CN106501787A - Coded Signals method for parameter estimation based on smooth pseudo derivative feedback - Google Patents

Abstract

The present invention relates to a kind of Coded Signals method for parameter estimation based on smooth pseudo derivative feedback, mainly solves the problems, such as that existing method can not take into account low signal-to-noise ratio with little amount of calculation.Implementation step is：1) Coded Signals of 13 Barker code sequential codings are produced；2) its power spectrum is obtained as FFT to Coded Signals；3) power spectrum is smoothed, and signal carrier frequency is estimated according to the three dB bandwidth power spectrum center of gravity of power spectrum after smooth；4) Coded Signals are carried out with smooth pseudo derivative feedback conversion, the amplitude sequence at carrier frequency is obtained；5) search amplitude sequence minimum undershoot spacing obtains signal element width, and calculates the subcode number included by adjacent undershoot；6) according to undershoot position and subcode number, the estimation of sequence of symhols is obtained.The present invention improves the estimated accuracy of the parameter to Coded Signals in the case of low signal-to-noise ratio, reduces amount of calculation, can be used for the accurate scouting to target.

Description

Coded Signals method for parameter estimation based on smooth pseudo derivative feedback

Technical field

The invention belongs to technical field of data processing, the two-phase volume of more particularly to a kind of smooth pseudo derivative feedback SPWVD Code bpsk signal method for parameter estimation, can be used for the accurate scouting to target in low probability of intercept radar.

Background technology

In order to reduce average emitted power, reduce the probability that signal is trapped, low probability of intercept radar is generally using having The pulse compression signal of broadband product when big.Phase-coded signal due to have higher range resolution ratio and stronger anti-scouting, Antijamming capability and become a kind of conventional pulse compression signal.Due to the echo-signal that radar is received often be buried in big In noise background, therefore, when using digital received, how the phase of phase-coded signal is rapidly estimated under low signal-to-noise ratio Related parameter has important practical significance.

For the Parameter Estimation Problem of bpsk signal, Wujiang is marked, and incomparably, Yu Chun is proposing " based on Wavelet Transform Phase-coded signal intrapulse feature is extracted " see aerospace electronic warfare, 2005 (3):38-40, extracts with wavelet transformation in text little Recognizing phase-coded signal, the extraction of wavelet ridge under conditions of low signal-to-noise ratio is affected the method for wave crest line by noise Very big, Signal parameter estimation precision is affected, and the method operand is big, is not suitable for engineer applied；Yin Jihao, Wang Ling, Chen Tian Qi proposes " a kind of multiple Coded Signals carrier frequency, code check and coded sequence method of estimation " and sees signal transacting, and 2006,22 (5):639-543, uses code element information and coding of Time-Frequency Analysis Method-Short Time Fourier Transform STFT to bpsk signal in text Sequence is estimated, but the noiseproof feature of STFT is poor, low to Signal parameter estimation precision in the environment of low signal-to-noise ratio；Lv Ming Long, Zhou Ming, Han Jun, Deng Jing propose " a kind of low signal-to-noise ratio Coded Signals Time-Frequency Analysis Method " and see radar science and skill Art, 2010 (6):Result after proposing to convert signal STFT in 549-552. texts carries out dual threshold Singularity detection, the party again Although method achieves the parameter Estimation under conditions of low signal-to-noise ratio to bpsk signal, but estimated accuracy is low, and is estimating Process needs to accumulate pulse, and required process time is long, computationally intensive.

Content of the invention

Present invention aims to the deficiency of above-mentioned existing method, propose a kind of based on smooth pseudo derivative feedback Coded Signals method for parameter estimation, with improve wide to biphase coding bpsk signal carrier frequency, code under Low SNR and The estimated accuracy of coded sequence, while reduce amount of calculation.

To achieve these goals, technical scheme includes as follows：

(1) biphase coding encoded by 13 Barker code sequences [1 111 1-1-1 1 1-1 1-1 1] is produced Signal s (t)；

(2) FFT is carried out to Coded Signals s (t), obtains its power spectrum Y (m)；

(3) power spectrum Y (m) is smoothed, the power spectrum Y after being smoothed_s(k)；

(4) according to smooth rear power spectrum Y_sK the three dB bandwidth power spectrum center of gravity of (), estimates signal carrier frequency

(5) amplitude sequence is obtained

5a) Coded Signals s (t) are carried out with smooth pseudo derivative feedback SPWVD conversion, two-dimentional amplitude-frequency matrix is obtained SPWVD (t, f),

5b) two-dimentional amplitude-frequency matrix SPWVD (t, f) is scanned in frequency dimension, signal carrier frequency is obtainedThe amplitude sequence at place Row

(6) symbol width of Coded Signals s (t) is calculated

6a) amplitude sequence is searched forEach undershoot position is obtained, adjacent undershoot interval delta is calculated；

6b) take minimum adjacent undershoot interval delta and be designated as Δ_min, then the estimate of signal element widthFor：

Wherein, T_sFor signal sampling period；

(7) subcode number l included by every segment data that undershoot is separated is calculated：L=Δs/Δ_min；

(8) sequence of symhols of Coded Signals is calculated

8a) subcode number l included according to undershoot position and by every segment data that undershoot is separated, estimates roughly Count out sequence of symhols

8b) the sequence of symhols to roughly estimatingAccording to the accurate estimation that equation below device obtains sequence of symhols

Wherein, | | | | it is to take norm computing,It is by the signal carrier frequency for estimatingSymbol widthSequence of symholsAnd the Coded Signals that time t is reconfigured out, argmin is to take optimal solution.

The present invention is had the advantage that compared with prior art：

1st, frequency estimation accuracy is high

The present invention is filtered process using improved power spectrum smoothing formula to the power spectrum of biphase coding bpsk signal, And signal carrier frequency is estimated according to the three dB bandwidth center of gravity of power spectrum after smooth, compared to prior art to time-frequency matrix maximum Sequence is averaged come the method for estimating carrier frequency, improves and the carrier frequency of biphase coding bpsk signal is estimated under Low SNR Meter precision.

2nd, the estimated accuracy of symbol width is high

The present invention is converted using smooth pseudo derivative feedback SPWVD and the symbol width of Coded Signals is estimated, Compared to the method that prior art is converted using ZAM, SPWVD conversion has more preferable time-frequency locality, improves in low noise Symbol width estimated accuracy than under the conditions of to Coded Signals.

3rd, amount of calculation is little

The present invention is mapped as signal using the phase information that smooth pseudo derivative feedback SPWVD becomes Coded Signals of changing commanders Amplitude information at carrier frequency, compared to the method that prior art adopts Short Time Fourier Transform, the parameter to Coded Signals Estimate repeatedly accumulate data and multiple threshold decisions, reduce amount of calculation.

With reference to the accompanying drawings and detailed description the present invention is described in further details.

Description of the drawings

Fig. 1 is the flowchart of the present invention；

Fig. 2 is the frequency estimation accuracy of Coded Signals obtained with the present invention with signal to noise ratio change curve；

Fig. 3 is that the symbol width estimated accuracy of the Coded Signals obtained with existing method with the present invention is become with signal to noise ratio Change curve comparison figure.

Specific embodiment

With reference to Fig. 1, the present invention realizes that step is as follows：

Step 1:Obtain Coded Signals s (t).

By 13 Barker code sequences [1 111 1-1-1 1 1-1 1-1 1] encoded two are produced as follows Phase encoded signal s (t)：

Wherein, SNR is signal to noise ratio, f_cFor carrier frequency, t is the time, and τ is echo time delay, T_PFor symbol width, n is Barker code sequence Row length, φ is initial phase, φ_iFor the phase place of each subpulse, for Coded Signals, φ_i∈ { 0, π }, works as Barker code When the code element of sequence is 1, φ_iπ is taken as, when the code element of Barker code sequence is -1, φ_iIt is taken as 0,It is that width is T_PRectangle Window function, n (t) are the Gaussian sequence for randomly generating.

Step 2:Obtain power spectrum Y (m) of Coded Signals s (t).

FFT is carried out to Coded Signals s (t) 2a), result F after FFT [s (t)], transformation for mula is obtained As follows：

Wherein, f is frequency；

2b) according to FFT after result F [s (t)], obtain power spectrum Y (m) of Coded Signals s (t)：

Wherein, time spans of the T for Coded Signals s (t), m carry out the length sequence number of FFT for signal.

Step 3:Power spectrum Y after being smoothed_s(k).

Power spectrum Y (m) is smoothed, the power spectrum signal Y after being smoothed_s(k)：

Wherein, M is smooth length, and k is spectral line sequence number.

Step 4:Calculate the carrier frequency of Coded Signals s (t)

4a) Y is set_sK in (), maximum amplitude is Y_s(k₀), calculate Y_sThe three dB bandwidth internal power spectrum center of gravity of (k)

Wherein, L is Y_sAll more than 0.5Y in (k)_s(k₀) spectral line quantity, k be three dB bandwidth in spectral line sequence number；

4b) willCorresponding frequency is used as the carrier frequency that estimates

Wherein, T_sFor the sampling period.

Step 5:Obtain amplitude sequence

5a) Coded Signals s (t) are carried out with smooth pseudo derivative feedback SPWVD conversion, two-dimentional amplitude-frequency matrix is obtained SPWVD(t,f)：

Wherein, g (τ) be time domain window function, h (τ) be frequency domain window function, s^*T () is the multiple common of Coded Signals s (t) Conjugate signal；

5b) two-dimentional amplitude-frequency matrix SPWVD (t, f) is scanned in frequency dimension, carrier frequency is obtainedThe amplitude sequence at place

Step 6:Calculate the symbol width of Coded Signals s (t)

6a) amplitude sequence is searched forEach undershoot position is obtained, and is calculated between adjacent undershoot Every Δ,

6b) take minimum adjacent undershoot interval and be designated as Δ_min, then the estimate of signal element widthFor：

Wherein, T_sFor signal sampling period.

Step 7:Calculate subcode number l included by every segment data that undershoot is separated：L=Δs/Δ_min.

Step 8:Calculate the sequence of symhols of Coded Signals

8a) subcode number l included according to undershoot position and by every segment data that undershoot is separated, estimates roughly Count out sequence of symhols

8b) the sequence of symhols to roughly estimatingAccording to the accurate estimation that equation below obtains sequence of symhols

Wherein, | | | | it is to take norm computing,It is by the signal carrier frequency for estimatingSymbol widthSequence of symholsAnd the Coded Signals that time t is reconfigured out, argmin is to take optimal solution.

The effect of the present invention can be further verified by following emulation.

1. experiment scene：

Radar return signal is two encoded by 13 Barker code sequences [1 111 1-1-1 1 1-1 1-1 1] Phase encoded signal s (t), signal carrier frequency f₀=75MHz, code check f_b=7.5MHz, sample frequency f_s=300MHz, receives in signal The noise of aliasing is white Gaussian noise that average is that 0, variance is 1.In the experiment for estimating Coded Signals carrier frequency, power spectrum Smooth points elect 20 as, and in the experiment for estimating signal element width and sequence of symhols, selections signal to noise ratio is -7dB, Smoothing Pseudo Wei The window function of Ge Na distribution SPWVD and ZAM distributions elects Hamming window as, and window length is respectively 33 and 65.

2. experiment content and result：

Test 1, the method for the present invention is used in the estimation to Coded Signals carrier frequency, by 500 Monte Carlo realities Test emulation and obtain signal frequency estimation accuracy result under different signal to noise ratios, as shown in Figure 2.

Figure it is seen that frequency estimation accuracy can be up to 96% when signal to noise ratio is -8dB, the side of the present invention is described Method is for signal carrier frequency is when estimating to be applied to low signal-to-noise ratio.

Test 2, the inventive method is used in the estimation to estimating signal element width, by 500 Monte Carlo Experiments Emulation has obtained the signal element width estimated accuracy result under different signal to noise ratios, as shown in Figure 3.

From figure 3, it can be seen that when letter is than being -7dB, estimation of the SPWVD converter techniques that the present invention is adopted to symbol width Up to 91%, the ZAM conversion that prior art is adopted only has 74% to the estimated accuracy of symbol width to high precision, and the inventive method is described Existing method is better than to the symbol width estimated accuracy of Coded Signals under conditions of low signal-to-noise ratio.

Claims (5)

1. the Coded Signals method for parameter estimation based on smooth pseudo derivative feedback, including：

(1) the Coded Signals s encoded by 13 Barker code sequences [1 111 1-1-1 1 1-1 1-1 1] is produced (t)；

(2) FFT is carried out to Coded Signals s (t), obtains its power spectrum Y (m)；

(3) power spectrum Y (m) is smoothed, the power spectrum Y after being smoothed_s(k)；

(4) according to smooth rear power spectrum Y_sK the three dB bandwidth power spectrum center of gravity of (), estimates signal carrier frequency

(5) amplitude sequence is obtained

5a) Coded Signals s (t) are carried out with smooth pseudo derivative feedback SPWVD conversion, two-dimentional amplitude-frequency matrix SPWVD is obtained (t, f),

5b) two-dimentional amplitude-frequency matrix SPWVD (t, f) is scanned in frequency dimension, signal carrier frequency is obtainedThe amplitude sequence at place

(6) symbol width of Coded Signals s (t) is calculated

6a) amplitude sequence is searched forEach undershoot position is obtained, adjacent undershoot interval delta is calculated；

6b) take minimum adjacent undershoot interval delta and be designated as Δ_min, then the estimate of signal element widthFor：

${\hat{T}}_b={\mathrm{\Δ}}_{\min }\·T_s,$

Wherein, T_sFor signal sampling period；

(7) subcode number l included by every segment data that undershoot is separated is calculated：L=Δs/Δ_min；

(8) sequence of symhols of Coded Signals is calculated

8a) subcode number l included according to undershoot position and by every segment data that undershoot is separated, roughly estimates Sequence of symhols

8b) the sequence of symhols to roughly estimatingAccording to the accurate estimation that equation below device obtains sequence of symhols

${\hat{P}}_m=\arg \min \left\{\right||\hat{s}({\hat{f}}_0,{\hat{T}}_b,{\tilde{P}}_m,t)-s\left(t\right)|\left|\right\},$

Wherein, | | | | it is to take norm computing,It is by the signal carrier frequency for estimatingSymbol widthCode MetasequenceAnd the Coded Signals that time t is reconfigured out, arg min are to take optimal solution.

2. method according to claim 1, Coded Signals s (t) that radar is received in its step (1), its are represented As follows：

$s\left(t\right)=10^(SNR/20)\left\{\underset{i=1}{\overset{n}{\Σ}}\exp \right\{j\left(2{\mathrm{\πf}}_c\right(t-\mathrm{\τ})+{\mathrm{\φ}}_i+\mathrm{\φ})\left\}{u}_{T_P}\left(\right(t-\mathrm{\τ})-{\mathrm{iT}}_P)\right\}+n\left(t\right),$

Wherein, SNR is signal to noise ratio, f_cFor carrier frequency, t is the time, and τ is echo time delay, T_PFor symbol width, n is that Barker code sequence is long Degree, φ is initial phase, φ_iFor the phase place of each subpulse, for Coded Signals, φ_i∈ { 0, π }, when code element is 1, φ_iπ is taken as, when code element is -1, φ_iIt is taken as 0,It is that width is T_PRectangular window function, n (t) is the Gauss white noise for randomly generating Sound sequence.

3. method according to claim 1, wherein step (3) is that power spectrum Y (m) to Coded Signals s (t) is carried out Smoothing processing, is carried out as follows：

$Y_s\left(k\right)=\frac{1}{M+1}\underset{m=k-\frac{M}{2}}{\overset{k+\frac{M}{2}}{\Σ}}|Y\left(m\right){|}^2,$

Wherein, M is smooth length, and k is spectral line sequence number, and m carries out the length sequence number of FFT, Y for signal_sK () is smooth rear work( Rate is composed.

4. according to power spectrum Y after smooth in method according to claim 1, its step (4)_sThe three dB bandwidth power spectrum of (k) Center of gravity estimation signal carrier frequencyCarry out as follows：

Smooth rear power spectrum Y 4a) is set_sK the maximum amplitude of () is Y_s(k₀), calculate Y_sThe three dB bandwidth internal power spectrum center of gravity of (k)

$\hat{k}=\frac{\underset{k=1}{\overset{L}{\Σ}}{\mathrm{kY}}_s\left(k\right)}{\underset{k=1}{\overset{L}{\Σ}}{Y}_s\left(k\right)},$

Wherein, L is Y_sAll more than 0.5Y in (k)_s(k₀) spectral line quantity, k be three dB bandwidth in spectral line sequence number；

Three dB bandwidth internal power is composed center of gravity 4b)Corresponding frequency is used as the signal carrier frequency that estimates

${\hat{f}}_0=\frac{\hat{k}}{{\mathrm{NT}}_s},$

Wherein, T_sFor signal sampling period.

5. Coded Signals s (t) are carried out Smoothing Pseudo Wigner point by method according to claim 1 in its step (5) Cloth SPWVD is converted, and its transformation for mula is as follows：

$SPWVD(t,f)=\∫\∫g(u-t)s(t+\frac{\mathrm{\τ}}{2})s^{*}(t-\frac{\mathrm{\τ}}{2})h\left(\mathrm{\τ}\right)e^{-j2\mathrm{\π}f\mathrm{\τ}}d\mathrm{\τ}du,$

Wherein, g (τ) be time domain window function, h (τ) be frequency domain window function, s^*T () is believed for the complex conjugate of Coded Signals s (t) Number.