FDA-MIMO airborne radar clutter range ambiguity resolution method based on code division orthogonal waveform

Abstract

The invention provides an FDA-MIMO airborne radar clutter range ambiguity resolution method based on a code division orthogonal waveform. The implementation steps are as follows: encoding the initial phase of the code division orthogonal waveform; designing a code division orthogonal waveform of the FDA-MIMO airborne radar; performing waveform separation on the target reflection echo baseband signal; calculating a secondary distance dependent compensation vector in a space-time two-dimensional joint frequency domain of the distance ambiguity region; and obtaining an FDA-MIMO airborne radar clutter solution range ambiguity result. The code division orthogonal waveform of the FDA-MIMO airborne radar designed according to the optimization result of the genetic algorithm has good orthogonality, and the defect that the ideal orthogonal waveform does not contain the actual waveform is avoided; and secondary distance-dependent compensation is carried out on the echo space-time snapshot data of the optimized distance ambiguity region of the code division orthogonal waveform through the secondary distance-dependent compensation vector, and the obtained distance ambiguity solving result has high implementability in practical engineering application.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of radar range resolution range ambiguity clutter signal processing, and relates to a FDA-MIMO airborne radar clutter range ambiguity resolution method based on code division orthogonal waveform, which can be used for airborne radar clutter suppression. BACKGROUND

[0002] Frequency diversity array (FDA) radar is a new type of array radar system. By introducing a frequency offset Δf smaller than the carrier frequency f0 of the first array element of the array input between adjacent array elements, the transmitting beam has both range and angle dependence. This feature breaks through the limitation of traditional phased array (PA) which can only control the angle dimension. Multiple-input multiple-output (MIMO) radar uses multiple transmitting antennas to transmit orthogonal waveforms, and the echoes are processed independently by multiple receiving antennas. The core is to improve the system degree of freedom through waveform diversity and spatial diversity.

[0003] FDA-MIMO radar exhibits unique performance in range ambiguity resolution by combining the range dimension regulation capability of FDA radar and the virtual aperture advantage of MIMO radar. When the FDA-MIMO airborne radar transmits the second transmitting pulse, if the target reflection signal of the first pulse has not arrived, it is impossible to find the original transmitting pulse corresponding to the echo signal, and it is also impossible to estimate the accurate echo time delay, so that range ambiguity, i.e. uncertainty in range, is generated. The existence of range ambiguity clutter seriously affects the target detection performance of airborne radar in strong clutter background.

[0004] The commonly used clutter suppression technique for airborne radar target detection in strong clutter background is space-time adaptive processing (STAP). In the research of space-time adaptive processing (STAP) method, an important prerequisite is that the clutter does not produce range ambiguity phenomenon. When range ambiguity occurs, the distance unit where the ground slow-moving target is located includes both near-range clutter and far-range clutter. Due to the inconsistent characteristics of near-range and far-range clutter, the accuracy of the clutter covariance matrix estimation is poor and inaccurate, which further deteriorates the performance of space-time adaptive processing and reduces the target detection performance of airborne radar.

[0005] FDA-MIMO airborne radar breaks through the limitation of traditional ambiguity resolution method by applying a small linear frequency offset to the transmitting array elements, so that the beam direction has range dependence. FDA-MIMO radar uses its inherent range-angle coupling characteristics to naturally separate different distance targets at the same angle in the spatial domain (beam pointing direction). Even if these targets fall into the same time-domain range gate due to PRF limitation, they can still be distinguished in the spatial dimension.

[0006] Existing FDA-MIMO airborne radar clutter resolution methods use a quadratic range-dependent compensation vector in the spatial-Doppler and frequency domains to compensate for the target's range ambiguity. This vector then separates the clutter from the different range ambiguity zones in the spatial-frequency domain. While this method is effective in resolving range ambiguity, its feasibility in practical engineering applications is limited because it relies on an ideal orthogonal waveform being introduced at the radar transmitter. Summary of the Invention

[0007] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and propose a FDA-MIMO airborne radar clutter resolution method based on code division orthogonal waveform to improve the feasibility in practical engineering applications.

[0008] To achieve the above object, the technical solution adopted by the present invention includes the following steps:

[0009] (1) Encode the initial phase of the code-division orthogonal waveform:

[0010] Initialize the frequency diversity array multiple-input multiple-output FDA-MIMO airborne radar. The FDA contains M transmitting array elements and N receiving array elements. The number of input antennas included in MIMO is equal to the number of transmitting array elements included in FDA. The number of output antennas is M×N. The initial phase of the code division orthogonal waveform of each transmitting array element is randomly encoded in the range of [0,2π] to obtain M initial phase coding sequences, where M≥8, N≥8, and the lth initial phase code of the mth transmitting array element is Φ m (l), m∈[1,M], l∈[1,L], L represents the length of the coding sequence;

[0011] (2) Design of code division orthogonal waveform for FDA-MIMO airborne radar:

[0012] Based on the genetic algorithm, M initial phase coding sequences are optimized and the m Optimization results of (l) The complex exponential x m (l) Calculate the complex envelope u of the code division orthogonal waveform to be designed at the current moment m (t), then through u m (t) Calculate the code division orthogonal waveform s of the FDA-MIMO airborne radar m (t), where t∈[0,T], T represents the width of the radar signal transmission pulse;

[0013] (3) Waveform separation of the target reflected echo baseband signal:

[0014] For each target echo signal r received by the receiving end n(t) Perform digital down-conversion and convert the baseband signal x of the echo after down-conversion n (g) Perform matched filtering to achieve x n (g) is separated to obtain the echo space-time snapshot data x of the nth receiving array element c (n);

[0015] (4) Calculate the quadratic distance-dependent compensation vector in the space-time two-dimensional joint frequency domain for different distance ambiguity zones:

[0016] Calculate the spatial compensation frequency of the two fuzzy zones at different distances where the target is located and through The calculated quadratic distance-dependent compensation vector Computing the Quadratic Distance-Dependent Compensation Vector in the Space-Time Two-Dimensional Joint Frequency Domain Among them, α represents the serial number of the distance fuzzy zone where the target is located, α∈{1,2};

[0017] (5) Obtain the FDA-MIMO airborne radar clutter resolution range ambiguity results:

[0018] Compensation vector via quadratic distance dependence The space-time snapshot data of the echo of the first and second range ambiguity zones x c (n) Perform secondary distance-dependent compensation to obtain compensated echo space-time snapshot data

[0019] Compared with the prior art, the present invention has the following advantages:

[0020] The present invention optimizes the code division orthogonal waveform after random phase encoding of the code division orthogonal waveform of each transmitting array element of the FDA-MIMO airborne radar based on a genetic algorithm, and designs the code division orthogonal waveform of the FDA-MIMO airborne radar based on the optimization result. Then, the quadratic range-dependent compensation vector is used to perform quadratic range-dependent compensation on the echo space-time snapshot data of two range ambiguity areas of the optimized code division orthogonal waveform to obtain a range ambiguity resolution result. The code division orthogonal waveform designed by the present invention has good orthogonality and practical engineering applicability, avoiding the defect of the ideal orthogonal waveform in the prior art that does not contain the actual waveform, and has high feasibility in practical engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a flow chart for implementing the present invention.

[0022] Figure 2 Schematic diagram of waveform separation at the receiving end of the present invention.

[0023] Figure 3The figure is a waveform autocorrelation function diagram of two channels of a code division MIMO orthogonal waveform designed based on a genetic algorithm when a phase coding length of the invention is 100.

[0024] Figure 4 The figure is a waveform cross-correlation function diagram of two channels of a code division MIMO orthogonal waveform designed based on a genetic algorithm when a phase coding length of the invention is 100.

[0025] Figure 5 The figure is a waveform autocorrelation function diagram of two channels of a code division MIMO orthogonal waveform designed based on a genetic algorithm when a phase coding length of the invention is 500.

[0026] Figure 6 The figure is a waveform cross-correlation function diagram of two channels of a code division MIMO orthogonal waveform designed based on a genetic algorithm when a phase coding length of the invention is 500.

[0027] Figure 7 The figure is a waveform autocorrelation function diagram of two channels of a code division MIMO orthogonal waveform designed based on a genetic algorithm when a phase coding length of the invention is 2048.

[0028] Figure 8 The figure is a waveform cross-correlation function diagram of two channels of a code division MIMO orthogonal waveform designed based on a genetic algorithm when a phase coding length of the invention is 2048.

[0029] Figure 9 The figure is a space-time two-dimensional distribution diagram of a range ambiguity clutter when a target is located in a first range ambiguity zone and a phase coding length of the invention is 100, 500 and 2048 respectively.

[0030] Figure 10 The figure is a space-time two-dimensional distribution diagram of a range ambiguity clutter after a secondary range dependence compensation algorithm is compensated when a target is located in a first range ambiguity zone and a phase coding length of the invention is 100, 500 and 2048 respectively.

[0031] Figure 11 The figure is a curve of an improvement factor of an original range ambiguity clutter spectrum and a spectrum after SRDC compensation when a target is located in a first range ambiguity zone.

[0032] Figure 12 The figure is a space-time two-dimensional distribution diagram of a range ambiguity clutter when a target is located in a second range ambiguity zone and a phase coding length of the invention is 100, 500 and 2048 respectively.

[0033] Figure 13 The figure is a space-time two-dimensional distribution diagram of a range ambiguity clutter after a secondary range dependence compensation algorithm is compensated when a target is located in a second range ambiguity zone and a phase coding length of the invention is 100, 500 and 2048 respectively.

[0034] Figure 14 Fig. 2 shows the original range ambiguity spectrum and the improved factor curve after the secondary range dependence compensation when the target is located in the second range ambiguity zone. DETAILED DESCRIPTION

[0035] The application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0036] Reference Figure 1 The application comprises the following steps:

[0037] Step 1) encoding the initial phase of the code division waveform:

[0038] The FDA-MIMO airborne radar includes M transmitting array elements and N receiving array elements. The number of input antennas of the MIMO is equal to the number of transmitting array elements of the FDA, the number of output antennas is MxN, and the initial phase of the code division orthogonal waveform of each transmitting array element is randomly encoded in the range of [0, 2π] to obtain M initial phase encoding sequences, wherein M≥8, N≥8, the lth initial phase encoding of the mth transmitting array element is Φ m (l), m∈[1, M], l∈[1, L], and L represents the length of the encoding sequence.

[0039] The initial phase of the code division waveform of each transmitting array element is randomly encoded in the range of [0, 2π] to obtain M initial phase encoding sequences, wherein M≥8, N≥8, the lth initial phase encoding of the mth transmitting array element is Φ m (l), m∈[1, M], l∈[1, L], and L represents the length of the encoding sequence.

[0040] If the number of radar transmitting array elements M and the number of receiving array elements N are too small, the degree of freedom obtained by the transmitting and receiving end of the FDA-MIMO radar will be too low, affecting the subsequent range ambiguity resolution performance. If M and N are too large, the orthogonality of the designed code division MIMO orthogonal waveform will be too low, which cannot separate the waveform well, affecting the subsequent range ambiguity resolution performance. In the embodiment, M=8, N=8. The encoding length L=500, 1000, 2048, and three groups of comparative experiments are set to compare the influence of different encoding lengths of the code division orthogonal waveform on the range ambiguity resolution performance.

[0041] Step 2) designing the transmitting signal of the FDA-MIMO airborne radar:

[0042] The initial phase encoding Φ m (l) is optimized based on the genetic algorithm, and the complex exponential x of the optimized initial phase encoding Φ is calculated. ​m (l), and then the x m (l) calculates the complex envelope u m (t) of the code division orthogonal waveform at the current time, and then the u m (t) calculates the code division orthogonal waveform s m (t) of the FDA-MIMO airborne radar, where t∈[0,T], and T represents the width of the radar signal transmission pulse.

[0043] The implementation steps of optimizing the M initial phase code sequences based on the genetic algorithm are as follows:

[0044] (2a) initialization parameters:

[0045] An initial population of samples of O is initialized, and the M initial phase code sequences are samples of the initial population. In each iteration, a pair of samples is randomly selected as the father and the mother, and the region composed of any [m,m+△m] rows and [l,l+△l] columns in the sample can be used as a chromosome for cross variation. The chromosome to be crossed and mutated in the sample is randomly generated. The integral sidelobe level ISL is selected as the cost function, the iteration number is set to k, the maximum iteration number is set to K, K≥100, the current population includes O groups of orthogonal code sequences, and k is set to 0. The minimum error ε is initialized to 0.001, and O is set to 500.

[0046] (2b) calculation of the cost function:

[0047] The integral sidelobe level ISL is used as the cost function, the autocorrelation function and the cross-correlation function of the code division orthogonal waveform are calculated, and the square of the modulus value of the autocorrelation function and the cross-correlation function of the code division orthogonal waveform is integrated to obtain the integral sidelobe level ISL of the code division orthogonal waveform. The modulus value is taken to obtain the fitness |ISL| of the current population, where:

[0048]

[0049] where represents the phase code sequence of the i-th channel, represents the phase code sequence of the e-th channel, represents the phase code sequence of the f-th channel, and f=e+1;

[0050] The integral sidelobe level ISL expression is:

[0051]

[0052] (2c) chromosome crossing and mutation:

[0053] Generate a random number in the range [0,1] as the crossover probability p through Monte Carlo experiments c , if p c If it is less than 0.9, perform chromosome crossover: randomly select two samples from the population as the father and mother respectively, generate the starting row number m of chromosome crossover in the range [1,M], generate the row number increment △i in the range [m,Mm], generate the starting column number l of chromosome crossover in the range [1,L], generate the row number increment △j in the range [l,Ll], and cross the chromosome segments of the father and mother corresponding to the hth row (1≤h≤M) to the h+△ith row (1≤h+△i≤M) and the lth column (1≤l≤L) to the l+△jth column (1≤l+△j≤L); otherwise, do not perform chromosome crossover; generate a random number in the range [0,1] as the crossover probability p v , if p v If it is less than 0.1, the chromosomes of the father and mother obtained by the crossover are mutated: the starting row number b of the chromosome crossover is generated in the range [1,M], the row number increment △b is generated in the range [b,Mb], the starting column number w of the chromosome crossover is generated in the range [1,L], and the row number increment △w is generated in the range [w,Lw]. The chromosome segments corresponding to the bth row (1≤b≤M) to the b+△bth row (1≤b+△b≤M) and the wth column (1≤w≤L) to the w+△wth column (1≤w+△w≤L) of the father and mother are selected, and random numbers are generated in the range [0,2π] as the mutated chromosome segments. The mutated chromosome segments and the unchanged chromosome segments form the new father and mother. Otherwise, the chromosome mutation operation is not performed.

[0054] Wherein h represents the starting row number of the chromosome segment selected when performing chromosome crossover, △i represents the increment of the number of rows of the chromosome segment selected when performing chromosome crossover; l represents the starting column number of the chromosome segment selected when performing chromosome crossover, △j represents the increment of the number of columns of the chromosome segment selected when performing chromosome crossover; b represents the starting row number of the chromosome segment selected when performing chromosome mutation, △b represents the increment of the number of rows of the chromosome segment selected when performing chromosome mutation; w represents the starting column number of the chromosome segment selected when performing chromosome mutation, △w represents the increment of the number of columns of the chromosome segment selected when performing chromosome mutation;

[0055] (2d) Get each initial phase code Φ m Optimization results of (l):

[0056] The offspring obtained by crossover mutation are used as the father and mother of the new generation to update the population and determine whether k≥K or |ISL|<ε is true. If so, each initial phase code Φ is obtained. m The optimal value of (l) Otherwise, let k = k + 1 and perform step (2b);

[0057] The optimized code division waveform phase As the phase of the transmitted waveform complex envelope, the complex exponential form x m (l) is represented, and the complex exponential x m (l) of the lth coded phase of the mth array element is multiplied by the rectangular function of the lth sub-pulse corresponding to it, and summed to obtain the complex envelope u m (t) of the transmitted signal.

[0058] By multiplying the complex envelope u m (t) of the transmitted waveform and the rectangular function corresponding to the code division orthogonal waveform pulse width T, the truncated complex envelope is obtained. After calculation, the complex exponential form of the angular frequency corresponding to each array element is obtained, and the truncated complex envelope is multiplied to obtain the code division orthogonal waveform s m (t) of the mth array element at the current time.

[0059] The complex exponential x m (l) of the current time, the complex envelope u m (t) of the transmitted waveform, and the transmitted signal s m (t) of the FDA-MIMO airborne radar, the calculation formulas are respectively:

[0060]

[0061] Where exp[·] represents the complex exponential function, j represents the complex unit, rect(·) represents the rectangular window function, T p represents the sub-pulse width occupied by each coded signal T p = T / L, f m represents the carrier frequency of the mth transmitting array element, f m = f0 + (m-1)△f, f0 represents the carrier frequency of the first array element, and△f represents the frequency offset between adjacent two transmitting array elements.

[0062] Step 3) Waveform separation of target reflection echo baseband signal:

[0063] The target echo signal r n (t) received by each receiving end is digitally down-converted, and the baseband signal x n (g) of the down-converted echo is matched filtered to realize the separation of x n (g), and the echo space-time snapshot data x n (n) corresponding to r c (t) is obtained, and the separation process is as follows Figure 2The echo signals received by the N receiving elements are digitally down-converted (mixed and AD sampled), and a matched filter cluster with a length of M is accessed after the digital down-conversion, MF m The mth matched filter of the matched filter cluster arranges the matched filtering result into MxN space-time snapshot data.

[0064] By adding a matched filter cluster with a length of M after each receiving element, the coefficients of the matched filter cluster are The mth transmitted signal component is obtained by matched filtering, and other signal components are filtered out. If the transmitted waveform is an ideal orthogonal waveform, the desired signal and irrelevant components can be completely separated, but in actual situations, an ideal orthogonal waveform cannot be obtained, so after matched filtering, other irrelevant signal components are introduced, which has a certain impact on subsequent processing. The degree of influence is related to the orthogonality of the designed code division waveform. The better the orthogonality, the lower the degree of influence, and vice versa, the greater the degree of influence.

[0065] Wherein, the target echo signal r n (t), the baseband signal x n (g) of the echo after down-conversion, and the echo space-time snapshot data x c (n) of the nth receiving element, the expressions are respectively:

[0066]

[0067] Wherein: ξ represents the echo reflection coefficient, τ0 represents the echo time delay, g represents the sampling point sequence number, and g=(t-τ0)f s , f s represents the sampling rate, r represents the distance from the target to the radar receiving array, c represents the speed of light, λ represents the wavelength of the radar transmitted signal, i represents the receiving matched filter traversal sequence number, d T represents the transmitting element spacing, d R represents the receiving element spacing, and θ represents the target pointing angle.

[0068] Step 4) Calculate the quadratic range-dependent compensation vector in the space-time two-dimensional joint frequency domain of different range ambiguity zones:

[0069] Since the FDA-MIMO transmitting pattern contains range information, a quadratic range compensation vector related to the range can be constructed, so that the range ambiguity is solved by performing quadratic range-dependent compensation on the echo signal.

[0070] Calculate the spatial compensation frequency f c {α} of the two different range ambiguity zones where the target is located, and the quadratic range-dependent compensation vector calculated by f c {α} ​ Computing quadratic range-dependent compensation vectors in joint space-time two-dimensional frequency domain wherein, alpha represents the serial number of the distance ambiguity zone where the target is located, alpha is in {1, 2};

[0071] wherein alpha is in {1, 2}, the spatial compensation frequency f c {α} , quadratic range-dependent compensation vector The expression is:

[0072]

[0073] wherein, when alpha = 1, R c {1} =R1, R1 is a set distance value in the main value distance zone; when alpha = 2, R c {2} =R1+R u , R u =c / 2f r , R u represents the maximum non-ambiguous distance, f r represents the radar pulse repetition frequency, represents the Kronecker product, 1 K is an M-row column vector with all elements being 1.

[0074] Step 5) obtaining the FDA-MIMO airborne radar range-ambiguous clutter result:

[0075] by means of the quadratic range-dependent compensation vector , the first and second range-ambiguous zone echo space-time snapshot data x c (n) is compensated by means of the quadratic range-dependent compensation, to obtain the compensated echo space-time snapshot data

[0076] The compensated echo space-time snapshot data The expression is:

[0077]

[0078] wherein, represents the Hadamard product.

[0079] The technical effects of the present application are further described below in combination with simulation experiments:

[0080] 1. Simulation conditions and contents

[0081] Simulation 1: The code division orthogonal waveform design result with a phase code length of 100 is simulated under the conditions of Table 1, and the result is shown in Figure 3 , Figure 4 .

[0082] Table 1

[0083]

[0084]

[0085] Simulation 2, simulation results of code division orthogonal waveform design when phase encoding length is 500 under the conditions of Table 2 are simulated, and the results are shown in Figure 5 , Figure 6 .

[0086] Table 2

[0087]

[0088] Simulation 3, simulation results of code division orthogonal waveform design when phase encoding length is 2048 under the conditions of Table 3 are simulated, and the results are shown in Figure 7 , Figure 8 .

[0089] Table 3

[0090]

[0091] Simulation 4, simulation results of target located in the first range ambiguity area to solve range ambiguity under the conditions of Table 4 are simulated, and the results are shown in Figure 9 , Figure 10 , Figure 11 .

[0092] Table 4

[0093]

[0094] Simulation 5, simulation results of target located in the second range ambiguity area to solve range ambiguity under the conditions of Table 5 are simulated, and the results are shown in Figure 12 , Figure 13 , Figure 14 .

[0095] Table 5

[0096]

[0097] 2. Analysis of simulation results:

[0098] Referring to Figure 3 , Figure 4 , wherein Figure 3 (a) and Figure 3(b) The waveform autocorrelation function plots for the first and fourth channels designed using the genetic algorithm for a phase coding length of 100 are shown. The horizontal axis represents the number of offset points, and the vertical axis represents the autocorrelation function value. As can be seen from the figure, except for the zero point, the waveform autocorrelation function values ​​are all below -15dB, indicating that the code division MIMO waveforms designed using the genetic algorithm have preliminary orthogonality. Figure 4 (a) and Figure 4 (b) shows the waveform cross-correlation function graphs for the first and fourth channels, and the third and eighth channels, respectively, designed using the genetic algorithm, when the phase coding length is 100. The horizontal axis represents the number of offset points, and the vertical axis represents the cross-correlation function value. As can be seen from the figure, the waveform cross-correlation function values ​​are all below -15dB, indicating that the code division MIMO waveforms designed using the genetic algorithm have preliminary orthogonality.

[0099] Simulation 2

[0100] Reference Figure 5 , Figure 6 ,in Figure 5 (a) and Figure 5 (b) The waveform autocorrelation functions of the first and fourth channels designed using the genetic algorithm for a phase coding length of 500 are plotted. The horizontal axis represents the number of offset points, and the vertical axis represents the autocorrelation function value. The figure shows that, except for the zero point, the autocorrelation function values ​​of the waveforms are all below -20 dB, indicating that the code division MIMO waveforms designed using the genetic algorithm have a certain degree of orthogonality. Figure 6 (a) and Figure 6 (b) shows the waveform cross-correlation function graphs for the first and fourth channels, and the third and eighth channels, respectively, designed using the genetic algorithm for a phase coding length of 500. The horizontal axis represents the number of offset points, and the vertical axis represents the cross-correlation function value. As can be seen from the figure, the waveform cross-correlation function values ​​are all below -20 dB, indicating that the code division MIMO waveforms designed using the genetic algorithm have a certain degree of orthogonality.

[0101] Simulation 3

[0102] Reference Figure 7 , Figure 8 ,in Figure 7 (a) and Figure 7 (b) The waveform autocorrelation function plots for the first and fourth channels designed using the genetic algorithm for a phase code length of 2048 are shown; the horizontal axis represents the number of offset points, and the vertical axis represents the autocorrelation function value. As can be seen from the figure, except for the zero point, the waveform autocorrelation function values ​​are all below -25dB, indicating that the code division MIMO waveform designed using the genetic algorithm has good orthogonality. Figure 8 (a) and Figure 8(b) are the waveform cross-correlation function graphs of the first and fourth channels and the third and eighth channels of the present application based on genetic algorithm design respectively when the phase encoding length is 2048. The abscissa represents the offset point number, and the ordinate represents the cross-correlation function value. As can be seen from the graph, the waveform cross-correlation function values are all below -25 dB, and the code division MIMO waveform designed by the genetic algorithm has good orthogonality.

[0103] Simulation 4

[0104] Reference Figure 9 (b) is the range ambiguity clutter spectrum distribution graph when the target is located in the first range ambiguity zone and the phase encoding length is 100. The abscissa represents the normalized Doppler frequency, the ordinate represents the normalized spatial frequency, and different gray values represent different clutter spectrum amplitudes. Figure 10 (b) is the range ambiguity clutter spectrum distribution graph after the secondary range-dependent compensation algorithm is compensated for the first range ambiguity zone clutter when the phase encoding length is 100. The abscissa represents the normalized Doppler frequency, the ordinate represents the normalized spatial frequency, and different gray values represent different clutter spectrum amplitudes. Figure 9 (a), 10(a) is the range ambiguity clutter spectrum and the range ambiguity clutter spectrum compensated by the secondary range-dependent algorithm under the condition of ideal orthogonal waveforms. The abscissa represents the normalized Doppler frequency, the ordinate represents the normalized spatial frequency, and different gray values represent different clutter spectrum amplitudes. Figure 11 (a), Figure 11 (b) is the original clutter spectrum and the improvement factor curve after secondary range-dependent compensation when the target is located in the first range ambiguity zone. The abscissa represents the Doppler frequency, and the ordinate represents the improvement factor value. Figure 9 (c) is the range ambiguity clutter spectrum distribution graph when the target is located in the first range ambiguity zone and the phase encoding length is 500. The abscissa represents the normalized Doppler frequency, the ordinate represents the normalized spatial frequency, and different gray values represent different clutter spectrum amplitudes. Figure 10 (c) is the range ambiguity clutter spectrum distribution graph after the secondary range-dependent compensation algorithm is compensated for the first range ambiguity zone clutter when the phase encoding length is 500. The abscissa represents the normalized Doppler frequency, the ordinate represents the normalized spatial frequency, and different gray values represent different clutter spectrum amplitudes. Figure 9 (d) is the range ambiguity clutter spectrum distribution graph when the target is located in the first range ambiguity zone and the phase encoding length is 2048. The abscissa represents the normalized Doppler frequency, the ordinate represents the normalized spatial frequency, and different gray values represent different clutter spectrum amplitudes. Figure 10(d) shows the clutter spectrum distribution after applying the quadratic range-dependent compensation algorithm to the clutter in the first range ambiguity zone when the phase encoding length is 2048. The horizontal axis represents the normalized Doppler frequency, and the vertical axis represents the normalized spatial frequency. Different grayscale values ​​represent different clutter spectrum amplitudes.

[0105] from Figure 9 (b) and Figure 10 (b) It can be seen that the clutter in the first and second range ambiguity zones in the spatial frequency domain can be distinguished. Due to the quadratic range dependence, the clutter is severely diffused in the spatial frequency domain. After the quadratic range dependence algorithm is used to compensate, the clutter in the first range ambiguity zone is distributed as [-1 / 4, 1 / 4] in the spatial frequency domain, while the clutter in the second range ambiguity zone is distributed as [-1 / 2, -1 / 4] ∪ [1 / 4, 1 / 2]. At this point, the clutter in the second range ambiguity zone has little effect on target detection in the first range ambiguity zone. Figure 11 It can be seen that when the code length is 100, the improvement factor performance curve has a notch in the second range ambiguity area, and the improvement factor performance curve in the first range ambiguity area still decreases to a certain extent, and has preliminary performance in solving range ambiguity clutter, but there is still a large gap between the performance of solving range ambiguity and the ideal orthogonal waveform conditions. Figure 9 (c) and Figure 10 (c) It can be seen that the clutter in the first and second range ambiguity zones in the spatial frequency domain can be distinguished. Due to the quadratic range dependence, the clutter is severely diffused in the spatial frequency domain. After quadratic range dependence compensation, the clutter in the first range ambiguity zone is distributed as [-1 / 4, 1 / 4] in the spatial frequency domain, while the clutter in the second range ambiguity zone is distributed as [-1 / 2, -1 / 4] ∪ [1 / 4, 1 / 2]. At this point, the clutter in the second range ambiguity zone has little effect on target detection in the first range ambiguity zone. Figure 11 It can be seen that when the code length is 500, the improvement factor performance curve has a notch in the second range ambiguity area, and the improvement factor performance curve in the first range ambiguity area still decreases to a certain extent, but it is improved to a certain extent compared with the code length of 100, and basically has the performance of solving range ambiguity clutter, but there is still a certain gap with the performance of solving range ambiguity under ideal orthogonal waveform conditions. Figure 9 (d) and Figure 10 (d) It can be seen that when the code length is 500, the clutter in the first range ambiguity zone and the second range ambiguity zone in the spatial frequency domain can be distinguished. Due to the quadratic range dependence, the clutter is severely diffused in the spatial frequency domain. After quadratic range dependence compensation, the clutter in the first range ambiguity zone is distributed in the spatial frequency domain as [-1 / 4, 1 / 4], while the clutter in the second range ambiguity zone is distributed as [-1 / 2, -1 / 4] ∪ [1 / 4, 1 / 2]. At this time, the clutter in the second range ambiguity zone has basically no effect on the target detection in the first range ambiguity zone.Figure 11 It can be seen that when the code length is 2048, the improvement factor performance curve has a notch in the second range ambiguity region, and the improvement factor performance curve in the first range ambiguity region is basically smooth, which is greatly improved compared with the code length of 100 and 500, has the performance of resolving range ambiguity clutter, and has a small gap with the performance of resolving range ambiguity under the condition of ideal orthogonal waveform. At this time, the clutter in the second range ambiguity region has basically no effect on the target detection in the first range ambiguity region.

[0106] Simulation 5

[0107] Reference Figure 12 (b) is a range ambiguity clutter spectrum distribution diagram when the target is located in the second range ambiguity region and the phase encoding length is 100. The horizontal axis represents the normalized Doppler frequency, the vertical axis represents the normalized spatial frequency, and different gray values represent different clutter spectrum amplitudes. Reference Figure 13 (b) is a range ambiguity clutter spectrum distribution diagram obtained after the second range-dependent compensation algorithm is compensated when the phase encoding length is 100. The horizontal axis represents the normalized Doppler frequency, the vertical axis represents the normalized spatial frequency, and different gray values represent different clutter spectrum amplitudes. Reference Figure 12 (a), 13a) is a range ambiguity clutter spectrum and a range ambiguity clutter spectrum compensated by a second range-dependent algorithm under the condition of ideal orthogonal waveform. The horizontal axis represents the normalized Doppler frequency, the vertical axis represents the normalized spatial frequency, and different gray values represent different clutter spectrum amplitudes. Reference Figure 14 , is the original clutter spectrum and the improvement factor curve after the second range-dependent compensation when the target is located in the second range ambiguity region. The horizontal coordinate represents the Doppler frequency, and the vertical coordinate represents the improvement factor value. Reference Figure 12 (c) is a range ambiguity clutter spectrum distribution diagram when the target is located in the second range ambiguity region and the phase encoding length is 500. The horizontal axis represents the normalized Doppler frequency, the vertical axis represents the normalized spatial frequency, and different gray values represent different clutter spectrum amplitudes. Reference Figure 13 (c) is a range ambiguity clutter spectrum distribution diagram obtained after the second range-dependent compensation algorithm is compensated for the first range ambiguity region when the phase encoding length is 500. The horizontal axis represents the normalized Doppler frequency, the vertical axis represents the normalized spatial frequency, and different gray values represent different clutter spectrum amplitudes. Reference Figure 12 (a), 13(a), is a range ambiguity clutter spectrum and a range ambiguity clutter spectrum compensated by a second range-dependent algorithm under the condition of ideal orthogonal waveform. The horizontal axis represents the normalized Doppler frequency, the vertical axis represents the normalized spatial frequency, and different gray values represent different clutter spectrum amplitudes. Reference Figure 14 , is the original clutter spectrum and the improvement factor curve after the second range-dependent compensation when the target is located in the second range ambiguity region. The horizontal coordinate represents the Doppler frequency, and the vertical coordinate represents the improvement factor value. Reference Figure 12(d) is the range ambiguity clutter spectrum distribution diagram when the target is located in the second range ambiguity zone and the phase encoding length is 2048. The horizontal axis represents the normalized Doppler frequency, the vertical axis represents the normalized spatial frequency, and different grayscale values ​​represent different clutter spectrum amplitudes. Figure 13 (d) is the clutter spectrum distribution diagram obtained after compensating the first range ambiguity area using the quadratic range-dependent compensation algorithm when the phase encoding length is 2048. The horizontal axis represents the normalized Doppler frequency, the vertical axis represents the normalized spatial frequency, and different grayscale values ​​represent different clutter spectrum amplitudes. Figure 12 (a), 13(a), are the range ambiguity clutter spectrum under ideal orthogonal waveform conditions and the range ambiguity clutter spectrum compensated by the quadratic range dependency compensation algorithm. The horizontal axis represents the normalized Doppler frequency, the vertical axis represents the normalized spatial frequency, and different grayscale values ​​represent different clutter spectrum amplitudes. Figure 14 , which is the original clutter spectrum and the improvement factor curve after quadratic range dependence compensation when the target is located in the second range ambiguity zone. The horizontal axis represents the Doppler frequency, and the vertical axis represents the improvement factor value.

[0108] from Figure 12 (b) and Figure 13 (b) It can be seen that the clutter in the first and second range ambiguity zones in the spatial frequency domain can be distinguished. Due to the quadratic range dependence, the clutter is severely diffused in the spatial frequency domain. After the quadratic range dependence algorithm is used to compensate, the clutter in the second range ambiguity zone is distributed as [-1 / 4, 1 / 4] in the spatial frequency domain, while the clutter in the first range ambiguity zone is distributed as [-1 / 2, -1 / 4] ∪ [1 / 4, 1 / 2]. Figure 14 It can be seen that when the code length is 100, the improvement factor performance curve has a notch in the first range ambiguity area, and the improvement factor performance curve in the second range ambiguity area still decreases to a certain extent. It has preliminary performance in resolving range ambiguity clutter, but there is still a certain gap between the performance and the ideal orthogonal waveform conditions. Figure 12 (c) and Figure 13 (c) It can be seen that the clutter in the first range ambiguity zone and the second range ambiguity zone in the spatial frequency domain can be distinguished. Due to the quadratic range dependence, the clutter is severely diffused in the spatial frequency domain. After quadratic range dependence compensation, the distribution of clutter in the second range ambiguity zone in the spatial frequency domain is [-1 / 4, 1 / 4], while the distribution of clutter in the first range ambiguity zone is [-1 / 2, -1 / 4] ∪ [1 / 4, 1 / 2]. It can be seen that when the code length is 500, the improvement factor performance curve has a notch in the first range ambiguity zone, and the improvement factor performance curve in the second range ambiguity zone still decreases to a certain extent, but it is improved to a certain extent compared to the code length of 100. It basically has the performance of resolving range ambiguity clutter, but there is still a certain gap with the performance of resolving range ambiguity under ideal orthogonal waveform conditions. From Figure 12 (d) andFigure 13 (d)It can be seen that the clutter in the first and second range ambiguities in the spatial frequency domain can be distinguished. Due to the quadratic range dependence, the clutter is severely spread in the spatial frequency domain. After the quadratic range dependence compensation, the clutter in the second range ambiguity is distributed in [-1 / 4, 1 / 4] in the spatial frequency domain, while the clutter in the first range ambiguity is distributed in [-1 / 2, -1 / 4]∪[1 / 4, 1 / 2]. At this time, the clutter in the first range ambiguity has little effect on the target detection in the second range ambiguity. From Figure 14 It can be seen that when the code length is 2048, the improvement factor performance curve has a notch in the first range ambiguity, and the improvement factor performance curve in the second range ambiguity is basically smooth, which is greatly improved compared with the code length of 100 and 500, has the performance of resolving range ambiguity clutter, and has a small gap with the performance of resolving range ambiguity under the ideal orthogonal waveform condition. At this time, the clutter in the first range ambiguity has little effect on the target detection in the second range ambiguity.

Claims

1. A method for resolving range ambiguity in FDA-MIMO airborne radar clutter based on code division orthogonal waveform, characterized in that: The steps include: (1) Encode the initial phase of the code-division orthogonal waveform: Initialize the frequency diversity array multiple-input multiple-output FDA-MIMO airborne radar. The FDA contains M transmitting array elements and N receiving array elements. The number of input antennas included in MIMO is equal to the number of transmitting array elements included in FDA. The number of output antennas is M×N. The initial phase of the code division orthogonal waveform of each transmitting array element is randomly encoded in the range of [0,2π] to obtain M initial phase coding sequences, where M≥8, N≥8, and the lth initial phase code of the mth transmitting array element is Φ m (l), m∈[1,M], l∈[1,L], L represents the length of the coding sequence; (2) Design of code division orthogonal waveform for FDA-MIMO airborne radar: Based on the genetic algorithm, M initial phase coding sequences are optimized and the m Optimization results of (l) The complex exponential x m (l) Calculate the complex envelope u of the current code division orthogonal waveform to be designed m (t), then through u m (t) Calculate the code division orthogonal waveform s of the FDA-MIMO airborne radar m (t), where t∈[0,T], T represents the width of the radar signal transmission pulse; (3) Waveform separation of the target reflected echo baseband signal: For each target echo signal r received by the receiving end n (t) Perform digital down-conversion and convert the baseband signal x of the echo after down-conversion n (g) Perform matched filtering to achieve x n (g) is separated to obtain the echo space-time snapshot data x of the nth receiving array element c (n); (4) Calculate the quadratic distance-dependent compensation vector in the space-time two-dimensional joint frequency domain for different distance ambiguity zones: Calculate the spatial compensation frequency f of the two fuzzy zones at different distances where the target is located c {α} and through f c {α} The calculated quadratic distance-dependent compensation vector Computing the Quadratic Distance-Dependent Compensation Vector in the Space-Time Two-Dimensional Joint Frequency Domain Among them, α represents the serial number of the distance fuzzy zone where the target is located, α∈{1,2}; (5) Obtain the FDA-MIMO airborne radar clutter resolution range ambiguity results: Compensation vector via quadratic distance dependence The space-time snapshot data of the echo of the first and second range ambiguity zones x c (n) Perform secondary distance-dependent compensation to obtain compensated echo space-time snapshot data 2. The method according to claim 1, characterized in that The genetic algorithm described in step (2) is used to encode each initial phase Φ m (l) Optimize and implement the steps as follows: Initialize an initial population with M initial phase coding sequences as samples, containing a total of O samples, and perform a roulette operation on the samples using the integrated sidelobe level (ISL) of the code-division orthogonal waveform as the cost function. Then, perform chromosome crossover and mutation on the paternal and maternal chromosomes after the roulette operation. Then, use the samples obtained after the roulette operation on the mutated new population as the optimal coding phase. Repeat multiple rounds until the fitness of the population falls below a preset threshold, and the optimization results of the M initial phase coding sequences are obtained.

3. The method according to claim 1, characterized in that Φ described in step (2) m Optimization results of (l) The complex exponential x m (l) The complex envelope u of the code-division orthogonal waveform at the current moment to be designed m (t), and the code division orthogonal waveform s of the FDA-MIMO airborne radar m (t), the calculation formulas are: Where exp[·] represents the complex exponential function, j represents the complex unit, and rect(·) represents the rectangular window function. T p express The corresponding sub-pulse width, T p =T / L,f m represents the carrier frequency of the mth transmitting array element, f m =f0+(m-1)△f, where f0 represents the carrier frequency of the first array element and △f represents the frequency offset between two adjacent transmitting array elements.

4. The method according to claim 1, wherein The target echo signal r described in step (3) n (t), baseband signal x of the echo after down-conversion n (g), and the echo space-time snapshot data x of the nth receiving array element c (n), the expressions are: Where: ξ represents the echo reflection coefficient, τ0 represents the echo delay, g represents the sampling point number, and g = (t-τ0)f s , f s represents the sampling rate, r represents the distance from the target to the radar receiving array, c represents the speed of light, λ represents the wavelength of the radar transmitting signal, i represents the traversal order of the receiving matched filter, d T Denotes the distance between transmitting elements, d R represents the receiving array element spacing, and θ represents the target pointing angle.

5. The method according to claim 1, wherein The spatial compensation frequency f described in step (4) c {α} , quadratic distance dependent compensation vector and the quadratic distance-dependent compensation vector in the space-time two-dimensional joint frequency domain The calculation formulas are: Among them, when α=1, R c {1} =R1, R1 is the distance value set in the main value distance zone; when α=2, R c {2} =R1+R u , R u =c / 2f r , R u represents the maximum unambiguous distance, f r Indicates the radar pulse repetition rate, represents the Kronecker product, 1 K is a column vector with M rows whose elements are all 1.

6. The method according to claim 1, characterized in that The compensated echo space-time snapshot data described in step (5) The expression is: Where ⊙ represents the Hadamard product.

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