CN103138799A - Modulation method of low sidelobe random frequency hopping pulse signal - Google Patents

Abstract

The invention provides a modulation method of a low sidelobe random frequency hopping pulse signal, relates to the modulation method of a frequency hopping pulse signal and solves the problems existing in a traditional modulation method of the low sidelobe random frequency hopping pulse signal that local accuracy optimization ability is bad, the modulation speed of the random frequency hopping pulse signal is low caused by low convergence speed. According to the modulation method of the low sidelobe random frequency hopping pulse, a self-correlation function of the random frequency hopping pulse signal is derived, the self-correlation function is used to calculate a deviation function of the random frequency hopping pulse signal and calculate an initialization frequency combination, the initialization frequency combination is brought into the deviation function to obtain an optimal frequency combination, stochastic disturbance is added, and the deviation function is updated. The updated deviation function is detected, a moment corresponding to the maximum value point of the deviation function is used, according to a gradient theory, the frequency combination is conducted with a-stage frequency adjustment, until a difference value of deviation functions of two adjacent stages is smaller than a set threshold, the frequency combination update is stopped, and the random frequency hopping pulse signal modulation is completed. The modulation method of the low sidelobe random frequency hopping pulse signal is applicable to the field of signal modulation.

Description

A kind of modulator approach of low secondary lobe random frequency hopping pulse signal

Technical field

The present invention relates to a kind of modulator approach of frequency hopping pulse signal.

Background technology

Radar gets its space and movable information by the echo of evaluating objects, in order to obtain the more accurate distance estimations of target, usually needs to launch the signal with larger bandwidth.The frequency stepped pulse trains signal is by the large resolution bandwidth of the synthetic acquisition of a plurality of narrow-band impulses, and its interpulse frequency interval is uniformly, and convenient owing to producing and processing, the frequency stepped pulse trains signal is widely applied in the high-resolution Range Imaging.But the first distance side lobe of frequency-stepped pulse signal is higher, Yue Da-13dB, and this causes adverse effect for the detection of weak target.In addition, for fear of fuzzy graing lobe of cycle occurring, also need to satisfy frequency step during the design frequency-stepped pulse signal and quantize interval and pulse duration product less than 1 parameter limit.If the interpulse frequency hopping interval of frequency hopping pulse signal is non-homogeneous, random, just obtain the random frequency hopping pulse signal, sort signal has jamproof potentiality.For the random frequency hopping pulse signal, because each pulse frequency in working band is random combine, the fuzzy graing lobe of its regularity will no longer occur, and corresponding distribution begins to be diffused as secondary lobe, and this makes the random frequency hopping pulse signal generally have higher side lobe levels.Distance side lobe to the random frequency hopping pulse signal suppresses and can process realization by mismatch, but this mode can cause the snr loss.The another kind of mode that reduces random frequency hopping pulse signal distance side lobe is Design of Signal, namely optimizes and chooses its frequency hopping combination used.

The random frequency hopping pulse signal modulation method of low secondary lobe roughly can be divided into two classes: 1, based on the relation of Fourier transform each other between signal auto-correlation function (being range ambiguity function) and power spectrum, construct a kind of central frequency distribution intensive, the sparse combination of frequency of band edge frequency distribution to be obtaining to have the random frequency hopping pulse signal of low distance side lobe, and it represents that method has nonlinear frequency modulation continuous wave pulse intercept method and based on the equal area partition method of window function.2, utilizing random intelligent evolution engine that this problem is optimized finds the solution.For first kind method, its realization is comparatively convenient, but because this class methods many places relate to approximate processing, it is difficult to obtain desired result when the pulse frequency number is less.For Equations of The Second Kind, because the problem equation of not requiring can be led continuously, random intelligent evolution technology is widely used in the multivariable optimization problem, but continuous for those problem equations and can lead situation, utilize the random frequency modulation on pulse signal modulating method of random intelligent evolution technology because there is local accurately optimizing ability, convergence rate causes the slow-footed problem of random frequency hopping pulse signal modulation slowly.

Summary of the invention

The present invention is local accurately optimizing ability for the random frequency hopping pulse signal modulation method that solves the low secondary lobe of tradition exists, convergence rate causes the slow problem of modulating speed of random frequency hopping pulse signal slowly, has proposed a kind of modulator approach of low secondary lobe random frequency hopping pulse signal.

The step of the modulator approach of a kind of low secondary lobe random frequency hopping pulse signal of the present invention:

A kind of modulator approach of low secondary lobe random frequency hopping pulse signal is characterized in that, its modulator approach is realized by following steps:

Step 1, will be to be modulated random frequency hopping pulse signal s (t) according to formula:

$\mathrm{\&chi;}\left(\mathrm{\&tau;}\right)=\frac{1}{N^2}{(1-\frac{\left|\mathrm{\&tau;}\right|}{T})}^2\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}{e}^{j2\mathrm{\&pi;}(f_n-f_m)\mathrm{\&tau;}}\left|\mathrm{\&tau;}\right|<T,---\left(1\right)$

Obtain the auto-correlation function χ (τ) of random frequency hopping pulse signal s (t) to be modulated, wherein, T is pulse duration, and N is the number of random frequency hopping pulse signal s (t) pulse within a signal period, f _nBe the frequency of n pulse within this signal period, f _mFrequency for m pulse within this signal period;

Step 2, the auto-correlation function χ (τ) that step 1 is obtained, according to formula:

E(τ)＝[χ(τ)-d(τ)] ² (2)

Obtain the departure function E (τ) of random frequency hopping pulse signal to be modulated, wherein, d (τ) is for having the target function of expectation sidelobe structure characteristics;

Step 3, utilize formula:

$\frac{i-1}{N-1}=\frac{f_{0,n}}{B}-\frac{k}{2\mathrm{\&pi;}}\sin \left(2\mathrm{\&pi;}\frac{{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA00002948214300012.png,HDA00002948214300021.png"\; state="\{\{state\}\}">f</figure-callout>}}_{0,n}}{B}\right)n=\mathrm{1,2},...,N---\left(3\right)$

Successively take step value as 21 k values of 0.1 selection, obtain 21 groups of initialization combination of frequencies in [0,2]; In formula, N is the pulse number in the signal period, and B is the bandwidth of random frequency hopping pulse signal;

The departure function E (τ) of the random frequency hopping pulse signal to be modulated that obtains in step 4,21 groups of initialization combination of frequencies substitution step 2 respectively that will obtain, obtain altogether 21 departure function E (τ), original frequency combination corresponding to departure function E (τ) that wherein side lobe levels is minimum made up f as optimum original frequency _0,1, f _0,2..., f _{0, N}

Step 5, the optimum initialization combination of frequency f that obtains to step 4 _0,1, f _0,2..., f _{0, N}Correspondence adds small random perturbation c successively ₁, c ₂..., c _N, obtain asymmetrical optimum initialization combination of frequency; Described small random perturbation c ₁, c ₂..., c _NIn c ₂..., c _N-1It is zero obeying average and mean square deviation is the normal distribution of B/ (20N), c ₁And c _NValue be zero;

The departure function E (τ) of the random frequency hopping pulse signal to be modulated that step 6, the asymmetrical optimum initialization combination of frequency substitution step 2 that step 5 is obtained obtain, the departure function E (τ) of random frequency hopping pulse signal to be modulated after obtaining to upgrade;

The peak point of departure function E (τ) output of random frequency hopping pulse signal to be modulated after upgrading in step 7, detecting step six, the peak value of the departure function E (τ) of random frequency hopping pulse signal to be modulated after main peak point is removed, detection error function E (τ) is in the output valve at main lobe width preset value D place simultaneously, relatively this output valve obtains maximum with the peak value of the departure function E (τ) that removes random frequency hopping pulse signal to be modulated after main peak point, thus moment τ corresponding to acquisition maximum _{I, max}

Step 8, moment τ that the maximum of departure function E (τ) is corresponding _{I, max}By the gradient principle, combination of frequency is carried out the frequency adjustment in a stage, a is the positive integer more than or equal to 2, and each stage obtains one group of combination of frequency after adjustment, obtains altogether the combination of frequency after a group is adjusted;

The departure function E (τ) of the random frequency hopping pulse signal to be modulated that the combination of frequency substitution step 2 after step 9, a group that step 8 is obtained are adjusted obtains obtains a departure function E (τ);

Whether the difference of the side lobe levels of adjacent two the departure function E of a departure function E (τ) (τ) that step 10, determining step nine obtain is less than setting threshold delta PSL, if judgment result is that be, the stop frequency combination is upgraded, combination of frequency after upgrading as modulation result, is completed the random frequency hopping pulse signal modulation; Otherwise, make a=a+1, carry out next stage and adjust, return to execution in step eight.

The present invention is a kind of modulator approach that is based upon on the gradient principle, with respect to existing method, result of use of the present invention is not subjected to the pulse frequency numeral system approximately, no matter the much equal amounts of calculation that can make of problem scale remain on less level to utilize simultaneously the gradient principle, accurately local accurate optimizing ability, compare with the random frequency hopping pulse signal modulation method of the low secondary lobe of tradition and adopt modulator approach of the present invention to make the convergence rate of random frequency hopping pulse signal improve approximately three orders of magnitude, to the saving on year-on-year basis consuming time of random frequency hopping pulse signal modulation more than 99%.

Description of drawings

Fig. 1 is the described random frequency hopping pulse signal of embodiment one carrier frequency varies schematic diagram.

Fig. 2 is the peak point output schematic diagram that has peak point in the described main lobe scope of embodiment one.

Fig. 3 is the peak point output schematic diagram that does not have peak point in the described main lobe scope of embodiment one.

Fig. 4 is the described main lobe division of embodiment one schematic diagram.

Fig. 5 is the random frequency hopping pulse signal target function schematic diagram with even sidelobe structure.

Fig. 6 is the signal target function schematic diagram with the sidelobe structure of successively decreasing.

Fig. 7 is N=64, and B=64kHz adjusts number of times in the adjustment process of employing the method for the invention during T=1ms and maximum adjustment amount concerns schematic diagram.

Fig. 8 is N=64, and B=64kHz adopts the adjustment number of times of the method for the invention and adjustment levelness to concern schematic diagram during T=1ms, in figure,

Curve 1 is the dynamic convergence curve of adjustment number of times and levelness,

Curve 2 keeps curve for the elite who adjusts number of times and levelness.

Fig. 9 is N=64, and B=64kHz adopts the method for the invention signal to be adjusted the oscillogram of acquisition during T=1ms.

Figure 10 is N=64, and B=64kHz adopts genetic algorithm signal to be adjusted the oscillogram of acquisition during T=1ms.

Figure 11 is N=64, B=64kHz, the secondary lobe oscillogram of successively decreasing that adopts the method for the invention to obtain during T=1ms.

Figure 12 is N=64, and B=64kHz adopts the secondary lobe part that the method for the invention obtains-5dB oscillogram that caves in during T=1ms.

Embodiment

Embodiment one, in conjunction with Fig. 1, Fig. 2, Fig. 3, Fig. 4, Fig. 5 and Fig. 6, present embodiment is described, the concrete steps of the modulator approach of the described a kind of low secondary lobe random frequency hopping pulse signal of present embodiment:

A kind of modulator approach of low secondary lobe random frequency hopping pulse signal is characterized in that, its modulator approach is realized by following steps:

Step 1, will be to be modulated random frequency hopping pulse signal s (t) according to formula:

$\mathrm{\&chi;}\left(\mathrm{\&tau;}\right)=\frac{1}{N^2}{(1-\frac{\left|\mathrm{\&tau;}\right|}{T})}^2\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}{e}^{j2\mathrm{\&pi;}(f_n-f_m)\mathrm{\&tau;}}\left|\mathrm{\&tau;}\right|<T,---\left(1\right)$

Obtain the auto-correlation function χ (τ) of random frequency hopping pulse signal s (t) to be modulated, wherein, T is pulse duration, and N is the number of random frequency hopping pulse signal s (t) pulse within a signal period, f _nBe the frequency of n pulse, f _mIt is the frequency of m pulse;

Described random frequency hopping pulse signal s (t) comprises N pulse in a wave period, the carrier frequency of each pulse is different, and pulse duration is T, and the pulse repetition period is T _r, the pulse repetition period is T _s=NT _r, an interior random frequency hopping pulse signal of signal period can be expressed as:

$s\left(t\right)=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{Ae}}^{j2\mathrm{\&pi;}{f}_{c}t}{e}^{j2\mathrm{\&pi;}{f}_{n}t}{\mathrm{rect}}_T(t-(n-1)T_r-\frac{T}{2})0\&le;t\&le;T_S$

Wherein, rect _T(t) being rectangular function, is 1 in-T/2＜t＜T/2, and all the other are zero.f _cBe signal carrier frequency, f _n(0≤n≤N) is each pulse frequency to ∈ [0, B], and B is frequency range; The carrier frequency varies of random frequency hopping pulse signal within a signal period, as shown in Figure 1;

Step 2, the auto-correlation function χ (τ) that step 1 is obtained, according to formula:

E(τ)＝[χ(τ)-d(τ)] ² (2)

Obtain the departure function E (τ) of random frequency hopping pulse signal to be modulated, wherein, d (τ) is for having the target function of expectation sidelobe structure characteristics;

Described target function with expectation sidelobe structure characteristics; Have the random frequency hopping pulse signal target function of even sidelobe structure, as shown in Figure 5, the concrete form of this function is:

$d\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}1,\left|\mathrm{\&tau;}\right|\&le;\mathrm{<figure-callout\; id="0"\; label="D"\; filenames="HDA00002948214300012.png,HDA00002948214300021.png"\; state="\{\{state\}\}">D</figure-callout>}\\ 0,D<\left|\mathrm{\&tau;}\right|<T\end{array}\right.$

Wherein, τ represents time variable,

Have the signal target function d (τ) of the sidelobe structure of successively decreasing, as shown in Figure 6, the concrete form of this function is:

$d\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{c}0\mathrm{dB},\left|\mathrm{\&tau;}\right|\&le;D\\ -110-10\left|\mathrm{\&tau;}\right|/\mathrm{TdB},D<\left|\mathrm{\&tau;}\right|<T\end{array}\right.$

Step 3, utilize formula:

$\frac{i-1}{N-1}=\frac{f_{0,n}}{B}-\frac{k}{2\mathrm{\&pi;}}\sin \left(2\mathrm{\&pi;}\frac{{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA00002948214300012.png,HDA00002948214300021.png"\; state="\{\{state\}\}">f</figure-callout>}}_{0,n}}{B}\right)n=\mathrm{1,2},...,N---\left(3\right)$

Successively take step value as 21 k values of 0.1 selection, obtain 21 groups of initialization combination of frequencies in [0,2]; In formula, N is the pulse number in the signal period, and B is the bandwidth of random frequency hopping pulse signal;

The departure function E (τ) of the random frequency hopping pulse signal to be modulated that obtains in step 4,21 groups of initialization combination of frequencies substitution step 2 respectively that will obtain, obtain altogether 21 departure function E (τ), original frequency combination corresponding to departure function E (τ) that wherein side lobe levels is minimum made up f as optimum original frequency _0,1, f _0,2..., f _{0, N}

Step 5, the optimum initialization combination of frequency f that obtains to step 4 _0,1, f _0,2..., f _{0, N}Correspondence adds small random perturbation c successively ₁, c ₂..., c _N, obtain asymmetrical optimum initialization combination of frequency; Described small random perturbation c ₁, c ₂..., c _NMiddle c ₂..., c _N-1It is zero obeying average and mean square deviation is the normal distribution of B/ (20N), c ₁And c _NValue be zero;

The departure function E (τ) of the random frequency hopping pulse signal to be modulated that step 6, the asymmetrical optimum initialization combination of frequency substitution step 2 that step 5 is obtained obtain, the departure function E (τ) of random frequency hopping pulse signal to be modulated after obtaining to upgrade;

The peak point of departure function E (τ) output of random frequency hopping pulse signal to be modulated after upgrading in step 7, detecting step six, the peak value of the departure function E (τ) of random frequency hopping pulse signal to be modulated after main peak point is removed, detection error function E (τ) is in the output valve at main lobe width preset value D place simultaneously, relatively this output valve obtains maximum with the peak value of the departure function E (τ) that removes random frequency hopping pulse signal to be modulated after main peak point, thus moment τ corresponding to acquisition maximum _{I, max}There is the side lobe peak point in main lobe width preset value D scope, and when this peak point is exported higher than the output of other peak point, as shown in Figure 2, this peak point can be adjusted reduction, output when the side lobe peak point that do not contain in main lobe width preset value D scope, as shown in Figure 3, main lobe width is retrained equally, effectively avoid main lobe separating phenomenon as shown in Figure 4, guaranteed the main lobe width requirement;

Step 8, utilize moment τ corresponding to maximum of departure function E (τ) _{I, max}, by the gradient principle, combination of frequency being carried out the adjustment of a stage frequency, a is the positive integer more than or equal to 2, obtains the combination of frequency after a group is adjusted;

Combination of frequency after step 9, a group that step 8 is obtained are adjusted is brought the departure function E (τ) of the random frequency hopping pulse signal to be modulated that step 2 obtains into, obtains a departure function E (τ);

Whether the difference of the side lobe levels of adjacent two the departure function E of a departure function E (τ) (τ) that step 10, determining step nine obtain is less than setting threshold delta PSL, if judgment result is that be, the stop frequency combination is upgraded, combination of frequency after upgrading as modulation result, is completed the random frequency hopping pulse signal modulation; Otherwise, make a=a+1, carry out next stage and adjust, return to execution in step eight.

Embodiment two, present embodiment are to the further illustrating of the modulator approach of the described a kind of low secondary lobe random frequency hopping pulse signal of embodiment one, the described moment τ that the maximum of departure function E (τ) is corresponding of step 8 _{I, max}By the gradient principle, combination of frequency is carried out the frequency adjustment in a stage, the method that obtains the combination of frequency after a group is adjusted is:

Steps A, moment τ that the maximum of departure function E (τ) is corresponding _{I, max}, according to formula:

$\mathrm{\&Delta;}{f}_{i,j}=\left\{\begin{array}{c}-\mathrm{\&eta;}\frac{\mathrm{dE}({\mathrm{\&tau;}}_{i,\max };\stackrel{\&OverBar;}{f})}{{\mathrm{df}}_j}|\stackrel{\&OverBar;}{f}={\stackrel{\&OverBar;}{f}}_i,j=\mathrm{2,3},...,N-1\\ 0,j=1,N\end{array}\right.---\left(4\right)$

Obtain current combination of frequency

Adjustment amount

Δ f _{I, j}It is the frequency adjustment amount of the i time iteration of j pulse; In formula, η is the stepping factor,

It is the combination of frequency of the i time iteration;

Step B, the current combination of frequency that utilizes steps A to obtain

Adjustment amount

According to formula:

${\stackrel{\&OverBar;}{f}}_{i+1}={\stackrel{\&OverBar;}{f}}_i+\mathrm{\&Delta;}{\stackrel{\&OverBar;}{f}}_i$

Combination of frequency is carried out L time upgrade, L=100 selects stepping factor η by steepest descent method, passes through formula:

$\frac{\mathrm{dE}({\mathrm{\&tau;}}_{i,\max };{\stackrel{\&OverBar;}{f}}_i+\mathrm{\&eta;\&Delta;}{\stackrel{\&OverBar;}{f}}_i)}{\mathrm{d\&eta;}}=0---\left(5\right)$

To combination of frequency

Carry out L time and adjust, obtain the adjustment amount of L combination of frequency

L=100 is to the peak frequency adjustment amount of each adjustment acquisition

Add up and average, obtaining L peak frequency adjustment amount

Average M;

Step C, with $\max \left[\mathrm{abs}\left(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{f}}_i\right)\right]=M/5^a,$ As maximum adjustment amount, will $\max \left[\mathrm{abs}\left(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{f}}_i\right)\right]=M/5^a$ Bring formula (4) into, to combination of frequency Carry out the adjustment of Q subgradient, Q 〉=100, the adjustment amount of Q combination of frequency of corresponding acquisition

And utilize formula

Combination of frequency is upgraded, obtains Q combination of frequency,

step D, Q the combination of frequency that step C is obtained be the departure function E (τ) of substitution random frequency hopping pulse signal to be modulated respectively, obtain Q departure function E (τ), record the result that occurs the optimum of side lobe levels in Q departure function E (τ), the elite who obtains departure function E (τ) keeps curve, until continuously W (W=100) inferior do not occur levelness lower as a result the time this stage adjust and finish, combination of frequency after the combination of frequency of selecting to occur in departure function E (τ) optimal result of side lobe levels was adjusted as a stage.

For performance of the present invention is described, adopt the optimum results of the inventive method and genetic algorithm to compare to 5 groups of different parameters simultaneously, the result that obtains in the test of homogeneous not due to random intelligent evolution technology is different, so different parameters is set to be utilized the method for the invention and adopts the modulator approach of random intelligent evolution technology respectively to move the result that obtains for 10 times and adjust the time used, as shown in table 1, in table 1 target function used as shown in Figure 2, main lobe width is set as D=2/B.

The modulator approach of table 1 the inventive method and the random intelligent evolution technology of employing is comparison sheet as a result

Can be accessed by table 1 adopts the method for the invention to modulate to signal the result that the result that obtains all is better than adopting the modulator approach of random intelligent evolution technology to obtain, especially count N when larger when pulse frequency, the side lobe levels that the method for the invention adjustment obtains adopts the modulator approach of random intelligent evolution technology that larger improvement is arranged, as N=64, B=64kHz, during T=1ms, the improvement amount of side lobe levels reaches 6.01dB.In addition, because the method for the invention is a kind of optimization method based on the gradient principle, its adjustment time is much smaller than the modulator approach time used of adopting random intelligent evolution technology, work as N=64, B=64kHz, adopt the adjustment process of the method for the invention during T=1ms as shown in Figure 7, and obtained the adjustment number of times of the method for the invention and adjust levelness concerning schematic diagram by Fig. 8.

Can find out from Fig. 9 and Figure 10, the time auto-correlation output of frequency hopping pulse signal all has smooth secondary lobe distributed architecture after the modulator approach adjustment of the method for the invention and the random intelligent evolution technology of employing.But the time auto-correlation output that the method for the invention adjustment obtains each side lobe peak point in the secondary lobe interval can reach par, has the low sidelobe structure on stricter Chebyshev's meaning by contrast.

Because auto-correlation output may not be optimal selection in the time of the inferior sidelobe structure of different occasions, we pass through to set expectation target function d (τ) realization to the control of signal distance ambiguity function sidelobe structure for this situation, as shown in FIG. 11 and 12, work as N=64, B=64kHz, during T=1ms, the adjustment with the sidelobe structure of successively decreasing waveform as a result as shown in figure 11, has the adjustment waveform of part-5dB sunk structure as shown in figure 12.Can find out that by Figure 11 and Figure 12 the method for the invention all has adjustment preferably to different sidelobe structure situations.

Claims (2)

1. the modulator approach of one kind low secondary lobe random frequency hopping pulse signal, is characterized in that, its modulator approach is realized by following steps:

Step 1, random frequency hopping pulse signal s (t) to be modulated are according to formula:

$\mathrm{\&chi;}\left(\mathrm{\&tau;}\right)=\frac{1}{N^2}{(1-\frac{\left|\mathrm{\&tau;}\right|}{T})}^2\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}{e}^{j2\mathrm{\&pi;}(f_n-f_m)\mathrm{\&tau;}}\left|\mathrm{\&tau;}\right|<T,---\left(1\right)$

Obtain the auto-correlation function χ (τ) of random frequency hopping pulse signal s (t) to be modulated, wherein, T is pulse duration, and N is the number of random frequency hopping pulse signal s (t) pulse within a signal period, f _nBe the frequency of n pulse within this signal period, f _mFrequency for m pulse within this signal period;

Step 2, the auto-correlation function χ (τ) that step 1 is obtained, according to formula:

E(τ)＝[χ(τ)-d(τ)] ² (2)

Obtain the departure function E (τ) of random frequency hopping pulse signal to be modulated, wherein, d (τ) is for having the target function of expectation sidelobe structure characteristics;

Step 3, utilize formula:

$\frac{i-1}{N-1}=\frac{f_{0,n}}{B}-\frac{k}{2\mathrm{\&pi;}}\sin \left(2\mathrm{\&pi;}\frac{f_{0,n}}{B}\right)n=\mathrm{1,2},...,N---\left(3\right)$

Successively take step value as 21 k values of 0.1 selection, obtain 21 groups of initialization combination of frequencies in [0,2]; In formula, N is the pulse number in the signal period, and B is the bandwidth of random frequency hopping pulse signal;

The departure function E (τ) of the random frequency hopping pulse signal to be modulated that obtains in step 4,21 groups of initialization combination of frequencies substitution step 2 respectively that will obtain, obtain altogether 21 departure function E (τ), original frequency combination corresponding to departure function E (τ) that wherein side lobe levels is minimum made up f as optimum original frequency _0,1, f _0,2..., f _{0, N}

Step 5, the optimum initialization combination of frequency f that obtains to step 4 _0,1, f _0,2..., f _{0, N}Correspondence adds small random perturbation c successively ₁, c ₂..., c _N, obtain asymmetrical optimum initialization combination of frequency; Described small random perturbation c ₁, c ₂..., c _NIn c ₂..., c _N-1It is zero obeying average and mean square deviation is the normal distribution of B/ (20N), c ₁And c _NValue be zero;

The departure function E (τ) of the random frequency hopping pulse signal to be modulated that step 6, the asymmetrical optimum initialization combination of frequency substitution step 2 that step 5 is obtained obtain, the departure function E (τ) of random frequency hopping pulse signal to be modulated after obtaining to upgrade;

The peak point of departure function E (τ) output of random frequency hopping pulse signal to be modulated after upgrading in step 7, detecting step six, the peak value of the departure function E (τ) of random frequency hopping pulse signal to be modulated after main peak point is removed, detection error function E (τ) is in the output valve at main lobe width preset value D place simultaneously, relatively this output valve obtains maximum with the peak value of the departure function E (τ) that removes random frequency hopping pulse signal to be modulated after main peak point, thus moment τ corresponding to acquisition maximum _{I, max}

Step 8, moment τ that the maximum of departure function E (τ) is corresponding _{I, max}By the gradient principle, combination of frequency is carried out the frequency adjustment in a stage, a is the positive integer more than or equal to 1, and each stage obtains one group of combination of frequency after adjustment, obtains altogether the combination of frequency after a group is adjusted;

The departure function E (τ) of the random frequency hopping pulse signal to be modulated that the combination of frequency substitution step 2 after step 9, a group that step 8 is obtained are adjusted obtains obtains a departure function E (τ);

Whether the difference of the side lobe levels of adjacent two the departure function E of a departure function E (τ) (τ) that step 10, determining step nine obtain is less than setting threshold delta PSL, if judgment result is that be, the stop frequency combination is upgraded, combination of frequency after upgrading as modulation result, is completed the random frequency hopping pulse signal modulation; Otherwise, make a=a+1, carry out next stage and adjust, return to execution in step eight.

2. the modulator approach of a kind of low secondary lobe random frequency hopping pulse signal described according to claim l, is characterized in that, the described moment τ that the maximum of departure function E (τ) is corresponding of step 8 _{I, max}By the gradient principle, combination of frequency is carried out the frequency adjustment in a stage, the method that obtains the combination of frequency after a group is adjusted is:

Steps A, moment τ that the maximum of departure function E (τ) is corresponding _{I, max}, according to formula:

$\mathrm{\&Delta;}{f}_{i,j}=\left\{\begin{array}{c}-\mathrm{\&eta;}\frac{\mathrm{dE}({\mathrm{\&tau;}}_{i,\max };\stackrel{\&OverBar;}{f})}{{\mathrm{df}}_j}|\stackrel{\&OverBar;}{f}={\stackrel{\&OverBar;}{f}}_i,j=\mathrm{2,3},...,N-1\\ 0,j=1,N\end{array}\right.---\left(4\right)$

Obtain current combination of frequency

Adjustment amount

Δ f _{I, j}It is the frequency adjustment amount of the i time iteration of j pulse; In formula, η is the stepping factor,

It is the combination of frequency of the i time iteration;

Step B, the current combination of frequency that utilizes steps A to obtain

Adjustment amount According to formula:

${\stackrel{\&OverBar;}{f}}_{i+1}={\stackrel{\&OverBar;}{f}}_i+\mathrm{\&Delta;}{\stackrel{\&OverBar;}{f}}_i$

Combination of frequency is carried out L time upgrade, L=100 selects stepping factor η by steepest descent method, passes through formula:

$\frac{\mathrm{dE}({\mathrm{\&tau;}}_{i,\max };{\stackrel{\&OverBar;}{f}}_i+\mathrm{\&eta;\&Delta;}{\stackrel{\&OverBar;}{f}}_i)}{\mathrm{d\&eta;}}=0---\left(5\right)$

To combination of frequency Carry out L time and adjust, obtain the adjustment amount of L combination of frequency

L=100 is to the peak frequency adjustment amount of each adjustment acquisition

Add up and average, obtaining L peak frequency adjustment amount Average M;

Step C, with $\max \left[\mathrm{abs}\left(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{f}}_i\right)\right]=M/5^a,$ As maximum adjustment amount, will $\max \left[\mathrm{abs}\left(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{f}}_i\right)\right]=M/5^a$ Bring formula (4) into, to combination of frequency

Carry out the adjustment of Q subgradient, Q 〉=100, the adjustment amount of Q combination of frequency of corresponding acquisition

And utilize formula

Combination of frequency is upgraded, obtain Q combination of frequency;

step D, Q the combination of frequency that step C is obtained be the departure function E (τ) of substitution random frequency hopping pulse signal to be modulated respectively, obtain Q departure function E (τ), record the result that occurs the optimum of side lobe levels in Q departure function E (τ), the elite who obtains departure function E (τ) keeps curve, until continuously W (W=100) inferior do not occur levelness lower as a result the time this stage adjust and finish, combination of frequency after the combination of frequency of selecting to occur in departure function E (τ) optimal result of side lobe levels was adjusted as a stage.

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