CN101951276B - Method for detecting and suppressing Gaussian fitting linear frequency-modulated jamming in direct sequence spread spectrum (DSSS) communication system - Google Patents

Abstract

The invention provides a method for detecting and suppressing Gaussian fitting linear frequency-modulated jamming in a direct sequence spread spectrum (DSSS) communication system. The characteristic that data frequency spectrum transmitted in an information channel in the DSSS communication system is similar to white noise is used, if the linear frequency-modulated jamming is exerted, a strong peak value exists on an instantaneous energy frequency spectrum and an obvious peak value line exists in a time-frequency energy distribution plane. At the receiving end of the DSSS communication system, the extreme point of each time point in the time-frequency energy distribution plane is tracked, so that the track of the peak value line is obtained. A linear regression technology is used to acquire parameters of the peak value so as to roughly estimate linear frequency-modulated slope rate and rotation angle alpha of fractional Fourier transform. According to the parameter alpha, the fractional Fourier transform is carried out on a signal, and an iterative Gaussian fitting process is used to exactly search to obtain the optimal alpha. The wave absorbing processing is performed in the optimal fractional Fourier transform domain so as to suppress the linear frequency-modulated jamming. The de-noised signals are output to the follow-up process.

Description

Gauss curve fitting linear frequency modulation Interference Detection and inhibition method in direct-sequence communications system

Technical field

The invention belongs to Wireless Data Transmission, Communication Anti-Jamming Techniques field, what relate to is detection and the inhibition method of in Direct Sequence Spread Spectrum Communication (abbreviation direct-sequence spread-spectrum communication), linear frequency modulation being disturbed.

Background technology

In the communications field, disturb and suppress always to be the focus that the researcher pays close attention to.Present stage has been obtained a large amount of comparatively ripe theory and achievements on Suppression of narrow band interference.The introducing of the multiple research tools such as adaptive-filtering, transform domain technology, the code ancillary technique more inhibition of arrowband interference provides how reliable and effective means.But along with deepening continuously and the raising of practical application request of research, broad-band interference suppresses to become again the party's new research focus that makes progress.In this case, existing treatment technology ubiquitous defective on broad-band interference suppresses makes people begin to seek the purpose that new handling implement realizes suppressing broad-band interference.

Spread spectrum technic has large capacity, anti-interference, low intercepting and capturing rate and can realize the advantage such as code division multiple access (CDMA), is widely used, and becomes the technical foundation of next generation mobile communication.In spread spectrum communication system, the application of direct sequence spread spectrum (Directsequence spread spectrum, DSSS) technology is the most general.There is very strong antijamming capability in the DSSS system, and still, when the intensity of external disturbance had surpassed the jamming margin of system, the performance of system will sharply descend, and at this moment, must introduce corresponding interference protection measure, normally before despreading, signal is carried out preliminary treatment.At present, the achievement in research in this field mostly concentrates in the inhibition of disturbing by the arrowband, and in recent years, the nonstationary interference in broadband more and more causes people's attention on the impact of spread spectrum system, and its common form is that linear frequency modulation (LFM:line frequency modulate) disturbs.With respect to the single frequency sinusoidal ripple, the linear frequency modulation interference is more obvious on the impact of DSSS system.

Disturb for linear frequency modulation, proposed the method that a lot of inhibition are disturbed.There is distinct disadvantage in prior art.The linear frequency modulation that Fourier transfer pair broadband becomes when especially quick disturbs helpless.The time-frequency distributions technology is owing to existing cross term, so a plurality of interference of None-identified.

The fractional order conversion is a kind of new time frequency analyzing tool that causes that in recent years people pay close attention to, and is that fractional order thought is promoted the new variation that obtains in various traditional conversion.Fractional Fourier Transform (FRFT:Fractional Fouriertransform) is a kind of special fractional order conversion, and fractional order thought is also to obtain from its popularization to traditional F ourier conversion.Disturb existing corresponding algorithm to propose at the special broad-band interference of Fractional Fourier Domain inhibition-linear frequency modulation.Its basic ideas are take anglec of rotation α as variable, observation signal is carried out Fractional Fourier Transform continuously, form signal energy at the two-dimensional parameter (α of fractional order or anglec of rotation α and chirp rate μ formation, μ) the Two dimensional Distribution on the plane, the two-dimensional search that carries out peak point by threshold value on this plane is realized detection and the parameter Estimation of signal.The most obvious shortcoming of these algorithms is exactly that the hunting zone is large, and computation burden is excessive.

Summary of the invention

The object of the present invention is to provide a kind of fast linear frequency modulation Interference Detection and inhibition method in direct-sequence communications system that can overcome the problems such as existing linear frequency modulation disturbance restraining method search volume based on Fractional Fourier Transform is large, heavy computational burden.

The object of the present invention is achieved like this:

(1) divide frame, will block into from the data f (x) that receiver obtains shorter, certain overlapping Frame f arranged ₁, f ₂..., f _K-1, f _K

(2) to each frame f _i(x), suppose that linear frequency modulation disturbs existence, utilize Fourier transition structure two dimension time-frequency figure in short-term, by the tracking to the peak line track, utilize linear regression technique to draw the anglec of rotation α that the peak line equation parameter namely roughly estimates chirp slope and Fractional Fourier Transform;

(3) verify hypothesis and parameter optimization, carry out Fractional Fourier Transform according to parameter alpha, if exist remarkable peak value to detect successfully, and parameter is carried out the iteration optimizing, utilize an iteration Gauss curve fitting process to carry out limited search and accurately estimate to obtain the exact value that linear frequency modulation disturbs the anglec of rotation α ' of slope and Fractional Fourier Transform;

(4) denoising is carried out wave absorption and is processed in the Fractional Fourier Transform territory, remove and disturb;

(5) judge whether to have processed all Frames;

(6) signal goes overlapping and restructuring, if treated all data f _i(x), go overlapping to the result data and the restructuring processing, the signal that obtains disturbing.

The present invention can also comprise:

1, described minute frame further comprises:

1) determine to contain the length of the pending signal f (x) that linear frequency modulation disturbs, represent with L;

2) determine that analysis frame is data frame length fr;

3) determine the front and back two overlapping parameter 2*p of frame (%), lap 2* Δ p=fr*2*p%, and 4*p%＜1, p%=10%;

4) sliding step before and after between two frames is d=fr-2* Δ p;

5) respectively mend the data 0 that length is Δ p before and after signal f (x), generate new data f (x), length is 2* Δ p+L;

6) if 2* Δ p+ (K-1) * is d＜2 Δ p+L＜2* Δ p+K*d, mend again (2* Δ p+K*d)-(2* Δ p+L)=K*d-L data 0 after newly-generated f (x), consist of new f (x), length is 2* Δ p+K*d;

7) f (x) is divided into K frame f ₁, f ₂..., f _K-1, f _K,

f _i(x)：f((i-1)*d+1)，...，f(2*Δp+i*d)。

2, to each frame f _i(x), carrying out linear frequency modulation parameter prediction meter further comprises:

1) to f _i(x) do fourier conversion in short-term

Wherein w (n) is window function, a kind of in rectangular window, Gaussian window, Hanning or Hamming window;

2) obtain corresponding energy spectrogram

spectrogram(m，ω)＝|F(m，ω)| ²；

3) at spectrogram (m, ω) time-frequency plane, follow the trail of the maximum curve, on time-frequency plane spectrogram (m, ω), choose, record each time point

On the maximum point position, consist of set P (m), 1≤m≤M;

4) if exist linear frequency modulation to disturb, it is adjacent that the some position in P (t-1) and P (t) must be arranged, and utilizes the abutment points in set P (m) to consist of line segment, uses the method for fitting of a polynomial, tries to achieve the coarse value that the line segment parameter is slope

Otherwise illustrate not exist linear frequency modulation to disturb in this frame that then i=i+1 turns and judge whether to have processed all Frame steps.

3, described hypothesis verification and parameter optimization are based on hypothesis verification and the parameter optimization of iteration Gauss curve fitting, and concrete grammar is:

1) utilize a stage to obtain

To f _i(x) carry out corresponding Fractional Fourier Transform Obtain Wherein

2) if

Exist linear FM signal to disturb, forward 3 to); If

Do not exist linear FM signal to disturb, or the linear frequency modulation interfering energy is very little is not enough to affect systematic function, forwards to and judge whether to have processed all Frame steps; Wherein μ is Average

σ is

Variance, a is regulatory factor;

3) if exist linear frequency modulation to disturb, the excursion of k is decided to be

Iterations ite=1 is set;

4) the parameter iteration optimizing begins

To two slope value k _Head, k _end, make respectively corresponding Fractional Fourier Transform, obtain

$\max \left({\left|F_{p_{\mathrm{end}}}\left(f_i\left(x\right)\right)\right|}^2\right);$

If | k _Head-k _end|＜Δ, $\mathrm{\Δ}=\frac{|k_{\mathrm{hend}}-k_{\mathrm{end}}|}{5};$

If If T=0.01, and iterations ite＜10 forward 7 to) finishing iteration;

5) Gaussian function fitting

Calculate k _m∈ (k _Head, k _end):

$k_m=\frac{\max \left({\left|F_{p_{\mathrm{head}}}\left(f_i\left(x\right)\right)\right|}^2\right)}{\max \left({\left|F_{p_{\mathrm{head}}}\left(f_i\left(x\right)\right)\right|}^2\right)+\max \left({\left|F_{p_{\mathrm{end}}}\left(f_i\left(x\right)\right)\right|}^2\right)}\·k_{\mathrm{head}}+\frac{\max \left({\left|F_{p_{\mathrm{end}}}\left(f_i\left(x\right)\right)\right|}^2\right)}{\max \left({\left|F_{p_{\mathrm{head}}}\left(f_i\left(x\right)\right)\right|}^2\right)+\max \left({\left|F_{p_{\mathrm{end}}}\left(f_i\left(x\right)\right)\right|}^2\right)}\·k_{\mathrm{end}}$

If the Gaussian function form is:

$y=A\·e^{-\frac{{(x-b)}^2}{c}}$

It is taken the logarithm obtains:

$\log \left(y\right)=-\frac{1}{c}{x}^2+\frac{2b}{c}x+\log \left(A\right)-\frac{b^2}{c}$

The same with chirped slop estimation, be worth according to the observation (y _i, x _i), come estimated parameter A, b, c with linear regression method; With Slope Parameters and corresponding Fractional Fourier Transform territory extreme value, as 3 couples of input value in (x, y) of Gaussian function fitting={ (k _Head, M _Head), (k _m, M _m), (k _end, M _end) estimate 3 parameters in Gaussian function

Put into parameter sets

Wherein

$M_{\mathrm{end}}=\max \left({\left|F_{p_{\mathrm{end}}}\right|}^2\right);$

If in the Gaussian function fitting parameter sets, continuous two values change little, namely

Forward 7 to) finishing iteration;

6) hill-climbing algorithm

If K _end=k _Head, k _Head=k _Head-Δ forwards 4 to);

If

K _Head=k _end, k _end=k _end+ Δ forwards 4 to);

If

K _Head=k _m, otherwise k _end=k _m, iterations ite=ite+1 forwards 4 to);

7) iteration finishes, and obtains

4, described denoising further comprises:

1) to f _i(x) make p rank Fractional Fourier Transform, obtain F _p(f _i(x));

2) obtain the extreme point position

3) utilize Gaussian window w _gRight

Carry out smoothly, obtain new

w _g～N (0,1) is standardized normal distribution, and its window length is

4) utilize

At l _MLeft side δ neighborhood be monotone increasing, and at l _MRight side δ neighborhood be the rule of monotone decreasing, right

Carry out second differnce, obtain l _MNear two valley points position l _v1, l _v2, and l is arranged _v1＜l _M＜l _v2

5) with F _p(f _i(x)) at [l _v1, l _v2] to be set to 0 be that wave absorption is processed to interval data, suppress linear frequency modulation and disturb,

$X_p\left(u\right)=F_p\left(u\right)=F_p\left(f_i\left(x\right)\right)=\left\{\begin{array}{cc}{F}_p\left(u\right)& \mathrm{if}(u<l_{v1})\mathrm{or}(u>l_{v2})\\ 0& ({\mathrm{<figure-callout\; id="1"\; label="l\; v"\; filenames="HSA00000291046000012.png,HSA00000291046000021.png"\; state="\{\{state\}\}">l</figure-callout>}}_v\&le;u\&le;l_{v2})\end{array}\right.;$

6) to the F after wave absorption _p(f _i(x)) do-p rank Fractional Fourier Transform, obtain

5, judged whether all Frames treated, and whether also existed linear frequency modulation to disturb to each frame cycle criterion to comprise:

1) judge whether Frame crosses the border, and exceeds process range, if i＞K forwards signal to and goes overlapping and restructuring;

2) with Frame f _i(x) again forward to each frame f _i(x), carry out linear frequency modulation parameter prediction meter.

6, described signal goes overlapping and recombinates further to comprise:

1) will

Go overlappingly by rule, consist of the signal after going to disturb

Step 1, remove

A last Δ p data;

Step 2, remove

P data of each Δ of head and the tail, 1＜i＜K;

Step 3, remove

A front Δ p data;

Step 4, the redundancy of removing Head and the tail connect, and consist of

2) remove

Head and the tail replenish 0, remove anterior Δ p 0, remove afterbody K*d-L+ Δ p 0;

3) signal after obtaining disturbing with isometric the going of input signal f (x)

The present invention has overcome that existing linear frequency modulation disturbance restraining method search volume based on Fractional Fourier Transform is large, the shortcoming of heavy computational burden.We's ratio juris is mainly utilize in direct-sequence communications system at the similar white noise of data spectrum of channel and have the characteristics of spreading gain.Jamming-to-signal ratio (disturbing the energy Ratios with signal) if less than spreading gain, does not need to carry out special processing, and system can correctly receive the decode data; In believing that if ratio is greater than spreading gain, data are disturbed by linear FM signal obviously in channel, the energy that disturbs of linear frequency modulation obviously is better than signal and very strong peak value must be arranged on the instantaneous energy frequency spectrum, must the time-there is obvious peak line correspondence linear FM signal in frequency Energy distribution on the plane.therefore can be by the tracking to the peak line track on time-frequency Energy distribution plane, utilize linear regression technique just can draw the anglec of rotation α that the peak line equation parameter can roughly estimate chirp slope and Fractional Fourier Transform, then carry out Fractional Fourier Transform according to parameter, if exist remarkable peak value to detect successfully (existing linear FM signal to disturb), then utilize an iteration Gauss curve fitting process to carry out limited search and accurately estimate to obtain the exact value that linear frequency modulation disturbs the anglec of rotation α ' of slope and Fractional Fourier Transform.Certainly exist the corresponding linear frequency modulation of a peak value in Fractional Fourier Transform territory, α ' rank and disturb, carry out carrying out corresponding Fractional Fourier inverse transformation after wave absorption is processed, can remove linear frequency modulation and disturb.

The simple description of basic principle of the present invention and foundation:

(1) relation of Fractional Fourier Transform and LFM

(background technology) as previously mentioned, the LFM signal has the energy accumulating characteristic in corresponding Fractional Fourier Transform territory, can produce pulse peak, so the suitable unknown parameter LFM signal of processing of Fractional Fourier Transform, separating signal of communication and LFM interference completed.Subject matter is how to find fast the fractional-order corresponding with LFM in parameter space.

(2) the quick estimation of the characteristics of spread spectrum communication and parameter

Spread spectrum communication system has spreading gain.In spread spectrum communication system at the similar white noise of data spectrum of channel.Jamming-to-signal ratio (disturbing the energy Ratios with signal) if less than spreading gain, does not need to carry out special processing, and system can correctly receive the decode data; If jamming-to-signal ratio is greater than spreading gain, data are disturbed by linear FM signal obviously in channel, the energy that disturbs of linear frequency modulation obviously is better than signal and very strong peak value must be arranged on the instantaneous energy frequency spectrum, must the time-there is obvious peak line correspondence linear FM signal in frequency Energy distribution on the plane.therefore can be by the tracking to the peak line track on time-frequency Energy distribution plane, utilize linear regression technique just can draw the anglec of rotation α that the peak line equation parameter can roughly estimate chirp slope and Fractional Fourier Transform, then carry out Fractional Fourier Transform according to parameter, if exist remarkable peak value to detect successfully (existing linear FM signal to disturb), then utilize an iteration Gauss curve fitting process to carry out limited search and accurately estimate to obtain the exact value that linear frequency modulation disturbs the anglec of rotation α ' of slope and Fractional Fourier Transform.Certainly exist the corresponding linear frequency modulation of a peak value in Fractional Fourier Transform territory, α ' rank and disturb, carry out carrying out corresponding Fractional Fourier inverse transformation after wave absorption is processed, can remove linear frequency modulation and disturb.

(3) parameter optimization: iteration Gauss curve fitting-hill-climbing algorithm

A LFM signal is only an impulse function in suitable fractional order Fourier domain.Therefore FRFT is k to given frequency modulation rate in certain fractional order Fourier domain the LFM signal has best aggregation properties, and

Area fraction rank Fourier domain maximum is monotone increasing,

Area fraction rank Fourier domain maximum is monotone decreasing.This has different monotonicities and similar with the point-symmetric characteristics of extreme value and normal distribution (Gaussian function) in optimal value both sides.Therefore utilize this characteristic, proposed a kind of detection and parameter estimation algorithm-Gauss curve fitting optimizing algorithm of LFM signal.

(4) divide frame: windowing is overlapping

Generally, the data of input can be a lot, directly carry out treatment system and bear very heavy.Therefore need to be with data truncation, segmentation (divided data frame) is processed and is helped to reduce computational load.The process of data truncation is equivalent to data are multiplied by a rectangular window in time domain, is equivalent to the convolution of frequency spectrum and the rectangular window frequency spectrum of data at frequency domain.By the frequency spectrum knowledge of finite-length rectangular window, we know that data and rectangular window must cause spectrum leakage at frequency domain in time domain multiplication.The edge of this leakage major effect data when returning time domain from the frequency domain inverse conversion.Therefore divide frame to adopt the limited overlapping method of front and back frame to initial data, eliminate this adverse effect.The present invention in an embodiment, the Duplication of front and back frame is 20% (being rear 20% front 20% overlapping with next frame of former frame), has just eliminated the impact of spectrum leakage fully.

(5) to the Adaptive Suppression of LFM at the pulse peak in Fourier territory, corresponding scores rank

More than introduced impact and the elimination of spectrum leakage problem on time domain.Disturb because will suppress LFM at Fractional Fourier Domain, therefore also must pay close attention to spectrum leakage to the impact of Fractional Fourier frequency spectrum.Cause the arrowband power expansion to contiguous scope at the Fractional Fourier Domain spectrum leakage, so LFM is no longer corresponding single-point pulse in Fourier territory, corresponding scores rank, but the pulse peak with sideband.Will suppress the LFM interference at Fractional Fourier Domain and will suppress the whole pulse peak that sideband arranged corresponding with it, in the situation of the intensity of pulse peak and width the unknown, the effect that simple threshold value method suppresses LFM is limited.The pulse peak that sideband is arranged that utilization of the present invention is corresponding with LFM, seek the balance point local minizing point of both sides (peak value) of signal energy and LFM interfering energy as the zone of wave absorption (inhibition peak value) in the monotonicity of peak point both sides spectrum energy, frequency spectrum in the balance point interval all is set to 0, reaches wave absorption and suppress the purpose that LFM disturbs.

(6) many LFM disturb and suppress

The present invention utilizes the method for estimating the straight line parameter on the time-frequency energy plane of Fourier structure in short-term, and the parameter that recycling is estimated suppresses LFM at Fractional Fourier Domain and disturbs.If there are many LFM to disturb, just determine that by the jamming-to-signal ratio of each interference its intensity in time-frequency energy plane upward peak is different, will produce the peak line of varying strength.Utilize this characteristic, the present invention adopts the method for circulation, suppresses a LFM the strongest at every turn and disturbs, and reaches and suppresses the purpose that many LFM disturb.

Spread spectrum communication neutral line frequency modulation Interference Detection as above and inhibition method have following feature: (1) divides frame to process the long data section in order to shorten data length, to reduce computation burden; (2) the appropriate overlapping processing of Frame has been eliminated spectrum leakage that data truncation causes to the impact of time domain; (3) utilize the LFM signal to have the energy accumulating characteristic in corresponding Fractional Fourier Transform territory, detect the LFM signal and go and disturb; (4) utilize in spread spectrum communication system at the similar white noise of data spectrum of channel and have the characteristic of spreading gain, reaching the quick estimation purpose of parameter; (5) the present invention proposes the Adaptive Suppression method at the pulse peak in Fourier territory, corresponding scores rank for LFM, utilize the sideband searching signal energy of pulse peak and the balance point of LFM interfering energy, determine that wave absorption is regional, reach wave absorption and suppress the purpose that LFM disturbs.(6) the present invention can disturb a plurality of LFM and suppress.

Description of drawings

Fig. 1 is the time-frequency figure of LFM signal.

Fig. 2 be with Fig. 1 in the Fourier Transform of Fractional Order territory of LFM signal parameter coupling.

Fig. 3 is the flow chart of linear frequency modulation disturbance restraining method.

Fig. 4 is data framing process schematic diagram.

Fig. 5 is signal f _iThe map of magnitudes of p rank Fractional Fourier Transform (x).

Fig. 6 is signal f _iThe amplitude maximum point Neighborhood Graph of p rank Fractional Fourier Transform (x).

Fig. 7 is superimposed structure

Embodiment

For example the present invention is described in more detail below in conjunction with accompanying drawing:

This method theory diagram comprises following 6 stages referring to Fig. 3: (1) minute frame, with data f (x) block into shorter, certain overlapping Frame f arranged ₁, f ₂..., f _K-1, f _K(2) to each frame f _i(x), suppose that linear frequency modulation disturbs existence, utilize Fourier transition structure two dimension time-frequency figure in short-term, by the tracking to the peak line track, utilize linear regression technique just can draw the anglec of rotation α that the peak line equation parameter can roughly estimate chirp slope and Fractional Fourier Transform; (3) verify hypothesis and parameter optimization: carry out Fractional Fourier Transform according to parameter alpha, if exist remarkable peak value to detect successfully, and parameter is carried out the iteration optimizing, utilize an iteration Gauss curve fitting process to carry out limited search and accurately estimate to obtain the exact value that linear frequency modulation disturbs the anglec of rotation α ' of slope and Fractional Fourier Transform; (4) denoising: carry out wave absorption in the Fractional Fourier Transform territory and process, remove and disturb; (5) judge whether to have processed all Frames; (6) signal goes overlapping and restructuring, if treated all data f _i(x), go overlapping to the result data and the restructuring processing, the signal that obtains disturbing.

Stage 1: minute frame

Generally, the data of input can be a lot, directly carry out treatment system and bear very heavy.Therefore need to be with data truncation, segmentation (divided data frame) is processed and is helped to reduce computational load.Process as shown in Figure 4.

(1) determine to contain the length of the pending signal f (x) that linear frequency modulation disturbs, represent L=120000 in this example with L;

(2) determine to analyze frame length fr, fr=24000 in this example;

(3) determine the front and back two overlapping parameter 2*p of frame (%), lap 2* Δ p=fr*2*p%, and 4*p%＜1 establishes p%=10% in this example, lap 2* Δ p=fr*2*p%=4800;

(4) sliding step before and after between two frames is d=fr-2* Δ p, d=24000-4800=19200 in this example;

(5) respectively mend the data 0 that length is Δ p before and after signal f (x), generate new data f (x), length is 2* Δ p+L, and f (x) length newly-generated in this example is 2* Δ p+L=124800;

(6) if 2* Δ p+ (K-1) * is d＜2 Δ p+L＜2* Δ p+K*d, mend again (2* Δ p+K*d)-(2* Δ p+L)=K*d-L data 0 after newly-generated f (x), consist of new f (x), length is 2* Δ p+K*d;

(4800+6*19200=120000)＜124800＜(4800+7*19200=139200) in this example, in 7*19200-120000=14400 data 0 of f (x) back benefit, consisting of new length is the data f (x) of 2* Δ p+K*d=139200

(7) f (x) is divided into K frame f ₁, f ₂..., f _K-1, f _K, and f _i(x): f ((i-1) * d+1) ..., f (2* Δ p+i*d)

The length that in this example, previous step is produced is that the f (x) of 2* Δ p+K*d=4800+7*19200=139200 is divided into 7 frames, and is as follows:

f ₁(x)：f(1)，...，f(24000)

f ₂(x)：f(19200+1)，...，f(43200)

f ₃(x)：f(38400+1)，...，f(62400)

f ₄(x)：f(57600+1)，...，f(81600)

f ₅(x)：f(76800+1)，...，f(100800)

f ₆(x)：f(96000+1)，...，f(120000)

f ₆(x)：f(11520+1)，...，f(139200)

Stage 2: to each frame f _i(x), carry out linear frequency modulation parameter prediction meter

(1) to f _i(x) do fourier conversion in short-term

Wherein w (n) is window function, can select rectangular window, Gaussian window, Hanning or Hamming window etc.

W in this example (n) is rectangular window, and the long M of window is that (log2 (fr)-3) power of 2 rounds, so the Matlab language description is M=2^floor (log2 (fr)-3).

(2) obtain corresponding energy spectrogram

spectrogram(m，ω)＝|F(m，ω)| ² (15)

(3) at spectrogram (m, ω) time-frequency plane, follow the trail of the maximum curve.On time-frequency plane spectrogram (m, ω), choose, record each time point

On the maximum point position, consist of set P (m), 1≤m≤M.

(4) if exist linear frequency modulation to disturb, it is adjacent that the some position in P (t-1) and p (t) must be arranged, and can utilize the abutment points formation line segment in set P (m).Can with the method (introduction of the scape technology of specifically passing away neutral line regression analysis) of fitting of a polynomial, try to achieve the coarse value of line segment parameter (slope)

Otherwise illustrate not exist linear frequency modulation to disturb in this frame, then i=i+1 turns the stage 5;

Stage 3: based on hypothesis verification and the parameter optimization of iteration Gauss curve fitting

By the definition of FRFT as can be known, a LFM signal is only an impulse function in suitable fractional order Fourier domain.Therefore FRFT has best aggregation properties to given LFM signal in certain fractional order Fourier domain, and

The zone is monotone increasing,

The zone is monotone decreasing, and this has different monotonicities and similar with the point-symmetric characteristics of extreme value and normal distribution (Gaussian function) in optimal value both sides.Therefore utilize this characteristic, proposed a kind of detection and parameter estimation algorithm-Gauss curve fitting optimizing algorithm of LFM signal.

(1) utilize a stage to obtain

To f _i(x) carry out corresponding Fractional Fourier Transform

Obtain

Wherein

(2) if

Exist linear FM signal to disturb, forward (3) to; If

Do not exist linear FM signal to disturb, or the linear frequency modulation interfering energy is very little is not enough to affect systematic function, can forwards the stage 5 to.Wherein μ is

Average

σ is

Variance, a is regulatory factor (can be made as spreading gain).

(3) if exist linear frequency modulation to disturb, the excursion of k is decided to be

Iterations ite=1 is set;

(4) the parameter iteration optimizing begins

To two slope value k _Head, k _end, make respectively corresponding Fractional Fourier Transform, obtain

$\max \left({\left|F_{p_{\mathrm{end}}}\left(f_i\left(x\right)\right)\right|}^2\right);$

If | k _Head-k _end|＜Δ,

If

Usually establish T=0.01, and iterations ite＜10, forward to

(7) finishing iteration;

(5) Gaussian function fitting

Calculate k _m∈ (k _Head, k _end):

$k_m=\frac{\max \left({\left|F_{p_{\mathrm{head}}}\left(f_i\left(x\right)\right)\right|}^2\right)}{\max \left({\left|F_{p_{\mathrm{head}}}\left(f_i\left(x\right)\right)\right|}^2\right)+\max \left({\left|F_{p_{\mathrm{end}}}\left(f_i\left(x\right)\right)\right|}^2\right)}\&CenterDot;k_{\mathrm{head}}+\frac{\max \left({\left|F_{p_{\mathrm{end}}}\left(f_i\left(x\right)\right)\right|}^2\right)}{\max \left({\left|F_{p_{\mathrm{head}}}\left(f_i\left(x\right)\right)\right|}^2\right)+\max \left({\left|F_{p_{\mathrm{end}}}\left(f_i\left(x\right)\right)\right|}^2\right)}\&CenterDot;k_{\mathrm{end}}$

If the Gaussian function form is:

$y=A\&CenterDot;e^{-\frac{{(x-b)}^2}{c}}$

It is taken the logarithm obtains:

$\log \left(y\right)=-\frac{1}{c}{x}^2+\frac{2b}{c}x+\log \left(A\right)-\frac{b^2}{c}$

The same with chirped slop estimation, also can be worth according to the observation (y _i, x _i), come estimated parameter A, b, c with linear regression method.With Slope Parameters and corresponding Fractional Fourier Transform territory extreme value, as 3 couples of input value in (x, y) of Gaussian function fitting={ (k _Head, M _Head), (k _m, M _m), (k _end, M _end) just in time can estimate 3 parameters in Gaussian function

Put into parameter sets

Wherein

$M_m=\max \left({\left|F_{p_m}\right|}^2\right),$ $M_{\mathrm{end}}=\max \left({\left|F_{p_{\mathrm{end}}}\right|}^2\right).$

If in the Gaussian function fitting parameter sets, continuous two values change little, namely

Forward (7) finishing iteration to;

(6) hill-climbing algorithm

If

K _end=k _Head, k _Head=k _Head-Δ forwards (4) to:

If

K _Head=k _end, k _end=k _end+ Δ forwards (4) to;

If K _Head=k _m, otherwise k _end=k _m, iterations ite=ite+1 forwards (4) to;

(7) iteration finishes, and obtains

Stage 4: denoising

(1) to f _i(x) make p rank Fractional Fourier Transform, obtain F _p(f _i(x));

(2) obtain the extreme point position

(3) utilize Gaussian window w _gRight

Carry out smoothly, obtain new

w _g～N (0,1) is standardized normal distribution, and its window length is

(4) utilize

At l _MLeft side δ neighborhood be monotone increasing, and at l _MRight side δ neighborhood be the rule (as shown in Figure 5 and Figure 6) of monotone decreasing, right

Carry out second differnce, obtain l _MNear two valley points position l _v1, l _v2, and l is arranged _v1＜l _M＜l _v2

(5) with F _p(f _i(x)) at [l _v1, l _v2] interval data are set to 0 (wave absorption processings), can suppress the linear frequency modulation interference.

$X_p\left(u\right)=F_p\left(u\right)=F_p\left(f_i\left(x\right)\right)=\left\{\begin{array}{cc}{F}_p\left(u\right)& \mathrm{if}(u<l_{v1})\mathrm{or}(u>l_{v2})\\ 0& ({\mathrm{<figure-callout\; id="1"\; label="l\; v"\; filenames="HSA00000291046000012.png,HSA00000291046000021.png"\; state="\{\{state\}\}">l</figure-callout>}}_v\&le;u\&le;l_{v2})\end{array}\right.$

(6) to the F after wave absorption _p(f _i(x)) do-p rank Fractional Fourier Transform, obtain

Stage 5: judged whether all Frames treated, and whether also existed linear frequency modulation to disturb to each frame cycle criterion

(1) judge whether Frame crosses the border (exceeding process range), if i＞K forwards the stage 6 to

(2) with Frame f _i(x) again forward the stage 2 to;

Stage 6: signal goes overlapping and restructuring

(1) will

Go overlappingly by rule, consist of the signal after going to disturb Process as shown in Figure 7;

The rule 1, remove A last Δ p data;

The rule 2, remove

P data of each Δ of head and the tail, 1＜i＜K;

The rule 3, remove

A front Δ p data;

Rule 4, the redundancy of removing

Head and the tail connect, and consist of

In this example,

Remove a last Δ p=2400 data, from

Arrive

P=2400 data of Δ before and after respectively removing,

Remove a front Δ p=2400 data, so consist of

Length is 7*fr-12* Δ p=7*24000-12*2400=139200

(2) remove

0 (remove anterior Δ p 0, remove afterbody K*d-L+ Δ p 0) that head and the tail replenish;

Removing previous step in this example produces

Front Δ p=2400 number reach according to this afterbody K*d-L+ Δ p=7*19200-120000+2400=16800,

Length become 139200-16800-2400=120000

(3) signal after obtaining disturbing with isometric the going of input signal f (x)

The interference signal of going of the final output of this example is Its length equals the length 120000 of input signal f (x).

Claims (7)

1. Gauss curve fitting linear frequency modulation Interference Detection and inhibition method in a direct-sequence communications system is characterized in that:

(1) divide frame, will block into from the data f (x) that receiver obtains shorter, certain overlapping Frame f arranged ₁, f ₂..., f _K-1, f _K

(2) to each frame f _i(x) carry out linear frequency modulation parameter prediction meter, suppose that linear frequency modulation disturbs existence, utilize Fourier transition structure two dimension time-frequency figure in short-term, by the tracking to the peak line track, utilize linear regression technique to draw the anglec of rotation α that the peak line equation parameter namely roughly estimates chirp slope and Fractional Fourier Transform;

(3) verify hypothesis and parameter optimization, carry out Fractional Fourier Transform according to parameter alpha, if exist remarkable peak value to detect successfully, and parameter is carried out the iteration optimizing, utilize an iteration Gauss curve fitting process to carry out limited search and accurately estimate to obtain the exact value that linear frequency modulation disturbs the anglec of rotation α of slope and Fractional Fourier Transform;

(4) denoising is carried out wave absorption and is processed in the Fractional Fourier Transform territory, remove and disturb;

(5) judge whether to have processed all Frames;

(6) signal goes overlapping and restructuring, if treated all data f _i(x), go overlapping to the result data and the restructuring processing, the signal that obtains disturbing.

2. Gauss curve fitting linear frequency modulation Interference Detection and inhibition method in direct-sequence communications system according to claim 1 is characterized in that described minute frame further comprises:

1) determine to contain the length of the pending signal f (x) that linear frequency modulation disturbs, represent with L;

2) determine that analysis frame is data frame length fr;

3) determine the front and back two overlapping parameter 2*p of frame (%), lap 2* Δ p=fr*2*p%, and 4*p%＜1, p%=10%;

4) sliding step before and after between two frames is d=fr-2* Δ p;

5) respectively mend the data 0 that length is Δ p before and after signal f (x), generate new data f (x), length is 2* Δ p+L;

6) if 2* Δ p+ (K-1) * is d＜2 Δ p+L＜2* Δ p+K*d, mend again (2* Δ p+K*d)-(2* Δ p+L)=K*d-L data 0 after newly-generated f (x), consist of new f (x), length is 2* Δ p+K*d;

7) f (x) is divided into K frame f ₁, f ₂..., f _K-1, f _K,

f _i(x)：f((i-1)*d+1)，...，f(2*Δp+i*d)。

3. Gauss curve fitting linear frequency modulation Interference Detection and inhibition method in direct-sequence communications system according to claim 2, is characterized in that each frame f _i(x) carrying out linear frequency modulation parameter prediction meter further comprises:

1) to f _i(x) do fourier conversion in short-term

Wherein w (n) is window function, a kind of in rectangular window, Gaussian window, Hanning or Hamming window;

2) obtain corresponding energy spectrogram

spectrogram(m，ω)＝|F(m，ω)| ²；

3) at spectrogram (m, ω) time-frequency plane, follow the trail of the maximum curve, on time-frequency plane spectrogram (m, ω), choose, record each time point

On the maximum point position, consist of set P (m), 1≤m≤M;

4) if exist linear frequency modulation to disturb, it is adjacent that the some position in P (t-1) and P (t) must be arranged, and utilizes the abutment points in set P (m) to consist of line segment, uses the method for fitting of a polynomial, tries to achieve the coarse value that the line segment parameter is slope

Otherwise illustrate not exist linear frequency modulation to disturb in this frame that then i=i+1 turns and judge whether to have processed all Frame steps.

4. Gauss curve fitting linear frequency modulation Interference Detection and inhibition method in direct-sequence communications system according to claim 3, is characterized in that described hypothesis verification and parameter optimization are based on hypothesis verification and the parameter optimization of iteration Gauss curve fitting, and concrete grammar is:

1) utilize a stage to obtain

To f _i(x) carry out corresponding Fractional Fourier Transform

Obtain Wherein $\hat{p}=2\widehat{\mathrm{\&alpha;}}/\mathrm{\&pi;}=-\frac{2\mathrm{arccot}\left(\hat{k}\right)}{\mathrm{\&pi;}};$

2) if

Exist linear FM signal to disturb, forward 3 to); If

Do not exist linear FM signal to disturb, or the linear frequency modulation interfering energy is very little is not enough to affect systematic function, forwards to and judge whether to have processed all Frame steps; Wherein μ is

Average

σ is

Variance, a is regulatory factor;

3) if exist linear frequency modulation to disturb, the excursion of k is decided to be

Iterations ite=1 is set;

4) the parameter iteration optimizing begins

To two slope value k _Head, k _end, make respectively corresponding Fractional Fourier Transform, obtain

$\max \left({\left|F_{p_{\mathrm{end}}}\left(f_i\left(x\right)\right)\right|}^2\right);$

If | k _Head-k _end|＜Δ, $\mathrm{\&Delta;}=\frac{|k_{\mathrm{head}}-k_{\mathrm{end}}|}{5};$

If

If T=0.01, and iterations ite＜10 forward 7 to) finishing iteration;

5) Gaussian function fitting

Calculate k _m∈ (k _Head, k _end):

$k_m=\frac{\max \left({\left|F_{p_{\mathrm{head}}}\left(f_i\left(x\right)\right)\right|}^2\right)}{\max \left({\left|F_{p_{\mathrm{head}}}\left(f_i\left(x\right)\right)\right|}^2\right)+\max \left({\left|F_{p_{\mathrm{end}}}\left(f_i\left(x\right)\right)\right|}^2\right)}\&CenterDot;k_{\mathrm{head}}+\frac{\max \left({\left|F_{p_{\mathrm{head}}}\left(f_i\left(x\right)\right)\right|}^{\text{2}}\right)}{\max \left({\left|F_{p_{\mathrm{head}}}\left(f_i\left(x\right)\right)\right|}^2\right)+\max \left({\left|F_{p_{\mathrm{end}}}\left(f_i\left(x\right)\right)\right|}^2\right)}\&CenterDot;k_{\mathrm{end}}$

If the Gaussian function form is:

$y=A\&CenterDot;e^{-\frac{{(x-b)}^2}{c}}$

It is taken the logarithm obtains:

$\log \left(y\right)=-\frac{1}{c}{x}^2+\frac{2b}{c}x+\log \left(A\right)-\frac{b^2}{c}$

The same with chirped slop estimation, be worth according to the observation (y _i, x _i), come estimated parameter A, b, c with linear regression method; With Slope Parameters and corresponding Fractional Fourier Transform territory extreme value, as 3 couples of input value in (x, y) of Gaussian function fitting={ (k _Head, M _Head), (k _m, M _m), (k _end, M _end) estimate 3 parameters in Gaussian function

Put into parameter sets

Wherein $M_{\mathrm{head}}=\max \left({\left|F_{p_{\mathrm{head}}}\right|}^2\right),$ $M_m=\max \left({\left|F_{p_m}\right|}^2\right),$ $M_{\mathrm{end}}=\max \left({\left|F_{p_{\mathrm{end}}}\right|}^2\right);$

If in the Gaussian function fitting parameter sets, continuous two values change little, namely

$|\hat{b}\left(\mathrm{ite}\right)-\hat{b}(\mathrm{ite}-1)|<0.1,$ $|\hat{c}\left(\mathrm{ite}\right)-1|<0.1,$ $k_{\mathrm{end}}=k_{\mathrm{head}}=\hat{b}\left(\mathrm{ite}\right),$ Forward 7 to) finishing iteration;

6) hill-climbing algorithm

If $\max \left({\left|F_{p_{\mathrm{head}}}\right|}^2\right)>\max \left({\left|F_{p_m}\right|}^2\right)>\max \left({\left|F_{p_{\mathrm{end}}}\right|}^2\right),$ K _end=k _Head, k _Head=k _Head-Δ forwards 4 to);

If $\max \left({\left|F_{p_{\mathrm{head}}}\right|}^2\right)<\max \left({\left|F_{p_m}\right|}^2\right)<\max \left({\left|F_{p_{\mathrm{end}}}\right|}^2\right),$ K _Head=k _end, k _end=k _end+ Δ forwards 4 to);

If $\frac{\max \left({\left|F_{p_{\mathrm{head}}}\right|}^2\right)+\max \left({\left|F_{p_m}\right|}^2\right)}{2}<\frac{\max \left({\left|F_{p_m}\right|}^2\right)+\max \left({\left|F_{p_{\mathrm{end}}}\right|}^2\right)}{2},$ K _Head=k _m, otherwise k _end=k _m, iterations ite=ite+1 forwards 4 to);

7) iteration finishes, and obtains $p=\underset{p}{\arg }\left[\max (\max \left({\left|F_{p_{\mathrm{head}}}\right|}^2\right),\max \left({\left|F_{p_{\mathrm{end}}}\right|}^2\right))\right].$

5. Gauss curve fitting linear frequency modulation Interference Detection and inhibition method in direct-sequence communications system according to claim 4 is characterized in that described denoising further comprises:

1) to f _i(x) make p rank Fractional Fourier Transform, obtain f _p(f _i(x));

2) obtain the extreme point position

3) utilize Gaussian window w _gRight

Carry out smoothly, obtain new

w _g～N (0,1) is standardized normal distribution, and its window length is

4) utilize

At l _MLeft side δ neighborhood be monotone increasing, and at l _MRight side δ neighborhood be the rule of monotone decreasing, right

Carry out second differnce, obtain l _MNear two valley points position l _v1, l _v2, and l is arranged _v1＜l _M＜l _v2

5) with F _p(f _i(x)) at [l _v1, l _v2] to be set to 0 be that wave absorption is processed to interval data, suppress linear frequency modulation and disturb,

$X_p\left(u\right)=F_p\left(u\right)=F_p\left(f_i\left(x\right)\right)=\left\{\begin{array}{cc}{F}_p\left(u\right)& \mathrm{if}(u<l_{v1})\mathrm{or}(u>l_{v2})\\ 0& (l_{v1}\&le;u\&le;l_{v2})\end{array}\right.;$

6) to the F after wave absorption _p(f _i(x)) do-p rank Fractional Fourier Transform, obtain

6. whether Gauss curve fitting linear frequency modulation Interference Detection and inhibition method in direct-sequence communications system according to claim 5, is characterized in that judging whether treated all Frames, and also exist the linear frequency modulation interference to comprise to each frame cycle criterion:

1) judge whether Frame crosses the border, and exceeds process range, if i＞K forwards signal to and goes overlapping and restructuring;

2) with Frame f _i(x) again forward to each frame f _i(x), carry out linear frequency modulation parameter prediction meter.

7. Gauss curve fitting linear frequency modulation Interference Detection and inhibition method in direct-sequence communications system according to claim 5 is characterized in that described signal goes overlappingly further to comprise with restructuring:

1) will

Go overlappingly by rule, consist of the signal after going to disturb

Step 1, remove

A last Δ p data;

Step 2, remove

P data of each Δ of head and the tail, 1＜i＜K;

Step 3, remove A front Δ p data;

Step 4, the redundancy of removing

Head and the tail connect, and consist of

2) remove

Head and the tail replenish 0, remove anterior Δ p 0, remove afterbody K*d-L+ Δ p 0;

3) signal after obtaining disturbing with isometric the going of input signal f (x)

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