CN103746722B - Method for estimating jump cycle and take-off time of frequency hopping signal - Google Patents

Abstract

The invention discloses a method for estimating the jump cycle and the take-off time of a frequency hopping signal. The method comprises the following steps: step one: obtaining a data sequence; step two: initializing parameters; step three: calculating the power spectrum of data in the i-th short-time window; step four: estimating the peak frequency and the peak-to-average power ratio of the data in the short-time window through the power spectrum; step five: judging whether the processing for the data of all short-time windows is completed, if the processing is not completed, returning to the third step, and if the processing is completed, returning to the sixth step; step six: estimating the initial moment of each jump of the frequency hopping signal; step seven: utilizing an alpha-TM algorithm to estimate the jump cycle and the take-off time. The method simultaneously utilizes the frequency characteristics and the energy features of the frequency hopping signal, and the robustness is good; through short-time Fourier transform, the calculated amount is small, the engineering practicability is high, and the method is suitable for quick and robust estimation of the parameters of the frequency hopping signal.

Description

A kind of Frequency Hopping Signal hop cycle and take-off time method of estimation

Technical field

The present invention relates to signal transacting field, particularly relate to a kind of Frequency Hopping Signal hop cycle and take-off time method of estimation.

Background technology

Frequency Hopping Signal has good anti-interference, low probability of intercept, anti-multipath and stronger multiple access networking capability, has been widely used in military and civilian communication, also started in recent years to be applied under water some to communication security, occasion that reliability requirement is higher.Hop cycle and take-off time are two basic parameters describing Frequency Hopping Signal.Under random background noise and non-condition for cooperation, quick, the high accuracy that realize these two parameters estimate it is finally reach the prerequisite of frequency-hopping system being scouted to interference object.

The current parameter Estimation to Frequency Hopping Signal adopts the method for time frequency analysis mostly, and the method for time frequency analysis is divided into the large class of linear processes two usually.Wigner-Ville distributes (Wigner-Ville Distribution, WVD) be typical Nonlinear time-frequency distribution, there is time frequency resolution the highest in theory, but for this kind of multicomponent data processing of Frequency Hopping Signal, there is serious cross term interference in WVD, makes it apply and be restricted.In order to overcome the interference of WVD cross term, there is a large amount of Frequency Hopping Signal parameter estimation algorithms improved based on WVD: as the people such as Zhao Jun propose a kind of employing smooth-switch method (Smoothed Pseudo WVD, SPWVD) method estimates the parameter of Frequency Hopping Signal, the method can suppress cross-interference terms effectively, but the method is to noise-sensitive, at low signal-to-noise ratio (SignaltoNoiseRatio, SNR) under, parameter Estimation performance sharply declines, and the very huge (Zhao Jun of amount of calculation, Zhang Chaoyang, Lai Lifeng, Deng. a kind of Frequency Hopping Signal Blind Parameter Estimation based on time frequency analysis. Circuits and Systems journal, 2003, 8 (3): 46-50.), SPWVD combines with wavelet transformation by Feng Tao and Yuan Chaowei, this method is just improved the method for estimation of Frequency Hopping Signal hop cycle, with the method for the people such as Zhao Jun without essential distinction (Feng Tao, Yuan Chaowei. based on the frequency parameter blind estimate of time-frequency crestal line. electronic letters, vol, 2011,39 (12): 2921-2925.), the people such as Guo Yi propose the method estimating Frequency Hopping Signal parameter based on SPW time frequency analysis, SPW and SPWVD compares and account for certain advantage in amount of calculation, but under low SNR, estimated accuracy declines greatly (Guo Yi, Zhang Eryang, Shen Rongjun. Frequency Hopping Signal time and frequency zone is analyzed and Blind Parameter Estimation. signal transacting, 2007,23 (2): 210-213.), Chen proposes the method for parameter estimation based on resetting SPWVD, the method increase the focusing of time-frequency distributions, but amount of calculation increases greatly (Chen T C.Joint signal parameter estimation offrequency-hopping communications.Communications, IET, 2012,6 (4): 381-389.).The above-mentioned method improved based on WVD, only make use of in time-frequency crestal line crest frequency or crest frequency energy feature, greatly affected by noise, in order to improve Parameter Estimation Precision, need to increase a large amount of amount of calculation, be not suitable for requirement realize fast Frequency Hopping Signal fast, the occasion of Highly precise FFT method.

Summary of the invention

In order to overcome the deficiencies in the prior art, the invention provides a kind of Frequency Hopping Signal hop cycle and take-off time method of estimation, amount of calculation is little, and realize simple, engineering practicability is strong, is applicable to the quick robust iterative of Frequency Hopping Signal parameter.

For achieving the above object, the present invention takes following technical scheme:

A kind of Frequency Hopping Signal hop cycle and take-off time method of estimation, comprise the steps:

(1) pending data sequence x (n) is obtained, n=0,1 ..., N-1, wherein the sampled point number of N corresponding to the Frequency Hopping Signal that detects;

(2) parameter initialization: the long M of short time-window, the short time-window that arrange Short Time Fourier Transform employing move stepping L, and the α value of α-TM algorithm; Calculate total short time-window number represent downward rounding operation, and initialization short time-window sequence number i=1;

(3) the power spectrum Y of the data in i-th short time-window is calculated _i(l ₂):

If the data sequence in i-th short time-window is x _i(m)=x (n _i), m=0,1 ... M-1, n _i=(i-1) L, (i-1) L+1 ..., (i-1) L+M-1, with formula (1) to x _im () does discrete Fourier transform:

$X_i\left(l_1\right)=\underset{m=0}{\overset{M-1}{\mathrm{\Σ}}}{x}_i\left(m\right)e^{-j\frac{2\mathrm{\π}}{M}{\mathrm{ml}}_1},l_1=\mathrm{0,1}...,M---\left(1\right)$

Wherein X _i(l ₁) representing the result of discrete Fourier transform, j represents imaginary unit, namely l ₁for X _i(l ₁) discrete frequency sequence number, then the data x in i-th short time-window _ithe power spectrum Y of (m) _i(l ₂) be:

$Y_i\left(l_2\right)=\frac{1}{M}{\left|X_i\left(l_1\right)\right|}^2,l_1=l_2$ And l ₂=0,1,2 ... M/2-1 (2)

Wherein, l ₂for Y _i(l ₂) discrete frequency sequence number;

(4) the power spectrum Y obtained by step (3) _i(l ₂) estimate the crest frequency f of data in i-th short time-window _iwith Peak-Average-Power Ratio PAR _i:

f _i＝(L _i-1)Δf (3)

${\mathrm{PAR}}_i=\frac{\max \left[Y_i\left(l_2\right)\right]}{\mathrm{mean}\left[Y_i\left(l_2\right)\right]-\max \left[Y_i\left(l_2\right)\right]/M}---\left(4\right)$

Wherein L _ifor all power spectrum Y _i(l ₂), l ₂=0,1,2 ... the discrete frequency sequence number that maximum in M/2-1 is corresponding, the frequency resolution of Δ f to be short time-window length the be discrete Fourier transform of M, Δ f=f _s/ M, f _sfor sample frequency, max [Y _i(l ₂)] be all power spectrum Y _i(l ₂), l ₂=0,1,2 ... maximum in M/2-1, mean [Y _i(l ₂)] be all power spectrum Y _i(l ₂), l ₂=0,1,2 ... the mean value of M/2-1;

(5) data sequence processing all short time-windows is judged whether: if i≤I-1, wherein then make i=i+1, and turn back to step (3), otherwise enter step (6);

(6) each initial time of jumping of Frequency Hopping Signal is estimated:

First, from the crest frequency sequence { f that all short time-windows are estimated _i, i=2,3 ..., I-1} and Peak-Average-Power Ratio sequence { PAR _i, i=2,3 ..., find out the short time-window sequence number simultaneously meeting formula (5) and formula (6) in I-1}, be designated as i _k, k=1,2 ... K:

|f _i-1-f _i+1|＞f _TH(5)

PAR _i＜min(PAR _i-1,PAR _i+1) (6)

Wherein K is the sum of the short time-window sequence number simultaneously meeting formula (5) and formula (6), f _tH=2 Δ f; f _irepresent the crest frequency of data in i-th short time-window, PAR _irepresent the Peak-Average-Power Ratio of data in i-th short time-window;

Then, formula (7) is utilized to estimate each initial time of jumping of Frequency Hopping Signal

${\hat{N}}_k^s=i_{k}L-M/2,k=\mathrm{1,2},...K---\left(7\right)$

(7) α-TM algorithm is utilized to estimate hop cycle with the take-off moment

Estimation procedure is as follows:

First, formula (8) is utilized to calculate sequence of differences

${\hat{N}}_k^d={\hat{N}}_{k+1}^s-{\hat{N}}_k^s,k=\mathrm{1,2}...,K-1---\left(8\right)$

Then, formula (9) is utilized to calculate $\{{\hat{N}}_k^d,k=\mathrm{1,2}...,K-1\}$ Result after sequence $\{{\hat{N}}_k^{\mathrm{ds}},k=\mathrm{1,2}...,K-1\}:$

${\hat{N}}_k^{\mathrm{ds}}=\mathrm{sort}\left({\hat{N}}_k^d\right),k=\mathrm{1,2}...,K-1---\left(9\right)$

Finally, formula (10) and (11) are utilized to estimate hop cycle with the take-off moment

${\hat{N}}_h=\frac{1}{(K-2k_0+1)}\underset{k=k_0}{\overset{K-k_0}{\mathrm{\Σ}}}{\hat{N}}_k^{\mathrm{ds}}---\left(10\right)$

${\hat{N}}_0=\frac{1}{K-2k_1}[\underset{k=k_1}{\overset{K+1-k_1}{\mathrm{\Σ}}}{\hat{N}}_k^s-\frac{(K-2k_1+2)(K-1)}{2}{\hat{N}}_h]---\left(11\right)$

Wherein represent sequence $\{{\hat{N}}_k^d,k=\mathrm{1,2}...,K-1\}$ Sort,

Further, in step (2), the long M value of short time-window is the integral number power of 2, and meets M < < N, and L value is 0 < α < 0.5.

Further, preferred α=0.25 of the present invention.

Further, x in step (3) _im the discrete Fourier transform of () is realized by fast Fourier transform.

Further, in step (7) to sequence sort, take descending sortord, or ascending sortord.

Beneficial effect:

(1) at present for estimating that the method for Frequency Hopping Signal parameter is the method based on WVD mostly, these class methods only make use of one in Frequency Hopping Signal time-frequency crestal line crest frequency or crest frequency energy feature, and greatly affected by noise, robustness is poor; And the high accuracy estimation in order to realize parameter, need to consume a large amount of amounts of calculation, realize complicated, which greatly limits the engineering practicability of these class methods.Method of estimation of the present invention make use of Frequency Hopping Signal time-frequency crestal line crest frequency and crest frequency energy feature simultaneously, robustness is strong, and be the method based on Short Time Fourier Transform, amount of calculation is little, realize simple, be applicable to the occasion requiring to realize Frequency Hopping Signal parameter Estimation fast, engineering practicability is strong.

(2) discrete Fourier transform calculating data sequence in this short time-window is needed when calculating the power spectrum in each window, and discrete Fourier transform can be realized by fast Fourier transform, fast Fourier transform is the very extensive and effective computational tool of a kind of use, which greatly enhances operation efficiency and the practicality of method of estimation, engineering reality can be applied to preferably.

(3) utilize α-TM algorithm to estimate hop cycle and take-off moment, the exceptional value that each jumping initial time that effectively can reduce estimation exists, on the impact of parameter estimation result, improves the robustness of parameter Estimation.

Accompanying drawing explanation

Fig. 1 is a kind of Frequency Hopping Signal hop cycle provided by the invention and take-off time method of estimation flow chart.

Fig. 2 is frequency hopping simulate signal frequency hopping pattern in the embodiment of the present invention.

Fig. 3 is frequency hopping simulate signal time-frequency crestal line in the embodiment of the present invention.

Fig. 4 be in the embodiment of the present invention when signal to noise ratio is-3dB, superposed the Received signal strength time-frequency figure after background noise.

Embodiment

Below in conjunction with accompanying drawing, the present invention is further described.

Before carrying out Frequency Hopping Signal hop cycle and take-off time estimation, need advanced row data acquisition and input, can sample frequency f be obtained by part of data acquisition _sthe initial sum end time of signal can be obtained by input, the termination of the signal detected and the difference of initial time are signal pulsewidth, sampling number corresponding to signal pulsewidth is set to N, after the sampling number N that signal initial time also obtains corresponding to signal pulsewidth being detected, Frequency Hopping Signal hop cycle and take-off time estimation can be carried out.

Principle of the present invention is the initial time utilizing the time-frequency crestal line of Frequency Hopping Signal to jump at each, there is crest frequency transition and the minimum feature of Peak-Average-Power Ratio simultaneously, first estimate the initial time of each jumping, thus estimate hop cycle and the take-off time parameter of Frequency Hopping Signal further.Frequency Hopping Signal hop cycle of the present invention and take-off moment method of estimation, first, search out in the time-frequency crestal line of Frequency Hopping Signal Short Time Fourier Transform and meet crest frequency transition and the minimum short time-window sequence number of Peak-Average-Power Ratio simultaneously, thus estimate the initial time of each jumping; Then, according to the initial time of each jumping estimated, the good α of robustness-TM algorithm is utilized to estimate hop cycle and the take-off time of Frequency Hopping Signal.

As shown in Figure 1, as shown in Figure 1, Frequency Hopping Signal hop cycle provided by the invention and take-off time method of estimation, specifically comprise the following steps:

(1) pending data sequence x (n) is obtained, n=0,1 ..., N-1

The real-time data collection of N number of sampled point will be received as pending data sequence x (n) from transducer, n=0,1 ..., N-1, or extract from detecting that the data of N number of sampled point that the signal moment is initial are as pending data sequence x (n) from memory, n=0,1 ... N-1, wherein the sampled point number of N corresponding to the Frequency Hopping Signal that detects.

(2) parameter initialization

The long M of short time-window, the short time-window that arrange Short Time Fourier Transform employing move stepping L, and the α value of α-TM algorithm, calculate total short time-window number represent downward rounding operation, the long M value of short time-window is the integral number power of 2, and meets M < < N, and L value is α is greater than 0 number being less than 0.5, initialization short time-window sequence number i=1.

(3) the power spectrum Y of the data in i-th short time-window is calculated _i(l ₂)

Data sequence in i-th short time-window is x _i(m)=x (n _i), m=0,1 ... M-1, n _i=(i-1) L, (i-1) L+1 ..., (i-1) L+M-1, with formula (1) to x _im () does discrete Fourier transform:

$X_i\left(l_1\right)=\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}{x}_i\left(m\right)e^{-j\frac{2\mathrm{\&pi;}}{M}{\mathrm{ml}}_1},l_1=\mathrm{0,1}...,M---\left(1\right)$

Wherein X _i(l ₁) representing the result of discrete Fourier transform, j represents imaginary unit, namely l ₁for X _i(l ₁) discrete frequency sequence number, then the data x in i-th short time-window _ithe power spectrum Y of (m) _i(l ₂) be:

$Y_i\left(l_2\right)=\frac{1}{M}{\left|X_i\left(l_1\right)\right|}^2,l_1=l_2$ And l ₂=0,1,2 ... M/2-1 (2)

Wherein, l ₂for Y _i(l ₂) discrete frequency sequence number.

X in formula (1) _im the discrete Fourier transform of () can be realized by fast Fourier transform, utilize fast Fourier transform can reduce the operand of algorithm, improves the computational efficiency of algorithm.

(4) by crest frequency and the Peak-Average-Power Ratio of data in power spectrum estimation i-th short time-window

The crest frequency f of data in i-th short time-window is calculated respectively with formula (3) and formula (4) _iwith Peak-Average-Power Ratio PAR _i:

f _i＝(L _i-1)Δf (3)

${\mathrm{PAR}}_i=\frac{\max \left[Y_i\left(l_2\right)\right]}{\mathrm{mean}\left[Y_i\left(l_2\right)\right]-\max \left[Y_i\left(l_2\right)\right]/M}---\left(4\right)$

Wherein L _ifor all power spectrum Y _i(l ₂), l ₂=0,1,2 ... the discrete frequency sequence number that maximum in M/2-1 is corresponding, the frequency resolution of Δ f to be short time-window length the be discrete Fourier transform of M, Δ f=f _s/ M, f _sfor sample frequency, max [Y _i(l ₂)] be all power spectrum Y _i(l ₂), l ₂=0,1,2 ... maximum in M/2-1, mean [Y _i(l ₂)] be all power spectrum Y _i(l ₂), l ₂=0,1,2 ... the mean value of M/2-1.

Wherein, Y is searched for _i(l ₂) the discrete frequency sequence number L of maximum and its correspondence _iwith calculating mean [Y _i(l ₂)] time, get l ₂=0,1,2 ... M/2-1, this is because the discrete Fourier transform of real data sequence is about Central Symmetry, therefore searches for power spectral value Y _i(l ₂) discrete frequency sequence number L corresponding to maximum _itime, l ₂only can get front M/2 point;

(5) data sequence processing all short time-windows is judged whether

If i≤I-1, then make i=i+1, and turn back to step (3), otherwise enter step (6);

(6) each initial time of jumping of Frequency Hopping Signal is estimated:

First, from crest frequency sequence { f _i, i=2,3 ..., I-1} and Peak-Average-Power Ratio sequence { PAR _i, i=2,3 ..., find out the short time-window sequence number simultaneously meeting formula (5) and formula (6) in I-1}, be designated as i _k, k=1,2 ... K:

|f _i-1-f _i+1|＞f _TH(5)

PAR _i＜min(PAR _i-1,PAR _i+1) (6)

Wherein K is the sum of the short time-window sequence number simultaneously meeting formula (5) and formula (6), f _tH=2 Δ f;

Then, formula (7) is utilized to estimate each initial time of jumping of Frequency Hopping Signal

${\hat{N}}_k^s=i_{k}L-M/2,k=\mathrm{1,2},...K---\left(7\right)$

In step (6), formula (5) is corresponding to the transition feature of Frequency Hopping Signal crest frequency, the minimum of the corresponding Frequency Hopping Signal Peak-Average-Power Ratio of formula (6), search meets the short time-window sequence number of formula (5) and formula (6) simultaneously, be actually and make use of the initial time of Frequency Hopping Signal in each jumping, there is the feature of the minimum and frequency transient of Peak-Average-Power Ratio simultaneously, relatively at present only by the existing method of one of them feature, the sane type of method provided by the invention is strong; In formula (5), get f _tH=2 Δ f are because the Frequency Estimation worst error that the fence effect of finite length discrete Fourier transform brings is Δ f, therefore occur that two difference on the frequencies are greater than 2 Δ f and can think and occurred frequency transient feature;

(7) α-TM algorithm is utilized to estimate hop cycle with the take-off moment

Estimation procedure is as follows:

First, formula (8) is utilized to calculate sequence of differences

${\hat{N}}_k^d={\hat{N}}_{k+1}^s-{\hat{N}}_k^s,k=\mathrm{1,2}...,K-1---\left(8\right)$

Then, formula (9) is utilized to calculate $\{{\hat{N}}_k^d,k=\mathrm{1,2}...,K-1\}$ Result after sequence $\{{\hat{N}}_k^{\mathrm{ds}},k=\mathrm{1,2}...,K-1\}:$

${\hat{N}}_k^{\mathrm{ds}}=\mathrm{sort}\left({\hat{N}}_k^d\right),k=\mathrm{1,2}...,K-1---\left(9\right)$

Finally, formula (10) and (11) are utilized to estimate hop cycle with the take-off moment

${\hat{N}}_h=\frac{1}{(K-2k_0+1)}\underset{k=k_0}{\overset{K-k_0}{\mathrm{\&Sigma;}}}{\hat{N}}_k^{\mathrm{ds}}---\left(10\right)$

${\hat{N}}_0=\frac{1}{K-2k_1}[\underset{k=k_1}{\overset{K+1-k_1}{\mathrm{\&Sigma;}}}{\hat{N}}_k^s-\frac{(K-2k_1+2)(K-1)}{2}{\hat{N}}_h]---\left(11\right)$

Wherein represent sequence $\{{\hat{N}}_k^d,k=\mathrm{1,2}...,K-1\}$ Sort,

In the 7th step, α-TM algorithm can effectively reduce the exceptional value existed, on the impact of parameter estimation result, improves the precision of parameter Estimation; α value in formula 9 and formula 10 is that 0.25 effect is better.

In embodiments of the invention, emulation Received signal strength model is:

$s\left(n\right)=A\left\{\begin{array}{c}\exp \left(j\frac{2\mathrm{\&pi;}{f}_{0}n}{f_s}\right)\mathrm{rect}\left(\frac{n}{N_0}\right)\\ +\underset{t=1}{\overset{T}{\mathrm{\&Sigma;}}}\exp \left(j\frac{2\mathrm{\&pi;}{f}_{t}n}{f_s}\right)\mathrm{rect}\left[\frac{n-(t-1)N_h-N_0}{N_h}\right]\\ +\exp \left(j\frac{2f_{T+1}n}{f_s}\right)\mathrm{rect}\left(\frac{t-k{N}_h-N_0}{N_L}\right)\end{array}\right\},n=\mathrm{0,1},...N-1---\left(12\right)$

Wherein A is signal amplitude, rect (n/N _x) for length be N _xrectangular window, f _sfor sample frequency, f ₀, f _t, t=1,2 ..., T, f _t+1hopping frequencies, N ₀for take-off time, N _hfor hop cycle, N _lfor the duration of incomplete jumping within the observation period at end, T is the number of complete jumping in observation time, and total observed length is N=N ₀+ TN _h+ N _l, wherein N ₀and N _hfor parameter to be estimated.

Simulate signal parameter is set to respectively: sample frequency f _s=2400Hz, comprises 8 jumping signals in observation time, wherein comprise T=6 and finish whole hop cycle, two incomplete hop cycles, and hop cycle is N _h=600 sampled points, take-off time N ₀=400 sampled points, that incomplete jumping length at end is N _l=300 sampled points, total observed length N=4300 sampled point, Hopping frequencies is respectively 400,360,420,340,380,300,320,440Hz; Superposition zero mean Gaussian white noise, variances sigma ²size determined by signal to noise ratio snr: SNR=10log ₁₀[A ²/ (2 σ ²)], the signal to noise ratio snr of noise is set to-3dB.

Simulate signal frequency hopping pattern as shown in Figure 2, has marked hop cycle and the take-off time of this Frequency Hopping Signal in Fig. 2, can understand the parameter of Frequency Hopping Signal intuitively; Be the time-frequency crestal line of simulate signal shown in Fig. 3, as can be seen from Figure 3, the time-frequency crestal line initial time of jumping at each of emulation Frequency Hopping Signal, shows crest frequency transition and the minimum feature of Peak-Average-Power Ratio simultaneously; Figure 4 shows that superposed the Received signal strength time-frequency figure after background noise, as can be seen from Figure 4, at the initial time that each is jumped, the power spectrum of signal is affected by noise larger in the inventive method embodiment when signal to noise ratio is-3dB.

With the sampled signal x (n) be subject to after noise pollution that the simulation of this simulate signal receives, n=0,1 ..., N-1, N=4300.X (n) is carried out to the estimation of hop cycle and take-off time below.

Embodiment 1: first, carries out parameter initialization, and arrange the long M=128 of short time-window, short time-window moves stepping L=32, and α=0.25 of α-TM algorithm calculates total short time-window number initialization window moves number of times i=1.

Then, there is crest frequency transition and the minimum feature of Peak-Average-Power Ratio simultaneously, estimate the initial time of each jumping in the initial time utilizing Frequency Hopping Signal time-frequency crestal line to jump at each, and actual value and the estimated value of each initial time of jumping are as shown in table 1:

Table 1

Actual value	400	1000	1600	2200	2800	3400	4000
								Estimated value	416	992	1600	2208	2784	3392	4032

Finally, α-TM algorithm is utilized to estimate the hop cycle estimated value of Frequency Hopping Signal relative error is $|{\hat{N}}_h-N_h|/N_h=0,$ Take-off moment estimated value ${\hat{N}}_0=395.2,$ Relative error is $|{\hat{N}}_0-N_0|/N_0=0.012.$

Embodiment 2: first, carries out parameter initialization, and arrange the long M=256 of short time-window, short time-window moves stepping L=64, and α=0.25 of α-TM algorithm calculates total short time-window number initialization window moves number of times i=1.

Then, there is crest frequency transition and the minimum feature of Peak-Average-Power Ratio simultaneously, estimate the initial time of each jumping in the initial time utilizing Frequency Hopping Signal time-frequency crestal line to jump at each, and actual value and the estimated value of each initial time of jumping are as shown in table 2:

Table 2

Actual value	400	1000	1600	2200	2800	3400	4000
								Estimated value	448	1024	1664	2240	2880	3456	4096

Finally, α-TM algorithm is utilized to estimate the hop cycle estimated value of Frequency Hopping Signal relative error is $|{\hat{N}}_h-N_h|/N_h=0.0133,$ Take-off moment estimated value ${\hat{N}}_0=428.8,$ Relative error is $|{\hat{N}}_0-N_0|/N_0=0.072.$

Embodiment 3: first, carries out parameter initialization, and arrange the long M=128 of short time-window, short time-window moves stepping L=32, and α=0.3 of α-TM algorithm calculates total short time-window number initialization window moves number of times i=1.

Then, there is crest frequency transition and the minimum feature of Peak-Average-Power Ratio simultaneously, estimate the initial time of each jumping in the initial time utilizing Frequency Hopping Signal time-frequency crestal line to jump at each, and actual value and the estimated value of each initial time of jumping are as shown in table 3:

Table 3

Actual value	400	1000	1600	2200	2800	3400	4000
								Estimated value	416	992	1600	2208	2816	3392	4160

Finally, α-TM algorithm is utilized to estimate the hop cycle estimated value of Frequency Hopping Signal relative error is take-off moment estimated value relative error is

As can be seen from the result of embodiment 1, embodiment 2 and embodiment 3, method of estimation of the present invention can obtain good estimated accuracy, and calculating simple, amount of calculation is little, is applicable to fast, high accuracy estimates the hop cycle of Frequency Hopping Signal and the occasion of take-off time parameter.

The above is only the preferred embodiment of the present invention; be noted that for those skilled in the art; under the premise without departing from the principles of the invention, can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (5)

1. Frequency Hopping Signal hop cycle and a take-off time method of estimation, is characterized in that comprising the steps:

(1) pending data sequence x (n) is obtained, n=0,1 ..., N-1, wherein the sampled point number of N corresponding to the Frequency Hopping Signal that detects;

(2) parameter initialization: the long M of short time-window, the short time-window that arrange Short Time Fourier Transform employing move stepping L, and the α value of α-TM algorithm; Calculate total short time-window number represent downward rounding operation, and initialization short time-window sequence number i=1;

(3) the power spectrum Y of the data in i-th short time-window is calculated _i(l ₂):

If the data sequence in i-th short time-window is x _i(m)=x (n _i), m=0,1 ... M-1, n _i=(i-1) L, (i-1) L+1 ..., (i-1) L+M-1, with formula (1) to x _im () does discrete Fourier transform:

$X_i\left(l_1\right)=\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}{x}_i\left(m\right)e^{-k\frac{2\mathrm{\&pi;}}{M}m{l}_1},l_1=\mathrm{0,1}...,M---\left(1\right)$

Wherein X _i(l ₁) representing the result of discrete Fourier transform, j represents imaginary unit, namely l ₁for X _i(l ₁) discrete frequency sequence number, then the data x in i-th short time-window _ithe power spectrum Y of (m) _i(l ₂) be:

$Y_i\left(l_2\right)=\frac{1}{M}{\left|X_i\left(l_1\right)\right|}^2,$ L ₁=l ₂and l ₂=0,1,2 ... M/2-1 (2)

Wherein, l ₂for Y _i(l ₂) discrete frequency sequence number;

(4) the power spectrum Y obtained by step (3) _i(l ₂) estimate the crest frequency f of data in i-th short time-window _iwith Peak-Average-Power Ratio PAR _i:

f _i＝(L _i-1)△f (3)

${\mathrm{PAR}}_i=\frac{\max \left[Y_i\left(l_2\right)\right]}{\mathrm{mean}\left[Y_i\left(l_2\right)\right]-\max \left[Y_i\left(l_2\right)\right]/M}---\left(4\right)$

Wherein L _ifor all power spectrum Y _i(l ₂), l ₂=0,1,2 ... the discrete frequency sequence number that maximum in M/2-1 is corresponding, the frequency resolution of △ f to be short time-window length the be discrete Fourier transform of M, △ f=f _s/ M, f _sfor sample frequency, max [Y _i(l ₂)] be all power spectrum Y _i(l ₂), l ₂=0,1,2 ... maximum in M/2-1, mean [Y _i(l ₂)] be all power spectrum Y _i(l ₂), l ₂=0,1,2 ... the mean value of M/2-1;

(5) data sequence processing all short time-windows is judged whether: if i≤I-1, wherein then make i=i+1, and turn back to step (3), otherwise enter step (6);

(6) each initial time of jumping of Frequency Hopping Signal is estimated:

First, from the crest frequency sequence { f that all short time-windows are estimated _i, i=2,3 ..., I-1} and Peak-Average-Power Ratio sequence { PAR _i, i=2,3 ..., find out the short time-window sequence number simultaneously meeting formula (5) and formula (6) in I-1}, be designated as i _k, k=1,2 ... K:

|f _i-1-f _i+1|>f _TH(5)

PAR _i<min(PAR _i-1,PAR _i+1) (6)

Wherein K is the sum of the short time-window sequence number simultaneously meeting formula (5) and formula (6), f _tH=2 △ f; f _irepresent the crest frequency of data in i-th short time-window, PAR _irepresent the Peak-Average-Power Ratio of data in i-th short time-window;

Then, formula (7) is utilized to estimate each initial time of jumping of Frequency Hopping Signal

${\hat{N}}_k^s=i_{k}L-M/2,k=\mathrm{1,2},...K---\left(7\right)$

(7) α-TM algorithm is utilized to estimate hop cycle with the take-off moment

Estimation procedure is as follows:

First, formula (8) is utilized to calculate sequence of differences

${\hat{N}}_k^d={\hat{N}}_{k+1}^s-{\hat{N}}_k^s,k=\mathrm{1,2}...K-1---\left(8\right)$

Then, formula (9) is utilized to calculate result after sequence

${\hat{N}}_k^{\mathrm{ds}}=\mathrm{sort}\left({\hat{N}}_k^d\right),k=\mathrm{1,2}...,K-1---\left(9\right)$

Finally, formula (10) and (11) are utilized to estimate hop cycle with the take-off moment

${\hat{N}}_h=\frac{1}{(K-2k_0+1)}\underset{k=k_0}{\overset{K-k_0}{\mathrm{\&Sigma;}}}{\hat{N}}_k^{\mathrm{ds}}---\left(10\right)$

${\hat{N}}_0=\frac{1}{K-2k_1+2}[\underset{k=k_1}{\overset{K+1-k_1}{\mathrm{\&Sigma;}}}{\hat{N}}_k^s-\frac{(K-2k_1+2)(K-1)}{2}{\hat{N}}_h]---\left(11\right)$

Wherein represent sequence sort,

2. a kind of Frequency Hopping Signal hop cycle according to claim 1 and take-off time method of estimation, it is characterized in that: in described step (2), the long M value of short time-window is the integral number power of 2, and meeting M < < N, L value is 0< α <0.5.

3. a kind of Frequency Hopping Signal hop cycle according to claim 2 and take-off time method of estimation, is characterized in that: α=0.25.

4. a kind of Frequency Hopping Signal hop cycle according to claim 1 and take-off time method of estimation, is characterized in that: x in described step (3) _im the discrete Fourier transform of () is realized by fast Fourier transform.

5. a kind of Frequency Hopping Signal hop cycle according to claim 1 and take-off time method of estimation, is characterized in that: to sequence in described step (7) sort, take descending sortord, or ascending sortord.