CN1790050A - Imperfect matching processing method for pseudo random multiplex modulated signal - Google Patents

Abstract

The invention discloses an incomplete matching disposal method of pseudorandom composite modulation FSK-to-PSK signal, which is characterized by the following: distributing the optimum energy signal on the frequency point of important object; extracting the incomplete disposal signal of matching-loss phase; making the relative function of radar launching signal and incomplete disposal signal approximate one-dimensional distant image of object; accomplishing the signal disposal; outputting the self-relative function of object one-dimensional distant image. The invention makes the radar obtain object diffusion character information and outputs larger signal-to-noise ratio, which displays important meaning to trace object and identify low observable object for radar.

Description

A kind of imperfect matching processing method of pseudo random multiplex modulated signal

Technical field

The invention belongs to the Radar Signal Processing technical field, specially refer to the treatment technology of pseudorandom complex modulated (FSK/PSK) radar signal.

Background technology

As everyone knows, radar is mainly used in search and targets such as tracking aircraft, naval vessel, and target echo is attended by clutters such as massif, rain, snow and wave usually, and clutter is often than strong many of target echo.Modern radar faces more abominable electromagnetic environment, various active and passive interference always with the radar synchronized development, low observability target (the being commonly called as stealthy target) technology that particularly in recent years develops rapidly has reduced target significantly to electromagnetic reflection.In order from this complex environment and various interference, to obtain target information, must requirement higher, that upgrade be proposed to the Radar Signal Processing technology.Traditional Radar Signal Processing method constantly obtains new breakthrough, and as the appearance of pulse compression (abbreviation pulse pressure) radar, it is a kind of actual realization of matched filter system, has solved the contradiction between radar horizon and the resolution effectively.

By document (open the prominent personage. modern signal processing. Beijing: publishing house of Tsing-Hua University, 1995), s (t) is a known signal, if filter impulse responses h _m(t) satisfy:

h _m(t)＝ks ^*(t ₀-t) (1)

K is a constant in the formula, t ₀For physically realizable the adding of wave filter delayed, subscript m is represented coupling, and * represents conjugation.Then wave filter is to response output signal-to-noise ratio (SNR) maximum of input signal s (t), and this wave filter is called matched filter.

Document (Huang Deshuan etc. high resolution radar intelligent signal processing technology. Beijing: China Machine Press, 2001) to point out: in the Narrow-band Radar signal, target is approximately point target, receives echo waveform s _R(t) and s emission signal s _T(t) basic identical, i.e. s _R(t) ≈ s _T(t), Dui Ying matched filter is designed to:

h _m(t)＝ks _T(t ₀-t) (2)

K is a constant in the formula, t ₀Delay for making physically realizable the adding of wave filter.Subscript T represents emission, and subscript R represents to receive, and subscript m is represented coupling.

In the wideband radar signal, point target becomes the appearance mark that extends along distance, and very big difference takes place for the echo and former the transmitting that transmit behind target reflection.The backward scattered impulse response of hypothetical target is h (t), then to s emission signal s _T(t) reception echoed signal s _R(t) can be expressed as:

s _R(t)＝s _T(t)h(t) (3)

 represents convolution in the formula.Corresponding matched filter is designed to:

h _m(t)＝ks _T(t ₀-t)h(t ₀-t) (4)

 represents convolution in the formula, and k is a constant, t ₀Delay for making physically realizable the adding of wave filter.Subscript T represents emission, and subscript R represents to receive, and subscript m is represented coupling.

For being distinguished, among the present invention above-mentioned processing procedure is called " matched filter processing method ", Fig. 1 is the theory diagram of this method.S among the figure _T(t) be the radar emission signal, subscript T represents emission, and target scattering is represented the influence of target to transmitting, h _m(t) be the impulse response of matched filter, subscript m is represented coupling, and R (τ) is the output after the matched filter processing, and the τ express time postpones.

Document (Luo Hong, Xu Xiaojian, Huang Peikang etc. the modeling and the prediction of target wideband radar characteristic signal. electronic letters, vol, 1999) point out: in optical zone, complex target generally can be regarded as and be made up of many isolated scattering centers.Radar emission and receiving wide-band signal are done inverse fourier transform to the frequency domain data H (ω) that obtains, and obtain the target one-dimensional range profile, are approximately the back scattering impulse response h (t) of target among the present invention.

$h\left(t\right)=\underset{-\∞}{\overset{+\∞}{\∫}}H\left(\mathrm{\ω}\right)e^{\mathrm{j\ωt}}\mathrm{d\ω}---\left(5\right)$

T express time in the formula, ω represents angular frequency.

The essence of matched filter processing method is by the design matched filter, realization receives purpose to the dissimilar couplings that transmit, obtaining maximum signal to noise ratio (SNR) simultaneously, obtain target information, the impulse response of matched filter and echoed signal are the relations of conjugate lens picture.In the Narrow-band Radar signal, obtain radar emission signal Doppler frequency and postpone and time delay information; In the wideband radar signal, obtain reflecting the distance images of target signature information.

Summary of the invention

The purpose of this invention is to provide a kind of non-complete matched signal treatment technology of the radar based on complex modulated (FSK/PSK) signal, can obtain the target scattering characteristic information, obtain bigger signal to noise ratio (S/N ratio) output in the hope of radar.

In order to describe the content among the present invention easily, at first do following term definition:

1. pseudo-random FSK (frequency shift keying)/PSK (phase-shift keying (PSK)) signal: pseudo-random FSK/psk signal is a kind of signal of realizing frequency hopping and phase modulation simultaneously, and wherein the FSK frequency hop sequences is followed the certain rule random variation, and PSK phase modulation sequence is a binary pseudo random sequence.

2. pseudo-random FSK/psk signal complex envelope form is as follows:

$s\left(t\right)=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}{c}_n\mathrm{\Π}\left(\frac{t-\mathrm{nT}}{T}\right)e^{j2\mathrm{\π}{a}_{n}t}---\left(6\right)$

N is the subpulse sum in the formula, and T is the subpulse width, c _nBe PSK sequence, a _nBe the frequency of n subpulse in pseudo-random FSK/psk signal, correspond to the FSK sequence, ∑ is represented all summations.

3. non-complete matching treatment signal: compare the processing signals of introducing the mismatch phase place with transmitting, be called non-complete matching treatment signal.

4. the complex envelope form of non-complete matching treatment signal is as follows:

$c\left(t\right)=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}{c}_n\mathrm{\Π}\left(\frac{t-\mathrm{nT}}{T}\right)e^{j(2\mathrm{\π}{a}_{n}t+{\mathrm{\Φ}}_n)}---\left(8\right)$

N is the subpulse sum in the formula, and T is the subpulse width, c _nBe PSK sequence, a _nFrequency for n subpulse in the non-complete matching treatment signal corresponds to the FSK sequence, and ∑ is represented all summations, Φ _nMismatch phase place for n subpulse in the non-complete matching treatment signal.

5. the non-complete matching treatment of multiplex modulated signal: the signal energy optimized distribution to target important frequencies point, and is extracted the mismatch phase place and produced non-complete matching treatment signal,, realize the process of signal Processing by the echoed signal simple crosscorrelation is received.

6. fundamental frequency:

f ₀＝1/T (10)

F in the formula ₀Be fundamental frequency, the minimum frequency of pseudo-random FSK/psk signal and non-complete matching treatment signal among its expression the present invention, T is the subpulse width.

7. rectangular window:

M represents counting of rectangular window in the formula.

The invention provides a kind of imperfect matching processing method (as shown in Figure 2) of pseudo random multiplex modulated signal, its feature comprises the steps:

The first step: obtain the target one-dimensional range profile:

The receiving radar broadband signal is done inverse fourier transform to the frequency domain data H (ω) that obtains, and obtains target one-dimensional range profile h (t);

$h\left(t\right)=\underset{-\∞}{\overset{+\∞}{\∫}}H\left(\mathrm{\ω}\right)e^{\mathrm{j\ωt}}\mathrm{d\ω}---\left(12\right)$

T express time in the formula, ω represents angular frequency;

Second step: to the target one-dimensional range profile h (t) that the first step obtains, adopt following method, obtain the frequency domain data of target one-dimensional range profile h (t);

At first, the target one-dimensional range profile h (t) that the first step is obtained is according to the Nyquist sampling thheorem, and 2 samplings obtain the target one-dimensional range profile of discretize;

Then, the target one-dimensional range profile sampling number that makes discretize is 2 integral multiple, if sampling number is not 2 integral multiple, the target one-dimensional range profile end zero padding of discretize is satisfied;

At last, utilize fft algorithm to realize the Fourier exchange of the target one-dimensional range profile h (t) that the first step obtains, obtain the frequency domain data of target one-dimensional range profile h (t);

The 3rd step: to the frequency domain data of the second target one-dimensional range profile h (t) that obtain of step, take absolute value, obtain the amplitude-frequency value of target one-dimensional range profile h (t) frequency domain data, obtain the phase frequency value of target one-dimensional range profile h (t) frequency domain data corresponding simultaneously with the amplitude-frequency value of target one-dimensional range profile h (t) frequency domain data;

The 4th step: utilize the amplitude-frequency value of the 3rd target one-dimensional range profile h (t) frequency domain data that obtain of step, method below adopting obtains pseudo-random FSK/psk signal;

At first, the 3rd all Frequency point place amplitude-frequency values that go on foot target one-dimensional range profile h (t) frequency domain data that obtains are sued for peace, again the amplitude-frequency value at all Frequency point places of target one-dimensional range profile h (t) frequency domain data divided by try to achieve above and value, obtain the normalization amplitude-frequency value of target one-dimensional range profile h (t) frequency domain data;

Then, the normalization amplitude-frequency of target one-dimensional range profile h (t) the frequency domain data subpulse sum N with pseudo-random FSK/psk signal on duty, round, obtain the degree matrix that each frequency multiplication occurs in pseudo-random FSK/psk signal, the element position of this degree matrix is represented the frequency of pseudo-random FSK/psk signal neutron pulse;

Then, randomly draw the plain position of each frequency multiplication occurrence number entry of a matrix in pseudo-random FSK/psk signal that obtains above, this frequency multiplication occurrence number matrix element position element value of randomly drawing is subtracted one, write down the element position that this is drawn into simultaneously, this positional value (frequency) is saved as first element value that element number equals subpulse sum N matrix; Equally, the plain position of each the frequency multiplication occurrence number entry of a matrix that is drawn into is for the second time saved as second element value that element number equals subpulse sum N matrix, by that analogy; If the plain position of each the frequency multiplication occurrence number entry of a matrix element value of randomly drawing is zero, just the back of this displacement to each frequency multiplication occurrence number matrix, and each frequency multiplication occurrence number matrix element position range that randomly draw next time subtracts one;

Repeat said process, all elements value up to each frequency multiplication occurrence number matrix is zero, that element number that obtains equals the matrix of subpulse sum N, is exactly the frequency matrix that each subpulse occurs in pseudo-random FSK/psk signal, and this frequency matrix multiply by fundamental frequency f ₀Obtain FSK sequence a _n

Follow again, utilize random function rand () to produce [0,1] and go up equally distributed number, when numerical value more than or equal to 0.5 the time, value+1, when numerical value less than 0.5 the time, value-1 produces the even biphase coding sequence that a length equals subpulse sum N, is phase-shift keying (PSK) PSK sequence c _n

At last, by the frequency shift keying fsk sequence a that obtains above _n, phase-shift keying (PSK) PSK sequence c _n, the N of appointment and T, according to following formula,

Pseudo-random FSK/psk signal complex envelope form is as follows:

$s\left(t\right)=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}{c}_n\mathrm{\Π}\left(\frac{t-\mathrm{nT}}{T}\right)e^{j2\mathrm{\π}{a}_{n}t}---\left(13\right)$

N is the subpulse sum in the formula, and T is the subpulse width, c _nBe PSK sequence, a _nBe the frequency of n subpulse in pseudo-random FSK/psk signal, correspond to the FSK sequence, ∑ is represented all summations;

Just can obtain pseudo-random FSK/psk signal;

The 5th step: the phase frequency value of utilizing the 3rd target one-dimensional range profile h (t) frequency domain data that obtain of step, extract the phase value at each frequency multiplication place one to one with the amplitude-frequency value of target one-dimensional range profile h (t) frequency domain data, with these phase values series arrangement successively, obtain frequency multiplication mismatch phasing matrix;

The 6th step: utilize the 5th to go on foot the frequency multiplication mismatch phasing matrix that obtains, method below adopting obtains each subpulse mismatch phase sequence;

At first, the degree matrix that each subpulse mismatch phase value is occurred in non-complete matching treatment signal equals the degree matrix that each frequency multiplication occurs in the 4th step in pseudo-random FSK/psk signal, the element position of this degree matrix is represented the frequency of non-complete matching treatment signal subspace pulse;

Then, the degree matrix that each the subpulse mismatch phase value that obtains is above occurred in non-complete matching treatment signal, randomly draw the plain position (element position is represented frequency) of each subpulse mismatch phase value occurrence number entry of a matrix, go on foot the frequency multiplication mismatch phasing matrix that obtains according to the 5th, the phase value of the frequency correspondence that each the subpulse mismatch phase value occurrence number matrix element position that obtains randomly drawing is represented, mismatch phase value as current subpulse in the non-complete matching treatment signal, the mismatch phase value of current subpulse equals first element value of subpulse sum N matrix as element number, and the element value of each the subpulse mismatch phase value occurrence number matrix element position that will randomly draw subtracts one;

In like manner, the phase value of the frequency correspondence that the element position of the degree matrix that each the subpulse mismatch phase value that is drawn into is for the second time occurred in non-complete matching treatment signal is represented, equal second element value of subpulse sum N matrix as element number, and the element value of each the subpulse mismatch phase value occurrence number matrix element position that will randomly draw subtracts one, by that analogy; If each subpulse mismatch phase value occurrence number matrix element position element value of randomly drawing is zero, just this displacement is arrived the back of each subpulse mismatch phase value occurrence number matrix, and each subpulse mismatch phase value occurrence number matrix element position range that randomly draw next time subtracts one;

Repeat said process, be zero up to each element value of each subpulse mismatch phase value occurrence number matrix;

At last, the element number that obtains is above equaled the matrix of subpulse sum N as each subpulse mismatch phase sequence, i.e. Φ _n

The 7th step: the pseudo-random FSK/psk signal and the 6th that utilized for the 4th step obtained goes on foot each the subpulse mismatch phase sequence that obtains, and method below adopting obtains non-complete matching treatment signal;

Go on foot each the subpulse mismatch phase sequence Φ that obtains with the 6th _nAdd the 4th one to one with each frequency and go on foot in the pseudo-random FSK/psk signal that obtains, obtain non-complete matching treatment signal;

Non-complete matching treatment complex envelope form is as follows:

$c\left(t\right)=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}{c}_n\mathrm{\Π}\left(\frac{t-\mathrm{nT}}{T}\right)e^{j(2\mathrm{\π}{a}_{n}t+{\mathrm{\Φ}}_n)}---\left(15\right)$

N is the subpulse sum in the formula, and T is the subpulse width, c _nBe PSK sequence, a _nFrequency for n subpulse in the non-complete matching treatment signal corresponds to the FSK sequence, and ∑ is represented all summations, Φ _nRepresent each subpulse mismatch phase sequence;

The 8th step: pseudo-random FSK/psk signal and the 7th that the 4th step was obtained goes on foot the non-complete matching treatment signal that obtains, and method below adopting obtains both cross correlation results;

At first,, get Fourier transform (FFT), obtain the frequency domain data of pseudo-random FSK/psk signal pseudo-random FSK/psk signal that the 4th step obtained;

Then,, get Fourier transform (FFT), obtain non-complete matching treatment signal frequency-domain data the non-complete matching treatment signal that the 7th step obtained;

Then, the frequency domain data conjugate points of the pseudo-random FSK/psk signal that obtains above is multiplied by the non-complete matching treatment signal frequency-domain data that face obtains;

At last, to the frequency domain data of pseudo-random FSK/psk signal of obtaining above and the conjugation dot product result of non-complete matching treatment signal frequency-domain data, negate Fourier transform (IFFT) obtains the cross correlation results of pseudo-random FSK/psk signal and non-complete matching treatment signal;

Formula is as follows:

$\mathrm{\χ}\left(v\right)=\frac{1}{T_d}\underset{-\∞}{\overset{\∞}{\∫}}s\left(t\right)c(t+v)\mathrm{dt}---\left(17\right)$

S in the formula (t) represents pseudo-random FSK/psk signal, and c (t) represents non-complete matching treatment signal, T _dThe duration (being presented as pulsewidth if be applied to radar signal) of expression signal s (t) and c (t), the v express time postpones;

The 9th step:, select rectangular window to the 8th pseudo-random FSK/psk signal that obtain of step and the cross correlation results of non-complete matching treatment signal;

The tenth step: utilize the 8th pseudo-random FSK/psk signal that obtain of step and the cross correlation results of non-complete matching treatment signal, method below adopting recovers the target one-dimensional range profile;

At first, mid point with the cross correlation results figure of the 8th pseudo-random FSK/psk signal that obtain of step and non-complete matching treatment signal is the center, left-right symmetric switch (IFFTSHIFT), take absolute value, obtain the mould value of pseudo-random FSK/psk signal and non-complete matching treatment signal cross correlation results;

Then, the both sides, mould value center of pseudo-random FSK/psk signal that obtains in the above and non-complete matching treatment signal cross correlation results, equal second rectangular window that goes on foot target one-dimensional range profile h (t) sampling number that obtains with length and multiply by pseudo-random FSK/psk signal and non-complete matching treatment signal cross correlation results figure, the target one-dimensional range profile that is restored out;

The target one-dimensional range profile that recovers as shown in the formula:

$\mathrm{\χ}\left(\mathrm{\τ}\right)=(T-|\mathrm{\τ}\left|\right)\underset{k=0}{\overset{K-1}{\mathrm{\Σ}}}{P}_k{e}^{j(2\mathrm{\π}{a}_k\mathrm{\τ}+{\mathrm{\Φ}}_k)}---\left(18\right)$

T represents the subpulse width in the formula, and the τ express time postpones, and K represents the sampling number of target one-dimensional range profile h (t), P _kThe normalization amplitude-frequency value of expression target one-dimensional range profile h (t) frequency domain data, a _kThe frequency of expression target one-dimensional range profile h (t) frequency domain data, Φ _kThe phase value of expression target one-dimensional range profile h (t) frequency domain data, ∑ is represented all summations;

The 11 step: that utilizes that target one-dimensional range profile h (t) that the first step obtains and the tenth step obtain recovers the target one-dimensional range profile, and method below adopting obtains the non-complete matching treatment output result of radar system;

At first, to the target one-dimensional range profile that recovers that the tenth step obtained, get Fourier transform (FFT), the frequency domain data of the target one-dimensional range profile that is restored out;

Then, the frequency domain data conjugation dot product second of the target one-dimensional range profile that recovers that obtains is above gone on foot the frequency domain data of the target one-dimensional range profile h (t) that obtains;

At last, the conjugation dot product result of the frequency domain data of the target one-dimensional range profile h (t) that the frequency domain data of the target one-dimensional range profile that recovers that obtains above and second step are obtained, negate Fourier transform (IFFT) obtains the non-complete matching treatment output result of radar system.

Non-complete matching treatment output result, formula is as follows:

$R\left(\mathrm{\τ}\right)=\underset{-\∞}{\overset{\∞}{\∫}}h\left(v\right)\mathrm{\χ}(v+\mathrm{\τ})\mathrm{dv}---\left(19\right)$

The τ express time postpones in the formula, and v represents correlation integral transition variable, h (v) represent the target one-dimensional range profile, χ (v) corresponding formula is as follows:

$\mathrm{\χ}\left(v\right)=\frac{1}{T_d}\underset{-\∞}{\overset{\∞}{\∫}}s\left(t\right)c(t+v)\mathrm{dt}---\left(20\right)$

S in the formula (t) represents pseudo-random FSK/psk signal, and c (t) represents non-complete matching treatment signal, T _dThe duration (being presented as pulsewidth if be applied to radar signal) of expression signal s (t) and c (t), the v express time postpones;

Through after the above step, just can realize non-complete matching treatment for pseudorandom complex modulated (FSK/PSK) signal.

Principle Analysis of the present invention:

The imperfect matching processing method principle is as follows:

As shown in Figure 3, non-complete matching treatment is output as:

$R\left(\mathrm{\τ}\right)=\frac{1}{T_d}\underset{-\∞}{\overset{\∞}{\∫}}[s(t-\mathrm{\τ})\⊗h\left(t\right)]\×c\left(t\right)\mathrm{dt}---\left(21\right)$

 represents convolution in the formula, * representing general multiplication, s (t) represents pseudo-random FSK/psk signal, c (t) represents non-complete matching treatment signal, T _dThe duration (being presented as pulsewidth if be applied to radar signal) of expression signal s (t) and c (t), the τ express time postpones, h (t) expression target one-dimensional range profile.The definition substitution (21) of convolution and change integration in proper order:

$R\left(\mathrm{\τ}\right)=\frac{1}{T_d}\underset{-\∞}{\overset{\∞}{\∫}}h\left(v\right)\underset{-\∞}{\overset{\∞}{\∫}}s(t-v-\mathrm{\τ})c\left(t\right)\mathrm{dtdv}---\left(22\right)$

Formula (22) integration is got:

$R\left(\mathrm{\τ}\right)=\underset{-\∞}{\overset{\∞}{\∫}}h\left(v\right)\mathrm{\χ}(v+\mathrm{\τ})\mathrm{dv}---\left(23\right)$

In the formula (23):

$\mathrm{\χ}\left(v\right)=\frac{1}{T_d}\underset{-\∞}{\overset{\∞}{\∫}}s\left(t\right)c(t+v)\mathrm{dt}---\left(24\right)$

Following theoretical derivation recovers the process of target one-dimensional range profile by the cross correlation results of pseudo-random FSK/psk signal s (t) and non-complete matching treatment signal c (t):

At first, the FSK sequence a that obtains by the 4th step _nWith the 6th each subpulse mismatch phase sequence Φ of obtaining of step _nProduction process, FSK sequence a as can be known _nWith each subpulse mismatch phase sequence Φ _nThe probability density function that occurs in the subpulse string is:

$f(a_n,{\mathrm{\Φ}}_n)=\underset{k=0}{\overset{K-1}{\mathrm{\Σ}}}{P}_k\mathrm{\δ}(a_n-a_k,{\mathrm{\Φ}}_n-{\mathrm{\Φ}}_k)---\left(25\right)$

K represents the sampling number of target one-dimensional range profile h (t), P in the formula _kThe normalization amplitude-frequency value of expression target one-dimensional range profile h (t) frequency domain data, a _kThe frequency of expression target one-dimensional range profile h (t) frequency domain data, Φ _kThe phase value of expression target one-dimensional range profile h (t) frequency domain data, ∑ is represented all summations.

When supposing non-complete matching treatment signal c (t) and pseudo-random FSK/psk signal s (t) cross correlation process, pseudo-random FSK/psk signal s (t) has passed through the time delay of a period of time, makes that time delay is τ, then:

$s^{*}(t-\mathrm{\τ})c\left(t\right)=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}{c}_n\mathrm{\Π}\left(\frac{t-\mathrm{\τ}-\mathrm{nT}}{T}\right)e^{-j2\mathrm{\π}{a}_n(t-\mathrm{\τ})}\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}{c}_m\mathrm{\Π}\left(\frac{t-\mathrm{mT}}{T}\right)e^{j(2\mathrm{\π}{a}_{m}t+{\mathrm{\Φ}}_m)}---\left(26\right)$

* asks conjugation in the formula.Gate function ∏ (t) has following Several Properties again:

$\mathrm{\&Pi;}\left(\frac{t-\mathrm{nT}}{T}\right)\mathrm{\&Pi;}\left(\frac{t-\mathrm{mT}}{T}\right)=\left\{\begin{array}{c}\mathrm{\&Pi;}\left(\frac{t-\mathrm{nT}}{T}\right)......n=\mathrm{<figure-callout\; id="0"\; label="m"\; filenames="A20041008151000222.png,A20041008151000223.png"\; state="\{\{state\}\}">m</figure-callout>}\\ 0......n\&NotEqual;m\end{array}\right.---\left(27\right)$

$\mathrm{\&Pi;}\left(\frac{t-\frac{\mathrm{\&Delta;}}{2}-\mathrm{nT}}{T}\right)\mathrm{\&Pi;}\left(\frac{t+\frac{\mathrm{\&Delta;}}{2}-\mathrm{nT}}{T}\right)=\mathrm{\&Pi;}\left(\frac{t}{|T-\mathrm{\&Delta;}|}\right)---\left(28\right)$

By ambiguity function character as can be known, the cross correlation function of radar signal, time delay τ＞0 is symmetrical with the result of τ＜0, gets τ＞0 here.

c _nBe the PSK sequence that obtained in the 4th step, it asked statistical average:

E(c _nc _m)＝δ(n-m) (29)

Formula (26) is asked statistical average, and formula (28), (29) substitution is obtained:

$E_{c_n}\left[s^{*}(t-\mathrm{\&tau;})c\left(t\right)\right]=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\mathrm{\&Pi;}\left(\frac{t}{|T-\mathrm{\&tau;}|}\right)e^{j(2\mathrm{\&pi;}{a}_n\mathrm{\&tau;}+{\mathrm{\&Phi;}}_n)}---\left(30\right)$

Continuation is to the Φ in the formula (30) _n, a _nAverage, simultaneously formula (25) substitution (30) formula got:

$E_{c_n,a_n,{\mathrm{\&Phi;}}_n}\left[s^{*}(t-\mathrm{\&tau;})c\left(t\right)\right]=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\mathrm{\&Pi;}\left(\frac{t}{|T-\mathrm{\&tau;}|}\right)\underset{k=0}{\overset{K-1}{\mathrm{\&Sigma;}}}{P}_k{e}^{j(2\mathrm{\&pi;}{a}_k\mathrm{\&tau;}+{\mathrm{\&Phi;}}_k)}---\left(31\right)$

The cross correlation function of deriving pseudo-random FSK/psk signal s (t) and non-complete matching treatment signal c (t) by formula (31) as shown in the formula:

$\mathrm{\&chi;}\left(\mathrm{\&tau;}\right)=\underset{-\&infin;}{\overset{+\&infin;}{\&Integral;}}{E}_{c_n,a_n,{\mathrm{\&Phi;}}_n}\left[s^{*}(t-\mathrm{\&tau;})c\left(t\right)\right]\mathrm{dt}$

$=\underset{-\&infin;}{\overset{+\&infin;}{\&Integral;}}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\mathrm{\&Pi;}\left(\frac{t}{T-\mathrm{\&tau;}}\right)\underset{k=0}{\overset{K-1}{\mathrm{\&Sigma;}}}{P}_k{e}^{j(2\mathrm{\&pi;}{a}_k\mathrm{\&tau;}+{\mathrm{\&Phi;}}_k)}\mathrm{dt}---\left(32\right)$

In formula (28) substitution formula (32), obtain the target one-dimensional range profile that from the cross correlation results of pseudo-random FSK/psk signal s (t) and non-complete matching treatment signal c (t), recovers:

$\mathrm{\&chi;}\left(\mathrm{\&tau;}\right)=(T-|\mathrm{\&tau;}\left|\right)\underset{k=0}{\overset{K-1}{\mathrm{\&Sigma;}}}{P}_k{e}^{j(2\mathrm{\&pi;}{a}_k\mathrm{\&tau;}+{\mathrm{\&Phi;}}_k)}---\left(33\right)$

T represents the subpulse width in the formula, and the τ express time postpones, and K represents the sampling number of target one-dimensional range profile h (t), P _kThe normalization amplitude-frequency value of expression target one-dimensional range profile h (t) frequency domain data, a _kThe frequency of expression target one-dimensional range profile h (t) frequency domain data, Φ _kThe phase value of expression target one-dimensional range profile h (t) frequency domain data, ∑ is represented all summations.

From formula (33) as can be seen, the sum term of back is the inverse fourier transform of target one-dimensional range profile frequency domain obviously, and (T-| τ |) is equivalent to add a quarter window.Therefore, in the imperfect matching processing method among the present invention, the cross correlation function of non-complete matching treatment signal and pseudo-random FSK/PSK radar signal is approximately equal to radar target-range image h (t).

Essence of the present invention is by the energy-optimised strong zone of target scattering that is assigned to signal, and extraction mismatch phase place produces non-complete matching treatment signal, make the cross correlation function of radar emission signal and non-complete processing signals be approximately equal to radar target-range image, final Radar Signal Processing is output as the autocorrelation function of target one-dimensional range profile, compare with impulse radar, can obtain bigger signal to noise ratio (S/N ratio), compare, can obtain more target information with existing matched filter processing technology.

The non-complete matched signal disposal route that the present invention proposes, significant to radar lock on and low observability identification of targets.

Description of drawings

Fig. 1 matched filter processing method theory diagram

S among the figure _T(t) be the radar emission signal, subscript T represents emission, and target scattering is represented the influence of target to transmitting, h _m(t) be the impulse response of matched filter, subscript m is represented the implication of mating, and R (τ) is the output after the matched filter processing, and the τ express time postpones.

Fig. 2 imperfect matching processing method process flow diagram

Fig. 3 imperfect matching processing method theory diagram

Among the figure: h (t) represents radar target-range image, the pseudo-random FSK/psk signal of s (t-τ) expression radar emission, and c (t) represents non-complete matching treatment signal, the result of the non-complete matching treatment of R (τ) expression, integration is The τ express time postpones.

Fig. 4, Fig. 5 and Fig. 6 are computer artificial result examples of the present invention

Among the figure: what the coordinate axis horizontal ordinate was represented is the range unit number, and what ordinate was represented is normalized range value;

Fig. 4 is the target one-dimensional range profile that sets;

Fig. 5 is the target one-dimensional range profile that recovers after pseudo-random FSK/psk signal and the non-complete matching treatment signal simple crosscorrelation;

The result of the complete matching treatment of Fig. 6 right and wrong.

Embodiment

Utilize imperfect matching processing method of the present invention to carry out signal Processing.Simulation result is shown in Fig. 4,5,6.Fig. 4 is that we one of setting counts is 64 target one-dimensional range profile.Emulation neutron pulse sum is taken as 64, subpulse width T is 1us, after Fig. 5 is pseudo-random FSK/psk signal and non-complete matching treatment signal simple crosscorrelation, the target one-dimensional range profile that windowing extracts, the normalized correlation coefficient of it and real goal one-dimensional range profile equals 0.8484.Based on the target one-dimensional range profile that obtains, can adopt the method for present existing one-dimensional range profile Target Recognition to carry out Target Recognition.Net result after the complete matching treatment of Fig. 6 right and wrong.By analyzing as can be known in the background technology, utilize the matched filter processing method, radar is output as the target one-dimensional range profile, and in the simulation result, the maximal value of ideally handling back output equals 0.63.The radar that utilizes imperfect matching processing method to obtain is output as the autocorrelation function of target one-dimensional range profile, this point can be found out from (23) formula, handle back output maximal value and approximate 0.85, be about under the matched filter processing method peaked 1.35 times, output power value is original 1.82 times.The present invention can be not extra the increase noise, this value can be regarded the raising multiple of system signal noise ratio again as.

In sum, utilize the imperfect matching processing method among the present invention, the Radar Signal Processing output signal-to-noise ratio is greatly improved, obtain the target scattering characteristic information simultaneously, significant to radar lock on and the low observability target of identification.

Claims (1)

1, a kind of imperfect matching processing method of pseudo random multiplex modulated signal, its feature comprises the steps:

The first step: obtain the target one-dimensional range profile:

The receiving radar broadband signal is done inverse fourier transform to the frequency domain data H (ω) that obtains, and obtains target one-dimensional range profile h (t);

$h\left(t\right)=\underset{-\&infin;}{\overset{+\&infin;}{\&Integral;}}H\left(\mathrm{\&omega;}\right)e^{\mathrm{j\&omega;t}}\mathrm{d\&omega;}$

T express time in the formula, ω represents angular frequency;

Second step: to the target one-dimensional range profile h (t) that the first step obtains, adopt following method, obtain the frequency domain data of target one-dimensional range profile h (t);

At first, the target one-dimensional range profile h (t) that the first step is obtained is according to the Nyquist sampling thheorem, and 2 samplings obtain the target one-dimensional range profile of discretize;

Then, the target one-dimensional range profile sampling number that makes discretize is 2 integral multiple, if sampling number is not 2 integral multiple, the target one-dimensional range profile end zero padding of discretize is satisfied;

At last, utilize fft algorithm to realize the Fourier transform of the target one-dimensional range profile h (t) that the first step obtains, obtain the frequency domain data of target one-dimensional range profile h (t);

The 3rd step: to the frequency domain data of the second target one-dimensional range profile h (t) that obtain of step, take absolute value, obtain the amplitude-frequency value of target one-dimensional range profile h (t) frequency domain data, obtain the phase frequency value of target one-dimensional range profile h (t) frequency domain data corresponding simultaneously with the amplitude-frequency value of target one-dimensional range profile h (t) frequency domain data;

The 4th step: utilize the amplitude-frequency value of the 3rd target one-dimensional range profile h (t) frequency domain data that obtain of step, method below adopting obtains pseudo-random FSK/psk signal;

At first, the 3rd all Frequency point place amplitude-frequency values that go on foot target one-dimensional range profile h (t) frequency domain data that obtains are sued for peace, again the amplitude-frequency value at all Frequency point places of target one-dimensional range profile h (t) frequency domain data divided by try to achieve above and value, obtain the normalization amplitude-frequency value of target one-dimensional range profile h (t) frequency domain data;

Then, the normalization amplitude-frequency of target one-dimensional range profile h (t) the frequency domain data subpulse sum N with pseudo-random FSK/psk signal on duty, round, obtain the degree matrix that each frequency multiplication occurs in pseudo-random FSK/psk signal, the element position of this degree matrix is represented the frequency of pseudo-random FSK/psk signal neutron pulse;

Then, randomly draw the plain position of each frequency multiplication occurrence number entry of a matrix in pseudo-random FSK/psk signal that obtains above, this frequency multiplication occurrence number matrix element position element value of randomly drawing is subtracted one, write down the element position that this is drawn into simultaneously, this positional value is saved as first element value that element number equals subpulse sum N matrix; Equally, the plain position of each the frequency multiplication occurrence number entry of a matrix that is drawn into is for the second time saved as second element value that element number equals subpulse sum N matrix, by that analogy; If the plain position of each the frequency multiplication occurrence number entry of a matrix element value of randomly drawing is zero, just the back of this displacement to each frequency multiplication occurrence number matrix, and each frequency multiplication occurrence number matrix element position range that randomly draw next time subtracts one;

Repeat said process, all elements value up to each frequency multiplication occurrence number matrix is zero, that element number that obtains equals the matrix of subpulse sum N, is exactly the frequency matrix that each subpulse occurs in pseudo-random FSK/psk signal, and this frequency matrix multiply by fundamental frequency f ₀, obtain FSK sequence a _n

Follow again, utilize random function rand () to produce [0,1] and go up equally distributed number, when numerical value more than or equal to 0.5 the time, value+1, when numerical value less than 0.5 the time, value-1 produces the even biphase coding sequence that a length equals subpulse sum N, is phase-shift keying (PSK) PSK sequence c _n

At last, by the frequency shift keying fsk sequence a that obtains above _n, phase-shift keying (PSK) PSK sequence c _n, the N of appointment and T, according to following formula,

Pseudo-random FSK/psk signal complex envelope form is as follows:

$s\left(t\right)=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{c}_n\mathrm{\&Pi;}\left(\frac{t-\mathrm{nT}}{T}\right)e^{j2\mathrm{\&pi;}{a}_{n}t}$

N is the subpulse sum in the formula, and T is the subpulse width, c _nBe PSK sequence, a _nBe the frequency of n subpulse in pseudo-random FSK/psk signal, correspond to the FSK sequence, ∑ is represented all summations;

Just can obtain pseudo-random FSK/psk signal;

The 5th step: the phase frequency value of utilizing the 3rd target one-dimensional range profile h (t) frequency domain data that obtain of step, extract the phase value at each frequency multiplication place one to one with the amplitude-frequency value of target one-dimensional range profile h (t) frequency domain data, with these phase values series arrangement successively, obtain frequency multiplication mismatch phasing matrix;

The 6th step: utilize the 5th to go on foot the frequency multiplication mismatch phasing matrix that obtains, method below adopting obtains each subpulse mismatch phase sequence;

At first, the degree matrix that each subpulse mismatch phase value is occurred in non-complete matching treatment signal equals the degree matrix that each frequency multiplication occurs in the 4th step in pseudo-random FSK/psk signal, the element position of this degree matrix is represented the frequency of non-complete matching treatment signal subspace pulse;

Then, the degree matrix that each the subpulse mismatch phase value that obtains is above occurred in non-complete matching treatment signal, randomly draw the plain position of each subpulse mismatch phase value occurrence number entry of a matrix, go on foot the frequency multiplication mismatch phasing matrix that obtains according to the 5th, the phase value of the frequency correspondence that each the subpulse mismatch phase value occurrence number matrix element position that obtains randomly drawing is represented, mismatch phase value as current subpulse in the non-complete matching treatment signal, the mismatch phase value of current subpulse equals first element value of subpulse sum N matrix as element number, and the element value of each the subpulse mismatch phase value occurrence number matrix element position that will randomly draw subtracts one;

In like manner, the phase value of the frequency correspondence that the element position of the degree matrix that each the subpulse mismatch phase value that is drawn into is for the second time occurred in non-complete matching treatment signal is represented, equal second element value of subpulse sum N matrix as element number, and the element value of each the subpulse mismatch phase value occurrence number matrix element position that will randomly draw subtracts one, by that analogy; If each subpulse mismatch phase value occurrence number matrix element position element value of randomly drawing is zero, just this displacement is arrived the back of each subpulse mismatch phase value occurrence number matrix, and each subpulse mismatch phase value occurrence number matrix element position range that randomly draw next time subtracts one;

Repeat said process, be zero up to each element value of each subpulse mismatch phase value occurrence number matrix;

At last, the element number that obtains is above equaled the matrix of subpulse sum N as each subpulse mismatch phase sequence, i.e. Φ _n

The 7th step: the pseudo-random FSK/psk signal and the 6th that utilized for the 4th step obtained goes on foot each the subpulse mismatch phase sequence that obtains, and method below adopting obtains non-complete matching treatment signal;

Go on foot each the subpulse mismatch phase sequence Φ that obtains with the 6th _nAdd the 4th one to one with each frequency and go on foot in the pseudo-random FSK/psk signal that obtains, obtain non-complete matching treatment signal;

Non-complete matching treatment complex envelope form is as follows:

$c\left(t\right)=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{c}_n\mathrm{\&Pi;}\left(\frac{t-\mathrm{nT}}{T}\right)e^{j(2\mathrm{\&pi;}{a}_{n}t+{\mathrm{\&Phi;}}_n)}$

N is the subpulse sum in the formula, and T is the subpulse width, c _nBe PSK sequence, a _nFrequency for n subpulse in the non-complete matching treatment signal corresponds to the FSK sequence, and ∑ is represented all summations, Φ _nRepresent each subpulse mismatch phase sequence;

The 8th step: pseudo-random FSK/psk signal and the 7th that the 4th step was obtained goes on foot the non-complete matching treatment signal that obtains, and method below adopting obtains both cross correlation results;

At first,, get Fourier transform, obtain the frequency domain data of pseudo-random FSK/psk signal pseudo-random FSK/psk signal that the 4th step obtained;

Then,, get Fourier transform, obtain non-complete matching treatment signal frequency-domain data the non-complete matching treatment signal that the 7th step obtained;

Then, the frequency domain data conjugate points of the pseudo-random FSK/psk signal that obtains above is multiplied by the non-complete matching treatment signal frequency-domain data that face obtains;

At last, to the frequency domain data of pseudo-random FSK/psk signal of obtaining above and the conjugation dot product result of non-complete matching treatment signal frequency-domain data, the negate Fourier transform obtains the cross correlation results of pseudo-random FSK/psk signal and non-complete matching treatment signal;

Formula is as follows:

$\mathrm{\&chi;}\left(v\right)=\frac{1}{T_d}\underset{-\&infin;}{\overset{\&infin;}{\&Integral;}}s\left(t\right)c(t+v)\mathrm{dt}$

S in the formula (t) represents pseudo-random FSK/psk signal, and c (t) represents non-complete matching treatment signal, T _dThe duration of expression signal s (t) and c (t), the v express time postpones;

The 9th step:, select rectangular window to the 8th pseudo-random FSK/psk signal that obtain of step and the cross correlation results of non-complete matching treatment signal;

The tenth step: utilize the 8th pseudo-random FSK/psk signal that obtain of step and the cross correlation results of non-complete matching treatment signal, method below adopting recovers the target one-dimensional range profile;

At first, mid point with the cross correlation results figure of the 8th pseudo-random FSK/psk signal that obtain of step and non-complete matching treatment signal is the center, the left-right symmetric switch takes absolute value, and obtains the mould value of pseudo-random FSK/psk signal and non-complete matching treatment signal cross correlation results;

Then, the both sides, mould value center of pseudo-random FSK/psk signal that obtains in the above and non-complete matching treatment signal cross correlation results, equal second rectangular window that goes on foot target one-dimensional range profile h (t) sampling number that obtains with length and multiply by pseudo-random FSK/psk signal and non-complete matching treatment signal cross correlation results figure, the target one-dimensional range profile that is restored out;

The target one-dimensional range profile that recovers as shown in the formula:

$\mathrm{\&chi;}\left(\mathrm{\&tau;}\right)=(T-|\mathrm{\&tau;}\left|\right)\underset{k=0}{\overset{K-1}{\mathrm{\&Sigma;}}}{P}_k{e}^{j(2\mathrm{\&pi;}{a}_k\mathrm{\&tau;}+{\mathrm{\&Phi;}}_k)}$

T represents the subpulse width in the formula, and the τ express time postpones, and K represents the sampling number of target one-dimensional range profile h (t), P _kThe normalization amplitude-frequency value of expression target one-dimensional range profile h (t) frequency domain data, a _kThe frequency of expression target one-dimensional range profile h (t) frequency domain data, Φ _kThe phase value of expression target one-dimensional range profile h (t) frequency domain data, ∑ is represented all summations;

The 11 step: that utilizes that target one-dimensional range profile h (t) that the first step obtains and the tenth step obtain recovers the target one-dimensional range profile, and method below adopting obtains the non-complete matching treatment output result of radar system;

At first, to the target one-dimensional range profile that recovers that the tenth step obtained, get Fourier transform, the frequency domain data of the target one-dimensional range profile that is restored out;

Then, the frequency domain data conjugation dot product second of the target one-dimensional range profile that recovers that obtains is above gone on foot the frequency domain data of the target one-dimensional range profile h (t) that obtains;

At last, the conjugation dot product result of the frequency domain data of the target one-dimensional range profile h (t) that the frequency domain data of the target one-dimensional range profile that recovers that obtains above and second step are obtained, the negate Fourier transform obtains the non-complete matching treatment output result of pseudo random multiplex modulated signal.

Formula is as follows:

$R\left(\mathrm{\&tau;}\right)=\underset{-\&infin;}{\overset{\&infin;}{\&Integral;}}h\left(v\right)\mathrm{\&chi;}(v+\mathrm{\&tau;})\mathrm{dv}$

The τ express time postpones in the formula, and v represents correlation integral transition variable, and h (v) represents the target one-dimensional range profile; X (v) corresponding formula is as follows:

$\mathrm{\&chi;}\left(v\right)=\frac{1}{T_d}\underset{-\&infin;}{\overset{\&infin;}{\&Integral;}}s\left(t\right)c(t+v)\mathrm{dt}$

S in the formula (t) represents pseudo-random FSK/psk signal, and c (t) represents non-complete matching treatment signal, T _dThe duration of expression signal s (t) and c (t), the v express time postpones.

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