CN114839606A - Coherent accumulation method of sparse frequency coding anti-interference waveform signal - Google Patents
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Abstract
The invention discloses a coherent accumulation method of a sparse frequency coding anti-interference waveform signal, which mainly solves the problem that a frequency agile signal cannot be accumulated by using a traditional coherent accumulation method due to nonlinear phase change of the frequency agile signal. The implementation scheme is as follows: the radar transmits a plurality of groups of sparse frequency coding signals to obtain baseband echo signals; performing pulse compression and classification on the baseband echo signals according to the carrier frequency; carrying out same-frequency coherent accumulation on each group of classified signals respectively; respectively carrying out speed compensation on each group of signals after the same-frequency coherent accumulation; rearranging each group of signals after the speed compensation according to the carrier frequency; constructing an objective function with optimized distance parameters according to the rearranged signals, and solving the objective function to obtain optimal distance parameters; and performing distance compensation on the rearranged signals by using the optimal distance parameters, and performing IFFT to obtain a pilot frequency coherent accumulation result. The invention improves the anti-interference performance of the frequency agile radar and can be used for realizing the target detection of the frequency agile radar.
Description
Technical Field
The invention belongs to the technical field of radars, and particularly relates to an anti-interference waveform signal coherent accumulation method which can be used for target detection of frequency agile anti-interference signals.
Background
The pulse-to-pulse frequency agility technology refers to that carrier frequencies of pulses of radar transmitting signals are rapidly changed according to random or pseudorandom codes, and a radar using the technology is called an agile frequency system radar. The frequency agility system radar has a series of advantages in practical application, such as: the interception probability is reduced, the anti-interference performance is improved, the detection distance is increased and the like. Therefore, the frequency agile system radar has a very wide application prospect in increasingly complex electromagnetic environments.
However, the pulse carrier frequency of the transmitted signal is randomly and quickly changed, so that the phase change of the echo signal is nonlinear, and is incompatible with the traditional algorithm for realizing signal coherent accumulation based on Fast Fourier Transform (FFT), and thus target detection cannot be realized by the traditional coherent accumulation method.
In order to coherently accumulate the frequency agile signals, it has been analyzed and studied in some published literature. The target detection method based on the two-dimensional reconstruction algorithm is provided in patent document with application number 201811125895.6 by the university of west ampere electronic technology, pulse signals with randomly and rapidly changed carrier frequencies are adopted in the method, a two-dimensional joint dictionary matrix corresponding to echo signals is constructed by searching the sparsity of a target scene, and the rapidly and rapidly changed frequency signals are subjected to coherent accumulation by adopting a two-dimensional reconstruction method to obtain the speed and distance information of a target. The method has the disadvantages that when the two-dimensional joint dictionary matrix is constructed, grids need to be artificially divided in a distance-speed area, the problem of grid mismatch is easy to occur, and large errors are generated between real target parameters and grid points of the grids.
A agile frequency signal target accumulation method based on same-frequency phase participating frequency rearrangement is provided in a doctor graduation paper published by Tian Rui, a research on a weak target detection key technology of a flood radar (Changsha: national defense science and technology university, 2018). The method has the disadvantages that each pulse carrier frequency in one pulse group must adopt a agile mode of random step frequency, the waveform design freedom is low, and the anti-interference performance in practical application is poor.
Disclosure of Invention
The invention aims to provide a coherent accumulation method of a sparse frequency coding anti-interference waveform signal aiming at the defects in the technology, so that the anti-interference performance of a frequency agile radar is improved by designing a transmitting waveform frequency coding mode, the problem of grid errors caused by artificial grid division is avoided by optimizing parameters of the frequency agile radar during pilot frequency coherent accumulation, and the target detection performance of the frequency agile radar is improved.
In order to achieve the purpose, the technical scheme of the invention comprises the following steps:
(1) the radar transmits a plurality of groups of sparse frequency coding signals to obtain a baseband echo signal s of the transmitted signals;
(2) performing pulse compression and classification on the baseband echo signal S according to the carrier frequency to obtain Q groups of classified signals { S 1 ,S 2 ,…,S q ,…,S Q Wherein Q is 0, 1.., Q-1 is a group number;
(3) signal after Q group classification S 1 ,S 2 ,…,S q ,…,S Q Respectively carrying out same-frequency coherent accumulation to obtain Q groups of signals (Y) after same-frequency coherent accumulation 1 ,Y 2 ,…,Y q ,…,Y Q }；
(4) For Q group signals after same frequency coherent accumulation { Y 1 ,Y 2 ,…,Y q ,…,Y Q Speed compensation is respectively carried out to obtain Q groups of speed compensated signals (Z) 1 ,Z 2 ,…,Z q ,…,Z Q }；
(5) The Q groups of speed compensated signals Z 1 ,Z 2 ,…,Z q ,…,Z Q Taking out column vectors of energy peak values in the signals, and arranging and combining the column vectors according to the carrier frequency to obtain a frequency-speed two-dimensional signal Z' after frequency rearrangement;
(6) compensating the frequency into uniform frequency interval, and obtaining the optimal distance parameter R by using a parameter optimization method est ：
(6a) Setting r as a distance parameter to be optimized, and constructing a distance compensation function by using the distance parameter:
wherein c is the speed of light, and F is a frequency set formed by arranging F in descending order;
(6b) using a distance compensation function H r Performing distance compensation on the frequency-speed two-dimensional signal Z' after frequency rearrangement and performing IFFT (inverse fast Fourier transform) conversion to obtain a signal x to be optimized after distance compensation;
(6c) constructing an objective function according to the distance-compensated signal x to be optimized:
where, i is 0, 1., N-1 is the rearranged frequency sequence number, N is the total number of pulses included in one pulse group, and x i For the ith value in the distance compensated signal x to be optimized,
is a distanceFrom the sum of the square of the absolute values of the N values in the compensated signal x to be optimized, | | | | is norm operation;
(6d) performing optimization solution on the objective function in the step (6c) by using a gradient descent method based on BFGS to obtain a distance parameter R, wherein the distance parameter R is the optimal distance parameter R est ；
(7) Optimizing the distance parameter R est Substituting distance compensation function H r And performing distance compensation on the frequency-speed two-dimensional signal Z' subjected to frequency rearrangement, and performing IFFT (inverse fast Fourier transform) to obtain a pilot frequency coherent accumulation result SS.
Compared with the prior art, the invention has the following advantages:
1. in the design of the transmitting waveform agility mode, the carrier frequency of each pulse in each pulse group is encoded in a sparse frequency mode, so that the agility degree of freedom of partial existing waveforms is higher, the probability of interception by an interference machine is reduced, the anti-interference performance is improved, and the application range of the invention is wider.
2. According to the method, the agile frequency-conversion echo signals are classified, the distance parameters are optimized through a parameter optimization method during pilot frequency coherent accumulation, the grids are divided without prior information, and the problem of grid errors caused by manual grid division is solved; meanwhile, a distance compensation function is constructed by using the distance parameters to obtain signals with uniform frequency intervals, the problem that distance item phases of the agile frequency conversion signals are incoherent due to non-uniform frequency intervals during the accumulation of the pilot frequency coherence in the prior art is solved, and the target detection performance of the agile frequency conversion system radar is improved.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a diagram showing the results of sparse frequency coded signal coherent accumulation by using the existing agile frequency signal target accumulation method based on same-frequency phase participating in frequency rearrangement;
FIG. 3 is a diagram of the results of sparse reconstruction of a sparse frequency encoded signal using a conventional compressive sensing method;
FIG. 4 is a distance parameter optimization curve for optimizing distance parameters using the method of the present invention;
fig. 5 is a diagram of the results of the coherent accumulation of the sparse frequency encoded signal using the method of the present invention.
Detailed Description
Embodiments and effects of the present invention will be described in further detail below with reference to the accompanying drawings.
Referring to fig. 1, the coherent accumulation method of the sparse frequency coding anti-interference waveform signal of the present invention comprises the following steps:
Assuming that a radar transmits M groups of pulses in a coherent processing interval, each group comprises N pulses, the pulse width, the bandwidth and the repetition frequency of all the pulses in the same pulse group are fixed, the frequency jumps randomly within a certain range, and f ═ f { (f) n |f n ＝f 0 +C n Δ f, N ═ 0, 1.., N-1} is the set of frequencies of the pulses, f n Is the frequency of the nth pulse in a pulse group, f 0 Is a center frequency, C n E {0,1, 2.,. 2N-1} is a frequency hopping sequence of the nth pulse in a pulse group, delta f is the minimum frequency hopping interval, and the frequency change rule of the pulses in each pulse group is the same;
the radar transmits the multiple groups of sparse frequency coding signals, and obtains a baseband echo signal of the transmitted signal:
wherein s is mn (t,t m ) The baseband echo signal of the nth pulse in the mth pulse group, t is the fast time, t m For a slow time, A mn The amplitude of the nth pulse in the mth group is defined as M, 0,1, a, M-1 is the serial number of the pulse group, N is 0,1, a, N-1 is the serial number of the pulse group, M is the number of the pulse group, N is the number of the pulses contained in each pulse group, rect () is a window function, T p Is the pulse width, gamma is the frequency modulation rate,
in the m-th pulse groupR is the radial distance of the target from the radar, v is the radial velocity of the target relative to the radar, and c is the speed of light.
2.1) carrying out pulse compression processing on the baseband echo signal to obtain a pulse-compressed signal:
wherein, S' mn (t,t m ) The signal of the nth pulse in the mth pulse group after pulse compression processing, B is the bandwidth, T r For pulse repetition time, sinc (·) is the sine function;
2.2) classifying the signals after pulse compression according to the carrier frequency size, and only keeping pulse pressure results with the same frequency in each class to obtain Q groups of classified signals, wherein the Q groups of classified signals are as follows:
wherein, Q is 0,1, Q-1 is a group number, and Q is the total number of the groups;
since the signals after pulse compression are classified according to the carrier frequency size, it can be seen that the total number of groups obtained after classification is the same as the number of pulses in one pulse group, i.e., Q is equal to N, and the group number Q and the pulse number N are also in one-to-one correspondence.
And 3, respectively carrying out same-frequency coherent accumulation on the Q groups of classified signals to obtain Q groups of signals subjected to same-frequency coherent accumulation.
At carrier frequency f 0 Corresponding signal S 0 (t, M) in the slow time domain 0 Speed resolution unit obtained from Fourier transform of MN point
For reference, for arbitrary carrier frequency f n In order to make its speed resolution cell secure in
Without changing, it is theoretically necessary to do for the slow time
Fourier transform of the points;
realizing same-frequency coherent accumulation by utilizing linear frequency modulation Z transformation CZT while realizing speed domain scale normalization to obtain Q groups of signals after same-frequency coherent accumulation, wherein the Q group of signals after same-frequency coherent accumulation is as follows:
wherein k is 0,1 n -1 is the speed unit number, M 0 Number of base points of CZT, M q The points of the q group CZT.
And 4, respectively carrying out speed compensation on the Q groups of signals subjected to same-frequency coherent accumulation to obtain Q groups of signals subjected to speed compensation.
4.1) after passing through the CZT, the energy of the target is accumulated at a point with the abscissa of the target point
The ordinate is
It can be seen that the coordinates of the target point are independent of the carrier frequency, i.e. at different carrier frequencies, the target energy is accumulated at the same position in the corresponding range-velocity plane, and thus the center carrier frequency f is obtained 0 Corresponding to a velocity v est ：
4.2) from the center carrier frequency f 0 Corresponding velocity v est Constructing Q speed compensation functions, wherein the carrier frequency is f n Corresponding q-th set of velocity compensation functions H vq Expressed as:
4.3) using the velocity compensation function pair H vq Respectively carrying out speed compensation on Q groups of signals subjected to same-frequency coherent accumulation, neglecting speed compensation errors and obtaining Q groups of signals subjected to speed compensation, wherein the Q group of signals subjected to speed compensation are as follows:
wherein,
compensated signal Z for q-th group of velocities q (k) The amplitude of the signal at the kth velocity unit.
And 5, obtaining a frequency-speed two-dimensional signal Z'.
Taking out the column vector of the energy peak value in the Q groups of signals after the speed compensation, and arranging and combining the column vector according to the carrier frequency to obtain a frequency-speed two-dimensional signal Z' after frequency rearrangement:
wherein, F n Is f n And the frequency of the nth frequency point is rearranged from small to large.
According to the frequency-velocity two-dimensional signal Z' obtained in the step 5, the energy peak value is at the k-th position in the frequency-velocity plane peak Line, and k peak Within a row
Thus, only the phase term remains in the Z' (n, k) plane
As the carrier frequency varies, when Z' (n, k) is directly IDFT in the frequency domain, the k-th peak The fixed phase difference cannot be guaranteed, leading to main lobe broadening and side lobes being seriously raised, so that frequency compensation needs to be carried out to uniform frequency intervals, but because distance information is unknown, when a distance compensation function is constructed, the unknown distance parameters need to be optimized and searched by using a parameter optimization method, and the optimal distance parameters are obtained, and the method is specifically realized as follows:
6.1) constructing a distance compensation function by using the distance parameters:
wherein r is a distance parameter to be optimized, and F is a frequency set formed by arranging F in a descending order;
6.2) using the distance compensation function H r Performing distance compensation and IFFT (inverse fast Fourier transform) on the frequency-speed two-dimensional signal Z' after frequency rearrangement to obtain a signal x to be optimized after distance compensation:
wherein x is i The ith value of the signal x to be optimized is i ═ 0, 1.. and N-1 is the rearranged frequency sequence number;
6.3) constructing an objective function according to the distance-compensated signal x to be optimized by taking the minimum waveform entropy as an optimal judgment criterion:
wherein,
the sum of the squares of the absolute values of the signals after the N IFFT transformations, | | · | | is norm operation;
6.4) carrying out optimization solution on the objective function in the step (6.3) by using a gradient descent method based on BFGS (bidirectional Forwarding-class-oriented generalized likelihood-service) to obtain a distance parameter R, wherein the distance parameter R is the optimal distance parameter R est 。
7, setting the optimal distance parameter R est Substituting distance compensation function H r In the method, distance compensation is carried out on the frequency-speed two-dimensional signal Z' after frequency rearrangement, and then IFFT transformation is carried out to obtain a pilot frequency coherent accumulation result SS:
wherein eta is the serial number of the high resolution unit,
for the frequency hopping interval of uniform frequency points obtained after distance compensation, f ═ f n |f n ＝f 0 +C n Δ f, N ═ 0, 1.., N-1} is the set of frequencies at which the pulses were transmitted.
The technical effects of the invention are further explained by simulation experiments as follows:
first, simulation parameter
Assuming that a radar transmits M-16 groups of pulses in a coherent processing interval, each group of pulses contains N-16 pulses, each pulse is a chirp signal, and the center frequency f 0 10GHz, 15MHz for the minimum hop interval Δ f, and f { f } for the set of pulses n |f n ＝f 0 +C n Δf,n＝0,1,...,N-1}，C n E {0,1, 2.,. 2N-1} is a frequency hopping sequence of the nth pulse in a pulse group, the radial distance between the target and the radar is 211m, and the radial speed of the target relative to the radar is 5 m/s.
Second, simulation content
And 2, under the conditions of the simulation experiment, performing sparse reconstruction on the sparse frequency coding signal by adopting the conventional compressed sensing method, and obtaining a result graph as shown in fig. 3.
And 3, under the condition of the simulation experiment, performing coherent accumulation on the sparse frequency coding signal by adopting the method disclosed by the invention to obtain a distance parameter optimization curve as shown in fig. 4, and a coherent accumulation result graph as shown in fig. 5.
Third, simulation result analysis
As can be seen from fig. 2, the coherent accumulation result obtained by using the existing target accumulation algorithm of frequency agile signals based on frequency rearrangement involving same frequency phase generates high side lobes and grating lobes in the range direction, so that the real range and speed information of the target cannot be obtained.
As can be seen from fig. 3, as a result obtained by performing sparse reconstruction on a sparse frequency coding signal by using the existing compressive sensing method, due to the problem of grid mismatch, a real parameter of a target is not matched with a preset distance-speed grid, so that a real target cannot be reconstructed accurately.
As can be seen from fig. 4, the method performs parameter optimization on the target distance parameter, the distance parameter optimization curve shows good convergence, the number of search iterations is small, and the calculation amount is small.
As can be seen from fig. 5, the coherent accumulation result obtained by the method of the present invention can effectively implement coherent accumulation of the frequency agile signal, and the obtained distance and speed information meet the resolution requirement under the simulation condition, so that the target detection of the frequency agile signal can be implemented.
Claims (8)
1. A coherent accumulation method of a sparse frequency coding anti-interference waveform signal is characterized by comprising the following steps:
(1) the radar transmits a plurality of groups of sparse frequency coding signals to obtain a baseband echo signal s of the transmitted signals;
(2) performing pulse compression and classification on the baseband echo signal s according to the carrier frequency to obtainTo Q groups of sorted signals S 1 ,S 2 ,…,S q ,…,S Q -wherein Q-0, 1, Q-1 is a group number;
(3) signal after Q group classification S 1 ,S 2 ,…,S q ,…,S Q Respectively carrying out same-frequency coherent accumulation to obtain Q groups of signals (Y) after same-frequency coherent accumulation 1 ,Y 2 ,…,Y q ,…,Y Q }；
(4) For Q group signals after same frequency coherent accumulation { Y 1 ,Y 2 ,…,Y q ,…,Y Q Speed compensation is respectively carried out to obtain Q groups of speed compensated signals (Z) 1 ,Z 2 ,…,Z q ,…,Z Q }；
(5) The Q groups of speed compensated signals Z 1 ,Z 2 ,…,Z q ,…,Z Q Taking out column vectors of energy peak values in the signals, and arranging and combining the column vectors according to the carrier frequency to obtain a frequency-speed two-dimensional signal Z' after frequency rearrangement;
(6) compensating the frequency into uniform frequency interval, and obtaining the optimal distance parameter R by using a parameter optimization method est ：
(6a) And (3) setting r as a distance parameter to be optimized, and constructing a distance compensation function by using the distance parameter:
wherein c is the speed of light, F is a sparse frequency coding set, and F is a frequency set formed by arranging F in a descending order;
(6b) using a distance compensation function H r Performing distance compensation on the frequency-speed two-dimensional signal Z' after frequency rearrangement and performing IFFT (inverse fast Fourier transform) conversion to obtain a signal x to be optimized after distance compensation;
(6c) constructing an objective function according to the distance-compensated signal x to be optimized:
wherein, i is 0,1, N-1 is the rearranged frequency number, NIs the total number of pulses, x, contained in a pulse group i For the ith value in the distance compensated signal x to be optimized,
the sum of the squares of the absolute values of N values in the signal x to be optimized after distance compensation is adopted, and | | · | | is norm operation;
(6d) performing optimization solution on the objective function in the step (6c) by using a gradient descent method based on BFGS to obtain a distance parameter R, wherein the distance parameter R is the optimal distance parameter R est ；
(7) Optimizing the distance parameter R est Substituting distance compensation function H r And performing distance compensation on the frequency-speed two-dimensional signal Z' after frequency rearrangement, and performing IFFT conversion to obtain a pilot frequency coherent accumulation result SS.
2. The method of claim 1, wherein the baseband echo signal s in (1) is represented as follows:
wherein s is mn (t,t m ) The baseband echo signal of the nth pulse in the mth pulse group, M is 0,1,.., M-1 is the pulse group number, N is 0, 1.., N-1 is the pulse number, M is the total number of pulse groups, N is the total number of pulses included in one pulse group, t is the fast time, t is the total number of pulses included in one pulse group m For slow time, rect (-) is a window function, T p Is pulse width, gamma is frequency modulation, f n The frequency of the nth pulse in a pulse group,
the signal echo delay of the nth pulse in the mth pulse group is obtained, R is the radial distance between the target and the radar, v is the radial speed of the target relative to the radar, and c is the speed of light.
3. The method of claim 1, wherein each set of signals classified in (2) is represented as follows:
wherein S is q (T, M) is a signal after the Q-th group classification, Q is 0,1,.., Q-1 is a group number, Q is a total number of groups, T is a fast time, M is 0,1,..., M-1 is a pulse group number, N is 0,1,.., N-1 is a pulse number, M is a total number of pulse groups, N is a total number of pulses included in one pulse group, B is a bandwidth, T is a bandwidth, and T is a total number of pulses included in one pulse group p For pulse width, sinc (·) is the sine function, R is the radial distance of the target from the radar, v is the radial velocity of the target relative to the radar, c is the speed of light, f n Is the frequency of the nth pulse in a pulse group, T r Is the pulse repetition time.
4. The method according to claim 1, wherein each group of signals after coherent accumulation in the same frequency in the (3) is represented as follows:
wherein, Y q (t, k) is a Q-th group of signals after coherent accumulation of same frequency, Q is 0,1,.., Q-1 is a group number, Q is the total number of groups, t is a fast time, k is 0,1,.., M q -1 is the speed unit number,
number of points for the q-th group of CZT transforms, M 0 For the number of datum points of the CZT transform, sinc (. cndot.) is a sine function, B is the bandwidth, c is the speed of light, R is the radial distance between the target and the radar, v is the radial velocity of the target relative to the radar, f n Is the frequency of the nth pulse in a pulse group, N is 0,1, N-1 is the pulse number, N is the total number of pulses contained in a pulse group, T r For pulse repetition time, f 0 As the center frequency, M is the total number of pulse groups.
5. The method of claim 1, wherein each set of signals obtained in (4) after velocity compensation is represented as follows:
wherein, Z q (k) For the Q-th group of speed compensated signals, Q is 0,1 q -1 is the speed unit number,
number of points for the q-th group of CZT transforms, M 0 Number of base points for CZT conversion, f 0 Is the center frequency, f n Is the frequency of the nth pulse in a pulse group, N is 0,1, N-1 is the pulse sequence number, N is the total number of pulses contained in a pulse group,
compensated signal Z for q-th group of velocities q (k) The amplitude of the signal at the kth velocity element, B is the bandwidth, c is the speed of light, sinc (·) is the sine function, R is the radial distance of the target from the radar, v is the radial velocity of the target relative to the radar, T r The pulse repetition time is M, the number of pulse groups.
6. The method according to claim 1, characterized in that the frequency-velocity two-dimensional signal Z' in (5) is represented as follows:
wherein Z' (k, Q) is a frequency-velocity two-dimensional signal corresponding to the kth velocity unit and the qth frequency, Q is 0,1 q -1 is the speed unit number,
number of points for the q-th group of CZT transforms, M 0 Number of base points for CZT conversion, f 0 Is the center frequency, f n Is the frequency of the nth pulse in a pulse group, N is 0,1, N-1 is the pulse sequence number, N is the total number of pulses contained in a pulse group,
the amplitude of the signal on the kth speed unit after the q-th group of speed compensation is carried out, B is the bandwidth, c is the speed of light, sinc (·) is a sine function, R is the radial distance between the target and the radar, v is the radial speed of the target relative to the radar, T r For pulse repetition time, M is the number of pulse groups, F n Is f n And the frequency of the nth frequency point is rearranged from small to large.
7. The method according to claim 1, wherein the signal x to be optimized in (6b) is represented as follows:
wherein x is i For the ith value in the signal x to be optimized, i is 0, 1.., N-1 is the rearranged frequency sequence number, N is 0, 1.., N-1 is the pulse sequence number, N is the total number of pulses included in a pulse group, R is the radial distance between the target and the radar, R is the distance parameter to be optimized, c is the speed of light, F is the number of pulses in the pulse group, and the number of pulses in the pulse group is the number of pulses in the pulse group n Is f n Frequency f of nth frequency point rearranged from small to large n The frequency of the nth pulse in a pulse group.
8. The method according to claim 1, wherein the inter-frequency coherent accumulation result SS in (7) is expressed as follows:
wherein SS (k) peak Eta) is the result of coherent accumulation of different frequencies at k peak The value of the line and the eta high resolution distance unit, eta is the serial number of the high resolution unit, k peak The number of lines where the energy peak value is located in the frequency-velocity plane, c is the speed of light, R is the radial distance between the target and the radar, N is 0,1 n -1 is the kth speed unit, M n For the number of points of the nth set of CZT transforms,
for the frequency hopping interval of uniform frequency points obtained after distance compensation, f ═ f n |f n ＝f 0 +C n Δ f, N ═ 0, 1.., N-1} is the set of frequencies of the transmit pulses, f n Is the frequency of the nth pulse in a pulse group, f 0 Is a center frequency, C n E {0,1, 2.,. 2N-1} is the frequency agile code for the nth pulse in a pulse group.
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