CN105578480B - The pre- decision method of lack sampling frequency spectrum perception towards wide-band modulation converter - Google Patents
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Abstract
The invention discloses a kind of pre- decision method of lack sampling frequency spectrum perception towards wide-band modulation converter mainly solves the problems, such as prior art false-alarm probability height and to calculate cost big.Its technical solution is: 1. receiving ends carry out compression sampling to the signal received, obtain the road m sample and calculate the time domain energy of each branch collecting sample；2. calculating test statistics r according to time domain energyJ, k；3. calculating the decision threshold γ of test statisticsJ, k；4 by test statistics compared with decision threshold, decision signal whether there is: if rJ, k>γJ, k, then it has been judged to signal, if all rJ, k≤γJ, k, then it is judged to no signal.The advantages of it is smaller that there is the present invention perceptual performance to be influenced by noise power, and computation complexity is low, effectively reduces influence of the non-sparsity of broadband Gaussian white noise to lack sampling frequency spectrum perception can be used in the broader frequency spectrum perception of analog signal compression sampling.
Description
Technical Field
The invention belongs to the technical field of communication, relates to a spectrum sensing technology, and further relates to an under-sampling spectrum sensing pre-judging method for a broadband modulation converter, which can be used for spectrum sensing in cognitive radio.
Background
The spectrum sensing is used as a foundation key technology of a cognitive radio system, can provide necessary feedback information for a dynamic closed-loop system, provides environmental information and decision basis for a cognitive radio system/network, provides guarantee for orderly and dynamically distributing and reasonably supervising a spectrum, and is a basis for improving the spectrum utilization rate, improving the transmission condition of a wireless channel, realizing network intellectualization, actively avoiding various interferences and effectively managing spectrum resources. The current spectrum sensing method is mainly focused on finding spectrum access opportunities in a narrower frequency range, and as known by Shannon's theorem, the maximum theoretical bit rate is directly determined by available bandwidth, an access spectrum provided by narrow-band spectrum sensing obviously cannot bear the communication rate required by a user, and a cognitive user needs to find more access opportunities in a wider frequency range by adopting broadband spectrum sensing. The classic Nyquist sampling theorem indicates that, in order to reconstruct an analog signal without distortion, the sampling frequency of the analog signal should be at least more than or equal to twice the signal spectrum bandwidth, and when a cognitive user performs broadband spectrum sensing, the user needs to acquire samples from a very wide frequency band with higher resolution and extremely low power consumption, which brings bottleneck constraints of acquisition front-end conversion speed, high throughput large-capacity cache space and the highest operating frequency of a back-end logic device to a digital signal processing mechanism based on the shannon-Nyquist sampling theorem.
The compressed sampling CS theory only needs a few non-adaptive linear measurement sample points, so that sparse analog signals on a time domain or other transformation domains can be recovered with a great probability by a convex optimization method, and the conversion of signals from analog to information can be directly realized according to the method, thereby providing a new theoretical basis for reducing the analog-digital conversion rate and relieving the digital signal processing pressure. In view of this, the method combines the compressive sampling and the broadband spectrum sensing, fully utilizes the sparse characteristic of the spectrum to be sensed, completes the information acquisition of the broadband spectrum at an analog-digital conversion speed far lower than the Nyquist sampling rate, and completes the broadband spectrum sensing in real time with extremely low digital signal processing overhead, and is one of effective ways for solving the bottleneck of broadband analog signal acquisition and high-speed digital signal transmission, storage and processing.
At present, the broadband spectrum sensing methods available for analog signal compression sampling can be roughly divided into two categories:
the first type is based on an analog information converter AIC, an AIC undersampling framework uses the addition of limited discrete multitone signals as an analog input signal model, the analog input signal is multiplied by a random symbol sequence, then integral accumulation and low-pass sampling are carried out, after a compressed acquisition sample is obtained, an original signal or the statistical characteristics of the original signal can be obtained by using a reconstruction method, and then occupancy rate judgment is completed by using a time domain or frequency domain energy detection method.
The second type is based on a broadband modulation converter MWC, the MWC under-sampling framework takes a limited union set with a translation invariant subspace as an analog input signal model, the input signal is multiplied by a periodic random symbol sequence on a plurality of branches to realize the down-conversion of different weight factors of input signal subspace decomposition, so that the necessary sampling rate is reduced, an infinite measurement vector system corresponding to continuous analog signal acquisition is converted into a multiple measurement vector system by constructing an under-sampling sample framework, then a branch set corresponding to an occupied frequency band is solved by utilizing an orthogonal matching tracking algorithm, and the MWC under-sampling framework has the advantages of reasonable signal model, real-time branch set determination, realization by using commercial devices and the like. However, due to the existence of white noise in the wideband frequency band, the wideband white noise is not sparse in the time domain, the frequency domain or other transform domains, and the following problems are easily caused by directly performing wideband spectrum sensing by adopting the undersampled samples of the wideband modulation transformer:
(1) although no main user signal exists in the broadband frequency band to be sensed and only white gaussian noise exists, the reconstruction algorithm of compressed sensing still gives the occupation situation in the frequency band according to sparsity, which causes serious false alarm probability;
(2) the processes of signal reconstruction and support set determination are carried out by utilizing the undersampled samples, so that great calculation cost is brought, and the operations are meaningless;
(3) the wrong spectrum sensing result influences the communication strategy, so that the communication of the secondary user is frequently interrupted, and the utilization rate of the frequency band is reduced.
Disclosure of Invention
The invention aims to overcome the defects of a spectrum sensing technology based on a broadband modulation converter, and provides an under-sampling spectrum sensing pre-judging method facing the broadband modulation converter, so that the influence of the non-sparsity of broadband white Gaussian noise on the under-sampling spectrum sensing is effectively reduced, the spectrum sensing accuracy is improved, the calculation cost is reduced, and the frequency band utilization rate is improved.
In order to achieve the above object, the present invention provides an undersampled spectrum sensing decision-making method for a wideband modulation converter, which includes the following steps:
(1) the receiving end carries out compression sampling on the received signal by using a broadband modulation converter to obtain m paths of samples yi(N), i is 1,2, …, m, N is 0,1, …, N-1, N is the number of sample points, and the time domain energy of each branch collected sample is calculated respectively
(2) Computing test statistics from time domain energy
Wherein,andrespectively obtaining time domain energy of a j-th branch and a k-th branch, wherein j is 2,3, …, m, k is 1,2, …, j-1, and m (m-1)/2 test statistics are obtained;
(3) calculating a test statistic rj,kIs determined by the decision threshold gammaj,k：
(3a) Dividing the time domain energy of the ith branchConversion to frequency domain energyWill test statistic rj,kConverted from the time domain to the frequency domain,
(3b) constructing a test statistic rj,kCumulative distribution function Pf：
Where ρ isj,kIs a correlation coefficient of a sum, taking the value as a function phi (·)Is expressed as
(3c) Cumulative distribution function P from test statisticsfCalculating a decision threshold gamma by using a constant false alarm criterionj,k：
Wherein, PfPresetting false alarm probability, phi, for each branch decision-1(. h) is the inverse of the phi (. h.);
(4) testing statistic r obtained in step (2)j,kAnd the threshold value gamma obtained in the step (3)j,kComparing, judging whether there is signal, if there is statistic rj,kGreater than a threshold gammaj,kIf so, judging that a signal exists; if there is no statistic rj,kGreater than a threshold gammaj,kThen it is judged as no signal.
The invention has the following advantages:
1. according to the invention, because a small amount of compressed sampling samples are utilized, the influence of the non-sparsity of the broadband white Gaussian noise on the undersampled spectrum sensing can be effectively reduced;
2. because the threshold value of the invention is irrelevant to the variance of the noise, the influence of the noise power on the perception performance is small, and the influence on the uncertainty of the noise can be effectively resisted;
3. the invention only needs a small amount of samples to carry out simple modular square operation, so the calculation complexity is low, and the real-time performance of frequency spectrum sensing can be met.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a simulation of the probability of correct detection under different signal-to-noise ratios according to the present invention;
FIG. 3 is a simulation of false alarm probability for different signal-to-noise ratios according to the present invention;
FIG. 4 is a comparison graph of detection probability simulation at different signal-to-noise ratios in the presence of noise uncertainty in accordance with the present invention;
fig. 5 is a simulation diagram of receiver performance curves under different false alarm probabilities in accordance with the present invention.
Detailed Description
The invention is used for the broadband spectrum sensing of analog signal compression sampling, and the sensing end receives signals on each sub-channel and processes the sampling of the received signals.
Referring to fig. 1, the implementation steps of the invention are as follows:
step 1, a sensing end calculates the time domain energy T of each branch acquisition samplei td。
The sensing end performs compression sampling on the received signal by using a broadband modulation converter to obtain m paths of samples yi(n),i＝1,2,…,m,n＝0,1,…,N-1；
Using a branch sample yi(n) calculating time domain energy
Wherein m is the number of the acquisition branches of the broadband modulation converter, and N is the number of the sample points.
Step 2, calculating a test statistic r according to the time domain energyj,k
Wherein,andthe time domain energies of the j-th and k-th branches, j 2,3, …, m, k 1,2, …, j-1,
and (3) calculating m (m-1)/2 test statistics according to different values of j and k.
Step 3, according to the preset false alarm probability, when the main user signal does not exist, calculating a judgment threshold gammaj,k。
When the primary user signal is absent, the received signal contains only noise, i.e., the input signal x (t) ═ ω (t), where ω (t) is assumed to be 0 in mean and 0 in varianceWhite gaussian noise, with a decision threshold gammaj,kThe calculation steps are as follows:
(3a) dividing the time domain energy of the ith branchConversion to frequency domain energyWill test statistic rj,kConverted from the time domain to the frequency domain,
(3b) constructing a test statistic rj,kCumulative distribution function Pf：
(3b1) Calculating Yi(k) Statistical properties of (a):
(3b11) according to the MWC compression acquisition structure of the broadband modulation converter, the branch sample y is subjected toi(n) performing discrete Fourier transform to obtain a branch sample spectrum Yi(k)：
Wherein, cilFor periodic pseudo-random + -1 sequences pi(t) a periodic Fourier series expansion coefficient, L being the number of subspaces required for complete representation of the input signal X (t) Fourier transform X (j Ω), L being calculated according to the formula,
wherein f isNYQIs the equivalent Nyquist sampling rate, f, of the MWCpIs the frequency of a random symbol sequence, fsIs the low pass sampling rate;
(3b12) in the absence of primary users, the input signal spectrum X (k) is mean 0 and varianceUsing the mean and variance of X (k), calculating branch sample spectrum Yi(k) The statistical properties of (a), comprising:
calculating Yi(k) Mean value of E [ Y ]i(k)]Sum variance D [ Y ]i(k)]Comprises the following steps:
E[Yi(k)]＝0，
calculating Yi(k) Mean of real partsSum varianceComprises the following steps:
calculating Yi(k) Mean of imaginary partSum varianceComprises the following steps:
calculating Yi(k) Real part and Yi(k) Correlation coefficient of imaginary part:(3b2) calculating branch sample spectrum Yi(k) Mean value of the squares of the modes E [ | | Yi(k)||2]And variance D [ | Y [ ]i(k)||2]：
Wherein,is the variance of the input signal spectrum x (k);
(3b3) calculating branch sample spectrum Yi(k) Correlation coefficient of modulo square:
(3b31) the correlation coefficients at different frequency points are:
cov[||Yp(a)||2,||Yq(b)||2]＝0，
(3b32) the correlation coefficients at the same frequency point are:
wherein p, q ═ 1, 2., m, p ≠ q, k ═ 0, 1., N-1,
in the formula cqmIs a periodic Fourier series expansion coefficient of a periodic pseudorandom + -1 sequence,the representation is taken in the real part,the expression takes the imaginary part;
(3b4) calculating the mean value E [ T ] of branch frequency domain energyi fd]Variance D [ T ]i fd]And correlation coefficient ρj,k：
(3b5) Cumulative distribution function F according to ratio of any two related Gaussian random variables G and HR(r) calculating a test statistic rj,kCumulative distribution function Pf：
FRThe expression of (r) is:
wherein, muGIs the mean of the gaussian random variable G,is the variance, mu, of the Gaussian random variable GHIs the mean value of the gaussian random variable H,is the variance of a Gaussian random variable H, and rho is the correlation coefficient of G and H.
When N is present>At 20 hours, Ti fdApproximately obey a Gaussian distribution with mean and variance, respectivelyAndandis rhoj,kFrom this, the test statistic r can be obtainedj,kThe cumulative distribution function of (a) is:
where ρ isj,kIs the j branch frequency domain energyAnd the kth branch frequency domain energyGamma is a system of tests
Measurement of rj,kOf the decision threshold, E [ ·]Represents the mean value, D [. cndot.)]Represents the variance;
(3c) cumulative distribution function P from test statisticsfUse of constantFalse alarm criterion, calculating decision threshold gammaj,k：
Wherein, PfPresetting false alarm probability, phi, for each branch decision-1(. cndot.) is the inverse of the phi (. cndot.) function.
And 4, step 4: testing statistic r obtained in step (2)j,kAnd the decision threshold value gamma obtained in the step (3)j,kAnd (3) comparing, judging whether a signal exists or not:
if there is a statistic rj,kGreater than a threshold gammaj,kIf so, judging that a signal exists;
if there is no statistic rj,kGreater than a threshold gammaj,kThen it is judged as no signal.
The effects of the present invention can be further illustrated by the following simulations:
A. simulation conditions
The equivalent sampling rate of a broadband modulation converter adopted by the simulation system is fNYQThe number of the acquisition branches is m-20, the period of the random symbol +/-1 sequence is Tp7.5ns, frequency fp＝1/TpThe number of equivalent random chips in one period is L-45, and the low-pass filtering cut-off frequency used by each channel is fsA single channel sampling rate of fs＝fp(ii) a In the frequency band (0, f)NYQ/2), there are 2 signals in total, and the symbol rate of each signal is srThe carrier frequency of each signal is randomly generated, the power of N signals is the same, the ratio of the total power of N signals to the noise power is defined as signal-to-noise ratio, 1000 times of simulation is carried out under each signal-to-noise ratio, and the preset false alarm probability is PfaAnd performing compression collection by using an MWC converter, wherein the number of used sample points K is 100.
B. Simulation content and results
Simulation 1: the signal-to-noise ratio is-20 dB to-10 dB and the preset false alarm probability PfaThe correct detection probability of the present invention was simulated under the condition of 0.01, and the simulation is shown in fig. 2.
As can be seen from fig. 2, when the signal-to-noise ratio is greater than or equal to-8 dB by using the number of undersampled sample points whose K is 100, the correct detection probability of the present invention can be greater than 98%, and the present invention can obtain an extremely superior pre-decision performance within a wider signal-to-noise ratio range.
Simulation 2: the signal-to-noise ratio is-20 dB to-10 dB and the preset false alarm probability PfaThe false alarm probability of the present invention is simulated under the condition of 0.01, and the simulation is shown in fig. 3.
As can be seen from fig. 3, the false alarm probability of the present invention is basically suppressed to be near the preset false alarm probability value within the range of the signal-to-noise ratio of-20 dB to-10 dB by using the number of the undersampled sample points where K is 100.
Simulation 3: under the conditions that the signal-to-noise ratio is-20 dB to-10 dB, the false alarm probability is 0.01 and the noise uncertainty rho is 1.4, the correct detection probability of the invention is simulated and compared with a simulation curve without the noise uncertainty, and the simulation result is shown in fig. 4.
As can be seen from fig. 4, when there is noise uncertainty, the correct detection probability of the present invention does not change much, and the performance curves of the present invention substantially coincide when there is noise uncertainty and there is no noise uncertainty, which indicates that the present invention can effectively combat noise uncertainty.
And (4) simulation: under the condition that the signal-to-noise ratio is-16 dB, a receiver performance curve of the under-sampling spectrum sensing pre-judging method for the broadband modulation converter is simulated, the receiver performance curve is compared with a simulation curve with the noise uncertainty rho of 1.4, and the simulation result is shown in fig. 5.
As can be seen from fig. 5, the pre-decision algorithm provided by the present invention can obtain superior perceptual performance under the conditions of a small false alarm probability and a low signal-to-noise ratio, and when there is noise uncertainty, the receiver performance curve of the present invention is also substantially unchanged, which indicates that the present invention has robustness to the noise uncertainty.
By combining the simulation result analysis, the invention can obtain more excellent perception performance under the conditions of smaller false alarm probability and lower signal-to-noise ratio, and the perception performance is basically unchanged when the noise uncertainty exists, which shows that the invention can effectively resist the noise uncertainty.
Claims (4)
1. An undersampled spectrum sensing pre-decision method for a broadband modulation converter comprises the following steps:
(1) the receiving end carries out compression sampling on the received signal by using a broadband modulation converter to obtain m paths of samples yi(N), i is 1,2, …, m, N is 0,1, …, N-1, N is the number of sample points, and the time domain energy T of each branch collecting sample is calculated respectivelyi td：
(2) Computing test statistics from time domain energy
Wherein,andrespectively obtaining time domain energy of a j-th branch and a k-th branch, wherein j is 2,3, …, m, k is 1,2, …, j-1, and m (m-1)/2 test statistics are obtained;
(3) calculating a test statistic rj,kIs determined by the decision threshold gammaj,k：
(3a) Dividing the time domain energy T of the ith branchi tdConversion into frequency domain energy Ti fdWill test the statistic rj,kConverted from the time domain to the frequency domain,
(3b) constructing a test statistic rj,kCumulative distribution function Pf：
Where ρ isj,kIs thatAndthe correlation coefficient is taken asD[·]Represents the variance, phi (·) is expressed as
(3c) Cumulative distribution function based on test statisticsPfCalculating a decision threshold gamma by using a constant false alarm criterionj,k：
Wherein phi-1(. h) is the inverse of the phi (. h.);
(4) testing statistic r obtained in step (2)j,kAnd the threshold value gamma obtained in the step (3)j,kComparing, judging whether there is signal, if there is statistic rj,kGreater than a threshold gammaj,kIf so, judging that a signal exists; if there is no statistic rj,kGreater than a threshold gammaj,kThen it is judged as no signal.
2. The under-sampling spectrum sensing decision-making method facing to the broadband modulation converter according to claim 1, wherein in step (1), each branch acquisition sample y is calculatedi(n) time domain energy Ti tdCalculated according to the following formula:
3. the under-sampling spectrum sensing pre-decision method facing to broadband modulation converter according to claim 1, wherein in step (3a), the time domain energy T of the ith branch is usedi tdConversion into frequency domain energy Ti fdIt is calculated according to the following formula using the Pasaval law of conservation of energy:
wherein, Yi(k) Is yi(N), i ═ 1,2, …, m, N ═ 0,1, …, N-1.
4. The under-sampled spectrum sensing decision-making method for wideband modulation transformer according to claim 1 or 3, wherein the test statistic r is constructed in step (3b)j,kCumulative distribution function PfThe method comprises the following steps:
(3b1) calculating Yi(k) Statistical properties of (a):
(3b11) according to the MWC compression acquisition structure of the broadband modulation converter, the branch sample y is subjected toi(n) performing discrete Fourier transform to obtain a branch sample spectrum Yi(k)：
Wherein, cilFor periodic pseudo-random + -1 sequences pi(t) a periodic Fourier series expansion coefficient, L being the number of subspaces required for complete representation of the input signal X (t) Fourier transform X (j Ω), L being calculated according to the formula,
wherein f isNYQIs the equivalent Nyquist sampling rate, f, of the MWCpIs the frequency of a random symbol sequence, fsIs the low pass sampling rate;
(3b12) in the absence of primary users, the input signal spectrum X (k) is mean 0 and varianceUsing the mean and variance of X (k), calculating branch sample spectrum Yi(k) Statistical properties of (a):
calculating Yi(k) Mean value of E [ Y ]i(k)]Sum variance D [ Y ]i(k)]Comprises the following steps:
E[Yi(k)]＝0，
calculating Yi(k) Mean of real partsSum varianceComprises the following steps:
calculating Yi(k) Mean of imaginary partSum varianceComprises the following steps:
calculating Yi(k) Real part and Yi(k) Correlation coefficient of imaginary part:
(3b2) calculating branch sample spectrum Yi(k) Mean value of the squares of the modes E [ | | Yi(k)||2]And variance D [ | Y [ ]i(k)||2]：
Wherein,is the variance of the input signal spectrum x (k);
(3b3) calculating branch sample spectrum Yi(k) Phase of mode squareThe correlation coefficient is as follows:
(3b31) the correlation coefficients at different frequency points are:
cov[||Yp(a)||2,||Yq(b)||2]＝0，
(3b32) the correlation coefficients at the same frequency point are:
wherein p, q ═ 1, 2., m, p ≠ q, k ═ 0, 1., N-1,
cpm、cqmis a periodic Fourier series expansion coefficient of a periodic pseudorandom + -1 sequence,the representation is taken in the real part,the expression takes the imaginary part;
(3b4) calculating the mean value E [ T ] of branch frequency domain energyi fd]Variance D [ T ]i fd]And correlation coefficient ρj,k：
(3b5) Cumulative distribution function F according to ratio of any two related Gaussian random variables G and HR(r) calculating a test statistic rj,kCumulative distribution function Pf：
FRThe expression of (r) is:
wherein, muGIs the mean of the gaussian random variable G,is the variance, mu, of the Gaussian random variable GHIs the mean value of the gaussian random variable H,the variance of a Gaussian random variable H is obtained, and rho is a correlation coefficient of G and H;
when N > 20, Ti fdApproximately obey a Gaussian distribution with mean and variance, respectivelyAnd andis rhoj,kFrom this, the test statistic r can be obtainedj,kThe cumulative distribution function of (a) is:
where ρ isj,kIs the j branch frequency domain energyAnd the kth branch frequency domain energyGamma is the test statistic rj,kOf the decision threshold, E [ ·]Represents the mean value, D [. cndot.)]The variance is indicated.
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| CN107181548A (en) * | 2017-05-15 | 2017-09-19 | 西安电子科技大学 | One kind compression frequency spectrum perception performance improvement method |
| CN107332566B (en) * | 2017-06-19 | 2020-09-08 | 四川大学 | MWC-based support set rapid recovery method |
| CN107426737B (en) * | 2017-09-22 | 2020-10-02 | 哈尔滨工业大学 | Broadband spectrum sensing method based on single-channel structure modulation broadband converter |
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| CN113765607B (en) * | 2021-03-15 | 2022-08-30 | 全球能源互联网研究院有限公司 | Frequency spectrum detection method and device |
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