CN113985364A - Non-uniform sub-bandwidth orthogonal frequency division multiplexing frequency modulation signal waveform optimization method - Google Patents

Non-uniform sub-bandwidth orthogonal frequency division multiplexing frequency modulation signal waveform optimization method Download PDF

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CN113985364A
CN113985364A CN202111415699.4A CN202111415699A CN113985364A CN 113985364 A CN113985364 A CN 113985364A CN 202111415699 A CN202111415699 A CN 202111415699A CN 113985364 A CN113985364 A CN 113985364A
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CN113985364B (en
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李亚超
丁明月
闫安
张鹏
王家东
张志军
陶慧斌
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Xidian University
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    • G—PHYSICS
    • 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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/36—Means for anti-jamming, e.g. ECCM, i.e. electronic counter-counter measures
    • G—PHYSICS
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/06—Systems determining position data of a target
    • G01S13/08—Systems for measuring distance only
    • G01S13/10—Systems for measuring distance only using transmission of interrupted, pulse modulated waves

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Abstract

The invention discloses a non-uniform sub-bandwidth orthogonal frequency division multiplexing frequency modulation signal waveform optimization method, which mainly solves the problems that the radar signal detection capability is insufficient and the fixed emission waveform of a radar system is mismatched with the current environment state in the prior art. The implementation scheme is as follows: solving the ideal waveform energy spectrum density epsilon under the maximum signal-noise-ratio criterion according to clutter, noise and the spectrum distribution information of the targetopt(f) (ii) a Establishing a relation model between waveform parameters of orthogonal frequency division multiplexing linear frequency modulation signals and energy spectrum density of the orthogonal frequency division multiplexing linear frequency modulation signals; establishing an objective function by taking the minimum mean square error between the waveform to be optimized and the energy spectral density of the ideal waveform as a criterion; and solving the objective function to obtain the parameters of the optimal waveform. The invention increases the signal-to-noise-and-noise ratio of the output signal, improves the target detection performance of the radar, has the characteristics of large product value of time width and bandwidth and low time domain peak average power ratio of signal waveform, and can be used for clutter suppression。

Description

Non-uniform sub-bandwidth orthogonal frequency division multiplexing frequency modulation signal waveform optimization method
Technical Field
The invention belongs to the technical field of digital signal processing, and particularly relates to a non-uniform sub-bandwidth orthogonal frequency division multiplexing frequency modulation signal waveform optimization method which can be used for suppressing clutter and improving the signal-to-noise-ratio of radar output signals.
Background
The important restriction of improving the detection and identification performance of the traditional radar target is that the fixed emission waveform of the traditional radar system is mismatched with the current environment state. Due to the dynamic change of the environment, the radar generally has difficulty in achieving the expected detection effect, and the detection performance of the radar system can be greatly improved by optimizing the transmitting waveform according to the current environment knowledge. The clutter is an important interference factor in a radar working environment, so that the waveform design work under the clutter environment is very important, and the problem of low radar detection performance under the change of a complex environment can be solved from the source by designing a radar transmitting waveform according to current clutter knowledge.
Waveform design refers to the optimization of parameters of a certain basic waveform according to the radar task requirements, so the selection of the basic waveform is also very important. The orthogonal frequency division multiplexing chirp signal is widely used because of its many excellent characteristics, it not only has a large time-bandwidth product, but also has the advantages of low peak-to-average power ratio and low range-doppler coupling, and it is a relatively ideal basic waveform.
Wangxing proposed in "MIMO SAR OFDM symbol diversity with random matrix modulation, IEEE Transactions on Geoscience and Remote Sensing, vol.53, No.3, pp.1615-1625, and mar.2015", a method for designing an orthogonal frequency division multiplexing chirp signal waveform suitable for MIMO SAR modulates a set of basic waveforms by a random matrix to obtain an orthogonal frequency division multiplexing chirp signal waveform with uniformly distributed sub-bandwidths and sub-bandwidths, which has the advantages of large time-bandwidth product, low time-frequency domain peak average power ratio and low distance-doppler coupling, but cannot effectively suppress clutter due to high time-domain autocorrelation function side lobes and flat frequency spectrum distribution.
Disclosure of Invention
The invention aims to provide a non-uniform sub-bandwidth orthogonal frequency division multiplexing frequency modulation signal waveform optimization method aiming at the defects of the prior art so as to increase the signal-to-noise-ratio of an output signal and improve the target detection performance of a radar.
The technical scheme of the invention is as follows: solving the ideal waveform energy spectrum density under the maximum signal-noise-ratio criterion according to the clutter and the spectrum distribution information of the target; establishing a relation model between waveform parameters of orthogonal frequency division multiplexing linear frequency modulation signals and energy spectrum density thereof, and establishing a target function by taking the minimum mean square error between an optimized waveform and ideal waveform energy spectrum density as a criterion; the parameters of the optimal waveform are obtained by solving the objective function, and the specific implementation comprises the following steps:
1) acquiring an ideal waveform and an orthogonal frequency division multiplexing linear frequency modulation signal s (t) with a non-uniform distribution sub bandwidth under an optimal signal-to-noise-ratio criterion;
2) calculating the signal noise-to-noise ratio according to the clutter and the spectrum density function of the target, and calculating the energy spectrum density epsilon of the ideal waveform under the optimal signal noise-to-noise ratio criterionopt(f)；
3) Calculating the energy spectral density epsilon (f) of the waveform of the orthogonal frequency division multiplexing linear frequency modulation signal with the non-uniformly distributed sub-bandwidth;
4) taking the minimum mean square error function of the energy spectral density obtained by calculation in 2) and 3) as an objective function, taking the total energy and the total bandwidth of the signal as constraints, and establishing a mathematical model of the following optimization problem;
Figure BDA0003375677130000021
s.t.max[Δesdn]≤μ,n＝0,1,...,N-10＜μ≤1
Figure BDA0003375677130000022
0＜Bn＜B,n＝0,1,...,N-1
Figure BDA0003375677130000023
wherein, Δ esdn＝|mean[ε(f)]-mean[εopt(f)]|,
Figure BDA0003375677130000024
B is the total bandwidth of the orthogonal frequency division multiplexing linear frequency modulation signal, and comprises N non-uniformly distributed sub-bandwidths; p is the sub-bandwidth vector to be optimized, BnIs the (N + 1) th sub-bandwidth, N0, 1., N-1; e is the total energy of the signal and mu is a positive number less than 1;
5) taking a group of random values as initial values of a sub-bandwidth vector P to be optimized, and solving the mathematical model in the step 4) through a sequence quadratic programming SQP solving tool of MATLAB software to obtain a sub-bandwidth vector P ' ═ B ' of the optimized orthogonal frequency division multiplexing linear frequency modulation signal '0,B′1,...,B′n,...,B′N-1]；B′nIs the N +1 th optimized sub-bandwidth, N ═ 0, 1.., N-1;
6) and determining the initial frequency and the frequency modulation rate of the sub-carrier according to the distribution value of the sub-bandwidth vector P' to obtain the optimized orthogonal frequency division multiplexing linear frequency modulation signal.
Compared with the prior art, the invention has the following advantages:
1. improving signal-to-noise ratio of output signal
The orthogonal frequency division multiplexing chirp signal waveforms designed by the prior art are uniform sub-temporal width and uniform sub-bandwidth waveforms. The clutter energy can not be suppressed from a frequency domain due to the uniform distribution of the frequency spectrum, and meanwhile, clutter can not be suppressed from a time domain due to the fact that the sidelobe of the autocorrelation function is too high due to the fact that part of subcarriers in the waveform are the same, so that the capability of suppressing the clutter by the waveform is poor.
The invention optimizes the sub-bandwidth vector of the waveform based on the maximum signal-to-noise-ratio criterion under the assistance of target and clutter prior knowledge, compared with the orthogonal frequency division multiplexing linear frequency modulation signal waveform with equal sub-bandwidth, the energy distribution of the designed emission waveform in the frequency domain is more reasonable, the clutter signal energy can be reduced while the target signal energy is enhanced, the signal-to-noise-ratio of the output signal is improved, and thus the purpose of inhibiting the clutter is achieved.
2. Has the advantages of multiple waveforms
Compared with the widely used phase coding waveform, the invention has low Doppler sensitivity because the designed waveform introduces the linear frequency modulation signal waveform;
compared with the traditional linear frequency modulation signal waveform, the designed waveform has a discontinuous sub-carrier wave structure, so that the method has lower range-Doppler coupling, and has important significance for accurate distance measurement and speed measurement of a radar;
compared with the basic orthogonal frequency division multiplexing linear frequency modulation signal, the designed waveform optimizes the sub-bandwidth vector of the waveform based on the maximum signal-to-noise-ratio criterion with the assistance of target and clutter prior knowledge, thereby not only improving the signal-to-noise-ratio of the output signal and having the capability of inhibiting clutter, but also having the characteristics of large time-width bandwidth, large time domain and low peak average power ratio.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a diagram of a model of a radar signal transmission channel according to the present invention;
fig. 3 is a waveform structure diagram of an orthogonal frequency division multiplexing chirp signal in the prior art;
FIG. 4 is a spectral distribution plot of clutter, targets, noise, and optimal waveforms in the present invention;
FIG. 5 is a diagram of an optimized waveform configuration according to the present invention;
FIG. 6 is a graph comparing the energy spectral density of the optimized waveform with the optimal waveform in the present invention;
fig. 7 is a graph comparing the output signal-to-noise ratio of the optimum waveform, and the equal sub-bandwidth ofdm chirp signal waveform in the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific examples.
Referring to fig. 1, the implementation steps of the invention are as follows:
step 1, obtaining an orthogonal frequency division multiplexing linear frequency modulation signal s (t) with non-uniformly distributed sub-bandwidth.
The existing basic waveform structure of orthogonal frequency division multiplexing chirp signal is shown in fig. 3, in which the horizontal axis represents a pulse time width T, which is uniformly divided into M sub-time widths Tp(ii) a The vertical axis represents the total bandwidth B of the signal, which is divided evenly into N sub-bandwidths BbEach slash in fig. 3 represents a subcarrier: the waveform structure only contains one group of subcarriers, namely only one subcarrier in each sub-pulse.
The invention is provided with K groups of subcarriers, the sub-bandwidths are non-uniformly distributed, and the acquisition of the orthogonal frequency division multiplexing linear frequency modulation signal s (t) of the non-uniformly distributed sub-bandwidths is realized as follows because no prior information exists:
1.1) this example takes a set of random values as the initial value P ═ B for the sub-bandwidth vector to be optimized0,B1,...,Bn,...,BN-1]In which B isnIs the (n + 1) th sub-bandwidth;
1.2) according to BnCalculating the starting frequency f of the kth subcarrier in the mth sub-pulsek,m：
Figure BDA0003375677130000041
Wherein f _ codek,mFrequency coding of a k subcarrier within an m sub-pulse;
1.3) according to the sub-bandwidth corresponding to the kth sub-carrier in the mth sub-pulse
Figure BDA0003375677130000045
Calculating the frequency modulation rate r of the kth subcarrier in the mth sub-pulsek,m：
Figure BDA0003375677130000042
Wherein T ispIs M sub-pulses uniformly distributed in one pulseThe time width of the rush;
1.4) according to the starting frequency fk,mAnd a frequency rk,mThe obtained orthogonal frequency division multiplexing linear frequency modulation signal s (t) with the non-uniform distribution sub bandwidth is as follows:
Figure BDA0003375677130000043
wherein u (t) is a unit step function, and t is time.
Step 2, calculating the energy spectrum density epsilon of the ideal waveform under the optimal signal-to-noise-ratio criterionopt(f)。
2.1) calculating the signal-noise-ratio of the chirp signal s (t) according to clutter, noise and a target spectral density function:
the radar signal transmission path is shown in FIG. 2, where s0(t) is a radar emission signal, a (t) is s0(t) a target echo generated by the action of a target impulse response h (t), c (t) s0(t) clutter echoes generated by the action of the clutter impulse response w (t), n (t) white noise, r (t) a receive filter, s0(t), c (t) and n (t) are independent of each other, and y (t) is a system output signal.
Calculating the target signal t from fig. 20Spectral density function at time of day of
Figure BDA0003375677130000044
According to clutter power spectral density Pww(f) Sum noise power spectral density Pnn(f) The computing system is at t0The clutter noise power spectral density function of the time output is
Figure BDA0003375677130000051
The system thus obtained is at t0Signal-to-noise ratio of time-of-day output signal
Figure BDA0003375677130000052
Comprises the following steps:
Figure BDA0003375677130000053
wherein S is0(f) For radar emission of signals s0(t), h (f) is the frequency spectrum of the target impulse response h (t), r (f) is the frequency spectrum of the receive filter r (t);
2.2) calculating the energy spectrum density epsilon of the ideal waveform under the optimal signal-to-noise-ratio criterionopt(f)：
2.2.1) construction of the equation for | S according to the Lagrangian multiplier method0(f)|2The objective function of (a) is:
Figure BDA0003375677130000054
wherein the content of the first and second substances,
Figure BDA0003375677130000055
is a known signal energy constraint;
2.2.2) order I (| S)0(f)|2) Is equal to 0, the energy spectral density epsilon of the optimal transmitting signal is obtainedopt(f) Comprises the following steps:
Figure BDA0003375677130000056
and 3, calculating the energy spectrum density epsilon (f) of the waveform of the orthogonal frequency division multiplexing linear frequency modulation signal with the non-uniformly distributed sub-bandwidth.
Transforming the orthogonal frequency division multiplexing linear frequency modulation signal s (t) with the non-uniformly distributed sub-bandwidth to a frequency domain to obtain a frequency domain linear frequency modulation signal S (f):
Figure BDA0003375677130000061
obtaining the energy spectrum density epsilon (f) of the orthogonal frequency division multiplexing linear frequency modulation signal waveform with non-uniformly distributed sub-bandwidth according to an energy spectrum density formula:
Figure BDA0003375677130000062
from the above equation, it can be seen that the signal energy spectral density is mainly related to the subcarrier modulation frequency and the start frequency, and both the modulation frequency and the start frequency are related to the sub-bandwidth, so that a more ideal epsilon (f) can be obtained by changing the sub-bandwidth.
And 4, constructing a mathematical model of the optimization problem.
Calculating the energy spectral density epsilon of the ideal waveformopt(f) And minimum mean square error function of energy spectral density epsilon (f) of chirp signal waveform
Figure BDA0003375677130000063
Calculating the Total energy of the Signal
Figure BDA0003375677130000064
Calculating the total bandwidth of a signal
Figure BDA0003375677130000065
Approximating ε (f) to ideal εopt(f) Establishing an objective function by taking a minimum mean square error function as a criterion, and taking the difference value delta esd of the objective function and each frequency bandnFor constraint, the total energy E of the signal is used as constraint, the sum of the sub-bandwidths meets the total bandwidth B as constraint, and a mathematical model for establishing the optimization problem is as follows:
Figure BDA0003375677130000066
s.t.max[Δesdn]≤μ,n＝0,1,...,N-1 0＜μ≤1
Figure BDA0003375677130000067
0＜Bn＜B,n＝0,1,...,N-1
Figure BDA0003375677130000068
wherein, Δ esdn＝|mean[ε(f)]-mean[εopt(f)]|,
Figure BDA0003375677130000069
And 5, solving the mathematical model of the optimization problem.
Because no prior information exists, a group of random values are taken as initial values of variables to be optimized in the step;
solving the constrained nonlinear programming optimization model by adopting a sequence quadratic programming SQP solving tool of MATLAB software to obtain a solved waveform sub-bandwidth vector P' of the orthogonal frequency division multiplexing linear frequency modulation signal:
P′＝[B′0,B′1,...,B′n,...,B′N-1]，
wherein, B'nIs the N +1 th optimized sub-bandwidth, N-0, 1, …, N-1.
And 6, calculating the optimized orthogonal frequency division multiplexing linear frequency modulation signal s' (t).
Determining the starting frequency f ' of the optimized sub-carrier according to the distribution value of the sub-bandwidth vector P ' after solution 'k,mAnd a frequency modulation rate r'k,m：
Figure BDA0003375677130000071
Wherein the content of the first and second substances,
Figure BDA0003375677130000072
the sub-bandwidth corresponding to the kth sub-carrier in the mth sub-pulse after optimization;
according to the starting frequency f 'of the optimized sub-carrier'k,mAnd a frequency modulation rate r'k,mObtaining an optimized orthogonal frequency division multiplexing linear frequency modulation signal s' (t):
Figure BDA0003375677130000073
the technical effects of the invention are further explained by simulation experiments as follows:
1. simulation conditions
Taking two orthogonal frequency division multiplexing chirp signals of 1 group of subcarriers and 2 groups of subcarriers, carrying out a simulation test on a computer by using MATLAB R2018b, wherein the parameters are shown in tables 1 and 2:
TABLE 1 simulation parameters for 1 set of subcarrier chirp signals
Bandwidth of 400MHz
Time width 8μs
Number of hour widths 8
Number of sub-bandwidths 8
Number of subcarrier groups 1
Frequency coding [8 6 1 3 5 4 2 7]
Noise power spectral density 1
Table 2 simulation parameters of 2 sets of subcarrier chirp signals
Bandwidth of 400MHz
Time width 8μs
Number of hour widths 8
Number of sub-bandwidths 8
Number of subcarrier groups 2
Frequency coding [5 7；4 1；7 3；1 5；3 8；2 6；8 4；6 2]
Noise power spectral density 1
2. Emulated content
Simulating 1, randomly generating a first group of noise, clutter signals and target impulse response, and calculating a corresponding spectral density function and an optimal waveform energy spectral density thereof, wherein the result is shown as a figure 4(a), and the optimal waveform spectral density function is used for designing an orthogonal frequency division multiplexing linear frequency modulation signal waveform to be optimized, which corresponds to the parameters in the table 1 and contains 1 group of subcarriers; randomly generating a second group of noise, clutter signals and target impulse response, and calculating a corresponding spectrum density function and an optimal waveform energy spectrum density thereof, wherein the result is shown in fig. 4(b), and the optimal waveform spectrum density function is used for designing the waveform of the orthogonal frequency division multiplexing linear frequency modulation signal to be optimized, which corresponds to the parameters in table 2 and contains 2 groups of subcarriers;
simulation 2, calculating a minimum mean square error function of a signal energy spectrum density function to be optimized and a corresponding optimal waveform energy spectrum density function thereof to obtain optimized signal waveform parameters, wherein the result is shown in fig. 5, wherein fig. 5(a) is an optimized waveform structure containing 1 group of subcarriers calculated by using the parameters of table 1, and fig. 5(b) is an optimized waveform structure containing 2 groups of subcarriers calculated by using the parameters of table 2;
simulation 3, calculating an energy spectrum density function of the optimized signal, wherein the result is shown in fig. 6, wherein fig. 6(a) is used for calculating the energy spectrum density of the optimized signal containing 1 group of subcarriers by using the parameters of table 1, and fig. 6(b) is used for calculating the energy spectrum density of the optimized signal containing 2 groups of subcarriers by using the parameters of table 2;
simulation 4, calculating the output signal-to-noise ratio of the optimized waveform, the output signal-to-noise ratio of the theoretical optimal waveform and the output signal-to-noise ratio of the original waveform, wherein the results are shown in fig. 7, wherein fig. 7(a) is the comparison of the optimized waveform containing 1 group of subcarriers, the theoretical optimal waveform and the output signal-to-noise ratio of the original waveform calculated by using the parameters in table 1, and fig. 7(b) is the comparison of the optimized waveform containing 2 groups of subcarriers, the theoretical optimal waveform and the output signal-to-noise ratio of the original waveform calculated by using the parameters in table 2;
3. analysis of simulation results
As can be seen from fig. 4, the energy spectrum densities of the optimal transmit waveforms are different under different target and clutter spectrum distributions, the distribution of the optimal waveform energy is mainly concentrated on the frequency band with stronger target energy, and in the frequency band with stronger clutter energy, the energy of the transmitted optimal waveform distribution is also very little even at the position where the target energy is also strong, which indicates that the waveform can effectively suppress clutter in the frequency domain.
As can be seen from fig. 6, the energy spectral density of the waveform obtained by the solution is substantially consistent with that of the theoretically optimal waveform, which illustrates the effectiveness of the optimization method of the present invention.
As can be seen from FIG. 7, compared with the orthogonal frequency division multiplexing linear frequency modulation signal waveform with equal bandwidth, the signal-to-noise ratio output by the designed target waveform in the optimization iteration is continuously increased and finally approaches the theoretically optimal signal-to-noise ratio, and the signal-to-noise ratio output in the whole process is improved by more than 2dB, which shows that the waveform can effectively suppress clutter and further improve the target detection performance of the radar.

Claims (5)

1. A non-uniform sub-bandwidth Orthogonal Frequency Division Multiplexing (OFDM) frequency modulation signal waveform optimization method is characterized by comprising the following steps:
1) acquiring an ideal waveform and an orthogonal frequency division multiplexing linear frequency modulation signal s (t) with a non-uniform distribution sub bandwidth under an optimal signal-to-noise-ratio criterion;
2) calculating the signal noise-to-noise ratio according to the clutter and the spectrum density function of the target, and calculating the energy spectrum density epsilon of the ideal waveform under the optimal signal noise-to-noise ratio criterionopt(f)；
3) Calculating the energy spectral density epsilon (f) of the waveform of the orthogonal frequency division multiplexing linear frequency modulation signal with the non-uniformly distributed sub-bandwidth;
4) taking a minimum mean square error function of the energy spectral density obtained by calculation in 2) and 3) as an objective function, taking total energy and total bandwidth of signals as constraints, and establishing a mathematical model of the following optimization problem:
Figure FDA0003375677120000011
s.t.max[Δesdn]≤μ,n＝0,1,...,N-1 0＜μ≤1
Figure FDA0003375677120000012
0＜Bn＜B,n＝0,1,...,N-1
Figure FDA0003375677120000013
wherein, Δ esdn＝|mean[ε(f)]-mean[εopt(f)]|,
Figure FDA0003375677120000014
B is the total bandwidth of the orthogonal frequency division multiplexing linear frequency modulation signal, and comprises N non-uniformly distributed sub-bandwidths; p is the sub-bandwidth vector to be optimized, BnIs the (N + 1) th sub-bandwidth, N0, 1., N-1; e is the total energy of the signal and mu is a positive number less than 1;
5) taking a group of random values as initial values of a sub-bandwidth vector P to be optimized, and solving the mathematical model in the step 4) through a sequence quadratic programming SQP solving tool of MATLAB software to obtain a sub-bandwidth vector P ' ═ B ' of the orthogonal frequency division multiplexing linear frequency modulation signal '0,B′1,...,B′n,...,B′N-1]；B′nIs the N +1 th optimized sub-bandwidth, N ═ 0, 1.., N-1;
6) and determining the initial frequency and the frequency modulation rate of the sub-carrier according to the distribution value of the sub-bandwidth vector P' to obtain the optimized orthogonal frequency division multiplexing linear frequency modulation signal.
2. The method of claim 1, wherein the orthogonal frequency division multiplexing chirp signal s (t) in 1) is represented as follows:
Figure FDA0003375677120000021
wherein the content of the first and second substances,
Figure FDA0003375677120000022
u (T) is a unit step function, TpIs M sub-time widths uniformly distributed in a pulse period, K is the number of sub-carriers in one sub-time width, fk,mIs the starting frequency, r, of the k sub-carrier within the m sub-pulsek,mF _ code, the modulation frequency of the k sub-carrier within the m sub-pulsek,mThe frequency of the k-th subcarrier within the m-th sub-pulse is encoded.
3. According to the rightThe method of claim 1, wherein the signal to noise ratio of 2) is calculated as a function of spectral density of the clutter and the target
Figure FDA0003375677120000023
Calculating ideal waveform energy spectrum density epsilon under the criterion of optimal signal-noise-ratioopt(f) The implementation is as follows:
3a) the computing system is at t0Signal-to-noise ratio of time instant output signal
Figure FDA0003375677120000024
Figure FDA0003375677120000025
Wherein, Pww(f) And Pnn(f) Power spectral density PSD, S of clutter and noise, respectively0(f) For radar emission of signals s0(t), h (f) is the frequency spectrum of the target impulse response h (t), r (f) is the frequency spectrum of the receive filter r (t);
3b) construction of the equation for | S according to the Lagrange multiplier method0(f)|2The objective function of (a) is:
Figure FDA0003375677120000026
wherein the content of the first and second substances,
Figure FDA0003375677120000027
is a known signal energy constraint;
3c) the derivative of the formula is equal to 0, and the energy spectrum density epsilon of the optimal transmitting signal is obtainedopt(f) Comprises the following steps:
Figure FDA0003375677120000031
4. the method of claim 1, wherein the energy spectral density e (f) of the non-uniformly distributed sub-bandwidth orthogonal frequency division multiplexing chirp signal waveform is calculated in 3) as follows:
Figure FDA0003375677120000032
wherein S (f) is the frequency spectrum of the OFDM chirp signal s (t),
Figure FDA0003375677120000033
Tpis M sub-time widths uniformly distributed in a pulse period, K is the number of sub-carriers in one sub-time width, BnIs the (N + 1) th sub-bandwidth, N0, 1., N-1; f. ofk,mIs the starting frequency, r, of the k sub-carrier within the m sub-pulsek,mF _ code, the modulation frequency of the k sub-carrier within the m sub-pulsek,mThe frequency of the k-th subcarrier within the m-th sub-pulse is encoded.
5. The method of claim 1, wherein 6) the start frequency and the tuning frequency of the sub-carriers are determined according to the distribution value of the sub-bandwidth vector P', by the following formula:
Figure FDA0003375677120000034
Figure FDA0003375677120000035
wherein the content of the first and second substances,
Figure FDA0003375677120000036
the sub-bandwidth T corresponding to the k sub-carrier in the m sub-pulse after optimizationpIs M sub-time widths, B 'uniformly distributed in the pulse period'nIs the n +1 sub-bandwidth of the sub-bandwidth vector P' after optimization，n＝0,1,...,N-1；f′k,mIs the optimized starting frequency of the k sub-carrier in the m sub-pulse'k,mF _ code optimized for the k sub-carrier within the m sub-pulsek,mThe frequency of the k-th subcarrier within the m-th sub-pulse is encoded.
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