frequency of the whole band, B₀Is the bandwidth of a single LFM pulse, T₀Is the pulse width, D, of a single LFM pulse_mThe value of the frequency modulation direction control parameter can only take 1 or-1. When the m-th LFM pulse is up-modulated, D_m1, when the m-th LFM pulse is down-modulated, D_m＝-1。

The resulting correlation function can be expressed as:

wherein R is_m,m(t) is the autocorrelation function of the mth LFM pulse, R_m,i(t) is the cross-correlation function between the mth LFM pulse and the other LFM pulses.

Due to the overlapping of the frequency bands and the opposite frequency modulation directions of the adjacent LFM pulse signals, a plurality of high cross-correlation functions (the cross-correlation peak is more than or equal to 0.1 times of the autocorrelation peak) are generated. These cross-correlation functions may be used together with the autocorrelation function to suppress range side lobes of the composite signal. Varying bandwidth B of LFM pulses₀Pulse width T₀And the overlapped frequency bandwidth Δ B (which is a negative value), the correlation function (see equation (2)) obtained in different combinations of parameters is examined, and the signal parameter of the LFM pulse having the lowest range side lobe is searched.

Taking M-2 as an example, an example of optimizing the desired signal parameters to obtain low range sidelobes is given.

Let f₀400kHz, bandwidth B of a single LFM pulse₀10kHz, 0.3ms pulse width T0, the frequency modulation direction between the two pulses being opposite, i.e. D₁＝1，D₂1, superposedThe value interval of the frequency bandwidth Delta B is [ -3, -1]kHz. Side lobes of the autocorrelation function r (t) of the composite signal are calculated. All results were normalized using the autocorrelation peak as the denominator and the results are shown in figure 2. As can be seen from fig. 2(a), the range side lobe of the combined signal takes the lowest value at Δ B ═ 2.4 kHz. As can be seen from fig. 2(b), the peak of the cross-correlation function between 2 LFM pulses is greater than 0.1 times the peak of the autocorrelation function. As can be seen from fig. 2(c), in the presence of a high cross-correlation function, the range sidelobes of the combined signal are suppressed to a low level, below 0.1 times the autocorrelation peak.

The specific contents related to the steps 3) to 4) are as follows:

and after the array parameters and the signal parameters are determined, transmitting the designed LFM pulse out, and collecting the echo.

For simplicity of description, the expansion loss and absorption loss of the signal in the propagation process are ignored. It is assumed that the stepped frequency system is relatively stationary with respect to the target during the irradiation process. Under these simplified conditions. Echo on the N-th (1, 2, …, N) receiving element, x_n(t), which can be expressed as:

wherein σ_pThe scattering intensity of the P-th scattering point (P is 1,2, …, P), P is the number of scattering points,is the time delay from a single transmit array element to the p-th scattering point,is the time delay from the p-th scattering point to the n-th receiving array element, Δ T represents the time interval between adjacent LFM pulses at the time of transmission, z_n(t) represents a noise term.

After obtaining the echoes, the practical correction is carried out on the echoes of different LFM pulses, the time delay (m-1) delta T introduced in the transmitting process is removed, and the time delay delta T is superposed to obtain the echoes of the signals:

and performing matched filtering processing on the echo by using copies of M LFM pulses to obtain MN matched filtering outputs. The output, y, of the mth matched filter obtained by processing the nth echo_m,n(t), which can be expressed as:

y_m,n(t)＝x_n(t)*h_m(t) (5)

wherein,

h_m(t)＝[s_m(T₀-t)]^c(6)

is an impulse response function of the mth matched filter]^cRepresents taking conjugation.

Bringing equations (4) and (6) into equation (5) and assuming that the transmitted signal is uncorrelated with noise, yields:

and performing beam forming processing on the MN matched filter outputs to obtain different beam outputs so as to obtain a two-dimensional or three-dimensional image of the target. Taking the ULA employed in phase-shift beamforming and two-dimensional imaging as an example, beamforming can be expressed as:

wherein, B_q(t) is the output of the qth (Q1, 2, …, Q), Q representing the number of beams,

for complex weighting on the nth receiving array element, A_nFor amplitude weighting, θ_qIs the pointing angle of the qth beam, and c is the signal propagation velocity.

The main flow of the present invention is shown in fig. 3, and the flow of processing echo at the receiving end is shown in fig. 4.

The embodiment of the invention is given by taking a typical underwater two-dimensional fan-scan imaging process as an example. The implementation example uses a computer to perform numerical simulation to check the effect of the method of the present invention.

Let the transmitted signal be a sound wave, whose propagation velocity under water is 1500 m/s. The transmitting array element is positioned at (0,0) meter, the receiving ULA is positioned at the x axis, the number of the array elements is N-48, and the distance between the array elements is equal to the half wavelength corresponding to the underwater 400kHz sound wave. The single point target lies in a plane z-0.1 meters, with angles and distances of (15 °,20 meters) respectively, where ° represents the angle unit.

The number of transmission pulses is M-2, and the corresponding signal parameters are the same as those in fig. 2 (c). The transmission time interval of adjacent LFM pulses is Δ T-20 ms. At the receiving end, the sampling frequency was set to 2000 kHz. The signal-to-noise ratio at each receiving array element is set to 4dB and the noise added is white gaussian noise. The beam forming pointing angles are from-45 deg. to 45 deg., spaced by 1 deg., i.e., a total of 91 beams are produced. The 91 beamformers each use Chebyshev weighting with a sidelobe level of-25 dB. When the intensity of each beam output is extracted, the absolute value is obtained according to the time sequence.

The echoes are processed according to the flow of figure 4. The imaging result when M is 2 is shown in fig. 5. As can be seen from the two-dimensional imaging results of fig. 5(a) and the range-dimensional slice of fig. 5(b), the range sidelobe can be reduced to 0.0748 using the method of the present invention. From the results of fig. 5, it is considered that the method of the present invention can obtain lower range side lobes.

According to the embodiment, it can be considered that the method for suppressing range side lobes in step frequency imaging by using the cross-correlation function proposed in the present invention is feasible.

Claims (1)

1. A method for suppressing range sidelobes in step frequency imaging using a cross-correlation function, comprising the steps of:

1) setting array parameters, wherein a transmitting array adopts an array system of a step frequency system, and a single transmitting array element is positioned on a coordinate origin; the receiving array is an N-element ULA, the ULA represents a uniform linear array, and the array element interval is d; using a two-dimensional coordinate system, the coordinates of a transmitting array element are (0,0), the coordinates of an nth receiving array element are { [ N-1- (N-1)/2] d,0}, and N is 1,2, … …, N;

2) designing a group of LFM pulses, wherein the number M of the pulses is more than or equal to2, the frequency bands of adjacent pulses are overlapped, the frequency modulation directions of the adjacent pulses are opposite, and the mth LFM pulse is set as s_m(t)，

$s_m\left(t\right)=\frac{1}{\sqrt{T_0}}rect\left(\frac{t}{T_0}\right)\exp \[j2{\mathrm{\πD}}_m(-\frac{B_0}{2}t+\frac{1}{2}\frac{B_0}{T_0}{t}^2)\]\exp \left(j2{\mathrm{\πf}}_{m}t\right)$

Wherein t represents time, f_m＝f₀-D_m(B₀+ Δ B)/2 is the center frequency of the mth LFM pulse, Δ B is the coincidence bandwidth, which is negative, f₀Is the center frequency of the whole band, B₀Is the bandwidth of a single LFM pulse, T₀Is the pulse width, D, of a single LFM pulse_mFor controlling parameters in the FM direction, when the m-th LFM pulse is up-regulatedFrequency-time, D_m1, when the m-th LFM pulse is down-modulated, D_m＝-1，m＝1,2,…,M；

Superposing the autocorrelation function and the cross-correlation function of all LFM pulses to obtain a synthesized correlation functionWherein R is_m,m(t) is the autocorrelation function of the mth LFM pulse, R_m,i(t) is a cross-correlation function between the mth LFM pulse and the other LFM pulses;

shaping the synthesized correlation function by utilizing the cross-correlation function and the autocorrelation function together, and obtaining a low-range side lobe while obtaining an expected range main lobe, namely the peak value of the range side lobe is less than or equal to 0.1 time of the peak value of the main lobe;

3) transmitting the M LFM pulses designed in the step 2) by using the array in the step 1) according to the time interval delta T, and collecting echoes, wherein the echo on the nth receiving array element is x_n(t)，

$x_n\left(t\right)=\underset{p=1}{\overset{p}{\Σ}}{\mathrm{\σ}}_p\underset{m=1}{\overset{M}{\Σ}}{s}_m\[t-{\mathrm{\τ}}_0^p-{\mathrm{\τ}}_{rn}^p-(m-1)\mathrm{\Δ}T\]+z_n\left(t\right)$

Wherein σ_pThe scattering intensity of the P-th scattering point is represented by P1, 2, …, and P is the number of scattering points,is the time delay from a single transmit array element to the p-th scattering point,is the time delay from the p-th scattering point to the n-th receiving array element, Δ T represents the time interval between adjacent LFM pulses at the time of transmission, z_n(t) represents a noise term;

4) after obtaining the echo, carrying out time delay correction and time domain superposition on the echoes of different LFM pulses to obtain the echo of the signalMatched filtering is carried out on the echo by copying M LFM pulses to obtain MN matched filtering outputs, and the mth matched filter processes the nth echo to obtain an output y_m,n(t)＝x_n(t)*h_m(t) wherein h_m(t)＝[s_m(T₀-t)]^cIs an impulse response function of the mth matched filter]^cRepresenting conjugation;

assuming that the transmitted signal is uncorrelated with noise, then

$y_{m,n}\left(t\right)=\underset{p=1}{\overset{p}{\Σ}}{\mathrm{\σ}}_p\[R_{m,m}(t-{\mathrm{\τ}}_0^p-{\mathrm{\τ}}_{rn}^p-T_0)+\underset{i\≠m}{\overset{M}{\underset{i=1}{\Σ}}}{R}_{m,i}(t-{\mathrm{\τ}}_0^p-{\mathrm{\τ}}_{rn}^p-T_0)\];$

And performing beam forming processing on the MN matched filter outputs to obtain different beam outputs so as to obtain a two-dimensional or three-dimensional image of the target.