CN103297160A - Spectrum sensing method and spectrum sensing device for goodness-of-fit test based on normalized eigenvalues - Google Patents

Abstract

The invention relates to the technical field of wireless communication and discloses a spectrum sensing method and a spectrum sensing device for goodness-of-fit test based on normalized eigenvalues. The method includes receiving signals on authorized spectrum bands by a spectrum sensing device, performing sampling filter on the received signals, then calculating a covariance matrix, performing eigenvalue decomposition on the covariance matrix, sorting eigenvalues from small to large, dividing the eigenvalues by sum of all the eigenvalues to obtain normalized eigenvalues, performing goodness-of-fit test on the normalized eigenvalues, and judging whether signals exist or not according to test results. The method and the device have the advantages of no need of authorized signal features, noise uncertainty and insensitivity and the like, and the device is excellent in performance.

Description

Spectrum sensing method and device based on goodness-of-fit test of normalized characteristic value

Technical Field

The present invention relates to the field of wireless communication technologies, and in particular, to a spectrum sensing method and apparatus without sending any characteristic information of a signal.

Background

The problem of scarce radio spectrum resources becomes more and more prominent with the rapid growth of wireless data services. The proposal of cognitive radio makes it possible to flexibly apply the already occupied spectrum resources. The development of cognitive radio technology greatly improves the spectrum utilization rate, relieves the contradiction between the increasing wireless service demand and the increasingly deficient spectrum resources, and is generally considered to be the best scheme for solving the problem of the current wireless spectrum utilization rate. Existing research shows that cognitive radio can improve communication system capacity and improve spectrum management efficiency.

In a cognitive radio system, how to judge whether signals of authorized users exist on a frequency spectrum is a problem to be solved firstly. This problem is called spectrum sensing or spectrum sensing. Commonly used spectrum sensing methods include: energy detection, matched filter detection, and cyclostationary detection. The energy detection complexity is low, but the performance thereof is seriously deteriorated by the uncertainty of the noise. Matched filtering is excellent but requires the characteristics of the transmitted signal to be known. The cyclostationary detection performance is also excellent, but the complexity is high, and the cyclostationary detection performance is limited in practical application.

Whether the frequency band is a signal or noise can be judged according to the covariance matrix of the received signal, and the theoretical basis of the operation is as follows. It is known that, in general, in the presence of a signal, the covariance matrix of the signal is not a diagonal matrix, but the covariance matrix of the received signal is a matrix with equal diagonal elements in the presence of only noise. Based on the theoretical basis, the traditional technical scheme provides a method for carrying out spectrum sensing by using the eigenvalue of the covariance matrix of the received signal, and the decision variable can be formed by the eigenvalue of the covariance matrix. And provides a construction method of decision variables, namely the ratio of the maximum and minimum characteristic values. In addition, the conventional technical solution also proposes a method of using a ratio of a geometric mean and an arithmetic mean of feature values as a decision variable. The advantage of these methods is that no a priori information of the transmitted signal is required, nor is any statistical property of the noise required. However, these methods do not utilize the distribution characteristics of the feature values.

Disclosure of Invention

The technical problem is as follows: in order to further improve the performance of the characteristic value detection method and avoid the influence of noise uncertainty, the invention provides a frequency spectrum detection method and a frequency spectrum detection device based on the goodness-of-fit test of a normalized characteristic value.

The technical scheme is as follows: the spectrum sensing method based on the goodness-of-fit test of the normalized characteristic value comprises the following steps:

(1) receiving a wireless signal on a frequency band to be sensed;

(2) sampling and filtering a received signal, calculating a covariance matrix of the signal, recording the covariance matrix as R, and setting the dimensionality of the covariance matrix as L multiplied by L;

(3) calculating eigenvalue decomposition of the covariance matrix to obtain ordered eigenvalues, wherein the eigenvalues are expressed as sigma from small to large₁,σ₂,…,σ_L；

(4) The normalized feature value, i.e. the sum of the feature values divided by all feature values, is calculated and the result is expressed as

(5) Calculating the cumulative probability of the normalized characteristic value according to the cumulative distribution function F (x) of the normalized characteristic value of the noise:

(ii) a The cumulative distribution function F (x) of the normalized characteristic value of the noise is obtained through theoretical calculation, or F (x) is made into a table form through simulation, and the cumulative probability of the normalized characteristic value is obtained through table lookup.

(6) And (3) calculating a decision variable T according to the goodness-of-fit test, judging that an authorized signal exists on the frequency spectrum when T is greater than a preset threshold, and judging that no authorized signal exists when T is less than the preset threshold, namely the frequency spectrum is idle.

The decision variable T is examined using Anderson-Darling,

$T=-\frac{\underset{l=1}{\overset{L}{\mathrm{\Σ}}}(2l-1)\left\{1n\right[F\left({\widetilde{\mathrm{\σ}}}_l\right)+1n[1-F\left({\widetilde{\mathrm{\σ}}}_{L+1-l}\right)]\}}{L}-L$

where ln (·) represents a natural logarithmic function.

Preferably, the method is suitable for spectrum sensing of single-antenna and multi-antenna systems.

Preferably, the method is suitable for cooperative sensing of multiple nodes.

Spectrum sensing device based on goodness of fit test of normalization eigenvalue includes: the device comprises a wireless signal sampling and filtering module, a covariance matrix calculation module, a characteristic value decomposition module, a characteristic value normalization calculation module, a normalized characteristic value cumulative probability calculation module, a decision variable calculation module and a decision module; wherein,

the wireless signal sampling and filtering module is used for obtaining a wireless signal of a perceived frequency band;

the covariance matrix calculation module is used for calculating a covariance matrix of the signal to be perceived;

the eigenvalue decomposition module is used for calculating the eigenvalue decomposition of the covariance matrix of the signal to be perceived;

the normalization calculation module of the characteristic value divides the characteristic value by the sum of all the characteristic values to obtain a normalized characteristic value;

the cumulative probability calculation module of the normalized characteristic values calculates the cumulative probability corresponding to each normalized characteristic value;

the decision variable calculation module calculates the inspection quantity according to the cumulative probability of the normalized characteristic value; adopting an Anderson-Darling goodness of fit test method;

the decision module includes a comparator for comparing a decision variable with a threshold.

By adopting the technical scheme, the invention has the following beneficial effects: in the stage of calculating the decision variable T, the method only needs simple addition and comparison operation, and compared with the spectrum sensing based on the characteristic value in the background technology, the complexity is very low, and the method is not sensitive to the uncertainty of noise. In addition, the invention is also suitable for spectrum sensing of a multi-antenna system.

Drawings

Fig. 1 is a flowchart of a spectrum sensing method according to an embodiment of the present invention;

fig. 2 is a block diagram of a spectrum sensing apparatus according to an embodiment of the present invention;

FIG. 3 is a block diagram of a decision variable calculation module when the Anderson-Darling goodness-of-fit test method is adopted according to an embodiment of the invention;

FIG. 4 is a diagram illustrating a comparison between the performance of an embodiment of the present invention and that of the prior art when the sampling point is 64 for a wireless microphone signal;

FIG. 5 is a diagram illustrating a performance comparison between an embodiment of the present invention and the background art when a sampling point is 128 for a wireless microphone signal;

FIG. 6 is a diagram illustrating performance comparison between an embodiment of the present invention and the background art when a sampling point is 32 for a multi-point cooperative spectrum sensing model;

fig. 7 is a schematic diagram illustrating performance comparison between the embodiment of the present invention and the background art when a sampling point is 64 for a multi-point cooperative spectrum sensing model.

Detailed Description

The present invention is further illustrated by the following examples, which are intended to be purely exemplary and are not intended to limit the scope of the invention, as various equivalent modifications of the invention will occur to those skilled in the art upon reading the present disclosure and fall within the scope of the appended claims.

The spectrum detection method based on the goodness-of-fit test of the normalized feature values, as shown in fig. 1, includes the following steps:

1) the frequency spectrum sensing device receives a wireless signal on a frequency band to be sensed;

2) after sampling and filtering the received signals, the frequency spectrum sensing device calculates a covariance matrix of the signals, which is marked as R and has dimension of L multiplied by L;

we discuss the computation of the signal covariance matrix in two scenarios separately.

Scene 1: the covariance matrix of the signal can be estimated by means of a moving average. It is assumed that the received signal sequence is represented as,

x(1),x(2),x(N),x(N+1),x(N+2),...,x(nN),x(nN+1),....

where N represents the number of oversampling points for the signal (or N can be modeled as the number of receive antennas for a multi-antenna receive system). We use a sliding window method to compute the covariance matrix of the received signal. Assuming a smoothing factor M, then,

[ equation 1]

Where K represents the number of vectors to be summed,

$x_n={\left[\begin{array}{cccc}x\left(\mathrm{nN}\right)& x(\mathrm{nN}+1)& ...& x(\mathrm{nN}+N-1)\end{array}\right]}^T$ [ formula of2]

${\hat{x}}_n={\left[\begin{array}{cccc}{x}_n^T& x_{n-1}^T& ...& x_{n-M+1}^T\end{array}\right]}^T$ [ equation 3 ]]

R is a matrix NM × NM, and let L ═ NM, then R is a matrix L × L.

Then, when only noise is present,

[ formula 4 ]]

Wherein, w_nDefinition of (1) and x_nSimilarly. We assume that the noise is white Gaussian with a variance of γ². Mathematically strictly speaking, R_wIs not a meshart matrix, however, R_wCan be approximated as a Wishart matrix.

Scene 2: the cooperative spectrum sensing model assumes a flat fading channel, and the number of cooperative nodes is L. Then, the received signal at the nth time may be expressed as,

$x_n={\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="HDA00003252520100021.png,HDA00003252520100031.png"\; state="\{\{state\}\}">P</figure-callout>}}^{\frac{1}{2}}{H}_n{s}_n+w_n$ [ equation 5]

Wherein x is_nIs a received signal vector of L x 1, s_nIs a K × 1 transmitted signal vector, H_nIs a standard Rayleigh fading channel matrix, P is an L × L receive correlation matrix, w_nIs independent and identically distributed Gaussian white noise with variance of gamma². Then, the covariance matrix of the received signal can be calculated by the following formula,

r is an L matrix. When there is only noise present, the noise is,

it can be seen that mathematically, R_wIs a Wishart matrix.

In order to improve the performance of the conventional detection technology, we propose to use the distribution characteristics of the feature values for detection. The basic principle is that the distribution of the eigenvalues is available in the presence of noise only. Therefore, we can check whether the eigenvalue distribution of the received signal is similar to that of the noise by Goodness of Fit Test. To avoid the detector being affected by the uncertainty of the noise, we further performed a goodness-of-fit test based on the normalized eigenvalues. To this end, we proceed to steps 3) and 4) to distribute the eigenvalues of the computation covariance matrix and the normalized eigenvalues.

3) The covariance matrix of the spectrum sensing device carries out eigenvalue decomposition, and the eigenvalue is expressed as sigma from small to large₁,σ₂,…,σ_L。

4) The spectrum sensing device calculates a normalized feature value, i.e. the feature value is divided by the sum of all feature values, and the result is expressed as

Below, we will perform a goodness-of-fit test of the normalized feature values.

5) The spectrum sensing device calculates the cumulative probability of the normalized characteristic value according to the cumulative distribution function F (x) of the normalized characteristic value of the noise:

in performing goodness-of-fit testing, one key step is to calculate the cumulative probability of the data to be tested. The calculation of the cumulative probability of the normalized characteristic value can be calculated by a theoretical formula, or the cumulative probability of the normalized characteristic value can be obtained by simulation and stored into a table for query. Next, we refer to R under the two signal models described above_wThe calculation method is used for deducing approximate expressions of the cumulative distribution function of the normalized characteristic value in the presence of noise respectively from theory.

Here, we assume that L ≧ K, which is reasonable in practical cases. According to R_wIs characterized in thatSum of eigenvalues equal to R_wTrace of (1), then R_wThe mean value of the sum of the characteristic values is L gamma². Therefore, when the cumulative distribution function of the normalized feature values is calculated only in the presence of noise, let us use L γ²As the sum of the approximated eigenvalues. Then, the cumulative distribution function of the normalized feature values we obtain below is an approximate expression.

From the cumulative distribution function of the asymptotic characteristic root of the mathematical Wishart matrix, we can calculate the cumulative distribution function as L γ by the following formula²To normalize the cumulative distribution function of the eigenvalues at the factor,

$F\left(x\right)=\{\begin{array}{cc}0& 0<x\&le;a/\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="HDA00003252520100021.png,HDA00003252520100031.png"\; state="\{\{state\}\}">L</figure-callout>}\\ \frac{1}{2\mathrm{\&pi;}}G\left(\mathrm{Lx}\right)+\frac{1}{2}& a/L<x\&le;b/L\\ 1& x>b/L\end{array}$

wherein, $a={(1-\sqrt{K/L})}^2,b={(1+\sqrt{K/L})}^2,$

$G\left(x\right)\stackrel{\mathrm{\&Delta;}}{=}\&Integral;\frac{1}{x}\sqrt{(x-a)(b-x)}\mathrm{dx}$

$=\sqrt{(x-a)(b-x)}-\sqrt{\mathrm{ab}}\arcsin \frac{(a+b)x-2\mathrm{ab}}{(b-a)x}-\frac{a<figure-callout\; id="2"\; label="+\; b"\; filenames="HDA00003252520100031.png,HDA00003252520100032.png"\; state="\{\{state\}\}">+</figure-callout>b}{2}\arcsin \left(\frac{a+b-2x}{b-a}\right)$

in practical implementation, the cumulative distribution function can be made into a table and stored in a memory so as to reduce the computational complexity. Preferably, a relatively accurate cumulative distribution of the normalized characteristic values can be obtained through simulation and can be made into a table. And obtaining the cumulative probability of the normalized characteristic value through table lookup.

6) And the frequency spectrum sensing device calculates a decision variable T according to the goodness-of-fit test. When T is greater than a preset threshold, the spectrum sensing device judges that an authorized signal exists on the spectrum, and when T is less than the preset threshold, the spectrum sensing device judges that no authorized signal exists, namely the spectrum is idle.

There are various methods for implementing goodness-of-fit tests. One particular example of this is the use of the Anderson-Darling test, namely:

$T=-\frac{\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}(2l-1)\left\{1n\right[F\left({\widetilde{\mathrm{\&sigma;}}}_l\right)+1n[1-F\left({\widetilde{\mathrm{\&sigma;}}}_{L+1-l}\right)]\}}{L}-L$ [ equation 6)]

In summary, through steps 1) to 6), a result of spectrum sensing can be obtained.

Compared with the traditional characteristic value spectrum detection method, the invention only increases the complexity of the calculation of the formula 6, thereby having low complexity.

The following describes the working steps of the spectrum sensing method of the present invention in further detail with reference to the block diagram.

As shown in fig. 1, first, a spectrum sensing device receives a wireless signal on a frequency band to be sensed, performs sampling filtering on the received signal, calculates a covariance matrix R of the signal, calculates eigenvalue decomposition of the covariance matrix to obtain ordered eigenvalues, then calculates a normalized eigenvalue, that is, the eigenvalue is divided by the sum of all eigenvalues, and finally calculates a decision variable T according to goodness-of-fit test, wherein when T is greater than a preset threshold, the spectrum sensing device determines that an authorized signal exists on the spectrum, and when T is less than the preset threshold, the spectrum sensing device determines that no authorized signal exists, that is, the spectrum is idle.

The spectrum sensing apparatus of the present invention is further described in detail below with reference to fig. 2 and 3. As shown in fig. 2, the spectrum sensing apparatus of the present invention includes: the device comprises a covariance matrix calculation module, a sorted eigenvalue decomposition module, a normalized eigenvalue calculation module, a goodness-of-fit test decision variable calculation module and a decision module. The wireless signal sampling and filtering module is used for obtaining signals of a perceived frequency band, the covariance matrix calculation module is used for calculating a covariance matrix of the signals to be perceived, the sorted eigenvalue decomposition module is used for solving eigenvalue decomposition of the covariance matrix and sorting the eigenvalues from small to large, and the normalized eigenvalue calculation module divides the eigenvalue by the sum of all eigenvalues. Fig. 3 shows a decision variable calculation module when the Anderson-Darling goodness-of-fit test method is adopted, which comprises a cumulative probability calculation module for normalizing feature values and a calculation module for Anderson-Darling test decision variable T, wherein the calculation of T is shown as [ formula 6 ].

The following practical simulation verifies that the performance of the method of the invention is compared with that of the background technology under the scene 1 and the scene 2 shown in fig. 4 to 7. We compare the energy detection under noise-free uncertainty, the background art including the maximum-minimum eigenvalue ratio detection and the geometric mean and arithmetic mean ratio detection of eigenvalues, the energy detection under noise uncertainty, and the patented technology. The technology and the detection of the maximum and minimum eigenvalue ratios are insensitive to noise uncertainty, that is, the performance of the noise uncertainty is not influenced by the existence of the noise uncertainty. The performance of the patented technology and the background art in the presence of noise uncertainty is shown in the figure. The noise uncertainty factor is 0.5 dB.

Fig. 4 and 5 are signal models of scene 1 as an example, the transmission signal is a wireless microphone signal, the number of sampling points is 64 points and 128 points, the sliding factor is 16, and the oversampling factor is 1. As can be seen from fig. 4, the method of the present invention is slightly worse than the energy detection without noise uncertainty, but is significantly better than the energy detection in the presence of noise uncertainty, the maximum and minimum eigenvalue ratio detection, and the geometric mean and arithmetic mean ratio detection of eigenvalues. As the number of samples increases to 128 points, it can be seen from fig. 5 that the patented method outperforms all other considered techniques, including energy detection where the noise variance is precisely known, when the detection probability is greater than 0.9.

FIGS. 6 and 7 are examples of signal models for scene 2, the signal generation being represented by equation 5]It is given. The elements of the receive correlation matrix P are generated by: the ith row and j column elements of the P matrix are equal to alpha^|i-j|Where α is equal to 0.9. Assume that the number L of cooperative antennas is 16. Fig. 6 and 7 show the detection performance when K =32 and K =64, respectively. As can be seen from fig. 6 and 7, the embodiments of the present invention are slightly worse than the energy detection without noise uncertainty, but significantly better than the energy detection in the presence of noise uncertainty, the maximum-minimum eigenvalue ratio detection, and the geometric mean and arithmetic mean ratio detection of eigenvalues.

It will be understood by those skilled in the art that all or part of the steps of the above methods may be implemented by instructing the relevant hardware through a program, and the program may be stored in a computer readable storage medium, such as a read-only memory, a magnetic or optical disk, and the like. Alternatively, all or part of the steps of the above embodiments may be implemented using one or more integrated circuits. Accordingly, each module/unit in the above embodiments may be implemented in the form of hardware, and may also be implemented in the form of a software functional module. The present invention is not limited to any specific form of combination of hardware and software.

Claims (7)

1. The spectrum sensing method based on the goodness-of-fit test of the normalized characteristic value is characterized by comprising the following steps of:

(1) receiving a wireless signal on a frequency band to be sensed;

(2) sampling and filtering a received signal, calculating a covariance matrix of the signal, recording the covariance matrix as R, and setting the dimensionality of the covariance matrix as L multiplied by L;

(3) calculating eigenvalue decomposition of the covariance matrix to obtain ordered eigenvalues, wherein the eigenvalues are expressed as sigma from small to large₁,σ₂,…,σ_L；

(4) The normalized feature value, i.e. the sum of the feature values divided by all feature values, is calculated and the result is expressed as

(5) Calculating the cumulative probability of the normalized characteristic value according to the cumulative distribution function F (x) of the normalized characteristic value of the noise:

(6) and (3) calculating a decision variable T according to the goodness-of-fit test, judging that an authorized signal exists on the frequency spectrum when T is greater than a preset threshold, and judging that no authorized signal exists when T is less than the preset threshold, namely the frequency spectrum is idle.

2. The spectrum sensing method based on the goodness-of-fit test of the normalized feature values of claim 1, wherein the cumulative distribution function f (x) of the normalized feature values of the noise is obtained by theoretical calculation, or f (x) is made into a table form by simulation, and the cumulative probability of the normalized feature values is obtained by table lookup.

3. The spectrum sensing method based on the goodness-of-fit test for normalized eigenvalues of claim 1, wherein: the decision variable T is examined using Anderson-Darling,

$T=-\frac{\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}(2l-1)\left\{1n\right[F\left({\widetilde{\mathrm{\&sigma;}}}_l\right)+1n[1-F\left({\widetilde{\mathrm{\&sigma;}}}_{L+1-l}\right)]\}}{L}-L$

where ln (·) represents a natural logarithmic function.

4. The method for spectrum sensing based on the goodness-of-fit test for normalized feature values of any one of claims 1-3, wherein: the method is suitable for spectrum sensing of single-antenna and multi-antenna systems.

5. The method for spectrum sensing based on the goodness-of-fit test for normalized feature values of any one of claims 1-3, wherein: the method is suitable for cooperative sensing of multiple nodes.

6. Spectrum sensing device based on goodness of fit test of normalization eigenvalue includes: the device comprises a wireless signal sampling and filtering module, a covariance matrix calculation module, a characteristic value decomposition module, a characteristic value normalization calculation module, a normalized characteristic value cumulative probability calculation module, a decision variable calculation module and a decision module; it is characterized in that the preparation method is characterized in that,

the wireless signal sampling and filtering module is used for obtaining a wireless signal of a perceived frequency band;

the covariance matrix calculation module is used for calculating a covariance matrix of the signal to be perceived;

the eigenvalue decomposition module is used for calculating the eigenvalue decomposition of the covariance matrix of the signal to be perceived;

the normalization calculation module of the characteristic value divides the characteristic value by the sum of all the characteristic values to obtain a normalized characteristic value;

the cumulative probability calculation module of the normalized characteristic values calculates the cumulative probability corresponding to each normalized characteristic value;

the decision variable calculation module calculates the inspection quantity according to the cumulative probability of the normalized characteristic value;

the decision module includes a comparator for comparing a decision variable with a threshold.

7. The spectrum sensing device according to claim 6, wherein: the decision variable calculation module adopts an Anderson-Darling goodness-of-fit inspection method.

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