CN105406929A - Frequency domain-based frequency spectrum sensing method - Google Patents

Abstract

The invention provides a frequency domain-based frequency spectrum sensing method, belongs to the field of signal detection, and solves a problem that an error exists in periodogram estimated variance obtained through spectral estimation based on a periodogram in the prior art. According to the frequency domain-based frequency spectrum sensing method, a received signal is subjected to down-conversion to be converted into a certain intermediate frequency signal, the intermediate frequency signal is subjected to sampling according to a certain sampling method, a power spectrum of the sampled signal is estimated through a Bartlett method based on fast Fourier transform, then the maximum of the power spectrum is used as test statistics, and is compared with a judgment threshold, if the maximum is greater than the threshold, a condition that the signal exists in a channel is determined, and if the maximum is smaller than the threshold, another condition that the signal does not exist in the channel is determined. In the method, frequency spectrum sensing is realized by use of the maximum of the power spectrum of the received signal, so that the detection capability of the frequency spectrum sensing under low signal noise ratio environments is greatly improved.

Description

Based on the frequency spectrum sensing method of frequency domain

Technical field

The present invention relates to a kind of frequency spectrum sensing method based on frequency domain.

Background technology

Frequency spectrum perception can adopt dualism hypothesis model:

$x\left(t\right)=\left\{\begin{array}{cc}n\left(t\right)& H_0\\ hs\left(t\right)+n\left(t\right)& H_1\end{array}\right.$

Wherein h represents channel gain, for Gaussian white noise channel, and h=1.So-called frequency-domain spectrum perception has judged whether signal s (t) according to the power spectrum of Received signal strength x (t) exactly, as shown in Figure 1.

Be easy to judge have no signal to exist on fixing frequency (frequency range) have the difference of no signal to be to estimate whether spectrum has projection by Fig. 1.Just meeting H in signal ₀and H ₁namely dualism hypothesis, also can carry out frequency spectrum perception by the frequency domain characteristic of signal.

Although can be easy to determine whether signal from figure, to be compared by thresholding in reality.Generally speaking, for given false alarm probability, instead can release threshold value (false alarm probability and detection probability all have direct relation with thresholding), according to threshold value and then obtain detection probability, whole flow process as shown in Figure 2.As can be seen from Fig., the core based on the frequency spectrum sensing method of frequency domain is power spectrum estimation.Power spectrum estimation mainly contains period map method and Bartlett method, Power estimation is carried out based on periodogram according to pertinent literature is known, poor-performing, therefore make improvements introduce Bart Lai Tefa (Bartlett method) power spectrum estimation to reduce periodogram estimate variance.

Summary of the invention

The object of the invention is existingly to carry out based on periodogram the problem that periodogram estimate variance that Power estimation obtains exists error to solve, and propose a kind of frequency spectrum sensing method based on frequency domain.

Based on a frequency spectrum sensing method for frequency domain, described method is realized by following steps:

Step one, carry out down-conversion operation to received signal, be transformed to intermediate-freuqncy signal, then intermediate-freuqncy signal is sampled;

Step 2, the data sequence with N point obtained of step one being sampled are divided into K data segment, and each data segment has M point data;

Step 3, Bart Lai Tefa based on fast Fourier transform, carry out periodogram power spectrum estimation to the data segment of each M of having point data;

Step 4, ask for the mean value of the periodogram power spectrum estimation result that step 3 obtains, namely obtain the power spectrum estimation value of Bart Lai Tefa;

Step 5, select the maximum of the power spectrum estimation value of Bart Lai Tefa; And determine decision threshold;

Step 6, the maximum of the power spectrum estimation value of Bart Lai Tefa step 5 selected as test statistics, and contrast by it with decision threshold, make the judgement of frequency spectrum perception result:

If the maximum of power spectrum is greater than decision threshold, then there is primary user's signal in channel;

If the maximum of power spectrum is less than decision threshold, then dereliction subscriber signal in channel.

Beneficial effect of the present invention is:

Due to the excellent statistical property of Bartlett method, therefore the present invention selects Bartlett method as the computing method method of power spectrum, after carrying out power spectrum estimation to received signal, the power spectrum of many discrete point in frequency can be obtained, therefore select that to be the problem that the present invention first needs to consider as basis for estimation.According to Cleaning Principle, the quality of detection perform depends on the signal ratio of selection check statistic, according to the character of FFT, FFT is adopted to calculate the frequency spectrum of signal and then adopt Bartlett method to carry out power spectrum estimation, the power spectrum of M point can be obtained, wherein must there is a maximum, the power of the signal that the frequency content corresponding to it is occupied is maximum.According to the character of white Gaussian noise, after Fourier transform is carried out to white Gaussian noise, because Fourier transform is linear transformation, so the noise stochastic variable obtained at each Frequency point remains white Gaussian noise, the variance of each Frequency point is equal, therefore the power of the noise of each Frequency point is equal, and the signal to noise ratio that therefore in M point, maximum power spectrum point is corresponding is maximum, therefore selects the value of maximum of points in M point power spectrum as test statistics.Now, dualism hypothesis model becomes:

$\left\{\begin{array}{cc}{P}_{max}\left(f\right)\&GreaterEqual;\mathrm{\&gamma;},& H_1\\ P_{max}\left(f\right)<\mathrm{\&gamma;},& H_0\end{array}\right.$

Wherein H0 represents that signal does not exist, and H1 represents that signal exists, and γ represents decision threshold.

After choosing Frequency point, determine decision threshold thresholding.And choosing power spectrum maximum as test statistics, this value and contrast with decision threshold, if be greater than thresholding, then have signal in channel, if be less than decision threshold, then no signal in channel.This method utilizing received signal power spectrum maximum to carry out frequency spectrum perception, substantially increases the detectability of frequency spectrum perception under low signal-to-noise ratio.

The present invention utilizes the concentration of energy character of power spectrum signal to detect signal, compares the accuracy that can significantly improve frequency spectrum perception in low signal-to-noise ratio situation with time domain energy perception.The variance that the inventive method is estimated is reduced to the 1/K of periodogram.

Accompanying drawing explanation

Fig. 1 is the perception principle figure that background technology of the present invention relates to based on Power estimation;

Fig. 2 is the frequency spectrum perception flow chart based on frequency domain that background technology of the present invention relates to;

Fig. 3 is that the Bartlett that the present invention relates to realizes block diagram;

Fig. 4 is the theoretical threshold value figure that the present invention relates to;

Fig. 5 is the relation that the false alarm probability that the present invention relates to and FFT count; In figure, abscissa thrshold represents threshold value, and ordinate represents false alarm probability;

Fig. 6 is the graph of a relation of false alarm probability and the noise variance that the present invention relates to; In figure, abscissa thrshold represents threshold value, and ordinate represents detection probability;

Fig. 7 is the graph of a relation between detection probability and number of data points that the present invention relates to; Wherein, abscissa SNR represents signal to noise ratio, and unit is dB, and ordinate represents detection probability;

Fig. 8 is the relation of Bartlett method detection probability and number of data points and the segments that the present invention relates to; Wherein, abscissa SNR represents signal to noise ratio, and unit is dB, and ordinate represents detection probability;

Fig. 9 is the relation of Bartlett method detection probability and false alarm probability and the number of data points that the present invention relates to; Wherein, abscissa SNR represents signal to noise ratio, and unit is dB, and ordinate represents detection probability;

Figure 10 is the relation of detection probability and the data length that the present invention relates to; Wherein, abscissa SNR represents signal to noise ratio, and unit is dB, and ordinate represents detection probability;

Figure 11 is the flow chart that the present invention relates to.

Embodiment

Embodiment one:

The frequency spectrum sensing method based on frequency domain of present embodiment, as shown in figure 11, described method is realized by following steps:

Step one, carry out down-conversion operation to received signal, be transformed to intermediate-freuqncy signal, then intermediate-freuqncy signal is sampled;

Step 2, the data sequence with N point obtained of step one being sampled are divided into K data segment, and each data segment has M point data;

Step 3, Bart Lai Tefa (Bartlett method) based on fast Fourier transform (FFT), carry out periodogram power spectrum estimation to the data segment of each M of having point data;

Step 4, ask for the mean value of the periodogram power spectrum estimation result that step 3 obtains, namely obtain the power spectrum estimation value of Bart Lai Tefa (Bartlett method);

Step 5, select the maximum of the power spectrum estimation value of Bart Lai Tefa (Bartlett method); And determine the decision threshold shown in Fig. 4;

Step 6, the maximum of the power spectrum estimation value of Bart Lai Tefa (Bartlett method) step 5 selected as test statistics, and contrast by it with decision threshold, make the judgement of frequency spectrum perception result:

If the maximum of power spectrum is greater than decision threshold, then there is primary user's signal in channel;

If the maximum of power spectrum is less than decision threshold, then dereliction subscriber signal in channel

Embodiment two:

With embodiment one unlike, the frequency spectrum sensing method based on frequency domain of present embodiment, when sampling to intermediate-freuqncy signal described in step one, samples according to the sample frequency meeting nyquist sampling theorem.

Embodiment three:

With embodiment one or two unlike, the frequency spectrum sensing method based on frequency domain of present embodiment, described in step 3 to the process that the data segment of each M of having point data carries out periodogram power spectrum estimation be, utilize the power spectrum based on Bart Lai Tefa (Bartlett method) estimated signal of fast Fourier transform (FFT), N point data sequence is divided into K nonoverlapping data segment, and each data segment is expressed as:

x _i(n)＝x(n+iM),i＝0,1，...K-1；n＝0,1，...M-1；

Wherein, x _in () represents each data segment, n represents the sequence number of data in each segmentation, and i represents the sequence number of each data segment, and K represents data segment number; M represents in each data segment containing number of data points;

Every one piece of data section periodogram is calculated by following formula:

$\begin{array}{cc}{P}_{xx}^i\left(f\right)=\frac{1}{M}|\underset{n=0}{\overset{M-1}{\&Sigma;}}{x}_i\left(n\right)e^{-i2\mathrm{\&pi;}fn}{|}^2,& i=0,1,\mathrm{...},K-1\end{array}$

Finally, K periodogram is averaged and obtains Bart Lai Tefa power spectrum estimation, as follows:

$P_{xx}^B\left(f\right)=\frac{1}{K}\underset{i=0}{\overset{K-1}{\&Sigma;}}{P}_{xx}^i\left(f\right).$

Embodiment four:

With embodiment three unlike, the frequency spectrum sensing method based on frequency domain of present embodiment, described in step 4 the average of the Power Spectrum Estimation Method is:

$E\&lsqb;P_{xx}^B\left(f\right)\&rsqb;=\frac{1}{K}\underset{i=0}{\overset{K-1}{\&Sigma;}}E\&lsqb;P_{xx}^i\left(f\right)\&rsqb;=E\&lsqb;P_{xx}^i\left(f\right)\&rsqb;$

Wherein, E represents mean value computation symbol;

Namely the average of the Power Spectrum Estimation Method and periodogram method of estimation is identical, is also the progressive unbiased esti-mator of true spectrum density, namely

$\underset{N\&RightArrow;\mathrm{\&infin;}}{\lim }E\&lsqb;P_{xx}^i\left(f\right)\&rsqb;=\underset{m=-\mathrm{\&infin;}}{\overset{\mathrm{\&infin;}}{\&Sigma;}}{\mathrm{\&gamma;}}_{xx}\left(m\right)e^{-i2\mathrm{\&pi;}fm}={\mathrm{\&Gamma;}}_{xx}\left(f\right)$

Meanwhile, the variance obtaining the Power Spectrum Estimation Method is:

$Var\&lsqb;P_{xx}^B\left(f\right)\&rsqb;=\frac{1}{K^2}\underset{i=0}{\overset{K-1}{\&Sigma;}}Var\&lsqb;P_{xx}^i\left(f\right)\&rsqb;=\frac{1}{K}Var\&lsqb;P_{xx}^i\left(f\right)\&rsqb;$

Can find out that variance is reduced to the 1/K of periodogram; Said process can adopt Fig. 3 to state.

Embodiment five:

With embodiment one, two or four unlike, the frequency spectrum sensing method based on frequency domain of present embodiment, determines described in step 5 that the process of decision threshold is,

The first, the computing formula according to probability and probability density function:

$F\left(x\right)={\&Integral;}_{\mathrm{\&gamma;}}^{\mathrm{\&infin;}}f\left(x\right)dt={\&Integral;}_{\mathrm{\&gamma;}}^{\mathrm{\&infin;}}\frac{a^K{t}^{K-1}{e}^{-at}}{(K-1)!}dt=\frac{{\&Integral;}_{\mathrm{\&gamma;}}^{\mathrm{\&infin;}}{a}^K{t}^{K-1}{e}^{-at}dt}{(K-1)!}=\frac{{\&Integral;}_{\mathrm{\&gamma;}}^{\mathrm{\&infin;}}{a}^K{t}^{K-1}{e}^{-at}dt}{\mathrm{\&Gamma;}\left(K\right)}$

Wherein, f (x) is probability density function, and F (x) represents the probability being greater than γ; K represents data segment number; t represents integration variable;

Above formula is arranged:

$F\left(x\right)=\frac{{\&Integral;}_{a\mathrm{\&gamma;}}^{\mathrm{\&infin;}}{t}^{K-1}{e}^{-t}dt}{\mathrm{\&Gamma;}\left(K\right)}=\frac{{\&Integral;}_{\frac{K\mathrm{\&gamma;}}{{\mathrm{\&sigma;}}_n^2}}^{\mathrm{\&infin;}}{t}^{K-1}{e}^{-t}dt}{\mathrm{\&Gamma;}\left(K\right)}$

From above formula, in integral expression participate in calculating, only appear in lower limit of integral, on integral expression any impact useless, when emulating the relation of Pf and threshold value, K and be all fixed value, detailed process is as follows:

First, defined variable x and y, and make y=x ³× exp (-x)/6, then circulate according to number of thresholds, utilize the eval function of MATLAB to obtain corresponding theoretical false alarm probability;

Matlab writes and solves integral process and be:

The second, determine theoretical thresholding:

By formula $F\left(x\right)=\frac{{\&Integral;}_{a\mathrm{\&gamma;}}^{\mathrm{\&infin;}}{t}^{K-1}{e}^{-t}dt}{\mathrm{\&Gamma;}\left(K\right)}=\frac{{\&Integral;}_{\frac{K\mathrm{\&gamma;}}{{\mathrm{\&sigma;}}_n^2}}^{\mathrm{\&infin;}}{t}^{K-1}{e}^{-t}dt}{\mathrm{\&Gamma;}\left(K\right)}$ Be expressed as:

$F\left(x\right)={\&Integral;}_{\mathrm{\&gamma;}}^{\mathrm{\&infin;}}f\left(x\right)dt={\&Integral;}_{\mathrm{\&gamma;}}^{\mathrm{\&infin;}}\frac{a^K{t}^{K-1}{e}^{-at}}{(K-1)!}dt=\frac{{\&Integral;}_{\mathrm{\&gamma;}}^{\mathrm{\&infin;}}{a}^K{t}^{K-1}{e}^{-at}dt}{(K-1)!}=\frac{{\&Integral;}_{\mathrm{\&gamma;}}^{\mathrm{\&infin;}}{a}^K{t}^{K-1}{e}^{-at}dt}{\mathrm{\&Gamma;}\left(K\right)}$

$pf=\frac{{\&Integral;}_{\frac{k\mathrm{\&gamma;}}{{\mathrm{\&sigma;}}_n^2}}^{\mathrm{\&infin;}}{t}^{k-1}{e}^{-t}dt}{\mathrm{\&Gamma;}\left(k\right)}===>pf\mathrm{\&Gamma;}\left(k\right)={\&Integral;}_{\frac{k\mathrm{\&gamma;}}{{\mathrm{\&sigma;}}_n^2}}^{\mathrm{\&infin;}}{t}^{k-1}{e}^{-t}dt$

When the value of pf gets 0.1 and k=4, now in above formula, the value of pf Γ (k) is 0.6, that is:

$pf\mathrm{\&Gamma;}\left(k\right)={\&Integral;}_{\frac{4\mathrm{\&gamma;}}{{\mathrm{\&sigma;}}_n^2}}^{\mathrm{\&infin;}}{t}^{4-1}{e}^{-t}dt={\&Integral;}_{\frac{4\mathrm{\&gamma;}}{{\mathrm{\&sigma;}}_n^2}}^{\mathrm{\&infin;}}{t}^3{e}^{-t}dt=0.6$

3rd, defining integration lower end variables z sum functions variable t, utilizes the Solve function in MATLAB to obtain above formula lower limit of integral z;

Write the code asking for lower limit of integral as follows:

Symsxt；

Solve(int(t ³*exp(-t),t,x,inf)-0.6,x)

Emulation needs other the theoretical thresholding used to see Fig. 4.

Embodiment six:

With embodiment five unlike, the frequency spectrum sensing method based on frequency domain of present embodiment, the process judged of making frequency spectrum perception result described in step 6 as, when the maximum of the power spectrum estimation value of the Bart Lai Tefa that will select (Bartlett method) is as test statistics, dualism hypothesis model used is:

$\left\{\begin{array}{cc}{P}_{max}\left(f\right)\&GreaterEqual;\mathrm{\&gamma;}& H_1\\ P_{max}\left(f\right)<\mathrm{\&gamma;}& H_0\end{array}\right.$

Wherein, H ₀represent to there is not signal, H ₁represent to there is signal, γ represents decision threshold.

Emulation experiment:

After having determined test statistics and thresholding, the frequency spectrum perception performance of the method proposed is emulated.Performance simulation launches from false alarm probability and detection probability two aspects.First, we introduce false alarm probability emulation and the checking of put forward the methods.First relation being exactly false alarm probability and FFT and counting, simulated conditions is sampling number 512 and 1024, segments K=4 (i.e. 128 every section FFT and 256 FFT), noise variance variance_2=8.Result as shown in Figure 5.Wherein--representation theory value, * represents actual emulation (following identical), and the two overlaps substantially; Left side on the right side of 512 point data is 1024 point data, and the two does not have difference substantially because Pf with count that it doesn't matter, and relevant with segments.

Then, we provide the relation of false alarm probability and noise variance, as shown in Figure 6.Simulated conditions is sampling number 512, segments K=4, variance_2=[4812].

We analyze the detection probability of put forward the methods by the relation with number of data points, false alarm probability, division number below.Fig. 7 gives the impact of number of data points on detection probability.

For stable Bartlett method, 1024 and 2048 results are overlap substantially, namely for frequency domain, receive substantially not the affecting detection perform of counting of data.

Fig. 8 gives the impact of division number on detection probability.As shown in Figure 8, same program has run 2 times, list is considered from the angle of stability, divide the Bartlett method detection perform of 16 sections very stable (cyan), and points 4 sections and 8 sections have certain fluctuation, and for stable Bartlett method, the impact of number of data points is very little (two cyan curve difference is little), also demonstrate the conclusion of Fig. 7.

Finally we analyze the impact of false alarm probability on detection probability, and result as shown in Figure 9.In addition, in order to compare the difference of time domain and frequency domain detection, emulate its detection perform, result as shown in Figure 10.

As upper surface analysis for Bartlett method frequency domain energy detects (16 sections), number of data points is very little on the impact detected, and is far superior to time domain energy and detects; Time domain energy detects then has relation with data length, and under certain condition, the more detection perform of data are better.

The present invention also can have other various embodiments; when not deviating from the present invention's spirit and essence thereof; those skilled in the art are when making various corresponding change and distortion according to the present invention, but these change accordingly and are out of shape the protection range that all should belong to the claim appended by the present invention.

Claims (6)

1. based on a frequency spectrum sensing method for frequency domain, it is characterized in that: described method is realized by following steps:

Step one, carry out down-conversion operation to received signal, be transformed to intermediate-freuqncy signal, then intermediate-freuqncy signal is sampled;

Step 2, the data sequence with N point obtained of step one being sampled are divided into K data segment, and each data segment has M point data;

Step 3, Bart Lai Tefa based on fast Fourier transform, carry out periodogram power spectrum estimation to the data segment of each M of having point data;

Step 4, ask for the mean value of the periodogram power spectrum estimation result that step 3 obtains, namely obtain the power spectrum estimation value of Bart Lai Tefa;

Step 5, select the maximum of the power spectrum estimation value of Bart Lai Tefa; And determine decision threshold;

Step 6, the maximum of the power spectrum estimation value of Bart Lai Tefa step 5 selected as test statistics, and contrast by it with decision threshold, make the judgement of frequency spectrum perception result:

If the maximum of power spectrum is greater than decision threshold, then there is primary user's signal in channel;

If the maximum of power spectrum is less than decision threshold, then dereliction subscriber signal in channel.

2. according to claim 1 based on the frequency spectrum sensing method of frequency domain, it is characterized in that: when intermediate-freuqncy signal being sampled described in step one, sample according to the sample frequency meeting nyquist sampling theorem.

3. according to claim 1 or 2 based on the frequency spectrum sensing method of frequency domain, it is characterized in that: described in step 3 to the process that the data segment of each M of having point data carries out periodogram power spectrum estimation be, utilize the power spectrum based on the Bart Lai Tefa estimated signal of fast Fourier transform, N point data sequence is divided into K nonoverlapping data segment, and each data segment is expressed as:

x _i(n)＝x(n+iM),i＝0,1，…K-1；n＝0,1，…M-1；

Wherein, x _in () represents each data segment, n represents the sequence number of data in each segmentation, and i represents the sequence number of each data segment, and K represents data segment number; M represents in each data segment containing number of data points;

Every one piece of data section periodogram is calculated by following formula:

$P_{xx}^i\left(f\right)=\frac{1}{M}|\underset{n=0}{\overset{M-1}{\&Sigma;}}{x}_i\left(n\right)e^{-i2\mathrm{\&pi;}fn}{|}^2,i=0,1,...,K-1$

Finally, K periodogram is averaged and obtains Bart Lai Tefa power spectrum estimation, as follows:

$P_{xx}^B\left(f\right)=\frac{1}{K}\underset{i=0}{\overset{K-1}{\&Sigma;}}{P}_{xx}^i\left(f\right).$

4. according to claim 3 based on the frequency spectrum sensing method of frequency domain, it is characterized in that: the average obtaining the Power Spectrum Estimation Method described in step 4 is:

$E\&lsqb;P_{xx}^B\left(f\right)\&rsqb;=\frac{1}{K}\underset{i=0}{\overset{K-1}{\&Sigma;}}E\&lsqb;P_{xx}^i\left(f\right)\&rsqb;=E\&lsqb;P_{xx}^i\left(f\right)\&rsqb;$

Wherein, E represents mean value computation symbol;

Namely the average of the Power Spectrum Estimation Method and periodogram method of estimation is identical, is also the progressive unbiased esti-mator of true spectrum density, namely

$\underset{N\&RightArrow;\mathrm{\&infin;}}{\lim }E\&lsqb;P_{xx}^i\left(f\right)\&rsqb;=\underset{m=-\mathrm{\&infin;}}{\overset{\mathrm{\&infin;}}{\&Sigma;}}{\mathrm{\&gamma;}}_{xx}\left(m\right)e^{-i2\mathrm{\&pi;}fm}={\mathrm{\&Gamma;}}_{xx}\left(f\right)$

Meanwhile, the variance obtaining the Power Spectrum Estimation Method is:

$Var\&lsqb;P_{xx}^B\left(f\right)\&rsqb;=\frac{1}{K^2}\underset{i=0}{\overset{K-1}{\&Sigma;}}Var\&lsqb;P_{xx}^i\left(f\right)\&rsqb;=\frac{1}{K}Var\&lsqb;P_{xx}^i\left(f\right)\&rsqb;$

5. according to claim 1,2 or 4 based on the frequency spectrum sensing method of frequency domain, it is characterized in that: described in step 5, determine that the process of decision threshold is,

The first, the computing formula according to probability and probability density function:

$F\left(x\right)={\&Integral;}_{\mathrm{\&gamma;}}^{\mathrm{\&infin;}}f\left(x\right)dt={\&Integral;}_{\mathrm{\&gamma;}}^{\mathrm{\&infin;}}\frac{a^K{t}^{K-1}{e}^{-at}}{(K-1)!}dt=\frac{{\&Integral;}_{\mathrm{\&gamma;}}^{\mathrm{\&infin;}}{a}^K{t}^{K-1}{e}^{-at}dt}{(K-1)!}=\frac{{\&Integral;}_{\mathrm{\&gamma;}}^{\mathrm{\&infin;}}{a}^K{t}^{K-1}{e}^{-at}dt}{\mathrm{\&Gamma;}\left(K\right)}$

Wherein, f (x) is probability density function, and F (x) represents the probability being greater than γ; K represents data segment number; t represents integration variable;

Above formula is arranged:

$F\left(x\right)=\frac{{\&Integral;}_{a\mathrm{\&gamma;}}^{\mathrm{\&infin;}}{t}^{K-1}{e}^{-t}dt}{\mathrm{\&Gamma;}\left(K\right)}=\frac{{\&Integral;}_{\frac{K\mathrm{\&gamma;}}{{\mathrm{\&sigma;}}_n^2}}^{\mathrm{\&infin;}}{t}^{K-1}{e}^{-t}dt}{\mathrm{\&Gamma;}\left(K\right)}$

From above formula, in integral expression participate in calculating, only appear in lower limit of integral, on integral expression any impact useless, when emulating the relation of Pf and threshold value, K and be all fixed value, detailed process is as follows:

First defined variable x and y, and make y=x ³× exp (-x)/6, then circulate according to number of thresholds, utilize the eval function of MATLAB to obtain corresponding theoretical false alarm probability;

The second, determine theoretical thresholding:

By formula $F\left(x\right)=\frac{{\&Integral;}_{a\mathrm{\&gamma;}}^{\mathrm{\&infin;}}{t}^{K-1}{e}^{-t}dt}{\mathrm{\&Gamma;}\left(K\right)}=\frac{{\&Integral;}_{\frac{K\mathrm{\&gamma;}}{{\mathrm{\&sigma;}}_n^2}}^{\mathrm{\&infin;}}{t}^{K-1}{e}^{-t}dt}{\mathrm{\&Gamma;}\left(K\right)}$ Be expressed as:

$F\left(x\right)={\&Integral;}_{\mathrm{\&gamma;}}^{\mathrm{\&infin;}}f\left(x\right)dt={\&Integral;}_{\mathrm{\&gamma;}}^{\mathrm{\&infin;}}\frac{a^k{t}^{k-1}{e}^{-at}}{(k-1)!}dt=\frac{{\&Integral;}_{\mathrm{\&lambda;}}^{\mathrm{\&infin;}}{a}^k{t}^{k-1}{e}^{-at}dt}{(k-1)!}=\frac{{\&Integral;}_{\mathrm{\&lambda;}}^{\mathrm{\&infin;}}{a}^k{t}^{k-1}{e}^{-at}dt}{\mathrm{\&Gamma;}\left(K\right)}$

$pf=\frac{{\&Integral;}_{\frac{k\mathrm{\&gamma;}}{{\mathrm{\&sigma;}}_n^2}}^{\mathrm{\&infin;}}{t}^{k-1}{e}^{-t}dt}{\mathrm{\&Gamma;}\left(k\right)}===>pf\mathrm{\&Gamma;}\left(k\right)={\&Integral;}_{\frac{k\mathrm{\&gamma;}}{{\mathrm{\&sigma;}}_n^2}}^{\mathrm{\&infin;}}{t}^{k-1}{e}^{-t}dt$

When the value of pf gets 0.1 and k=4, now in above formula, the value of pf Γ (k) is 0.6, that is:

$pf\mathrm{\&Gamma;}\left(k\right)={\&Integral;}_{\frac{4\mathrm{\&gamma;}}{{\mathrm{\&sigma;}}_n^2}}^{\mathrm{\&infin;}}{t}^{4-1}{e}^{-t}dt={\&Integral;}_{\frac{4\mathrm{\&gamma;}}{{\mathrm{\&sigma;}}_n^2}}^{\mathrm{\&infin;}}{t}^3{e}^{-t}dt=0.6$

3rd, defining integration lower end variables z sum functions variable t, utilizes the Solve function in MATLAB to obtain above formula lower limit of integral z.

6. according to claim 5 based on the frequency spectrum sensing method of frequency domain, it is characterized in that: the process judged of making frequency spectrum perception result described in step 6 as, when the maximum of the power spectrum estimation value of the Bart Lai Tefa that will select is as test statistics, dualism hypothesis model used is:

$\left\{\begin{array}{cc}{P}_{max}\left(f\right)\&GreaterEqual;\mathrm{\&gamma;},& H_1\\ P_{max}\left(f\right)<\mathrm{\&gamma;},& H_0\end{array}\right.$

Wherein, H ₀represent to there is not signal, H ₁represent to there is signal, γ represents decision threshold.