CN113608177B - Radar high-robustness low-sidelobe waveform design method - Google Patents

Radar high-robustness low-sidelobe waveform design method Download PDF

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CN113608177B
CN113608177B CN202110869722.0A CN202110869722A CN113608177B CN 113608177 B CN113608177 B CN 113608177B CN 202110869722 A CN202110869722 A CN 202110869722A CN 113608177 B CN113608177 B CN 113608177B
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冯翔
赵宜楠
李风从
赵占锋
周志权
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Harbin Institute of Technology Weihai
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    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract

A radar high-stability low-sidelobe waveform design method belongs to the technical field of radar communication and is used for solving the problems of low stability, poor interception resistance and poor performance of inhibiting autocorrelation range sidelobes of the existing radar waveform design method. The technical points of the invention comprise: by adopting the idea of particle distributed projection, the chaotic waveform initialization, the waveform index evaluation value and the resampling idea are integrated into the iterative optimization of the constant modulus waveform sequence, and the constant modulus phase coding waveform meeting the engineering requirements is designed. Compared with the existing waveform design method, the method avoids the influence of the stagnation effect of the non-convex local area on the waveform design, and has stronger capability of inhibiting the side lobe interference of the distance of a specific interval. By applying the method, the waveform design has stronger robustness, better anti-interception performance and lower related side lobe, and the conventional radar, the MIMO radar, the cognitive radar and the like have better detection performance.

Description

Radar high-robustness low-sidelobe waveform design method
Technical Field
The invention relates to the technical field of radar detection, in particular to a radar high-stability low-sidelobe waveform design method.
Background
In recent years, unmanned aerial vehicle combat shows huge combat advantages in middle east and middle asian region conflicts. The land-based radar waveform agility level becomes an important means for improving the radar combat performance and battlefield viability. Signal interception, repeater interference, and shadowing interference are the most common forms in the field of radar electronic countermeasure today. In order to fully utilize the power of a transmitter and maximize the radar detection distance, the waveform constant modulus becomes the necessary condition for practical engineering. However, the traditional radar is limited by the form of a transmitted signal, has poor anti-interception performance and limited capability of inhibiting shielding interference. The distance side lobe of strong scatterers such as lighthouses and high-rise buildings in urban operations often influences the target detection of the unmanned aerial vehicle, and meanwhile, the enemy unmanned aerial vehicle often has the signal acquisition capacity. Therefore, the characteristics of anti-interception, low side lobe and constant modulus of radar waveform become objective requirements.
Aiming at the problem of low side lobe waveform design, typical solutions in current research include a cyclic algorithm family (e.g., CAN algorithm, see document [1 ]), an alternative projection algorithm (e.g., ISAA algorithm, see document [2 ]), a main optimization algorithm (e.g., MM algorithm, see document [3 ]), a gradient descent algorithm (e.g., PGD algorithm, see document [4 ]), and the like. In engineering, the mathematical modeling and optimization problem is non-convex due to waveform constant modulus constraint, waveform design robustness is crucial, and the iterative algorithm commonality problem is poor in solving stability of the non-convex problem caused by algorithm initialization and is difficult to meet engineering practice. In recent years, a popular relaxation alternative projection algorithm (such as an RSAP algorithm, see a document [5]; such as a Chinese patent document with a patent number of ZL 201510346063.7 and a name of a multi-input multi-output radar waveform design method) alleviates the problem of non-convex optimization stagnation to a certain extent by relying on a relaxation optimization mechanism, but also has the problem that the side lobe suppression effect is influenced because an initial point is selected and falls into a local area.
Disclosure of Invention
In view of the above problems, the invention provides a radar high-stability low-sidelobe waveform design method, which is used for solving the problems of low stability, poor anti-interception performance and poor range sidelobe suppression performance of the existing radar constant-modulus waveform design method.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a radar high-robustness low-sidelobe waveform design method comprises the following steps:
constructing a low-interception constant-modulus phase coding waveform set;
step two, constructing a waveform optimization objective function;
solving a waveform optimization objective function by utilizing a particle distributed projection idea, and specifically comprising the following steps of:
constructing a waveform sequence iterative projection mechanism, realizing waveform iterative projection by using waveform sequences stored at the previous moment and the next moment, and obtaining a low-interception constant modulus phase coding waveform set after iterative projection;
constructing a waveform sequence index evaluation function, and calculating all waveform sequences in the low-interception constant modulus phase coding waveform set after iterative projection according to a sidelobe suppression mean value calculation formula in an autocorrelation sidelobe interference interval to obtain a corresponding index evaluation value; screening out a waveform sequence with the minimum sidelobe suppression mean value as an optimal waveform sequence;
thirdly, constructing a particle resampling mechanism, and extracting a waveform sequence in the low-interception constant modulus phase coding waveform set after iterative projection by using a resampling method according to the index evaluation value to obtain a new low-interception constant modulus phase coding waveform set;
step four, circularly and iteratively executing the step one-step three, and when the difference value of the sidelobe suppression mean values of the optimal waveform sequences generated by two adjacent iterations is smaller than a preset error or the iteration times is larger than a preset total number, stopping the iteration and outputting the optimal waveform sequence corresponding to the minimum sidelobe suppression mean value.
Further, the low-intercept constant-modulus phase-encoding waveform set in the first step is constructed as follows:
if there are M waveform sequences in the waveform set and the length of the phase encoding unit of each waveform sequence is N, the low-interception constant modulus phase encoding waveform set is represented as:
Figure BDA0003188504000000021
in the above formula, the mth low-intercept constant-modulus phase-encoding waveform sequence is represented by
Figure BDA0003188504000000022
ψ n ∈[0,2π]Representing the phase of the nth symbol, taken from [0,2 π]The value is obtained.
Go to oneStep by step, generating a symbol phase ψ using a modified Logistic mapping power method n The generation formula is as follows:
ψ n+1 ＝mod(μ·ψ n ·(2π-ψ n ),2π)
wherein mu represents a chaotic branch parameter; mod (·) represents the remainder taking operation.
Further, the waveform optimization objective function in step two is constructed as follows:
Figure BDA0003188504000000023
wherein the content of the first and second substances,
Figure BDA0003188504000000024
representing an ideal waveform
Figure BDA0003188504000000025
The frequency spectrum of (a);
Figure BDA0003188504000000026
representing an FFT matrix; c denotes a spreading matrix.
Further, the specific process of the first step is as follows: order to
Figure BDA0003188504000000027
Representing the mth waveform sequence at the time t-1; the corresponding ideal waveform autocorrelation sequence is represented as:
Figure BDA0003188504000000028
wherein the mapping template
Figure BDA0003188504000000029
Q l Representing the ith autocorrelation sidelobe interference interval; the iterative projection process using the front and rear time waveforms is as follows:
firstly, obtaining an ideal frequency domain waveform sequence, namely a frequency spectrum, corresponding to the mth waveform sequence at the time t-1 by using the following formula (1):
Figure BDA0003188504000000031
wherein, angle () represents the phase taking operation;
then, according to the ideal frequency domain waveform sequence obtained above, a projection waveform sequence at time t satisfying a constant modulus constraint is obtained by using the following formula (2):
Figure BDA0003188504000000032
then, an iterative difference vector is obtained by subtracting the t-time projection waveform sequence and the t-1-time waveform sequence obtained above by using the following formula (3):
Figure BDA0003188504000000033
then, obtaining an ideal frequency domain waveform sequence, namely a frequency spectrum, corresponding to the waveform sequence at the time t by using the following formula (4);
Figure BDA0003188504000000034
wherein the content of the first and second substances,
Figure BDA0003188504000000035
representing a waveform sidelobe expression meeting the requirement of ideal low sidelobe constraint;
then, obtaining a projection waveform sequence at the t +1 moment by using the following formula (5);
Figure BDA0003188504000000036
then, the correction terms of the waveform sequences at the time t +1, the time t and the time t-1 are obtained by the following formula (6):
Figure BDA0003188504000000037
then, a correction term factor is constructed:
Figure BDA0003188504000000038
and finally, obtaining a waveform sequence after the iterative projection correction at the time t by using the following formula (8):
Figure BDA0003188504000000039
further, in the third step, the calculation formula of the mean value of sidelobe suppression in the sidelobe interference interval is as follows:
Figure BDA00031885040000000310
wherein p represents the number of range units in the sidelobe interference interval;
Figure BDA00031885040000000311
α(x m ) Representing a sequence of waveforms x m The auto-correlation sequence of (a) is,
Figure BDA0003188504000000041
representing an ideal waveform
Figure BDA0003188504000000042
The autocorrelation sequence of (a).
Further, the evaluation function of the waveform sequence index in the third step is expressed as follows:
Figure BDA0003188504000000043
the index evaluation value obtained by calculation according to the formula is normalized as follows:
Figure BDA0003188504000000044
further, the resampling method in the third step adopts a deterministic resampling method, and performs sampling by using the index evaluation value of the waveform sequence and the cumulative distribution function thereof, and the specific steps include:
first, a cumulative distribution function of each waveform sequence index evaluation value is calculated:
Figure BDA0003188504000000045
then, order
Figure BDA0003188504000000046
Representing random numbers taken from uniformly distributed 0 to 1, defining a comparison threshold
Figure BDA0003188504000000047
Initializing the number of samples num (j) =0, j =1, · M of each waveform sequence;
then, sequentially comparing the M comparison thresholds u i And a cumulative distribution function W j Performing a cyclic comparison of if u i ＜W j Then the number of samples num (j) is increased;
and finally, sequentially comparing the M sampling numbers num (j) with 0, if num (j) > 0, reserving and copying the jth waveform sequence num (j) times, thereby obtaining a new low-interception constant modulus phase coding waveform set after resampling.
Further, the value range of the chaotic branch parameter μ is as follows: mu is more than 3.6 and less than 4.
The beneficial technical effects of the invention are as follows:
the waveform designed according to the method of the invention can effectively avoid the shielding interference of strong scatterers, enhance the anti-interception performance, and is more beneficial to the detection and tracking of targets, and the method has the following advantages:
(1) As for the generation mode of the integrated constant modulus phase coding, the radar waveform sequence provided by the invention has an accurate expression:
Figure BDA0003188504000000048
Figure BDA0003188504000000049
ψ n+1 ＝mod(μ·ψ n ·(2π-ψ n ),2π)
the diversity of waveform sequence initialization is enhanced by an integrated waveform generation mode, and a code phase unit replaces a hardware random phase coding mode by a deterministic chaotic phase generation mechanism, so that the engineering realizability and the anti-interception performance are increased.
(2) For the conversion from the mathematical problem to the engineering problem, the method can be regarded as parallel fitting approximation of a distributed waveform sequence, so that the GPU and FPGA hardware can conveniently realize on-line calculation, and excessive factors considered in advance are avoided.
(3) In terms of avoiding the constant modulus non-convex stagnation problem, the index value is evaluated according to the waveform sequence, a new waveform set is obtained by adopting a resampling mode, and the method can be regarded as carrying out parallelization synchronous optimization searching on a plurality of local optimal areas, so that the problem that a single initial point determines the optimal waveform is avoided.
(4) In terms of waveform optimization effect, the radar waveform design method provided by the invention has high stability, and the suppression of autocorrelation distance sidelobe is stronger than that of the methods provided by the documents [1] to [5], and is more convenient for engineering design.
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The invention may be better understood by referring to the following description in conjunction with the accompanying drawings, in which like reference numerals are used throughout the figures to indicate like or similar parts. The accompanying drawings, which are incorporated in and form a part of this specification, illustrate preferred embodiments of the present invention and, together with the detailed description, serve to further illustrate the principles and advantages of the invention.
Fig. 1 shows an overall flow diagram of a radar high-robustness low-sidelobe waveform design method according to an embodiment of the invention.
Fig. 2 shows a schematic diagram of a distributed optimization flow of a radar high-robustness low-sidelobe waveform design method according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of radar signal autocorrelation sidelobe suppression in a single specific area.
Fig. 4 is a schematic diagram of radar signal autocorrelation sidelobe suppression in a plurality of specific areas.
Fig. 5 is a graph comparing the mean values of sidelobe suppression of radar signals in a plurality of experiments.
Detailed Description
Exemplary embodiments of the present invention will be described hereinafter with reference to the accompanying drawings. In the interest of clarity and conciseness, not all features of an actual implementation are described in the specification. It will of course be appreciated that in the development of any such actual embodiment, numerous implementation-specific decisions must be made to achieve the developers' specific goals, such as compliance with system-related and business-related constraints, which will vary from one implementation to another. Moreover, it will be appreciated that such a development effort might be complex and time-consuming, but would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of this disclosure. It should be noted that, in order to avoid obscuring the present invention with unnecessary details, only the device structures and/or processing steps closely related to the solution according to the present invention are shown in the drawings, and other details not so related to the present invention are omitted.
The invention aims to provide a constant-modulus low-sidelobe phase-coded radar waveform design method which has lower range sidelobe suppression depth, high interception resistance and high robustness. Starting from the idea of particle distributed projection, the invention introduces a chaotic phase generation mechanism, a sequence iterative projection mechanism and a resampling mechanism to improve the waveform design performance.
As shown in fig. 1 and 2, a method for designing a radar high-robustness low-sidelobe waveform includes the following steps:
step 1: a low-interception constant-modulus phase coding waveform set structure;
assuming that there are M waveform sequences in the waveform set and the coding unit length of the waveform sequence is N, the waveform sequence set is expressed as:
Figure BDA0003188504000000061
in order to maximize the transmission power of the radar transmitter, in the formula,
Figure BDA0003188504000000062
indicating that the nth symbol phase is taken from [0,2 π]Values, since the random phase hardware generation mechanism is complex, the phase code is generated by an improved Logistic mapping dynamic method, as follows:
ψ n+1 ＝mod(μ·ψ n ·(2π-ψ n ),2π)
wherein the chaotic branch parameter is more than 3.6 and less than mu and less than 4, and the phase sequence phi 1 ...ψ N ]From a deterministic, known first symbol phase psi 1 And the branch parameter mu can be generated iteratively, so that a random phase hardware mechanism is avoided; the statistic characteristics of the chaotic sequence generated by the method are consistent with white noise, the randomness is strong, the confidentiality is good, and the method is suitable for resisting the interception of phase coding waveforms; and ψ of an m-th waveform and an m + 1-th waveform 1 Often different, the phases of the subsequent code elements have no mathematical relationship; the waveform set can contain any plurality of waveform sequences, the number of the sequences corresponds to the number of parallel operation units, and the hardware aspect can be conveniently realized through GPU parallel computation.
Step 2: constructing a mathematical engineering problem of waveform optimization;
the autocorrelation sidelobe suppression approximation interval is determined using scene prior information or by transmitting a conventional waveform in advance. To reduce/attenuate strong scatterer range sidelobe interference, transmit waveform x should be made m The autocorrelation sequence of (a) (x) m ) Satisfies the following conditions:
Figure BDA0003188504000000063
α(x m )＝[α 0 (x m )...α N-1 (x m ) 0 α -N+1 (x m )...α -1 (x m )] T
Figure BDA0003188504000000064
wherein the content of the first and second substances,
Figure BDA0003188504000000065
representing an ideal waveform
Figure BDA0003188504000000066
The corresponding autocorrelation sequence; that is, the transmit waveform x m Should approximate the ideal waveform as much as possible
Figure BDA0003188504000000067
Range side lobe characteristic of (1), Q l Representing the ith autocorrelation sidelobe interference interval; hadamard product operation, mapping template, indicating a matrix or vector
Figure BDA0003188504000000071
From the pascal equivalence between the time-domain correlation property and the spectral amplitude:
Figure BDA0003188504000000072
Figure BDA0003188504000000073
which represents the FFT matrix, is,
Figure BDA0003188504000000074
a power spectrum representing a sequence of waveforms;
Figure BDA0003188504000000075
and f m Respectively characterizing ideal waveforms
Figure BDA0003188504000000076
And design waveform x m The frequency spectrum of (a) is,
Figure BDA0003188504000000077
c is the spreading matrix, and C is the spreading matrix,
Figure BDA0003188504000000078
(·) * representing a conjugate taking operation; the objective function of the waveform design can be written as:
Figure BDA0003188504000000079
and 3, step 3: evaluating the performance of the waveform sidelobe suppression;
defining the interference interval Q with side lobes l The mean value of the inner sidelobe suppression is used as a qualitative index (aver _ nominal) to measure the quality of a designed waveform; this qualitative index applies for each waveform sequence. The qualitative calculation formula is:
Figure BDA00031885040000000710
where p represents the number of distance elements within the sidelobe suppression interval. The smaller the mean side lobe suppression value is, the better the range side lobe suppression effect is.
And 4, step 4: constructing a particle distributed projection framework to solve the mathematical problem of waveform design; as shown in fig. 2, the algorithm framework comprises three substeps:
step 41, constructing a waveform sequence iterative projection mechanism, and realizing waveform iterative projection by using the waveform sequences stored at the previous moment and the next moment; waveform sequence iterative projection mechanism
Figure BDA00031885040000000711
Can be expressed as:
Figure BDA00031885040000000712
wherein, it is made
Figure BDA00031885040000000713
Representing the mth waveform sequence at the time point of t-1; the corresponding ideal waveform autocorrelation sequence is represented as:
Figure BDA00031885040000000714
the iterative projection process of the waveforms at the front and rear time instants is as follows:
firstly, obtaining an ideal frequency domain waveform sequence corresponding to the waveform sequence at the time t-1 by using the following formula (1):
Figure BDA00031885040000000715
then, obtaining a projection waveform sequence at the time t meeting the constant modulus constraint by using the following formula according to the obtained ideal frequency domain waveform sequence:
Figure BDA0003188504000000081
then, the obtained t-time projection waveform sequence and the t-1-time waveform sequence are subjected to difference to obtain an iterative difference value vector:
Figure BDA0003188504000000082
then, obtaining ideal frequency domain waveform sequences corresponding to the waveform sequences at the time t according to the above, as formula (4); projecting a waveform sequence at the t +1 moment, as shown in formula (5);
Figure BDA0003188504000000083
wherein the content of the first and second substances,
Figure BDA0003188504000000084
representing a waveform sidelobe expression meeting the requirement of ideal low sidelobe constraint;
Figure BDA0003188504000000085
further, the correction terms of the waveform sequences at the t +1 moment, the t moment and the t-1 moment are obtained by the following formula (6):
Figure BDA0003188504000000086
then, a correction term factor is constructed:
Figure BDA0003188504000000087
and finally, obtaining a waveform sequence after the iterative projection correction at the time t by using the following formula (8):
Figure BDA0003188504000000088
the sidelobe suppression mean value can be expressed as:
Figure BDA0003188504000000089
step 42, constructing a waveform sequence index evaluation function, calculating all sequences in the constant modulus phase coding waveform set according to a sidelobe suppression mean value calculation formula in a sidelobe interference interval to obtain an index evaluation value corresponding to the waveform sequence, and screening out the waveform sequence with the optimal sidelobe suppression mean value (namely the waveform sequence with the minimum sidelobe suppression mean value); the waveform sequence index evaluation function is constructed as follows:
Figure BDA00031885040000000810
the index evaluation value is normalized to obtain:
Figure BDA00031885040000000811
step 43, constructing a particle resampling mechanism, and extracting the waveform sequence set by using a resampling method according to the index evaluation value to obtain a new waveform sequence set;
the resampling method can adopt methods such as hierarchical resampling, deterministic resampling, residual resampling and the like, and the method adopts deterministic resampling and utilizes a waveform sequence set obtained by resampling to replace an original waveform sequence set. The deterministic resampling in the invention utilizes the index evaluation value of a waveform sequence and the cumulative distribution function of the evaluation value to sample, and comprises the following specific steps:
first, a cumulative distribution function of each waveform sequence index evaluation value is calculated:
Figure BDA0003188504000000091
then, let
Figure BDA0003188504000000092
Representing random numbers taken from uniformly distributed 0 to 1, defining a comparison threshold
Figure BDA0003188504000000093
Initializing the number of samples num (j) =0, j =1, · M of each waveform sequence;
then, M comparison thresholds u are sequentially compared i I = 1.. M and the cumulative distribution function W j Performing a cyclic comparison of if u i ＜W j Then the number of samples num (j) is increased;
finally, sequentially comparing the M sampling numbers num (j), j =1, so, M and 0, if num (j) > 0, reserving and copying the sampling sequence num (j) times, and obtaining a resampling waveform sequence.
The steps are completed, the task objective function is constructed and solved, the waveform is optimized according to the particle distributed projection algorithm framework in the step 4, and the iteration number num of the evolutionary projection is set; if the difference value of the optimal averer _ default (x) generated by two adjacent iterations (step 41-step 43 complete loop is called one iteration) is smaller than the given error epsilon or the iteration number of the algorithm is larger than the given total num, the algorithm stops and outputs the waveform averer _ default (x) corresponding to the optimal averer _ default index best ) Else, continuing the substep step in step 4.
To verify the effectiveness of the method of the invention, it is assumed that the strong scatterer is located in the single sidelobe interference interval Q l ＝[2:40]And a multi-sidelobe interference interval Q l ＝[2:20]∪[30:50](ii) a Any constant modulus waveform sequence in the emission waveform sequence set is as follows:
Figure BDA0003188504000000094
wherein psi 1 ∈[0,2π]And phi n A phase generated for improved chaotic mapping; sequence code length N =150; aggregate size M =10; the number of algorithm iterations num =200; iteration threshold, i.e. given error, is epsilon =10 -2 (ii) a And stopping the algorithm and outputting the optimal waveform (the waveform corresponding to the optimal aver _ sideval index) until the difference value of the optimal aver _ sideval (x) generated by two adjacent iterations is smaller than a given error epsilon or the iteration times of the algorithm are larger than a given total num.
Simulation comparison is carried out on the method (PFSP in Table 1) of the invention, a weighted CAN algorithm (WeCAN) in document [1], an alternative projection algorithm (ISAA) in document [2], a relaxed alternative projection algorithm (RSAP) in a patent (with the patent number of ZL 201510346063.7 and the name of a multi-input multi-output radar waveform design) and a constant modulus phase gradient optimization (PGD) algorithm, and the algorithms adopt consistent termination conditions; the method can obtain the optimization effects of 330dB and 328dB in the single sidelobe interval and the multi-sidelobe interval, and the good anti-interference performance of the method is shown in table 1 (10 times of test mean values), fig. 3 and fig. 4.
TABLE 1 different algorithms inhibit specific interval sidelobe comparisons
Figure BDA0003188504000000101
Fig. 3 is a schematic diagram of radar signal autocorrelation sidelobe suppression in a single specific sidelobe suppression region [ 2. Through multiple simulation tests, it can be seen from fig. 3 that the five algorithms in table 1 achieve the best interference interval sidelobe suppression effect, which is consistent with the performance difference in table 1.
Fig. 4 is a schematic diagram of radar signal autocorrelation sidelobe suppression in a plurality of specific sidelobe suppression regions [2, 30. Through multiple simulation tests, it can be seen from fig. 4 that the five algorithms in table 1 achieve the best interference interval sidelobe suppression effect, and the PFSP algorithm of the method for suppressing the multi-sidelobe interval still has the advantage (-328 dB) similar to that of a single interval, which is not possessed by other algorithms.
Fig. 5 is a comparison graph of the sidelobe suppression mean value of the radar signal in multiple tests, and comparing the method of the present invention with a typical RSAP algorithm, it can be seen from fig. 5 that the sidelobe suppression mean value obtained in 20 tests by the method of the present invention is relatively stable, and the RSAP algorithm has a slightly poor iteration robustness due to multiple fluctuations of the optimized sidelobe suppression mean value caused by each initialization difference.
Compared with the existing waveform design method, the method has better waveform design robustness, avoids the defect of poor solution stability caused by the initialization difference of the iterative algorithm under the constant modulus non-convex constraint, and has lower correlation side lobe. By applying the particle distributed projection constant modulus waveform coding design method, the conventional MIMO radar has better detection performance.
While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this description, will appreciate that other embodiments can be devised which do not depart from the scope of the invention as described herein. The present invention has been disclosed in an illustrative rather than a restrictive sense, and the scope of the present invention is defined by the appended claims.
The documents cited in the present invention are as follows:
[1] cyclic Algorithm New, CAN, see the literature for a computational approach, he H, li J, stoica P.; cambridge University Press,2012.
[2] Alternate projection coding waveform design based on rank-deficient fourier transform, zhao yinan, li feng yi, wangjun, qiao xian forest; journal of electronics, 2014, 06.
[3].Song J,Babu P,Palomar D P.Optimization methods for designing sequences with low autocorrelation sidelobes[J].IEEE Transactions on Signal Processing,2015,63(15):3998-4009.
[4].Esmaeili-Najafabadi H,Leung H,Moo P W.Unimodular waveform design with desired ambiguity function for cognitive radar[J].IEEE Transactions on Aerospace and Electronic Systems,2019,56(3):2489-2496.
[5].Feng X,Zhao Y,Zhou Z,et al.Waveform design with low range sidelobe and high Doppler tolerance for cognitive radar[J].Signal Processing,2017,139:143-155.

Claims (9)

1. A radar high-robustness low-sidelobe waveform design method is characterized by comprising the following steps:
constructing a low-interception constant modulus phase coding waveform set;
step two, constructing a waveform optimization objective function;
solving a waveform optimization objective function by utilizing a particle distributed projection idea, and specifically comprising the following steps of:
constructing a waveform sequence iterative projection mechanism, realizing waveform iterative projection by using waveform sequences stored at the previous moment and the next moment, and obtaining a low-interception constant modulus phase coding waveform set after iterative projection;
constructing a waveform sequence index evaluation function, and calculating all waveform sequences in the low-interception constant modulus phase coding waveform set after iterative projection according to a sidelobe suppression mean value calculation formula in an autocorrelation sidelobe interference interval to obtain a corresponding index evaluation value; screening out a waveform sequence with the minimum sidelobe suppression mean value as an optimal waveform sequence;
thirdly, constructing a particle resampling mechanism, and extracting a waveform sequence in the low-interception constant modulus phase coding waveform set subjected to iterative projection by using a resampling method according to the index evaluation value to obtain a new low-interception constant modulus phase coding waveform set;
step four, circularly and iteratively executing the step one-step three, and when the difference value of the sidelobe suppression mean values of the optimal waveform sequences generated by two adjacent iterations is smaller than a preset error or the iteration times is larger than a preset total number, stopping the iteration and outputting the optimal waveform sequence corresponding to the minimum sidelobe suppression mean value.
2. The method according to claim 1, wherein in step one, the low-intercept constant modulus phase-coded waveform set is constructed as follows:
if there are M waveform sequences in the waveform set and the length of the phase encoding unit of each waveform sequence is N, the low-interception constant modulus phase encoding waveform set is represented as:
Figure FDA0004054474820000011
in the above formula, the mth low-interception constant-modulus phase-encoding waveform sequence is represented by
Figure FDA0004054474820000012
Representing the nth symbol phase, taken from [0,2 π]The value is obtained.
3. The method of claim 2, wherein a symbol phase psi is generated by using an improved Logistic mapping dynamic method n The generation formula is as follows:
ψ n+1 ＝mod(μ·ψ n ·(2π-ψ n ),2π)
wherein mu represents a chaotic branch parameter; mod (·) represents the remainder taking operation.
4. The method according to claim 3, wherein the waveform optimization objective function in step two is constructed as follows:
Figure FDA0004054474820000021
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0004054474820000022
representing an ideal waveform
Figure FDA0004054474820000023
The frequency spectrum of (a);
Figure FDA0004054474820000024
representing an FFT matrix; c denotes a spreading matrix.
5. The method according to claim 4, wherein the specific process of the first step is as follows: order to
Figure FDA0004054474820000025
Figure FDA0004054474820000026
Representing the mth waveform sequence at the time t-1; the corresponding ideal waveform autocorrelation sequence is represented as:
Figure FDA0004054474820000027
wherein the mapping template
Figure FDA0004054474820000028
Figure FDA0004054474820000029
Q l Representing the ith autocorrelation sidelobe interference interval; the iterative projection process using the front and rear time waveforms is as follows:
firstly, obtaining an ideal frequency domain waveform sequence, namely a frequency spectrum, corresponding to the mth waveform sequence at the time point of t-1 by using the following formula (1):
Figure FDA00040544748200000210
wherein, angle () represents the phase taking operation;
then, according to the ideal frequency domain waveform sequence obtained above, a projection waveform sequence at time t satisfying a constant modulus constraint is obtained by using the following formula (2):
Figure FDA00040544748200000211
then, an iterative difference vector is obtained by subtracting the t-time projection waveform sequence and the t-1-time waveform sequence obtained as described above by using the following formula (3):
Figure FDA00040544748200000212
then, obtaining an ideal frequency domain waveform sequence, namely a frequency spectrum, corresponding to the waveform sequence at the time t by using the following formula (4);
Figure FDA00040544748200000213
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00040544748200000214
expressing a waveform side lobe expression meeting the requirement of ideal low side lobe constraint;
then, obtaining a projection waveform sequence at the t +1 moment by using the following formula (5);
Figure FDA00040544748200000215
then, the correction terms of the waveform sequences at the time t +1, the time t and the time t-1 are obtained by the following formula (6):
Figure FDA00040544748200000216
then, a correction term factor is constructed:
Figure FDA0004054474820000031
and finally, obtaining a waveform sequence after the iterative projection correction at the time t by using the following formula (8):
Figure FDA0004054474820000032
6. the method according to claim 5, wherein the mean value of sidelobe suppression in the sidelobe interference interval in step three or two is calculated as:
Figure FDA0004054474820000033
wherein p represents the number of range units in the sidelobe interference interval;
Figure FDA0004054474820000034
α(x m ) Representing a sequence of waveforms x m The auto-correlation sequence of (a) is,
Figure FDA0004054474820000035
representing an ideal waveform
Figure FDA0004054474820000036
The autocorrelation sequence of (a).
7. The method according to claim 6, wherein the evaluation function of the waveform sequence index in step three is expressed as follows:
Figure FDA0004054474820000037
the index evaluation value obtained by calculation according to the formula is normalized as follows:
Figure FDA0004054474820000038
8. the radar high-robustness low-sidelobe waveform design method according to claim 7, wherein the resampling method in the third step adopts a deterministic resampling method, and sampling is performed by using an index evaluation value of a waveform sequence and a cumulative distribution function thereof, and the specific steps include:
first, a cumulative distribution function of each waveform sequence index evaluation value is calculated:
Figure FDA0004054474820000039
then, order
Figure FDA00040544748200000310
Is taken from a uniform distribution of between 0 and 1Random number, defining a comparison threshold
Figure FDA00040544748200000311
Initializing the number of samples num (j) =0, j =1, · M of each waveform sequence;
then, M comparison thresholds u are sequentially compared i And cumulative distribution function W j Performing a cyclic comparison of if u i ＜W j Then the number of samples num (j) is increased;
and finally, sequentially comparing the M sampling numbers num (j) with 0, if num (j) > 0, reserving and copying the jth waveform sequence num (j) times, thereby obtaining a new low-interception constant modulus phase coding waveform set after resampling.
9. The method according to claim 8, wherein the chaotic branch parameter μ has a value range of: mu is more than 3.6 and less than 4.
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