CN104243369A - Wake-up signal detection method for underwater acoustic communication MODEM - Google Patents

Abstract

The invention provides a wake-up signal detection method for an underwater acoustic communication MODEM. The method includes the steps that two repeated two-phase code signals generated by a balanced Gold sequence are selected as wake-up signals, sliding correlation treatment between adjacent data block pairs different in length is adopted in a receiving end, a data block start moment corresponding to the maximum correlation value is wake-up signal arrival time, the difference between the length of a data block corresponding to the maximum correlation value and the length of each sent wake-up signal is the Doppler time stretching length, and therefore the wake-up signal arrival time and the Doppler time stretching length are jointly estimated; a current correlation value is obtained in the mode that a product of start data of the currently adjacent data block pairs at last time is subtracted from the sum of a former correlation value and a product of tail data of the currently adjacent data block pairs, the calculation amount is far smaller than that of multiple sliding copy correlation devices, and the method can be conducted in real time under the conditions of dormancy of the underwater acoustic communication MODEM and the low clock frequency of a processor and is high in practicality.

Description

A kind of wake-up signal detection method for underwater sound communication MODEM

Technical field

The invention belongs to technical field of underwater acoustic communication, be specifically related to a kind of detection method of underwater sound MODEM wake-up signal.

Background technology

Underwater sound MODEM majority is battery-powered, low power dissipation design need be considered, dormancy mechanism on duty is one of effective means of saving power consumption, underwater sound MODEM is in the resting state of low-power consumption at one's leisure, fraction circuit is only had to be in the state of working on power, once detect that wake-up signal is by opening the power supply of follow-up related circuit module, carries out communications transmit or reception.At present, common underwater sound MODEM wake-up signal is the CW pulse combined of multiple different frequency, the frequency energy adopting FFT process to obtain CW pulse compares with thresholding, carry out adjudicating and detecting, the frequency selective fading of underwater acoustic channel may make some frequency energy be less than pre-determined threshold, and cause undetected, the time-frequency characteristics of CW pulse in addition clearly, very easily intercepted and captured, be not suitable for the application scenario of covert communications.The pulse signal of large Timed automata is low by intercept probability, and adopt correlation processing technique to realize detecting, operand is higher.Under underwater sound MODEM is in resting state, the clock frequency of processor requires lower, if adopt the wake-up signal of pulse signal as underwater sound MODEM of large Timed automata, requires very high to the operation efficiency detected, and gives to detect in real time and brings great challenge.In underwater sound communication network, underwater sound MODEM network node launches wake-up signal to destination address node, and while often wishing reliably to wake destination address node up, non-destination address node is not waken up, and requires that the wake-up signal of different node has good orthogonality.

Summary of the invention

The present invention is directed to the shortcoming that wake-up signal is is easily intercepted and captured, loss is high that above-mentioned underwater sound MODEM adopts at present and the very high problem of wake-up signal detection calculations efficiency requirements, provide a kind of wake-up signal detection method for underwater sound communication MODEM.

The present invention for achieving the above object, takes following technical scheme to realize:

A kind of wake-up signal detection method for underwater sound communication MODEM, it is characterized in that: the biphase coded signal that the balanceable Gold sequence selecting two to repeat generates is as wake-up signal, receiving terminal first completes the Combined estimator to the wake-up signal time of advent and Doppler time collapsing length, recycling Doppler estimated result chooses the reference signal of corresponding Doppler time collapsing length, utilize and arrive time Estimate result intercepting Received signal strength, and carry out the logical down-sampled even lack sampling process of band, the signal obtained and reference signal make slip relevant treatment, complete wake-up signal detect by comparing correlation and pre-determined threshold, specifically comprise following committed step:

Step one: the sequence selecting " 0 " and " 1 " number to differ from 1 from Gold sequence race is balanceable Gold sequence, and the balanceable Gold sequence chosen repeats once, carries out dual polarization process, add rectangular window, with carrier frequency mixing, the real part of the number of winning the confidence, generates wake-up signal s (t):

Wherein g (n) be balanceable Gold sequence chip, T _cfor chip period, L is sequence length, w _cfor carrier frequency, G (t) is window function;

Step 2: adopt the adjacent data blocks of multiple Length discrepancy between slip relevant treatment carry out the Combined estimator of the wake-up signal time of advent and Doppler time collapsing length, by a front correlation, current correlation adds that current adjacent data blocks deducts previous adjacent data blocks to most end mantissa obtain most initial data product according to product, as formula 3, formula 4, except calculating the correlation of initial time, each correlation value calculation only subtracts computing containing once taking advantage of to add and once take advantage of, compare copy relevant treatment operand significantly to reduce

$R(n,\hat{k})=\underset{m=n}{\overset{n+(M+\hat{k})/2-1}{\mathrm{\Σ}}}x(m-M-\hat{k}+1)x(m-\frac{M}{2}-\frac{\hat{k}}{2}+1)---\left(3\right)$

$R(n,\hat{k})=R(n-1,\hat{k})+x\left(n\right)x(n-\frac{M}{2}-\frac{\hat{k}}{2})-x(n-\frac{M}{2}-\frac{\hat{k}}{2})x(n-M-\hat{k})---\left(4\right)$

When during with M → ∞, correlation is maximum, as formula 5, corresponding by finding maximum correlation peaks be wake-up signal to estimate the time of advent, be Doppler time collapsing length to estimate;

$R(n_0+\frac{M}{2}+\frac{k}{2}-1,k)=\underset{M\→\∞}{\lim }\underset{m=0}{\overset{(M+k)/2-1}{\mathrm{\Σ}}}x(n_0+m)x(n_0+m-\frac{M}{2}-\frac{k}{2})$

$=\underset{M\→\∞}{\lim }\underset{m=0}{\overset{(M+k)/2-1}{\mathrm{\Σ}}}[s^{\′}(m,k)+w_2(n_0+m)][s^{\′}(m,k)+w_3(n_0+m-\frac{M}{2}-\frac{k}{2})]$

$=\underset{M\→\∞}{\lim }\underset{m=0}{\overset{(M+k)/2-1}{\mathrm{\Σ}}}{s}^{\′}(m,k)s^{\′}(m,k)+\underset{M\→\∞}{\lim }\underset{m=0}{\overset{(M+k)/2-1}{\mathrm{\Σ}}}{s}^{\′}(m,k)w_3(n_0+m-\frac{M}{2}-\frac{k}{2})+---\left(5\right)$

$\underset{M\→\∞}{\lim }{w}_2(n_0+m)s^{\′}(m,k)+\underset{M\→\∞}{\lim }{w}_2(n_0+m)w_3(n_0+m-\frac{M}{2}-\frac{k}{2})$

$=\underset{m=0}{\overset{(M+k)/2-1}{\mathrm{\Σ}}}{s}^{\′}(m,k)s^{\′}(m,k)$

$x\left(n\right)=\left\{\begin{array}{cc}{w}_1\left(n\right)& n=\mathrm{0,1},...,n_0-1\\ s^{\′}(n-n_0,\frac{k}{2})+w_2\left(n\right)& n=n_0,n_0+1,...,n_0+\frac{M}{2}+\frac{k}{2}-1\\ s^{\′}(n-n_0-\frac{M}{2}-\frac{k}{2},\frac{k}{2})+w_3\left(n\right)& n=n_0+\frac{M}{2}+\frac{k}{2},n_0+\frac{M}{2}+\frac{k}{2}+1,...,n_0+M+k-1\\ w_4\left(n\right)& n=n_0+M+k,n_0+M+k+1,...,N-1\end{array}\right.---\left(6\right)$

The x (n) of formula 6 is the data received, w ₁(n), w ₂(n), w ₃(n) and w ₄n () be independent noise mutually; The s ' (n) of formula 7 is only containing the biphase coded signal of a balanceable Gold sequence, N _cfor the sample points of each chip; for having n unknown time of advent ₀with unknown Doppler stre tch time span isoparametric signal, at interval on be non-zero; Formula 5 also shows, improve sample rate, then M is larger, and the auto-correlation of the correlative relative signal of signal, noise and noise is less, can improve estimated performance;

Step 3: after completing the Combined estimator of the wake-up signal time of advent and Doppler time collapsing length, the down-sampled process of extracted at equal intervals to received signal again, if wake-up signal centre frequency and bandwidth ratio larger, also can adopt bandpass under sampling technology, reduce sampling number M, thus reduce the operand of step 4;

Step 4: in the reference signal of the multiple different Doppler time collapsing lengths of this locality preservation, choose the reference signal corresponding with step 2 Doppler estimated result, and in time range less before and after the time of advent that step 2 is estimated, by step 3 down-sampled after signal slide relevant to reference signal, the detection of wake-up signal is completed by comparing maximum related value and pre-determined threshold size, as formula 8

$T^{\′}\left(x\right)=\underset{n_0\∈[{\hat{n}}_0-m,{\hat{n}}_0+m]}{\max }\underset{n=n_0}{\overset{n_0+(M+\hat{k})/2-1}{\mathrm{\Σ}}}x\left(n\right)s^{\′}(n-n_0,\hat{k})---\left(8\right)$

If maximum related value is greater than thresholding, wake-up signal detected, otherwise wake-up signal do not detected.

Beneficial effect of the present invention is:

1, present invention employs balanceable Gold sequence design biphase coded signal as wake-up signal, time-frequency characteristics is not obvious, balanceable Gold sequence carrier leak is less, low intercepting and capturing and good concealment, in addition balanceable Gold sequence is Gold sequence race preferably oneself, the better sequence of cross correlation, is applied to underwater sound communication network, while waking destination address node up, non-destination address node is not waken up, thus can improve the energy efficiency of network.

2, the present invention adopt the adjacent data blocks of multiple Length discrepancy between slip relevant treatment carry out the Combined estimator of the wake-up signal time of advent and Doppler stre tch time span, utilize to arrive time Estimate result intercept signal and choose the local reference signal corresponding with Doppler's estimated result of preserving and carry out coherent detection, its operand is much smaller than the operand of multiple slip copy correlator, can when underwater sound MODEM dormancy processor clock frequency comparatively real time execution under low condition, there is good practicality.

Accompanying drawing explanation

Fig. 1 is wake-up signal design frame chart;

Fig. 2 is the time-frequency figure of wake-up signal;

Fig. 3 is the ambiguity function of the biphase signaling of the balanceable Gold sequence structure of long 511;

Fig. 4 is the correlated results that the adjacent data blocks of different length is right;

Fig. 5 is the Combined estimator block diagram of the wake-up signal time of advent and Doppler time collapsing length;

Fig. 6 is the Performance comparision that under different sample rate, Doppler is estimated;

Fig. 7 is that wake-up signal detects general diagram.

Embodiment

Below in conjunction with specific embodiment and accompanying drawing the present invention will be further described:

1, wake-up signal design

Fig. 1 is wake-up signal design frame chart, and the sequence selecting " 0 " and " 1 " number to differ from 1 from Gold sequence race is balanceable Gold sequence, and the balanceable Gold sequence chosen repeats once, carry out dual polarization process, add rectangular window, with carrier frequency mixing, the real part of the number of winning the confidence, generates wake-up signal as formula 1.The chip that the g (n) of formula 1 is balanceable Gold sequence, T _cfor chip period, L is sequence length, w _cfor carrier frequency.

The time-frequency figure of wake-up signal s (t) has obvious line spectrum unlike CW pulse, its feature is not obvious, as Fig. 2, the more non-equilibrium Gold sequence of balanced code Gold sequence has better spectral characteristic, carrier leak is less, and by force, balanceable Gold sequence is better than oneself, cross correlation sequence of non-equilibrium Gold sequence for Anti TBIgG and detection ability, be applied to underwater sound communication network, the energy efficiency of network can be improved.

2, the dualism hypothesis of wake-up signal detects

The biphase coded signal of balanceable Gold sequence design has " drawing pin type " ambiguity function, to Doppler shift and time deviation all very sensitive, as Fig. 3, time and the Doppler time collapsing length of wake-up signal arrival receiving terminal underwater sound MODEM are all unknown, therefore the dualism hypothesis test problems of unknown signaling parameter in noise can be regarded as to the detection of wake-up signal

$\begin{array}{cc}{H}_0:x\left(n\right)=w\left(n\right)& n=\mathrm{0,1},...,N-1\\ H_1:x\left(n\right)=s(n-n_0,k)+w\left(n\right)& n=\mathrm{0,1}...,N-1\end{array}---\left(3\right)$

The s (n) of formula 3 is without the wake-up signal postponed and do not have Doppler time flexible, and interval [0, M-1] is non-zero, s (n-n ₀, k) for having n unknown time of advent ₀with the isoparametric signal of unknown Doppler stre tch time span k, interval [0, M+k-1] is non-zero, if

$\frac{p(x;{\hat{n}}_0,\hat{k},H_1)}{p(x;H_0)}>\mathrm{\γ}---\left(4\right)$

H should be sentenced ₁,

$\frac{p(x;{\hat{n}}_0,\hat{k},H_1)}{p(x;H_0)}=\underset{n={\hat{n}}_0}{\overset{{\hat{n}}_0+M-1}{\mathrm{\Π}}}\exp \{-\frac{1}{{2\mathrm{\σ}}^2}[2x\left(n\right)s(n-{\hat{n}}_0,\hat{k})+s{(n-{\hat{n}}_0,\hat{k})}^2\left]\right\}>\mathrm{\γ}---\left(5\right)$

Take the logarithm in above formula both sides, if

$-\frac{1}{{2\mathrm{\σ}}^2}\underset{n={\hat{n}}_0}{\overset{{\hat{n}}_0+M-1}{\mathrm{\Σ}}}[-2x\left(n\right)s(n-{\hat{n}}_0,\hat{k})+s{(n-{\hat{n}}_0,\hat{k})}^2]>1\mathrm{n\γ}---\left(6\right)$

H should be sentenced ₁, then statistic is the correlation of Received signal strength and reference signal, as shown in the formula, in formula, σ is noise variance, and ε is the energy of signal, detects to obtain detection probability by NP, as formula 9.

$T\left(x\right)=\underset{n={\hat{n}}_0}{\overset{{\hat{n}}_0+M-1}{\mathrm{\Σ}}}x\left(n\right)s(n-{\hat{n}}_0,\hat{k})>{\mathrm{\σ}}^{2}1\mathrm{n\γ}+\frac{1}{2}\underset{n={\hat{n}}_0}{\overset{{\hat{n}}_0+M-1}{\mathrm{\Σ}}}s{(n-{\hat{n}}_0,\hat{k})}^2={\mathrm{\γ}}^{\′}---\left(7\right)$

$\mathrm{\ϵ}=\underset{n=0}{\overset{M-1}{\mathrm{\Σ}}}s{(n,\hat{k})}^2=\underset{n={\hat{n}}_0}{\overset{{\hat{n}}_0+M-1}{\mathrm{\Σ}}}s{(n-{\hat{n}}_0,\hat{k})}^2---\left(8\right)$

$P_D=Q(Q^{-1}\left(P_{\mathrm{FA}}\right)-\sqrt{\frac{\mathrm{\ϵ}}{{\mathrm{\σ}}^2}})---\left(9\right)$

Estimated value at H ₁maximum-likelihood estimator MLE, the wake-up signal time of advent and Doppler stre tch time when that is to say that ASSOCIATE STATISTICS amount is maximum, statistic also can formulate 10, wherein K/2 is the maximum Doppler stre tch time, formula 10 shows the relevant treatment that Likelihood ration test LRT needs the time, frequency carries out two dimension, traditional method is the direct employing Received signal strength copy signal slip relevant treatment of multiple different Doppler shift of preserving from this locality generally, operand is comparatively large, cannot detect in real time in the lower situation of underwater sound MODEM processor clock frequency.Therefore right to how to reduce estimation operand be realize wake-up signal detect key.

$T\left(x\right)=\underset{\hat{k}\∈[-K/2,K/2],{\hat{n}}_0\∈[0,N-M]}{\max }\underset{n={\hat{n}}_0}{\overset{{\hat{n}}_0+M-1}{\mathrm{\Σ}}}x\left(n\right)s(n-{\hat{n}}_0,\hat{k})---\left(10\right)$

3, the Combined estimator of the wake-up signal time of advent and Doppler time collapsing length

The unknown time of advent and Doppler cause MLE to estimate the main cause that operand is large, if can estimate probable ranges and the Doppler accurately of time of arrival (toa), the operand of formula 10 can decline.The wake-up signal of the present invention's design contains two Gold sequence repeated, invention adopt multiple Length discrepancy adjacent data blocks between slip relevant treatment carry out the wake-up signal time of advent and Doppler time collapsing length Combined estimator, by a front correlation, current correlation adds that current adjacent data blocks deducts previous adjacent data blocks to most end mantissa obtain most initial data product according to product, except calculating the correlation of initial time, each correlation value calculation is only containing once adding and once subtracting computing, compares copy relevant treatment operand and significantly reduces.Specific as follows, at H ₁lower Received signal strength can be written as,

$x\left(n\right)=\left\{\begin{array}{cc}{w}_1\left(n\right)& n=\mathrm{0,1},...,n_0-1\\ s^{\′}(n-n_0,\frac{k}{2})+w_2\left(n\right)& n=n_0,n_0+1,...,n_0+\frac{M}{2}+\frac{k}{2}-1\\ s^{\′}(n-n_0-\frac{M}{2}-\frac{k}{2},\frac{k}{2})+w_3\left(n\right)& n=n_0+\frac{M}{2}+\frac{k}{2},n_0+\frac{M}{2}+\frac{k}{2}+1,...,n_0+M+k-1\\ w_4\left(n\right)& n=n_0+M+k,n_0+M+k+1,...,N-1\end{array}\right.---\left(11\right)$

, n in formula 11 ₀for signal reaches the time, for the Doppler stre tch time, the s ' (n) of formula 12 is only containing the biphase coded signal of a balanceable Gold sequence, wherein N _cfor the sample points of each chip, then length is adjacent data blocks between correlation output be formula 13, suppose noise w ₁(n), w ₂(n), w ₃(n) and w ₄n separate between (), signal s ' (n) is independent with noise, when during with M → ∞, export the auto-correlation into s ' (n, k), now correlation is maximum, and obtains wake-up signal and reach time Estimate estimate with Doppler time collapsing length as formula 14.Fig. 4 be when being 10dB without Doppler's situation and SNR different length data block between correlation output, can find out that correlation output is maximum when the Doppler stre tch time, k was 0.The computing of formula 13 can be resolved into a front correlation and be added that current adjacent data blocks deducts a front adjacent data blocks to most initial data product, as formula 15 to most end mantissa according to product.Fig. 5 is for realizing the algorithm block diagram of Combined estimator, formula 10 shows that a relevant treatment is containing M*K multiply-add operation, and formula 15 relevant treatment is only containing 2*K multiply-add operation, and operand declines to a great extent.

$R(n,\hat{k})=\underset{m=n}{\overset{n+(M+\hat{k})/2-1}{\mathrm{\Σ}}}x(m-M-\hat{k}+1)x(m-\frac{M}{2}-\frac{\hat{k}}{2}+1)---\left(13\right)$

$R(n_0+\frac{M}{2}+\frac{k}{2}-1,k)=\underset{M\→\∞}{\lim }\underset{m=0}{\overset{(M+k)/2-1}{\mathrm{\Σ}}}x(n_0+m)x(n_0+m-\frac{M}{2}-\frac{k}{2})$

$=\underset{M\→\∞}{\lim }\underset{m=0}{\overset{(M+k)/2-1}{\mathrm{\Σ}}}[s^{\′}(m,k)+w_2(n_0+m)][s^{\′}(m,k)+w_3(n_0+m-\frac{M}{2}-\frac{k}{2})]$

$=\underset{M\→\∞}{\lim }\underset{m=0}{\overset{(M+k)/2-1}{\mathrm{\Σ}}}{s}^{\′}(m,k)s^{\′}(m,k)+\underset{M\→\∞}{\lim }\underset{m=0}{\overset{(M+k)/2-1}{\mathrm{\Σ}}}{s}^{\′}(m,k)w_3(n_0+m-\frac{M}{2}-\frac{k}{2})+$

$\underset{M\→\∞}{\lim }{w}_2(n_0+m)s^{\′}(m,k)+\underset{M\→\∞}{\lim }{w}_2(n_0+m)w_3(n_0+m-\frac{M}{2}-\frac{k}{2})$

$=\underset{m=0}{\overset{(M+k)/2-1}{\mathrm{\Σ}}}{s}^{\′}(m,k)s^{\′}(m,k)---\left(14\right)$

$R(n,\hat{k})=R(n-1,\hat{k})+x\left(n\right)x(n-\frac{M}{2}-\frac{\hat{k}}{2})-x(n-\frac{M}{2}-\frac{\hat{k}}{2})x(n-M-\hat{k})---\left(15\right)$

4, the logical down-sampled or lack sampling of band

Formula 15 shows, when balanceable Gold sequence length is fixed, sample rate is higher, then M is larger, and the auto-correlation of the correlative relative signal of signal, noise and noise is less, and the performance of estimation is better, Fig. 6 is the estimated performance comparing two kinds of sample rates, shows that sample rate is higher, and estimated performance is better.And formula 7 shows that M is larger, related operation amount is larger, can the down-sampled process of extracted at equal intervals to received signal, if wake-up signal centre frequency and bandwidth ratio larger, also can adopt bandpass under sampling technology, reduce sampling number M, thus reduce the related operation amount of formula 7.

5, based on wake-up signal detect

The result of Fig. 4 shows, maximum related value is with the n time of advent ₀different change is less, and formula 15 obtains be only the n time of advent ₀rough estimate, but maximum related value is very sensitive to the change of k value, therefore can obtain Doppler more accurately and estimate.? rough estimate and under accurate estimation, LRT can be rewritten as formula 16, and m wherein gets T _c* L/16 time span, as long as formula 16 shows at n ₀near carry out slip relevant treatment, by maximum related value being compared with thresholding, if be greater than thresholding, then wake-up signal detected, the detection of whole wake-up signal is as Fig. 7.

$T^{\′}\left(x\right)=\underset{n_0\∈[{\hat{n}}_0-m,{\hat{n}}_0+m]}{\max }\underset{n=n_0}{\overset{n_0+(M+\hat{k})/2-1}{\mathrm{\Σ}}}x\left(n\right)s^{\′}(n-n_0,\hat{k})---\left(16\right)$

The present invention is not limited to above-mentioned execution mode, no matter its execution mode does any change, every employing thinking provided by the present invention, is all one distortion of the present invention, all should thinks within the protection range of invention.

Claims (1)

1. the wake-up signal detection method for underwater sound communication MODEM, it is characterized in that: the biphase coded signal that the balanceable Gold sequence selecting two to repeat generates is as wake-up signal, receiving terminal first completes the Combined estimator to the wake-up signal time of advent and Doppler time collapsing length, recycling Doppler estimated result chooses the reference signal of corresponding Doppler time collapsing length, utilize and arrive time Estimate result intercepting Received signal strength, and carry out the logical down-sampled even lack sampling process of band, the signal obtained and reference signal make slip relevant treatment, complete wake-up signal detect by comparing correlation and pre-determined threshold, specifically comprise following committed step:

Step one: the sequence selecting " 0 " and " 1 " number to differ from 1 from Gold sequence race is balanceable Gold sequence, and the balanceable Gold sequence chosen repeats once, carries out dual polarization process, add rectangular window, with carrier frequency mixing, the real part of the number of winning the confidence, generates wake-up signal s (t):

Wherein g (n) be balanceable Gold sequence chip, T _cfor chip period, L is sequence length, w _cfor carrier frequency, G (t) is window function;

Step 2: adopt the adjacent data blocks of multiple Length discrepancy between slip relevant treatment carry out the Combined estimator of the wake-up signal time of advent and Doppler time collapsing length, by a front correlation, current correlation adds that current adjacent data blocks deducts previous adjacent data blocks to most end mantissa obtain most initial data product according to product, as formula 3, formula 4, except calculating the correlation of initial time, each correlation value calculation only subtracts computing containing once taking advantage of to add and once take advantage of, compare copy relevant treatment operand significantly to reduce

$R(n,\hat{k})=\underset{m=n}{\overset{n+(M+\hat{k})/2-1}{\mathrm{\Σ}}}x(m-M-\hat{k}+1)x(m-\frac{M}{2}-\frac{\hat{k}}{2}+1)---\left(3\right)$

$R(n,\hat{k})=R(n-1,\hat{k})+x\left(n\right)x(n-\frac{M}{2}-\frac{\hat{k}}{2})-x(n-\frac{M}{2}-\frac{\hat{k}}{2})x(n-M-\hat{k})---\left(4\right)$

When during with M → ∞, correlation is maximum, as formula 5, corresponding by finding maximum correlation peaks be wake-up signal to estimate the time of advent, be Doppler time collapsing length to estimate;

$R(n_0+\frac{M}{2}+\frac{k}{2}-1,k)=\underset{M\→\∞}{\lim }\underset{m=0}{\overset{(M+k)/2-1}{\mathrm{\Σ}}}x(n_0+m)x(n_0+m-\frac{M}{2}-\frac{k}{2})$

$=\underset{M\→\∞}{\lim }\underset{m=0}{\overset{(M+k)/2-1}{\mathrm{\Σ}}}[s^{\′}(m,k)+w_2(n_0+m)][s^{\′}(m,k)+w_3(n_0+m-\frac{M}{2}-\frac{k}{2})]$

$=\underset{M\→\∞}{\lim }\underset{m=0}{\overset{(M+k)/2-1}{\mathrm{\Σ}}}{s}^{\′}(m,k)s^{\′}(m,k)+\underset{M\→\∞}{\lim }\underset{m=0}{\overset{(M+k)/2-1}{\mathrm{\Σ}}}{s}^{\′}(m,k)w_3(n_0+m-\frac{M}{2}-\frac{k}{2})+---\left(5\right)$

$\underset{M\→\∞}{\lim }{w}_2(n_0+m)s^{\′}(m,k)+\underset{M\→\∞}{\lim }{w}_2(n_0+m)w_3(n_0+m-\frac{M}{2}-\frac{k}{2})$

$=\underset{m=0}{\overset{(M+k)/2-1}{\mathrm{\Σ}}}{s}^{\′}(m,k)s^{\′}(m,k)$

$x\left(n\right)=\left\{\begin{array}{cc}{w}_1\left(n\right)& n=\mathrm{0,1},...,n_0-1\\ s^{\′}(n-n_0,\frac{k}{2})+w_2\left(n\right)& n=n_0,n_0+1,...,n_0+\frac{M}{2}+\frac{k}{2}-1\\ s^{\′}(n-n_0-\frac{M}{2}-\frac{k}{2},\frac{k}{2})+w_3\left(n\right)& n=n_0+\frac{M}{2}+\frac{k}{2},n_0+\frac{M}{2}+\frac{k}{2}+1,...,n_0+M+k-1\\ w_4\left(n\right)& n=n_0+M+k,n_0+M+k+1,...,N-1\end{array}\right.---\left(6\right)$

The x (n) of formula 6 is the data received, w ₁(n), w ₂(n), w ₃(n) and w ₄n () be independent noise mutually; The s ' (n) of formula 7 is only containing the biphase coded signal of a balanceable Gold sequence, N _cfor the sample points of each chip; for having n unknown time of advent ₀with unknown Doppler stre tch time span isoparametric signal, at interval on be non-zero; Formula 5 also shows, improve sample rate, then M is larger, and the auto-correlation of the correlative relative signal of signal, noise and noise is less, can improve estimated performance;

Step 3: after completing the Combined estimator of the wake-up signal time of advent and Doppler time collapsing length, the down-sampled process of extracted at equal intervals to received signal again, if wake-up signal centre frequency and bandwidth ratio larger, also can adopt bandpass under sampling technology, reduce sampling number M, thus reduce the operand of step 4;

Step 4: in the reference signal of the multiple different Doppler time collapsing lengths of this locality preservation, choose the reference signal corresponding with step 2 Doppler estimated result, and in time range less before and after the time of advent that step 2 is estimated, by step 3 down-sampled after signal slide relevant to reference signal, the detection of wake-up signal is completed by comparing maximum related value and pre-determined threshold size, as formula 8

$T^{\′}\left(x\right)=\underset{n_0\∈[{\hat{n}}_0-m,{\hat{n}}_0+m]}{\max }\underset{n=n_0}{\overset{n_0+(M+\hat{k})/2-1}{\mathrm{\Σ}}}x\left(n\right)s^{\′}(n-n_0,\hat{k})---\left(8\right)$

If maximum related value is greater than thresholding, wake-up signal detected, otherwise wake-up signal do not detected.