CN103235288A - Frequency domain based ultralow-sidelobe chaos radar signal generation and digital implementation methods - Google Patents

Abstract

The invention relates to frequency domain based ultralow-sidelobe chaos radar signal generation and digital implementation methods. The generation method includes the steps: firstly, generating a chaotic mapping sequence; secondly, starting from a frequency domain, enabling frequency domain amplitude of chaos radar signals to be constant, and utilizing the chaotic mapping sequence generated in the first step for frequency modulation of radar signals in a frequency domain form; and thirdly, taking the chaos radar signals generated in the second step as the frequency domain form of the radar signals, and performing inverse Fourier transformation to obtain a frequency domain form of frequency domain based ultralow-sidelobe chaos radar signals. The digital implementation method includes utilizing the frequency domain based ultralow sidelobe chaos radar signals generated by the generation method for quantization and truncation so as to achieve digital implementation of the frequency domain based ultralow-sidelobe chaos radar signals. The methods have the advantages that limitation that the chaos radar signals are high in sidelobe is solved, peak sidelobe ratio is decreased, detectability of dim targets can be enhanced, and the like.

Description

ULTRA-LOW SIDE LOBES chaos radar signal based on frequency domain generates and the Digital Implementation method

Technical field

The present invention relates to the chaos radar signal design field, particularly utilize the chaotic maps design based on the ULTRA-LOW SIDE LOBES chaos radar signal field of frequency domain in the noise radar.

Background technology

Noise radar be a kind of with noise source as transmitting or the radar of signal modulation format because the random nature that transmits, noise radar has very excellent low probability of intercept performance and electronics anti-jamming capacity.Its ambiguity function is desirable drawing pin type, has high distance and velocity resolution simultaneously.Therefore, as far back as the sixties in 20th century US and European some countries just given widely concern to noise radar.But, owing to be subjected to the restriction of manufacturing process and the technical merit of electronic devices and components at that time, substantially all be in the theoretical analysis stage for the research of noise radar.After the eighties in 20th century, along with the appearance of solid state microwave device and VLSI (very large scale integrated circuit) allows the realization of noise signal become possibility, just increase gradually for the action oriented research of noise radar.

Chaos is very general phenomenon of nature, and a large amount of dynamical systems of occurring in nature can be thought Chaos dynamic system.Chaotic signal is the noise-like signal that is produced by deterministic system, and chaotic signal has character such as initial value susceptibility, aperiodicity and long-term unpredictability.To the research of chaotic signal, launch from the later stage eighties.Leon O Chua has at first studied the chaos phenomenon in the second order digital filter, and uses the chaos digital wave filter to produce pseudo random number.People such as Torhu Kohda have studied the pseudo-random sequence that is produced by the chaos Nonlinear Mapping, have provided a simple adequate condition of this class mapping generation Bernoulli sequence.Than noise signal, chaotic signal is more prone to produce and control, utilizes chaotic signal to replace noise signal to realize that noise radar is a kind of good selection.

But the existing secondary lobe of the chaotic fm radar signal that chaos sequence obtains that utilizes is than higher.So proposed many improved methods.Document Bin, C., et al., Chaotic Signals with Weak-Structure Used for High Resolution Radar Imaging.2009:p.325-330. has proposed to utilize the weak structure characteristic to instruct the generation of chaotic maps, and has proposed multistage Bernoulli chaotic maps with this; Document Yang, J., et al.Frequency modulated radar signals based on high dimensional chaotic maps.in Signal Processing (ICSP), 2010IEEE10th International Conference on.2010. utilizes the higher-dimension chaotic maps to produce chaotic fm signal, reduces the secondary lobe of radar signal autocorrelation function with this; Document Yunkai, D., H.Yinghui, and G.Xupu, Hyper Chaotic Logistic Phase Coded Signal and Its Sidelobe Suppression.Aerospace and Electronic Systems, IEEE Transactions on, 2010.46 (2): p.672-686. utilize hyperchaos Logistic phase encoding to come suppressed sidelobes in conjunction with the Tikhonov method.

But said method does not take into full account the reason that secondary lobe produces.The inverse Fourier transform of the power spectrum density of the autocorrelation function of radar signal, the autocorrelation function of flat power spectral density correspondence are the desirable Dirac functions that does not have secondary lobe.Produce in the process of chaos radar signal at digital form, secondary lobe mainly contains two factors: power spectrum unevenness and the quantizing noise of signal model.In order to reduce the secondary lobe of chaos radar signal, can reduce quantizing noise by increasing the quantification word length on the hardware, but cost is bigger, effect is also undesirable.

Summary of the invention

The objective of the invention is to, utilizing the chaotic maps sequence to produce in the process of chaotic fm radar signal for overcoming prior art, the defective that the radar signal secondary lobe is higher the invention provides a kind of ULTRA-LOW SIDE LOBES chaos radar signal based on frequency domain and generates and the Digital Implementation method.

For achieving the above object, the invention provides a kind of ULTRA-LOW SIDE LOBES chaos radar signal generation method based on frequency domain, described method comprises following steps:

Step 1) produces the chaotic maps sequence: the form of one-dimensional discrete chaotic maps is written as f: φ → φ, the mapping function of this one-dimensional discrete chaotic maps represents to be written as φ _N+1=g (φ _n), it utilizes described mapping function to try to achieve the chaotic maps sequence

Initial value φ (0)=φ with seasonal described one-dimensional discrete chaotic maps ₀Be the stochastic variable in the codomain scope; φ wherein _N+1Be stochastic variable φ _nUpdating value after the conversion of one-dimensional discrete chaotic maps, g () is the Nonlinear Mapping function, makes the chaotic maps sequence

Has fractal characteristic.Described chaotic maps sequence comprises Bernoulli Jacob (Bernoulli) sequence of mapping, logistic (Logistic) sequence of mapping and tent (Tent) sequence of mapping;

Step 2) the chaotic maps sequence of utilizing step 1) to produce is carried out signal frequency modulation, obtains the chaotic fm radar signal:

From frequency domain, the frequency domain amplitude that makes chaos radar signal is constant, utilizes the chaotic maps sequence that the radar signal of frequency domain form is carried out frequency modulation simultaneously, and the general expression-form based on the chaotic fm radar signal of frequency domain of generation is:

S(f)＝Aexp[j2πKΦ(f)]，

Wherein j is imaginary number, and A is the amplitude of radar signal frequency domain form, and K is modulation index, and Φ (f) is the phase place of radar signal frequency domain form,

Satisfy simultaneously:

Be the one dimension chaotic maps sequence of frequency domain form, f is the variable of frequency domain form, and K φ (f) is the rate of change of radar signal frequency domain form phase place, i.e. the frequency of radar signal frequency domain form, and the corresponding time domain scope of this chaos radar signal is:

Kφ _min≤t≤Kφ _max，

T represents the time, is the variable of time domain form,

T with

Be relation of equal value, because the frequency response of frequency domain form is exactly the time on time domain.

Produce the radar signal of described frequency domain form by the Digital Discrete mode, the discrete expression form of the described chaotic fm radar signal based on frequency domain that then obtains is: $\begin{array}{c}S\left(\mathrm{n\Δf}\right)=\mathrm{Aexp}\left(j2\mathrm{\πK\Φ}(\mathrm{n\Δf}\right)\\ =\mathrm{Aexp}\left(j2\mathrm{\πK}\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\φ}}_k\mathrm{\Δf}\right)\end{array}$ ,n∈[0,N-1]

Namely

Wherein N is the number of sampled point, φ _kBe the value in the discrete chaos sequence, Δ f is the frequency resolution of radar signal, and integration is limited to [0, B] interval, and wherein B is the bandwidth of signal, and has:

$\mathrm{\Δf}=\frac{B}{N},$

The range resolution of this radar signal is:

$\mathrm{\Δr}=\frac{c}{2B};$

Step 3) is with step 2) the chaotic fm radar signal that produces is as the frequency domain form of radar signal, carries out inverse Fourier transform, obtains the time domain form based on the ULTRA-LOW SIDE LOBES chaos radar signal of frequency domain:

The chaos radar signal based on frequency domain form that obtains behind the chaotic maps sequence frequency modulation is carried out inverse Fourier transform, and the general expression-form that obtains the chaos radar signal of time domain form is:

s(t)＝F ^-1{S(f)}＝F ^-1{Aexp[j2πKΦ(f)]}，

Then have, to the chaos radar signal based on frequency domain form that obtains behind the discrete chaotic maps sequence frequency modulation inverse Fourier transform of dispersing, the expression-form that obtains the discrete chaos radar signal of time domain form becomes:

$s\left(n\right)=\mathrm{IDFT}\left\{S\left(n\right)\right\}$

$=\mathrm{IDFT}\left\{\mathrm{Aexp}\left(j2\mathrm{\π}\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\φ}}_k\right)\right\}$

$=\frac{1}{N}\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}A\·\exp \left(j2\mathrm{\πK}\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\φ}}_k\right)\·\exp \left(j\frac{2\mathrm{\πnm}}{N}\right)$

Corresponding signal duration and time sampling interval are respectively:

$T_r=\frac{1}{\mathrm{\Δf}}=\frac{N}{B},$

$\mathrm{\Δt}=\frac{T_r}{B}=\frac{1}{B}.$

Based on the above-mentioned ULTRA-LOW SIDE LOBES chaos radar signal generation method based on frequency domain, the present invention also provides a kind of ULTRA-LOW SIDE LOBES chaos radar signal Digital Implementation method based on frequency domain, utilize the resulting ULTRA-LOW SIDE LOBES chaos radar signal based on frequency domain of the ULTRA-LOW SIDE LOBES chaos radar signal generation method based on frequency domain of the present invention to quantize and block, obtain the Digital Implementation based on the ULTRA-LOW SIDE LOBES chaos radar signal of frequency domain;

As the improvement project of above-mentioned technology, described quantification realizes with 14 word lengths;

As the improvement project of above-mentioned technology, described threshold value of blocking is elected 3 δ as.

Compared with prior art, the invention has the advantages that:

The present invention can overcome in having the process of utilizing the chaotic maps sequence to produce chaos radar signal now, the defective that secondary lobe is higher.The ULTRA-LOW SIDE LOBES chaos radar signal based on frequency domain that the present invention produces has smooth power spectrum density, extremely low peak sidelobe ratio (PSLR), the ambiguity function that has desirable drawing pin type simultaneously.The I/Q road of radar signal time domain form has with the similar pseudo-phase space structure of Gaussian noise close to normal distribution.The chaos radar signal that the present invention produces has the ability of stronger detection weak target, simultaneously, has stronger antijamming capability and low probability of intercept characteristic.

Description of drawings

Fig. 1 is the ULTRA-LOW SIDE LOBES chaos radar signal generation based on frequency domain of the present invention and the structural representation of Digital Implementation method.

Fig. 2 is based on the ULTRA-LOW SIDE LOBES chaos radar signal time domain form of frequency domain.

Fig. 3 is based on the probability distribution of the time domain form amplitude of frequency domain chaos radar signal.

Fig. 4 is based on the autocorrelation function of the time domain form of frequency domain chaos radar signal.

Fig. 5 is based on the ambiguity function of frequency domain chaos radar signal.

Fig. 6 is based on the distance of frequency domain chaos radar signal ambiguity function to the cross section.

Fig. 7 is quantification and blocks the back based on frequency domain chaos radar signal time domain form.

Fig. 8 is quantification and blocks the back based on frequency domain chaos radar signal autocorrelation function.

Fig. 9 is quantification and blocks the back based on the power spectrum density of frequency domain chaos radar signal.

Figure 10 is quantification and blocks the back based on the ambiguity function of frequency domain chaos radar signal.

Figure 11 be quantize and block the back based on the distance of frequency domain chaos radar signal ambiguity function to the cross section.

The hardware that Figure 12 is based on the chaos radar signal of frequency domain bears results and the performance comparison.

Embodiment

Below in conjunction with the drawings and specific embodiments a kind of generation of ULTRA-LOW SIDE LOBES chaos radar signal and Digital Implementation method based on frequency domain of the present invention described in further detail.

Shown in Figure 1, the invention provides a kind of ULTRA-LOW SIDE LOBES chaos radar signal generation method based on frequency domain, described method comprises following steps:

Step 1) produces the chaotic maps sequence:

The form of one-dimensional discrete chaotic maps is written as f: φ → φ, the mapping function of this one-dimensional discrete chaotic maps represents to be written as φ _N+1=g (φ _n), it utilizes described mapping function to try to achieve the chaotic maps sequence

Initial value φ (0)=φ with seasonal described one-dimensional discrete chaotic maps ₀Be the stochastic variable in the codomain scope, because chaotic maps can not change probability density function, initial value has at random guaranteed that chaos sequence is a stationary stochastic process.

φ wherein _N+1Be stochastic variable φ _nUpdating value after the conversion of one-dimensional discrete chaotic maps, g () is the Nonlinear Mapping function, makes the chaotic maps sequence

Has fractal characteristic.Described chaotic maps sequence comprises Bernoulli Jacob (Bernoulli) sequence of mapping, logistic (Logistic) sequence of mapping and tent (Tent) sequence of mapping.

Above-mentioned three kinds of one dimension chaotic maps are represented to concern as shown in the table:

By last table as can be known: for Bernoulli Jacob (Bernoulli) mapping, the codomain scope is

Carry out step 2) the radar signal frequency modulation of frequency domain form before, need carry out following conversion earlier:

φ _n'＝φ _n+0.5

φ wherein _n' be Bernoulli Jacob (Bernoulli) sequence of mapping φ _nUpdating value before carrying out frequency domain form radar signal frequency modulation guarantees that the chaos sequence codomain that frequency modulation is used is [0,1].

Step 2) the chaotic maps sequence of utilizing step 1) to produce is carried out signal frequency modulation, obtains the chaotic fm radar signal:

According to Wei Na-khintchine's theorem, the autocorrelation function of radar signal is the inverse Fourier transform of power spectrum density.When power spectrum density was constant, the autocorrelation function of radar signal was desirable delta function.For the autocorrelation function of the radar signal that makes design has low secondary lobe, need make radar signal have smooth power spectrum density.Therefore, we are in the process of design ULTRA-LOW SIDE LOBES chaos radar signal, from frequency domain, the frequency domain amplitude that makes chaos radar signal is constant, utilize the chaotic maps sequence that the radar signal of frequency domain form is carried out frequency modulation simultaneously, the general expression-form based on the chaotic fm radar signal of frequency domain of generation is:

S(f)＝Aexp[j2πKΦ(f)]，

Wherein j is imaginary number, and A is the amplitude of radar signal frequency domain form, and K is modulation index, and Φ (f) is the phase place of radar signal frequency domain form,

Satisfy simultaneously:

Be the one dimension chaotic maps sequence of frequency domain form, f is the variable of frequency domain form, and K φ (f) is the rate of change of radar signal frequency domain form phase place, i.e. the frequency of radar signal frequency domain form.

The power spectrum density of radar signal is:

P(S(f))＝|S(f)| ²＝|Aexp[j2πKΦ(f)]| ²＝A ²

Obviously, the chaos radar signal that designs with said method has smooth power spectrum density.

Simultaneously, the corresponding time domain scope of this chaos radar signal is:

Kφ _min≤t≤Kφ _max，

T represents the time, is the variable of time domain form,

T with

Be relation of equal value, because the frequency response of frequency domain form is exactly the time on time domain.

Produce the radar signal of described frequency domain form by the Digital Discrete mode, the discrete expression form of the described chaotic fm radar signal based on frequency domain that then obtains is:

$S\left(\mathrm{n\Δf}\right)=\mathrm{Aexp}\left(j2\mathrm{\πK\Φ}(\mathrm{n\Δf}\right)$

,n∈[0,N-1]

$=\mathrm{Aexp}\left(j2\mathrm{\πK}\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\φ}}_k\mathrm{\Δf}\right)$

Namely

Wherein N is the number of sampled point, φ _kBe the value in the discrete chaos sequence, Δ f is the frequency resolution of radar signal, and integration is limited to [0, B] interval, and wherein B is the bandwidth of signal, and has:

$\mathrm{\Δf}=\frac{B}{N},$

The range resolution of this radar signal is:

$\mathrm{\Δr}=\frac{c}{2B};$

Step 3) is with step 2) the chaotic fm radar signal that produces is as the frequency domain form of radar signal, carries out inverse Fourier transform, obtains the time domain form based on the ULTRA-LOW SIDE LOBES chaos radar signal of frequency domain:

The chaos radar signal based on frequency domain form that obtains behind the chaotic maps sequence frequency modulation is carried out inverse Fourier transform, and the general expression-form that obtains the chaos radar signal of time domain form is:

s(t)＝F ^-1{S(f)}＝F ^-1{Aexp[j2πKΦ(f)]}，

Then have, to the chaos radar signal based on frequency domain form that obtains behind the discrete chaotic maps sequence frequency modulation inverse Fourier transform of dispersing, the expression-form that obtains the discrete chaos radar signal of time domain form becomes:

$s\left(n\right)=\mathrm{IDFT}\left\{S\left(n\right)\right\}$

$=\mathrm{IDFT}\left\{\mathrm{Aexp}\left(j2\mathrm{\π}\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\φ}}_k\right)\right\}$

$=\frac{1}{N}\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}A\·\exp \left(j2\mathrm{\πK}\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\φ}}_k\right)\·\exp \left(j\frac{2\mathrm{\πnm}}{N}\right)$

Corresponding signal duration and time sampling interval are respectively:

$T_r=\frac{1}{\mathrm{\Δf}}=\frac{N}{B},$

$\mathrm{\Δt}=\frac{T_r}{B}=\frac{1}{B}.$

After the chaotic maps sequence carried out frequency modulation to the radar signal of frequency domain form, carry out inverse Fourier transform again, just can obtain the time domain form based on the chaos radar signal of frequency domain.The duration of radar signal is 40us in the emulation, and the number of sampled point is 800, and corresponding signal bandwidth is 20MHz; Simultaneously, the amplitude variance of the radar signal time domain in the emulation is

As shown in Figure 2, in emulation, use mutually homoscedastic Gaussian noise as a comparison, three kinds of envelope relations based on the chaos radar signal of frequency domain are inconsistent, and Bernoulli Jacob (Bernoulli) mapping is more smooth than the chaotic radar letter envelope of logistic (Logistic) mapping and tent (Tent) mapping generation, simultaneously also more close to Gaussian noise.And the chaos radar signal that logistic (Logistic) mapping and tent (Tent) mapping generate has the envelope of fluctuating.

Fig. 3 has showed the probability distribution based on the chaos radar signal time domain form of frequency domain, probability density distribution with Gaussian noise contrasts simultaneously, as seen from Figure 3, chaos radar signal and the Gaussian noise based on Bernoulli Jacob (Bernoulli) mapping has very approaching probability density distribution.Simultaneously, the probability density distribution of the chaos radar signal of this base of a fruit of logic-based (Logistic) mapping and tent (Tent) mapping also has similar shapes, and just probability density distribution is narrower, higher.

The autocorrelation function of noise radar has reflected the characteristic of distance to resolution.As seen from Figure 4, based on the PSLR of the autocorrelation function of the chaos radar signal of frequency domain all-below the 30dB.In the application of radar high-resolution imaging, can avoid weak target to be covered by the secondary lobe of strong scattering target on every side significantly, thereby improve the accuracy of radar imagery.

Fig. 5 and Fig. 6 have showed the ambiguity function based on the frequency domain chaos radar signal respectively, and corresponding distance is to the cross section.As we can see from the figure, the resolution of radar signal correspondence is 7.5m, just is the resolution of 20MHz bandwidth correspondence.As seen from Figure 6, about-300dB, this can consider the influence of secondary lobe fully to the PSLR in cross section for chaos radar signal distance.This is that the zero Doppler cross section that obtains through inverse Fourier transform should be desirable delta function because the power spectrum density of radar signal is normal value.And the zero Doppler cross section of Gaussian noise signal ambiguity function has only-50dB about, this causes owing to power spectrum is uneven.

Shown in Figure 1, based on the above-mentioned ULTRA-LOW SIDE LOBES chaos radar signal generation method based on frequency domain, the present invention also provides a kind of ULTRA-LOW SIDE LOBES chaos radar signal Digital Implementation method based on frequency domain, utilize the resulting ULTRA-LOW SIDE LOBES chaos radar signal based on frequency domain of the ULTRA-LOW SIDE LOBES chaos radar signal generation method based on frequency domain of the present invention to quantize and block, obtain the Digital Implementation based on the ULTRA-LOW SIDE LOBES chaos radar signal of frequency domain.

Under many circumstances, chaos radar signal produces by digital form, then through launching by up-conversion after the digital-to-analog conversion again.Because current DDS(Direct Digital frequency synthesis) quantification word length generally is 14 to the maximum, therefore considers also to quantize to realize with 14 word lengths based on the chaos radar signal of frequency domain.

For the radar signal with normal distribution, owing to there is a spot of sampled point to have very large amplitude, if we do not quantize all amplitudes with not blocked, so, under the same signal amplitude situation of DDS output, average power can be very little.In order to improve average power, we block the ULTRA-LOW SIDE LOBES chaos radar signal based on frequency domain.By the standardized normal distribution table as can be known, the probability of signal amplitude in 3 δ reached more than 99%, therefore, the threshold value of blocking is chosen as 3 δ, wherein δ is the standard deviation of the amplitude of described ULTRA-LOW SIDE LOBES chaos radar signal time domain form based on frequency domain, can try one's best like this and not destroy the probability distribution of chaos radar signal.Thereby under DDS output same signal amplitude situation, increase the average power of output, thereby improve signal to noise ratio (S/N ratio).

Quantize and block after the result as shown in Figure 7, through after quantizing and blocking, do not have what variation substantially based on the chaos radar signal of Bernoulli Jacob (Bernoulli) mapping.To block effect apparent in view and this base of a fruit of logic-based (Logistic) mapping and tent (Tent) shine upon, and the peak value of the time domain amplitude of radar signal changes to 1 from 1.5.

Fig. 8 showed quantize and block after the chaos radar signal autocorrelation function, as seen from Figure 8, what variation the autocorrelation function of radar signal does not have substantially.The PSLR of the autocorrelation function of the chaos radar signal of three kinds of mappings all-below the 30dB.

Fig. 9 represented to quantize and block after the chaos radar signal power spectrum density.Because the influence that quantizes and block, radar signal changes, and it is uneven that smooth power spectrum density becomes.Truncation effect based on the chaos radar signal of Bernoulli Jacob (Bernoulli) mapping is not obvious, and the power spectrum density fluctuation mainly causes by quantizing, and fluctuation range is in 2dB; The chaos radar signal power spectrum fluctuation of this base of a fruit of logic-based (Logistic) mapping and tent (Tent) mapping is by quantification and block due to the acting in conjunction, and fluctuation range is in 4dB; And the power spectrum density fluctuation range of Gaussian noise has surpassed 10dB.

Figure 10 and Figure 11 have represented respectively to quantize and have blocked back chaos radar signal ambiguity function and corresponding distance to the cross section.Can see that from Figure 10 and Figure 11 after quantification and blocking, the resolution character of radar signal does not change, and all is the 7.5m of 20MHz correspondence.But, because the power spectrum density of radar signal no longer is normal value, thereby cause the PSLR of radar signal to increase.Wherein, PSLR to the cross section is lower than-40dB based on the distance of the chaos radar signal ambiguity function of Bernoulli Jacob (Bernoulli) mapping, the PSLR that this base of a fruit of logic-based (Logistic) mapping and tent (Tent) shine upon is lower than-30dB, and the peak value secondary lobe of Gaussian noise has only-26dB about.Wherein the peak sidelobe ratio of the chaos radar signal that produces of Bernoulli Jacob (Bernoulli) mapping is lower than-40dB, this be more smooth than all the other several signals by its power spectrum due to.

Use Tektronix MSO70404 to gather the chaos radar signal based on frequency domain that DDS produces, and itself and warble (Chirp) signal and Gaussian noise are compared.The signal that collects is carried out matched filtering and relevant treatment, the result as shown in figure 12, the waveform sectional drawing of left column for gathering is respectively I road and the Q road of radar signal, the centre is classified the auto-correlation processing result as, right column is the result of matched filtering.

After 5 kinds of signals that oscillograph is collected carried out relevant treatment respectively, the peak sidelobe ratio of warble (Chirp), Bernoulli Jacob (Bernoulli), logistic (Logistic), tent (Tent) and Gaussian noise (gauss noise) was respectively :-13.8dB ,-28.51dB ,-26.54dB ,-27.24dB ,-20.94dB.After the matched filtering processing, the peak sidelobe ratio of 5 kinds of signals is respectively :-13.78dB ,-35.9dB ,-31.21dB ,-32.1dB ,-20.21dB.This experiment has proved absolutely the outstanding low sidelobe performance based on the chaos radar signal model of frequency domain.

In a word, the invention provides a kind of ULTRA-LOW SIDE LOBES chaos radar signal based on frequency domain and generate and the Digital Implementation method, wherein, carry out signal frequency modulation with the chaotic maps sequence, with the frequency domain form of the signal behind the frequency modulation as radar signal.Obtain the time domain form of radar signal through inverse Fourier transform then, namely based on the ULTRA-LOW SIDE LOBES chaos radar signal of frequency domain.This method has smooth power spectrum density than traditional chaotic fm radar signal, thereby makes the secondary lobe of related function lower.The higher limitation of secondary lobe when the invention solves chaos radar signal can increase the detectability of weak target, promotes anti-electromagnetic interference (EMI) and the low probability of intercept characteristic of radar signal simultaneously.

It should be noted last that above embodiment is only unrestricted in order to technical scheme of the present invention to be described.Although the present invention has been described in detail with reference to embodiment, those of ordinary skill in the art is to be understood that, technical scheme of the present invention is made amendment or is equal to replacement, do not break away from the spirit and scope of technical solution of the present invention, it all should be encompassed in the middle of the claim scope of the present invention.

Claims (9)

1. ULTRA-LOW SIDE LOBES chaos radar signal generation method based on frequency domain comprises following steps:

Step 1) produces the chaotic maps sequence;

Step 2) from frequency domain, the frequency domain amplitude that makes chaos radar signal is constant, and the chaotic maps sequence of utilizing step 1) to produce is simultaneously carried out frequency modulation to the radar signal of frequency domain form, obtains the chaotic fm radar signal based on frequency domain;

Step 3) is with step 2) the chaotic fm radar signal that produces is as the frequency domain form of radar signal, carries out inverse Fourier transform, obtains the time domain form based on the ULTRA-LOW SIDE LOBES chaos radar signal of frequency domain.

2. a kind of ULTRA-LOW SIDE LOBES chaos radar signal generation method based on frequency domain according to claim 1 is characterized in that described chaotic maps sequence comprises Bernoulli Jacob's sequence of mapping, logistic sequence of mapping and tent sequence of mapping.

3. a kind of ULTRA-LOW SIDE LOBES chaos radar signal generation method based on frequency domain according to claim 2 is characterized in that for described Bernoulli Jacob's sequence of mapping, the codomain scope is

Before carrying out the radar signal frequency modulation of frequency domain form, need to carry out earlier following conversion:

φ _n'＝φ _n+0.5，

φ wherein _n' be Bernoulli Jacob's sequence of mapping φ _nUpdating value before carrying out frequency domain form radar signal frequency modulation guarantees that the chaos sequence codomain that frequency modulation is used is [0,1].

4. a kind of ULTRA-LOW SIDE LOBES chaos radar signal generation method based on frequency domain according to claim 1, it is characterized in that, comprise in the described step 1): the form of one-dimensional discrete chaotic maps is written as f: φ → φ, the mapping function of this one-dimensional discrete chaotic maps represents to be written as φ _N+1=g (φ _n), it utilizes described mapping function to try to achieve the chaotic maps sequence

Initial value φ (0)=φ with seasonal described one-dimensional discrete chaotic maps ₀Be the stochastic variable in the codomain scope; φ wherein _N+1Be stochastic variable φ _nUpdating value after the conversion of one-dimensional discrete chaotic maps, g () is the Nonlinear Mapping function, makes the chaotic maps sequence

Has fractal characteristic.

5. a kind of ULTRA-LOW SIDE LOBES chaos radar signal generation method based on frequency domain according to claim 1 is characterized in that described step 2) in the general expression-form based on the chaotic fm radar signal of frequency domain that obtains be:

S(f)＝Aexp[j2πKΦ(f)]，

Wherein j is imaginary number, and A is the amplitude of radar signal frequency domain form, and K is modulation index, and Φ (f) is the phase place of radar signal frequency domain form,

Satisfy simultaneously:

φ

(f) be the one dimension chaotic maps sequence of frequency domain form, f is the variable of frequency domain form, and K φ (f) is the rate of change of radar signal frequency domain form phase place, i.e. the frequency of radar signal frequency domain form, and the corresponding time domain scope of this chaos radar signal is:

Kφ _min≤t≤Kφ _max，

T represents the time, is the variable of time domain form, and t and K φ (f) are relations of equal value, because the frequency response of frequency domain form is exactly the time on time domain.

6. a kind of ULTRA-LOW SIDE LOBES chaos radar signal generation method based on frequency domain according to claim 5, it is characterized in that, produce the radar signal of described frequency domain form by the Digital Discrete mode, the discrete expression form of the described chaotic fm radar signal based on frequency domain that then obtains is:

$S\left(\mathrm{n\Δf}\right)=\mathrm{Aexp}\left(j2\mathrm{\πK\Φ}(\mathrm{n\Δf}\right)$

,n∈[0,N-1]

$=\mathrm{Aexp}\left(j2\mathrm{\πK}\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\φ}}_k\mathrm{\Δf}\right)$

Namely

Wherein N is the number of sampled point, φ _kBe the value in the discrete chaos sequence, Δ f is the frequency resolution of radar signal, and integration is limited to [0, B] interval, and wherein B is the bandwidth of signal, and has:

$\mathrm{\Δf}=\frac{B}{N},$

The range resolution of this radar signal is:

$\mathrm{\Δr}=\frac{c}{2B}.$

7. a kind of ULTRA-LOW SIDE LOBES chaos radar signal generation method based on frequency domain according to claim 1 or 5 is characterized in that, obtains in the described step 3) based on the general expression-form of the time domain of the ULTRA-LOW SIDE LOBES chaos radar signal of frequency domain being:

s(t)＝F ^-1{S(f)}＝F ^-1{Aexp[j2πKΦ(f)]}，

Then have, to the chaos radar signal based on frequency domain form that obtains behind the discrete chaotic maps sequence frequency modulation inverse Fourier transform of dispersing, the expression-form that obtains the discrete chaos radar signal of time domain form becomes:

$S\left(n\right)=\mathrm{IDFT}\left\{S\left(n\right)\right\}$

$=\mathrm{IDFT}\left\{\mathrm{Aexp}\left(j2\mathrm{\π}\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\φ}}_k\right)\right\}$

$=\frac{1}{N}\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}A\·\exp \left(j2\mathrm{\πK}\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\φ}}_k\right)\·\exp \left(j\frac{2\mathrm{\πnm}}{N}\right)$

Corresponding signal duration and time sampling interval are respectively:

$T_r=\frac{1}{\mathrm{\Δf}}=\frac{N}{B},$

$\mathrm{\Δt}=\frac{T_r}{N}=\frac{1}{B}.$

8. ULTRA-LOW SIDE LOBES chaos radar signal Digital Implementation method based on frequency domain, utilize the resulting ULTRA-LOW SIDE LOBES chaos radar signal based on frequency domain of the described ULTRA-LOW SIDE LOBES chaos radar signal generation method based on frequency domain of one of claim 1-7 to quantize and block, obtain the Digital Implementation based on the ULTRA-LOW SIDE LOBES chaos radar signal of frequency domain.

9. a kind of ULTRA-LOW SIDE LOBES chaos radar signal Digital Implementation method based on frequency domain according to claim 8, it is characterized in that, described threshold value of blocking is elected 3 δ as, and wherein δ is the standard deviation of the amplitude of described ULTRA-LOW SIDE LOBES chaos radar signal time domain form based on frequency domain.

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