CN105578480A - Undersampling frequency spectrum perception pre-decision method orienting broadband modulation converter - Google Patents

Abstract

The invention discloses an undersampling frequency spectrum perception pre-decision method orienting a broadband modulation converter, and mainly solves the problems in the prior art that false alarm probability is high and computation cost is high. The technical scheme is that 1. a receiving end performs compressive sampling on received signals so that m paths of samples are obtained and time domain energy of each branch of acquired samples is computed; 2. test statistics r<j,k> is computed according to time domain energy; 3. the decision threshold gamma<j,k> of test statistics is computed; and 4. test statistics is compared with the decision threshold, and existence of signals is decided: the signals exist through decision if r<j,k> is greater than gamma<j,k>, and the signals do not exist through decision if r<j,k> is less than or equal to gamma<j,k>. The undersampling frequency spectrum perception pre-decision method has advantages that influence of noise power on perception performance is low, computation complexity is low and influence of broadband Gaussian white noise non-sparsity on undersampling frequency spectrum perception can be effectively reduced, and the undersampling frequency spectrum perception pre-decision method can be used for broadband frequency spectrum perception of analog signal compressive sampling.

Description

Towards the pre-decision method of lack sampling frequency spectrum perception of wide-band modulation converter

Technical field

The invention belongs to communication technical field, relate to frequency spectrum perception technology, further relate to a kind of pre-decision method of lack sampling frequency spectrum perception towards wide-band modulation converter, can be used for the frequency spectrum perception in cognitive radio.

Background technology

Frequency spectrum perception is as the founder key technology of cognitive radio system, can be the feedback information that Dynamic Closed Loop system provides necessary, for cognitive radio system/network provides environmental information and decision-making foundation, for in order dynamically spectrum allocation may and reasonably spectrum regulatory provide safeguard, be the raising availability of frequency spectrum, improve wireless channel transmission conditions, intelligent network, the basis of initiatively hiding various interference, effectively carrying out dynamic spectrum resource management.Current frequency spectrum sensing method is mostly absorbed in narrower frequency range, is found frequency spectrum access chance, from Shannon theorem, available bandwidth directly determines theoretical maximum bit rate, the access frequency spectrum that narrow band spectrum perception provides obviously can not carry the traffic rate of user's request, and cognitive user needs to adopt broader frequency spectrum perception to find out in wider frequency range simultaneously and more accesses chance.Classical Nyquist sampling thheorem is pointed out, in order to undistorted reconstruct analog signal, the sample frequency of analog signal at least should be more than or equal to the twice of signal spectrum bandwidth, when cognitive user carries out broader frequency spectrum perception, need with higher resolution and extremely low power consumption collecting sample from very wide frequency range, this digital signal processor system of giving based on Shannon-nyquist sampling theorem brings and gathers front end conversion speed, height handles up large capacity cache space and the 'bottleneck' restrictions of back-end logic device operation highest frequency.

Compression sampling CS theory only needs the non-self-adapting linear measurement sample point of only a few, just can recover analog signal sparse in time domain or other transform domains by the method for convex optimization with great probability, directly can realize the conversion of signal from analog to information according to the method, this is reduce Analog-digital Converter speed and alleviate Digital Signal Processing pressure to provide new theoretical foundation.Given this, compression sampling is combined with broader frequency spectrum perception, make full use of the sparse characteristic treating perceived spectral, to complete the information gathering of broader frequency spectrum far below the analog-to-digital conversion rate of Nyquist sample rate, and completing broader frequency spectrum perception in real time with extremely low Digital Signal Processing expense, is solve one of broadband analog signal collection and high-speed digital signal transmission, storage and the effective way processing bottleneck.

At present, the broader frequency spectrum cognitive method that can be used for analog signal compression sampling is broadly divided into two classes:

The first kind is based on analog information transducer AIC, AIC lack sampling framework with finite discrete multi-tone signal add and for analog input signal model, by analog input signal is multiplied with random mark sequence, then the sampling of integration cumulative sum low pass is carried out, after obtaining compression collecting sample, reconstructing method can be utilized to draw primary signal or its statistical property, degree judgement is completed again by time domain or frequency domain energy detection method, this collection framework realizes simple, but when recovering continuous spectra signal in broadband, the predicament that input signal model mismatch produces the higher-dimension complex matrix computing that great reconstructed error or input signal model accurately bring can be faced.

Equations of The Second Kind is based on wide-band modulation converter MWC, MWC lack sampling framework is using the limited union with translation invariant subspace as analog input signal model, by input signal is multiplied with cycle random mark sequence on multiple branch road, realize the different weight factor down-conversions of input signal Subspace Decomposition, thus reduce required sampling rate, by converting unlimited measurement vector corresponding for continuous analog signals collecting to multiple measurement vector system to lack sampling sample framework establishment, then orthogonal matching pursuit algorithm is utilized to obtain support corresponding to occupied frequency range, it is reasonable that MWC lack sampling framework has signal model, support determines the advantages such as real-time and the realization of useful commercial device.But owing to there is white noise in the frequency range of broadband, broadband white noise is not sparse on time domain, frequency domain or other transform domains, adopts the lack sampling sample of wide-band modulation converter, directly carry out broader frequency spectrum perception, easily cause following problem:

(1) although there is not any primary user's signal in the broadband frequency range treating perception, only there is white Gaussian noise, the restructing algorithm of compressed sensing still can take situation according to openness providing in frequency band, and this will cause serious false alarm probability;

(2) process utilizing lack sampling sample to carry out signal reconstruction and support to determine, bring great calculation cost, and these computings is insignificant;

(3) strategy of the frequency spectrum perception Influence on test result communication of mistake, brings secondary user's communication and frequently interrupts, reduce the utilance of frequency band.

Summary of the invention

The object of the invention is to the above-mentioned deficiency of the frequency spectrum perception technology overcome based on wide-band modulation converter, a kind of pre-decision method of lack sampling frequency spectrum perception towards wide-band modulation converter is proposed, to effectively reduce the non-openness impact on lack sampling frequency spectrum perception of broadband Gaussian white noise, promote frequency spectrum perception accuracy, reduce calculation cost, improve band efficiency.

In order to complete above-mentioned purpose, the pre-decision method of lack sampling frequency spectrum perception towards wide-band modulation converter that the present invention proposes, comprises the steps:

(1) receiving terminal utilizes wide-band modulation converter to carry out compression sampling to the received signal, obtains m road sample y _i(n), i=1,2 ..., m, n=0,1 ..., N-1, N are sample points, and calculate the time domain energy of each branch road collecting sample respectively

(2) test statistics is calculated according to time domain energy

Wherein, with be respectively the time domain energy of jth branch road and kth branch road, j=2,3 ..., m, k=1,2 ..., j-1, obtains m (m-1)/2 test statistics;

(3) test statistics r is calculated _j,kdecision threshold γ _j,k:

(3a) by the time domain energy of i-th branch road be transformed into frequency domain energy by test statistics r _j,kfrequency domain is transformed into by time domain,

(3b) test statistics r is built _j,kcumulative distribution function P _f:

$P_f=1-\mathrm{\&Phi;}\left(\frac{\sqrt{N}{\mathrm{\&gamma;}}_{j,k}-\sqrt{N}}{\sqrt{1-2{\mathrm{\&gamma;}}_{j,k}{\mathrm{\&rho;}}_{j,k}+{{\mathrm{\&gamma;}}_{j,k}}^2}}\right)$

Wherein ρ _j,kbe with coefficient correlation, value is Φ () function expression is $\mathrm{\&Phi;}\left(x\right)={\&Integral;}_{-\mathrm{\&infin;}}^x{e}^{-t^2}dt;$

(3c) according to the cumulative distribution function P of test statistics _f, utilize CFAR criterion, calculate decision threshold γ _j,k:

${\mathrm{\&gamma;}}_{j,k}=\frac{{\&lsqb;{\mathrm{\&Phi;}}^{-1}(1-P_f)\&rsqb;}^2{\mathrm{\&rho;}}_{j,k}-N+\sqrt{({\mathrm{\&rho;}}_{j,k}^2-1)({\&lsqb;{\mathrm{\&Phi;}}^{-1}(1-P_f)\&rsqb;}^4-2N{\&lsqb;{\mathrm{\&Phi;}}^{-1}(1-P_f)\&rsqb;}^2)}}{{\&lsqb;{\mathrm{\&Phi;}}^{-1}(1-P_f)\&rsqb;}^2-N},$

Wherein, P _ffor the default false alarm probability of each branch decision, Φ ^-1() is the inverse function of Φ () function;

(4) by test statistics r that step (2) obtains _j,kthe threshold value γ obtained with step (3) _j,krelatively, signal is determined whether, if there is statistic r _j,kbe greater than thresholding γ _j,k, then signal has been judged to; If there is not any statistic r _j,kbe greater than thresholding γ _j,k, then no signal is judged to.

The present invention has the following advantages:

1, the present invention is owing to utilizing a small amount of compression sampling sample, can effectively reduce the non-openness impact on lack sampling frequency spectrum perception of broadband Gaussian white noise;

2, the present invention has nothing to do due to its threshold value and noise variance, so perceptual performance is less by the impact of noise power, and effectively can resist the impact on noise uncertainty;

3, the present invention carries out simple computing module-square owing to only needing a small amount of sample, therefore computation complexity is low, can meet the real-time of frequency spectrum perception.

Accompanying drawing explanation

Fig. 1 is realization flow figure of the present invention;

Fig. 2 is the present invention's correct detection probability analogous diagram under different signal to noise ratio;

Fig. 3 is the present invention's false alarm probability analogous diagram under different signal to noise ratio;

Fig. 4 is in the present invention when there is noise uncertainty, detection probability simulation comparison figure under different signal to noise ratio;

Fig. 5 is the present invention's receiver performance curve analogous diagram under different false alarm probability.

Embodiment

The present invention is used for the broader frequency spectrum perception of analog signal compression sampling, and perception end is at each received over subchannels signal, and sampling to received signal processes.

With reference to Fig. 1, performing step of the present invention is as follows:

Step 1, perception end calculates the time domain energy T of each branch road collecting sample _i ^td.

Perception end utilizes wide-band modulation converter to carry out compression sampling to the received signal, obtains m road sample y _i(n), i=1,2 ..., m, n=0,1 ..., N-1;

Utilize branch road sample y _in () calculates time domain energy

$T_i^{td}=\underset{n=0}{\overset{N-1}{\&Sigma;}}|y_i\left(n\right){|}^2,$

Wherein, m is the collection circuitry number of wide-band modulation converter, and N is sample points.

Step 2, calculates test statistics r according to time domain energy _j,k

$r_{j,k}=\frac{T_j^{td}}{T_k^{td}},$

Wherein, with be respectively the time domain energy of jth and k branch road, j=2,3 ..., m, k=1,2 ..., j-1,

M (m-1)/2 test statistics is calculated according to the different values of j and k.

Step 3, according to the false alarm probability preset, when primary user's signal does not exist, calculates decision threshold γ _j,k.

When primary user's signal does not exist, Received signal strength only comprises noise, i.e. input signal x (t)=ω (t), suppose ω (t) for average be 0, variance is white Gaussian noise, its decision threshold γ _j,kcalculation procedure as follows:

(3a) by the time domain energy of i-th branch road be transformed into frequency domain energy by test statistics r _j,kfrequency domain is transformed into by time domain,

(3b) test statistics r is built _j,kcumulative distribution function P _f:

(3b1) Y is calculated _ithe statistical property of (k):

(3b11) structure is gathered, to branch road sample y according to wide-band modulation converter MWC compression _in () carries out discrete Fourier transform, obtain branch road sample spectra Y _i(k):

$Y_i\left(k\right)=\underset{l=-L_0}{\overset{L_0}{\&Sigma;}}{C}_{il}X(k-\ln ),k\&Element;\&lsqb;0,N),$

Wherein, c _ilfor cycle pseudorandom ± 1 sequence p _ithe cycle Fourier series expansion coefficient of (t), L is the subspace number required for complete expression input signal x (t) Fourier transform X (j Ω), and L can calculate according to following formula,

Wherein, f _nYQthe equivalent Nyquist sampling rate of MWC, f _pthe frequency of random mark sequence, f _sit is low pass sampling rate;

(3b12) in the non-existent situation of primary user, input signal spectrum X (k) is average is 0, variance is discrete random variable, utilize average and the variance of X (k), calculate branch road sample spectra Y _ithe statistical property of (k), it comprises:

Calculate Y _iaverage E [the Y of (k) _i(k)] and variance D [Y _i(k)] be:

E[Y _i(k)]＝0， $D\&lsqb;Y_i\left(k\right)\&rsqb;={\mathrm{\&sigma;}}_{\mathrm{\&omega;}}^2,$

Calculate Y _ithe average of (k) real part and variance for:

Calculate Y _ithe average of (k) imaginary part and variance for:

Calculate Y _i(k) real part and Y _ithe coefficient correlation of (k) imaginary part: (3b2) branch road sample spectra Y is calculated _ithe average E of (k) mould square [|| Y _i(k) || ²] and variance D [|| Y _i(k) || ²]:

$\begin{array}{cc}E\&lsqb;\left|\right|Y_i\left(k\right)|{|}^2\&rsqb;={\mathrm{\&sigma;}}_{\mathrm{\&omega;}}^2,& D\&lsqb;\left|\right|Y_i\left(k\right)|{|}^2\&rsqb;={\mathrm{\&sigma;}}_{\mathrm{\&omega;}}^4\end{array};$

Wherein, it is the variance of input signal spectrum X (k);

(3b3) branch road sample spectra Y is calculated _ithe coefficient correlation of (k) mould square:

(3b31) coefficient correlation on different frequent points is:

cov[||Y _p(a)|| ²,||Y _q(b)|| ²]＝0，

(3b32) coefficient correlation on identical frequency is:

$\mathrm{cov}\&lsqb;\left|\right|Y_p\left(k\right)|{|}^2,|\left|Y_q\left(k\right)\right|{|}^2\&rsqb;=\frac{{\mathrm{\&sigma;}}_w^4({\mathrm{\&rho;}}_0^2+{\mathrm{\&rho;}}_1^2+{\mathrm{\&rho;}}_2^2+{\mathrm{\&rho;}}_3^2)}{2},$

Wherein p, q=1,2 ..., m, p ≠ q, k=0,1 ..., N-1,

C in formula _qmfor the cycle Fourier series expansion coefficient of cycle pseudorandom ± 1 sequence, represent and get real part, represent and get imaginary part;

(3b4) the average E [T of branch road frequency domain energy is calculated _i ^fd], variance D [T _i ^fd] and correlation coefficient ρ _j,k:

$E\&lsqb;T_i^{fd}\&rsqb;=E\&lsqb;\frac{1}{N}\underset{k=0}{\overset{N-1}{\&Sigma;}}|Y_i\left(k\right){|}^2\&rsqb;={\mathrm{\&sigma;}}_{\mathrm{\&omega;}}^2$

$D\&lsqb;T_i^{fd}\&rsqb;=D\&lsqb;\frac{1}{N}\underset{k=0}{\overset{N-1}{\&Sigma;}}|Y_i\left(k\right){|}^2\&rsqb;=\frac{{\mathrm{\&sigma;}}_{\mathrm{\&omega;}}^4}{N}$

$\begin{array}{c}{\mathrm{\&rho;}}_{j,k}=\frac{Cov\&lsqb;T_j^{fd},T_k^{fd}\&rsqb;}{\sqrt{D\&lsqb;T_j^{fd}\&rsqb;D\&lsqb;T_k^{fd}\&rsqb;}}\\ =\frac{\frac{1}{N^2}\&lsqb;\underset{k=0}{\overset{N-1}{\&Sigma;}}(Cov\&lsqb;|Y_j\left(k\right){|}^2,|Y_k\left(k\right){|}^2\&rsqb;)\&rsqb;}{\sqrt{D\&lsqb;T_j^{fd}\&rsqb;D\&lsqb;T_k^{fd}\&rsqb;}}\\ =\frac{({\mathrm{\&rho;}}_0^2+{\mathrm{\&rho;}}_1^2+{\mathrm{\&rho;}}_2^2+{\mathrm{\&rho;}}_3^2)}{2}\end{array}$

(3b5) according to the cumulative distribution function F of any two correlated Gaussian stochastic variable G and H ratio _rr (), calculates test statistics r _j,kcumulative distribution function P _f:

F _rr the expression formula of () is:

$\begin{array}{c}{F}_R\left(r\right)=\mathrm{Pr}(G/H<r)\\ =\mathrm{\&Phi;}\left(\frac{{\mathrm{r\&mu;}}_H-{\mathrm{\&mu;}}_G}{\sqrt{{\mathrm{\&sigma;}}_G^2-2{\mathrm{r\&rho;\&sigma;}}_G{\mathrm{\&sigma;}}_H+r^2{\mathrm{\&sigma;}}_H^2}}\right)\end{array}$

Wherein, μ _gfor the average of Gaussian random variable G, for the variance of Gaussian random variable G, μ _hfor the average of Gaussian random variable H, for the variance of Gaussian random variable H, ρ is the coefficient correlation of G and H.

As N>20, T _i ^fdapproximate Gaussian distributed, its average and variance are respectively with with coefficient correlation be ρ _j,k, test statistics r can be obtained thus _j,kcumulative distribution function be:

$\begin{array}{c}{P}_f=P(\frac{T_j^{fd}}{T_k^{fd}}\&GreaterEqual;\mathrm{\&gamma;})=1-P(\frac{T_j^{fd}}{T_k^{fd}}<\mathrm{\&gamma;})\\ =1-\mathrm{\&Phi;}\left(\frac{\mathrm{\&gamma;}E\&lsqb;T_k^{fd}\&rsqb;-E\&lsqb;T_j^{fd}\&rsqb;}{\sqrt{{(D\&lsqb;T_j^{fd}\&rsqb;)}^2-2{\mathrm{\&gamma;\&rho;}}_{j,k}D\&lsqb;T_j^{fd}\&rsqb;D\&lsqb;T_k^{fd}\&rsqb;+{\mathrm{\&gamma;}}^2(D\&lsqb;T_k^{fd}\&rsqb;)}}\right)\\ =1-\mathrm{\&Phi;}\left(\frac{\sqrt{N}\mathrm{\&gamma;}-\sqrt{N}}{\sqrt{1-2{\mathrm{\&gamma;\&rho;}}_{j,k}+{\mathrm{\&gamma;}}^2}}\right)\end{array}$

Wherein ρ _j,kit is jth branch road frequency domain energy with kth branch road frequency domain energy coefficient correlation, γ be inspection system

Metering r _j,kdecision threshold, E [] represents average, and D [] represents variance;

(3c) according to the cumulative distribution function P of test statistics _f, utilize CFAR criterion, calculate decision threshold γ _j,k:

${\mathrm{\&gamma;}}_{j,k}=\frac{{\&lsqb;{\mathrm{\&Phi;}}^{-1}(1-P_f)\&rsqb;}^2{\mathrm{\&rho;}}_{j,k}-N+\sqrt{({\mathrm{\&rho;}}_{j,k}^2-1)({\&lsqb;{\mathrm{\&Phi;}}^{-1}(1-P_f)\&rsqb;}^4-2N{\&lsqb;{\mathrm{\&Phi;}}^{-1}(1-P_f)\&rsqb;}^2)}}{{\&lsqb;{\mathrm{\&Phi;}}^{-1}(1-P_f)\&rsqb;}^2-N},$

Wherein, P _ffor the default false alarm probability of each branch decision, Φ ^-1() is the inverse function of Φ () function.

Step 4: the test statistics r that step (2) is obtained _j,kthe judging threshold γ obtained with step (3) _j,kcompare, determine whether signal:

If there is statistic r _j,kbe greater than thresholding γ _j,k, then signal has been judged to;

If there is not any statistic r _j,kbe greater than thresholding γ _j,k, then no signal is judged to.

Effect of the present invention can be further illustrated by following emulation:

A, simulated conditions

The equivalent sampling speed of the wide-band modulation converter that analogue system adopts is f _nYQ=6GHz, collection circuitry number is m=20, and the cycle of random mark ± 1 sequence is T _p=7.5ns, frequency are f _p=1/T _p, in one-period, the random chip number of equivalence is L=45, and each passage low-pass filtering cut-off frequency used is f _s/ 2, single channel sampling rate is f _s=f _p; At frequency range (0, f _nYQ/ 2) in, co-exist in N=2 signal, the chip rate of each signal is s _r=1.024MBaud, the carrier frequency of each signal produces at random, and the power of N number of signal is identical, and the ratio of the gross power and noise power that define N number of signal is signal to noise ratio, and under each signal to noise ratio, carry out 1000 emulation, the false alarm probability preset is P _fa, utilize MWC converter to carry out compression collection, sample points K=100 used.

B, emulation content and result

Emulation 1: be-20dB ~-10dB and default false alarm probability P in signal to noise ratio _faunder the condition of=0.01, emulate correct detection probability of the present invention, emulation as shown in Figure 2.

As seen from Figure 2, utilize K=100 lack sampling sample points, when signal to noise ratio is more than or equal to-8dB, correct detection probability of the present invention can reach and be greater than 98%, and the present invention can obtain very superior pre-judgement performance in wider SNR ranges.

Emulation 2: be-20dB ~-10dB and default false alarm probability P in signal to noise ratio _faunder the condition of=0.01, emulate false alarm probability of the present invention, emulation as shown in Figure 3.

As seen from Figure 3, utilize K=100 lack sampling sample points, in the scope of signal to noise ratio-20dB ~-10dB, false alarm probability of the present invention suppresses substantially near default false alarm probability value, and the threshold value that the present invention calculates is reasonable, effectively can overcome the generation of false-alarm.

Emulation 3: signal to noise ratio be-20dB ~-10dB, false alarm probability be 0.01 and noise uncertainty ρ=1.4 condition under, correct detection probability of the present invention is emulated, and itself and the simulation curve that there is not noise uncertainty are contrasted, simulation result is as shown in Figure 4.

As seen from Figure 4, when there is noise uncertainty, correct detection probability of the present invention not too large change, performance curve of the present invention overlaps substantially when there is noise uncertainty and there is not noise uncertainty, illustrates that the present invention can effectively to antinoise uncertainty.

Emulation 4: be under the condition of-16dB in signal to noise ratio, the present invention is emulated towards the receiver performance curve of the pre-decision method of lack sampling frequency spectrum perception of wide-band modulation converter, and itself and the simulation curve that there are noise uncertainty ρ=1.4 are contrasted, simulation result is as shown in Figure 5.

As seen from Figure 5, the pre-decision algorithm that the present invention provides can under less false alarm probability and lower signal to noise ratio condition, obtain comparatively superior perceptual performance, when there is noise uncertainty, receiver performance curve of the present invention is also substantially constant, illustrates that the present invention has robustness to noise uncertainty.

Comprehensive above-mentioned analysis of simulation result, the present invention under less false alarm probability and lower signal to noise ratio condition, can obtain comparatively superior perceptual performance, when there is noise uncertainty, perceptual performance is substantially constant, illustrates that the present invention can effectively to antinoise uncertainty.

Claims (4)

1., towards the pre-decision method of lack sampling frequency spectrum perception of wide-band modulation converter, comprise the steps:

(1) receiving terminal utilizes wide-band modulation converter to carry out compression sampling to the received signal, obtains m road sample y _i(n), i=1,2 ..., m, n=0,1 ..., N-1, N are sample points, and calculate the time domain energy of each branch road collecting sample respectively

(2) test statistics is calculated according to time domain energy

Wherein, with be respectively the time domain energy of jth branch road and kth branch road, j=2,3 ..., m, k=1,2 ..., j-1, obtains m (m-1)/2 test statistics;

(3) test statistics r is calculated _j,kdecision threshold γ _j,k:

(3a) by the time domain energy of i-th branch road be transformed into frequency domain energy T _i ^fd, by test statistics r _j,kfrequency domain is transformed into by time domain,

(3b) test statistics r is built _j,kcumulative distribution function P _f:

Wherein ρ _j,kbe with coefficient correlation, value is Φ () function expression is

(3c) according to the cumulative distribution function P of test statistics _f, utilize CFAR criterion, calculate decision threshold γ _j,k:

Wherein, P _ffor the default false alarm probability of each branch decision, Φ ^-1() is the inverse function of Φ () function;

(4) by test statistics r that step (2) obtains _j,kthe threshold value γ obtained with step (3) _j,kcompare, determine whether signal, if there is statistic r _j,kbe greater than thresholding γ _j,k, then signal has been judged to; If there is not any statistic r _j,kbe greater than thresholding γ _j,k, then no signal is judged to.

2. the pre-decision method of lack sampling frequency spectrum perception towards wide-band modulation converter according to claim 1, wherein calculates each branch road collecting sample y in step (1) _ithe time domain energy of (n) calculate according to following formula:

3. the pre-decision method of lack sampling frequency spectrum perception towards wide-band modulation converter according to claim 1, wherein in step (3a) by the time domain energy of i-th branch road be transformed into frequency domain energy T _i ^fd, be utilize handkerchief Savall law of conservation of energy, calculate according to following formula:

Wherein, Y _ik () is y _ithe discrete Fourier transform of (n), i=1,2 ..., m, n=0,1 ..., N-1.

4. the pre-decision method of lack sampling frequency spectrum perception towards wide-band modulation converter according to claim 1, wherein builds test statistics r in step (3b) _j,kcumulative distribution function P _f, carry out as follows:

(3b1) Y is calculated _ithe statistical property of (k):

(3b11) structure is gathered, to branch road sample y according to wide-band modulation converter MWC compression _in () carries out discrete Fourier transform, obtain branch road sample spectra Y _i(k):

Wherein, c _ilfor cycle pseudorandom ± 1 sequence p _ithe cycle Fourier series expansion coefficient of (t), L is the subspace number required for complete expression input signal x (t) Fourier transform X (j Ω), and L can calculate according to following formula,

Wherein, f _nYQthe equivalent Nyquist sampling rate of MWC, f _pthe frequency of random mark sequence, f _sit is low pass sampling rate;

(3b12) in the non-existent situation of primary user, input signal spectrum X (k) is average is 0, variance is discrete random variable, utilize average and the variance of X (k), calculate branch road sample spectra Y _ithe statistical property of (k):

Calculate Y _iaverage E [the Y of (k) _i(k)] and variance D [Y _i(k)] be:

E[Y _i(k)]＝0，

Calculate Y _ithe average of (k) real part and variance for:

Calculate Y _ithe average of (k) imaginary part and variance for:

Calculate Y _i(k) real part and Y _ithe coefficient correlation of (k) imaginary part:

(3b2) branch road sample spectra Y is calculated _iaverage E [the ‖ Y of (k) mould square _i(k) ‖ ²] and variance D [‖ Y _i(k) ‖ ²]:

Wherein, it is the variance of input signal spectrum X (k);

(3b3) branch road sample spectra Y is calculated _ithe coefficient correlation of (k) mould square:

(3b31) coefficient correlation on different frequent points is:

cov[‖Y _p(a)‖ ²,‖Y _q(b)‖ ²]＝0，

(3b32) coefficient correlation on identical frequency is:

Wherein p, q=1,2 ..., m, p ≠ q, k=0,1 ..., N-1,

c _pm, c _qmfor the cycle Fourier series expansion coefficient of cycle pseudorandom ± 1 sequence, represent and get real part, represent and get imaginary part;

(3b4) the average E [T of branch road frequency domain energy is calculated _i ^fd], variance D [T _i ^fd] and correlation coefficient ρ _j,k:

(3b5) according to the cumulative distribution function F of any two correlated Gaussian stochastic variable G and H ratio _rr (), calculates test statistics r _j,kcumulative distribution function P _f:

F _rr the expression formula of () is:

Wherein, μ _gfor the average of Gaussian random variable G, for the variance of Gaussian random variable G, μ _hfor the average of Gaussian random variable H, for the variance of Gaussian random variable H, ρ is the coefficient correlation of G and H.

As N>20, T _i ^fdapproximate Gaussian distributed, its average and variance are respectively with with coefficient correlation be ρ _j,k, test statistics r can be obtained thus _j,kcumulative distribution function be:

Wherein ρ _j,kit is jth branch road frequency domain energy with kth branch road frequency domain energy coefficient correlation, γ is test statistics r _j,kdecision threshold, E [] represents average, and D [] represents variance.