CN103973381A

CN103973381A - Cooperative spectrum detection method based on Cholesky matrix decomposition

Info

Publication number: CN103973381A
Application number: CN201410211226.6A
Authority: CN
Inventors: 李赞; 周福辉; 杨鼎; 高锐; 关磊; 黄海燕; 刘向丽; 齐佩汉; 胡伟龙; 熊天意
Original assignee: Xidian University
Current assignee: Xidian University; Xian Cetc Xidian University Radar Technology Collaborative Innovation Research Institute Co Ltd
Priority date: 2014-05-19
Filing date: 2014-05-19
Publication date: 2014-08-06
Anticipated expiration: 2034-05-19
Also published as: CN103973381B

Abstract

The invention discloses a cooperative spectrum detection method based on Cholesky matrix decomposition. The cooperative spectrum detection method based on Cholesky matrix decomposition mainly solves the problems that an existing energy detection algorithm is subjected to large uncertain influences of noise, and needs prior information, and a detection threshold cannot be easily determined. The method comprises the implementation steps that (1) detection users collect data of frequency bands according to the frequency bands to be detected, and upload the data to a processing center; (2) the processing center builds a normalization covariance matrix according to the data uploaded to the processing center, and carries out Cholesky decomposition on the normalization covariance matrix; (3) detection statistics are calculated by using the decomposition result, and the probability distribution of the detection statistics is analyzed; (4) a judgment threshold under a target false alarm probability is calculated according to the probability distribution of the detection statistics; (5) the processing center compares the detection statistics and the detection threshold, and judges whether a main user signal exists or not. The cooperative spectrum detection method based on Cholesky matrix decomposition has the advantages of being high in noise uncertainty resistance capacity, accurate in detection threshold and high in detection performance, and can be applied to wireless communication.

Description

Cooperation spectrum detection method based on Cholesky matrix decomposition

Technical Field

The invention belongs to the technical field of wireless communication, and relates to a frequency spectrum detection method which can be used for frequency spectrum detection in a cognitive network and a cognitive radio system.

Background

With the development of the perception network and the popularization of the perception network in daily life, the research of the key technology facing the perception network is paid extensive attention. The spectrum detection technology is an important key technology in the sensing network, and whether to utilize the current frequency band is determined by detecting whether the frequency band is idle or not. Meanwhile, with the development of wireless communication and mobile communication, people have higher and higher requirements on communication technology and more services are required, so that limited spectrum resources become increasingly scarce. Under the current static spectrum allocation framework, many spectrum resources are allocated to some specific services, so that the utilization rate of the spectrum is low. Mitola et al propose a concept of cognitive radio in order to improve the current situation of low spectrum utilization, and the main idea is to search for an idle frequency band in an authorized frequency band, and allow a detection user to detect and access to the current idle frequency band on the premise of not affecting normal communication of the authorized user, thereby greatly improving the spectrum utilization. In order to access to the idle frequency band, the detecting user must accurately detect the spectrum occupancy around the detecting user, so the spectrum detecting technology has a key role in cognitive radio. The technology comprises a spectrum detection method and a cooperative spectrum detection method.

The existing frequency spectrum detection methods mainly comprise three methods:

1) and (4) detecting energy. And detecting whether a user exists or not by calculating the energy of the received signal and determining whether the main user exists or not according to the energy of the signal. The method is simple to implement and easy to determine the detection threshold. However, in the case of low snr, the method cannot work properly effectively due to interference from factors such as deep fading and multipath fading. Moreover, this method is subject to noise uncertainty and is limited in practical applications.

2) Detection based on cyclostationarity. And detecting whether the main user exists or not by using the peak characteristic of the main user signal at the cyclic frequency and the non-peak characteristic of the noise at the cyclic frequency. The method has good noise immunity, needs the prior information of the main user and has high complexity. The system efficiency is low in cognitive radio, and the practical application is limited.

3) Detection based on eigenvalue decomposition. And (3) the detection user utilizes the correlation of the main user signal to construct detection statistic by carrying out eigenvalue decomposition on the covariance matrix. The method can resist the problem of noise uncertainty, and the performance is superior to that of energy detection. However, this method can only use infinite sampling points to determine the approximate detection threshold, and its detection performance is reduced.

The cooperative spectrum detection is that each detection user determines whether a main user exists or not through cooperation. The existing cooperative spectrum detection method comprises the following steps:

1) collaborative detection based on energy detection. And determining whether the main user exists or not by cooperation of all the detection users by using an energy detection method. Although the method is simple to implement, the method is easily interfered by uncertain noise, and is easily interfered by factors such as deep fading, multipath fading and the like under the condition of low signal to noise ratio, so that the method cannot effectively and normally work.

2) Cyclostationary based cooperative detection. And determining whether the main user exists or not by cooperation of all detection users by using a detection method based on cyclostationarity. The method has good anti-manufacturing performance, but high complexity, needs the prior knowledge of the main user signal, cannot realize blind detection, and is limited in practice.

3) Collaborative detection based on eigenvalue decomposition. And determining whether the main user exists or not by cooperation of each detection user by using a detection method based on characteristic value decomposition. The method can resist the influence of noise uncertainty, has good detection performance, but is difficult to accurately determine the detection threshold, and causes limitation to practical application.

Disclosure of Invention

The invention aims to provide a cooperative spectrum detection method based on Cholesky matrix decomposition aiming at the defects of the prior art, so as to improve the anti-noise uncertainty capacity, reduce the detection complexity, accurately determine a decision threshold and improve the detection performance of a main user signal.

In order to achieve the above object, the technical method of the present invention comprises the steps of:

(1) defining a user signal occupying a current frequency band as a master user, defining the user signal trying to occupy the frequency band as a detection user by detecting whether the master user exists on the current frequency band, and defining equipment for determining whether the master user signal exists in the current frequency band as a processing center by fusing and analyzing data collected by each detection user;

(2) each detection user acquires data of the frequency band according to the frequency band to be observed to obtain x_i(N), wherein N ═ 1.., N; 1, M, N are the number of sampling points of each detection user, M is the number of detection users, and each detection user will collect data x_i(n) uploading to a processing center;

(3) the processing center uploads data x according to each detection user_i(n) constructing a detection statistic T_ξ：

(3.1) the processing center uploads the data x according to each detection user_i(n) constructing a data matrix X and a covariance matrix R_xWherein the data matrix X is:

X = [\begin{matrix} x_{1} (1) & x_{1} (2) & . . . & x_{1} (N) \\ x_{2} (1) & x_{2} (2) & . . . & x_{2} (N) \\ . & . & . & . \\ . & . & . & . \\ . & . & . & . \\ x_{M} (1) & x_{M} (2) & . . . & x_{M} (N) \end{matrix}],

the covariance matrix is:

R_{x} = \frac{1}{N} {XX}^{H},

wherein (·)^HTranspose for Heimiian;

(3.2) processing center based on covariance matrix R_xCalculating a normalized covariance matrix R'_x：

Wherein,setting noise variance for the processing center, wherein N is the number of sampling points of each detection user;

(3.3) processing center normalized covariance matrix R'_xPerforming Cholesky decomposition to obtain a decomposed upper triangular matrix, namely:

R'_x＝L^TL，

where L is an upper triangular matrix, which is represented as:

L = [\begin{matrix} l_{11} & l_{12} & . . . & l_{1 M} \\ 0 & l_{22} & . . . & l_{2 M} \\ . & . & . & . \\ . & . & . & . \\ . & . & . & . \\ 0 & 0 & . . . & l_{MM} \end{matrix}],

wherein l_ijIs the ith row and jth column element of the upper triangular matrix L, i is 1.

(3.4) the processing center constructs a detection statistic T according to the upper triangular matrix L obtained after decomposition_ξ：

Wherein ζ₁，ζ_MRespectively a maximum eigenvalue and a minimum eigenvalue of the upper triangular matrix L;

(4) processing center based on detection statistic T_ξCalculating a detection threshold gamma_ξ：

Wherein,andrespectively, the maximum eigenvalue ζ in step (3.4)₁And minimum eigenvalue ζ_MThe average value of (a) of (b),andrespectively, maximum eigenvalue ζ₁And minimum eigenvalue ζ_MVariance of (P)_faThe false alarm probability is represented by the value range of (0,1) phi^-1(. h) is the inverse of the cumulative quantity distribution function of the standard normal distribution, (. phi.);

(5) detecting statistic T obtained in step (3.4)_ξAnd (4) obtaining the detection threshold gamma_ξMaking a comparison when T_ξ≥γ_ξAnd judging that the master user exists, namely the frequency spectrum of the current frequency band is occupied by a certain user, otherwise, judging that the master user does not exist, namely the frequency spectrum of the current frequency band is in an idle state, and allowing the detected user to utilize.

The invention has the following advantages:

1. the invention utilizes the correlation of the main user signal to carry out detection, and the detection performance is superior to a cooperative detection scheme based on the ratio of the maximum characteristic value to the minimum characteristic value and a cooperative detection scheme based on the ratio of the maximum characteristic value to the matrix trace.

2. The invention is a totally blind detection method, without any prior information about the primary user, the channel and the noise.

3. The invention obtains the closed expression of the detection threshold based on the Cholesky decomposition of the finite random matrix according to the random matrix theory, and can obtain the accurate detection threshold corresponding to the target false alarm probability under any sampling point number.

4. The invention can quickly determine the detection threshold, reduces the complexity of frequency spectrum detection and can be widely applied in practice.

Drawings

FIG. 1 is a flow chart of an implementation of the present invention;

FIG. 2 is a graph comparing the cumulative quantity distribution of the probability distribution of the maximum eigenvalue of the normalized covariance matrix obtained for theory and simulation in the absence of primary user signals;

FIG. 3 is a comparison graph of the cumulative quantity distribution curve of the probability distribution of the minimum eigenvalue of the normalized covariance matrix obtained for theory and simulation under the condition that a primary user signal does not exist in the present invention;

FIG. 4 is a comparison graph of cumulative quantity distribution curves of probability distribution of the ratio of the maximum eigenvalue to the minimum eigenvalue of the normalized covariance matrix obtained for theory and simulation under the condition that a main user signal does not exist in the present invention;

FIG. 5 is a comparison graph of SNR-probability of detection obtained by the present invention, the prior collaborative detection method based on the ratio of the maximum eigenvalue to the minimum eigenvalue, and the prior collaborative detection method based on the ratio of the maximum eigenvalue to the matrix trace;

FIG. 6 is a ROC curve comparison graph obtained by the present invention, the conventional collaborative detection method based on the ratio of the maximum to minimum eigenvalues, and the conventional collaborative detection method based on the ratio of the maximum eigenvalue to the matrix trace.

Detailed Description

Referring to fig. 1, the implementation steps of the invention are as follows:

step 1, each detection user collects data and reports the data to a processing center.

1.1) each detection user filters out the signal of the frequency band by a corresponding filter according to the frequency band of the signal to be detected;

1.2) under the precondition of satisfying the sampling theorem, the data of the frequency band are collected to obtain the collected data x_i(N), wherein N ═ 1.., N; 1, wherein N is the number of sampling points of each detection user, and M is the number of detection users;

1.3) data x to be collected_iAnd (n) reporting to a processing center.

Step 2, the processing center according to the reported data x_i(n) to obtain a normalized covariance matrix R'_x。

2.1) the processing center constructs an M-row N-column data matrix X according to the data reported by each detection user:

X = [\begin{matrix} x_{1} (1) & x_{1} (2) & . . . & x_{1} (N) \\ x_{2} (1) & x_{2} (2) & . . . & x_{2} (N) \\ . & . & . & . \\ . & . & . & . \\ . & . & . & . \\ x_{M} (1) & x_{M} (2) & . . . & x_{M} (N) \end{matrix}],

wherein, N is the sampling point number of each detection user, and M is the number of the detection users;

2.2) the processing center calculates the covariance according to the constructed data matrix XMatrix R_x：

R_{x} = \frac{1}{N} {XX}^{H},

Wherein (·)^HTranspose for Heimiian;

2.3) processing center based on covariance matrix R_xCalculating a normalized covariance matrix R'_x：

Wherein,the noise variance set for the processing center takes the value of (0, + ∞).

Step 3, the processing center performs normalization on the covariance matrix R'_xCholesky decomposition is performed as follows:

R'_x＝L^TL，

where L is an upper triangular matrix, which is represented as:

L = [\begin{matrix} l_{11} & l_{12} & . . . & l_{1 M} \\ 0 & l_{22} & . . . & l_{2 M} \\ . & . & . & . \\ . & . & . & . \\ . & . & . & . \\ 0 & 0 & . . . & l_{MM} \end{matrix}],

wherein l_ijThe ith row and j column elements of the upper triangular matrix L are i 1.

Step 4, the processing center calculates the detection statistic T according to the upper triangular matrix L_ξ。

The processing center calculates M eigenvalues of the upper triangular matrix L to be zeta according to probability theory knowledge₁,ζ₂,...,ζ_MTherein ζ of₁≥ζ₂≥...≥ζ_MCalculating a detection statistic T based on the maximum eigenvalue and the minimum eigenvalue_ξIt is expressed as:

wherein ζ₁，ζ_MRespectively, the maximum eigenvalue and the minimum eigenvalue of the upper triangular matrix L.

Step 5, the processing center detects the statistic T according to the detection_ξAnalysis of the detection statistic T in the absence of a primary user signal_ξProbability distribution of (2).

5.1) probability distribution of diagonal elements of the upper triangular matrix L

Normalizing covariance matrix R 'in the absence of primary user signals'_xFor the Wishart matrix, the diagonal element L of the upper triangular matrix L_iiIndependently of one another, and not a negative number, wherein i 1Obeying a chi-square distribution with the degree of freedom of N-i +1, and expressing as follows by the formula:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>l</mi> <mi>ii</mi> </msub> <mo>&GreaterEqual;</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>l</mi> <mi>ii</mi> <mn>2</mn> </msubsup> <mo>~</mo> <msubsup> <mi>χ</mi> <mrow> <mi>N</mi> <mo>-</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math>

wherein,expressing chi-square distribution with the degree of freedom of N-i + 1;

5.2) cumulative quantity distribution function of probability distribution of maximum eigenvalue of upper triangular matrix L

From the characteristics of the upper triangular matrix, i.e. the eigenvalues of the upper triangular matrix L are the diagonal elements of L, as obtained from the analysis of step 5.1), the diagonal elements of the upper triangular matrix L are non-negative and mutually independent, and therefore, the eigenvalues of the upper triangular matrix L are also non-negative and mutually independent,

from the above analysis, the maximum eigenvalue ζ can be obtained₁The cumulative quantity distribution function of the probability distribution is formulated as:

<math> <mrow> <msub> <mi>F</mi> <msub> <mi>ζ</mi> <mn>1</mn> </msub> </msub> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mi>l</mi> <mn>11</mn> </msub> <mo>≤</mo> <mi>y</mi> <mo>,</mo> <msub> <mi>l</mi> <mn>22</mn> </msub> <mo>≤</mo> <mi>y</mi> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>l</mi> <mi>MM</mi> </msub> <mo>≤</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>Π</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <mi>P</mi> <mrow> <mo>(</mo> <msubsup> <mi>l</mi> <mi>ii</mi> <mn>2</mn> </msubsup> <mo>≤</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>Π</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <msup> <mi>y</mi> <mn>2</mn> </msup> </msubsup> <mfrac> <mrow> <msup> <mi>x</mi> <mfrac> <mrow> <mi>N</mi> <mo>-</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> </msup> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <mi>x</mi> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> <mrow> <msup> <mn>2</mn> <mfrac> <mrow> <mi>N</mi> <mo>-</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> </msup> <mi>Γ</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>N</mi> <mo>-</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>dx</mi> <mo>,</mo> </mrow> </math>

wherein,is the maximum eigenvalue ζ₁The cumulant distribution function of probability distribution (c), wherein y is (— infinity, + ∞), N is the number of sampling points per detected user, M is the number of detected users, and Γ (·) is a gamma function.

5.3) probability distribution of minimum eigenvalues of the upper triangular matrix L

Obtaining a minimum eigenvalue ζ according to the characteristic value which is the diagonal element of the upper triangular matrix L obtained in the step 5.2) and the nonnegativity and independence of the diagonal element of the upper triangular matrix L_MIs formulated as:

<math> <mrow> <msub> <mi>F</mi> <msub> <mi>ζ</mi> <mi>M</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mi>P</mi> <mrow> <mo>(</mo> <msubsup> <mi>l</mi> <mn>11</mn> <mn>2</mn> </msubsup> <mo>&GreaterEqual;</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> <mo>,</mo> <msubsup> <mi>l</mi> <mn>22</mn> <mn>2</mn> </msubsup> <mo>&GreaterEqual;</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msubsup> <mi>l</mi> <mi>MM</mi> <mn>2</mn> </msubsup> <mo>&GreaterEqual;</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mtext>=1-</mtext> <munderover> <mi>Π</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msubsup> <mo>&Integral;</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> <mrow> <mo>+</mo> <mo>∞</mo> </mrow> </msubsup> <mfrac> <mrow> <msup> <mi>x</mi> <mfrac> <mrow> <mi>N</mi> <mo>-</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> </msup> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <mi>x</mi> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> <mrow> <msup> <mn>2</mn> <mfrac> <mrow> <mi>N</mi> <mo>-</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> </msup> <mi>Γ</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>N</mi> <mo>-</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>dx</mi> <mo>,</mo> </mrow> </math>

whereinRepresents the minimum eigenvalue ζ_MThe cumulant distribution function of probability distribution (c), wherein y is (— infinity, + ∞), N is the number of sampling points per detected user, M is the number of detected users, and Γ (·) is a gamma function.

5.4) maximum eigenvalue ζ₁And minimum eigenvalue ζ_MApproximately gaussian distribution of

According to the central limit theorem, the maximum eigenvalue ζ can be calculated₁And minimum eigenvalue ζ_MIs approximated as a Gaussian distribution byRepresents the maximum eigenvalue ζ₁The average value of (a) of (b),represents the maximum eigenvalue ζ₁The variance of (a) is determined,represents the minimum eigenvalue ζ_MThe average value of (a) of (b),represents the minimum eigenvalue ζ_MThe formula of (a) is respectively expressed as:

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>u</mi> <msub> <mi>ζ</mi> <mn>1</mn> </msub> </msub> <mo>=</mo> <munderover> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mo>∞</mo> </mrow> <mrow> <mo>+</mo> <mo>∞</mo> </mrow> </munderover> <mi>y</mi> <msubsup> <mi>F</mi> <msub> <mi>ζ</mi> <mn>1</mn> </msub> <mo>′</mo> </msubsup> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mi>dy</mi> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>σ</mi> <msub> <mi>ζ</mi> <mn>1</mn> </msub> <mn>2</mn> </msubsup> <mo>=</mo> <munderover> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mo>∞</mo> </mrow> <mrow> <mo>+</mo> <mo>∞</mo> </mrow> </munderover> <msup> <mrow> <mo>(</mo> <mi>y</mi> <mo>-</mo> <msub> <mi>u</mi> <msub> <mi>ζ</mi> <mn>1</mn> </msub> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msubsup> <mi>F</mi> <msub> <mi>ζ</mi> <mn>1</mn> </msub> <mo>′</mo> </msubsup> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mi>dy</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <msub> <mi>ζ</mi> <mi>M</mi> </msub> </msub> <mo>=</mo> <munderover> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mo>∞</mo> </mrow> <mrow> <mo>+</mo> <mo>∞</mo> </mrow> </munderover> <mi>y</mi> <msubsup> <mi>F</mi> <msub> <mi>ζ</mi> <mi>M</mi> </msub> <mo>′</mo> </msubsup> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mi>dy</mi> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>σ</mi> <msub> <mi>ζ</mi> <mi>M</mi> </msub> <mn>2</mn> </msubsup> <mo>=</mo> <munderover> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mo>∞</mo> </mrow> <mrow> <mo>+</mo> <mo>∞</mo> </mrow> </munderover> <msup> <mrow> <mo>(</mo> <mi>y</mi> <mo>-</mo> <msub> <mi>u</mi> <msub> <mi>ζ</mi> <mi>M</mi> </msub> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msubsup> <mi>F</mi> <msub> <mi>ζ</mi> <mi>M</mi> </msub> <mo>′</mo> </msubsup> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mi>dy</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math>

wherein,for the maximum eigenvalue ζ obtained in step 5.2)₁Is calculated as a function of the cumulative amount distribution of the probability distribution,for the minimum eigenvalue ζ obtained in step 5.3)_MA cumulative amount distribution function of the probability distribution of (a);

5.5) detection statistic T_ξProbability distribution of

Suppose maximum eigenvalue ζ₁And minimum eigenvalue ζ_MIndependently of each other according to ζ₁And ζ_MThe detection statistic T can be obtained by Gaussian approximate distribution_ξThe probability distribution of (c) is:

whereinDetecting a statistic T for the absence of a primary user signal_ξPhi (-) is the cumulative distribution function of a standard normal distribution, which is expressed as follows:

<math> <mrow> <mi>Φ</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mo>∞</mo> </mrow> <mi>x</mi> </munderover> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mi>u</mi> <mn>2</mn> </msup> <mn>2</mn> </mfrac> </mrow> </msup> <mi>du</mi> <mo>,</mo> </mrow> </math>

wherein the value of the independent variable x is (- ∞, + ∞).

Step 6, the processing center detects the statistic T according to the detection_ξCalculating a decision threshold gamma of the probability distribution_ξ。

The detection statistic T obtained according to the step 5_ξCalculating a detection threshold gamma_ξThe following were used:

wherein P is_faThe false alarm probability of detection is represented, and the value is (0,1), phi^-1(. cndot.) is the inverse of the cumulative quantity distribution function of the standard normal distribution, Φ (·).

Step 7, the processing center detects the statistic T according to the detection_ξAnd a detection threshold gamma_ξAnd judging whether a main user signal exists or not.

The processing center obtains the detection statistic T calculated in the step 4_ξAnd the detection threshold gamma calculated in the step 6_ξAnd comparing to judge whether the main user signal exists:

when T is_ξ≥γ_ξAnd judging that the master user exists, namely the frequency spectrum of the current frequency band is occupied by a certain user, otherwise, judging that the master user does not exist, namely the frequency spectrum of the current frequency band is in an idle state, and allowing the detected user to utilize.

The spectrum detection effect of the invention can be further illustrated by the following simulation:

A. simulation conditions

The main user signal is a BPSK signal, the adopted noise is Gaussian white noise with the mean value of 0 and the variance of 1, and the simulation method is 10000000 Monte Carlo simulations. For the simulations 1-3, the number of detected users and the number of sampling points are respectively set to 10 and 20; 20 and 40 and 100, the false alarm probability is set to 0.1. For simulation 4, the signal-to-noise ratio was set from-8 dB to 8dB, the number of detected users and the number of sampling points were set to 40 and 100, respectively, and the false alarm probability was set to 0.1. For simulation 5, the number of detected users and the number of sampling points were set to 40 and 100, respectively, and the signal-to-noise ratio was set to 0 dB.

B. Emulated content

Simulation 1: in the absence of a main user signal, the cumulative distribution of the probability distribution of the maximum eigenvalue of the normalized covariance matrix is compared with respect to theory and simulation, and the result is shown in fig. 2, where "simulated CDF" represents the experimental cumulative distribution function curve of the maximum eigenvalue of the present invention. "approximate CDF" means the theoretical cumulative mass distribution function curve of the maximum eigenvalue of the present invention. "10 and 20", "20 and 40", "40 and 100" respectively represent three different setting combinations of the number of detected users and the number of sampling points.

Simulation 2: in the absence of a primary user signal, the cumulative distribution of the probability distribution of the minimum eigenvalue of the normalized covariance matrix is compared for theoretical and simulation, and the result is shown in fig. 3, where "simulated CDF" represents the experimental cumulative distribution function curve of the maximum eigenvalue of the present invention. "approximate CDF" means the theoretical cumulative mass distribution function curve of the maximum eigenvalue of the present invention. "10 and 20", "20 and 40", "40 and 100" respectively represent three different setting combinations of the number of detected users and the number of sampling points.

Simulation 3: in the absence of a main user signal, the cumulative distribution of the probability distribution of the ratio of the maximum eigenvalue to the minimum eigenvalue of the normalized covariance matrix is compared for theoretical and simulation, and the result is shown in fig. 4, where "simulated CDF" represents the experimental cumulative distribution function curve of the maximum eigenvalue of the present invention. "approximate CDF" means the theoretical cumulative mass distribution function curve of the maximum eigenvalue of the present invention. "10 and 20", "20 and 40", "40 and 100" respectively represent three different setting combinations of the number of detected users and the number of sampling points.

And (4) simulation: the anti-noise performance of the method of the present invention, the conventional cooperative detection method based on the ratio of the maximum eigenvalue to the minimum eigenvalue, and the conventional cooperative detection method based on the ratio of the maximum eigenvalue to the matrix trace are compared, and the results are shown in fig. 5. Wherein, the maximum eigenvalue and trace algorithm represents a cooperative detection scheme based on the ratio of the maximum eigenvalue to the trace of the matrix, the maximum and minimum eigenvalue algorithm represents a cooperative detection scheme based on the ratio of the maximum eigenvalue to the minimum eigenvalue, and the proposed method represents the method of the invention.

And (5) simulation: the results of comparing the ROC curves of the present invention method, the existing cooperative detection method based on the ratio of the maximum to the minimum eigenvalues, and the existing cooperative detection method based on the ratio of the maximum eigenvalues to the matrix traces are shown in fig. 6. Wherein, the maximum eigenvalue and trace algorithm represents a cooperative detection scheme based on the ratio of the maximum eigenvalue to the trace of the matrix, the maximum minimum eigenvalue algorithm represents a cooperative detection scheme based on the ratio of the maximum eigenvalue to the minimum eigenvalue, and the proposed scheme represents the method of the invention.

C. Simulation result

As can be seen from fig. 2, fig. 3 and fig. 4, the experimental cumulant distribution curve obtained by the present invention is substantially identical to the theoretical cumulant distribution curve under the condition that the number of detected users and the number of sampling points are small, so that the present invention has high accuracy of the detection threshold, requires a small number of detected users and a small number of sampling points, and can be widely applied in practice.

As can be seen from fig. 5 and 6, when the signal-to-noise ratio is between-8 dB and 8dB, the detection performance of the present invention is better than the cooperative detection scheme based on the ratio of the maximum eigenvalue to the minimum eigenvalue and the cooperative detection scheme based on the ratio of the maximum eigenvalue to the matrix trace, which indicates that the present invention can be more widely applied in practice.

The simulation result and analysis are integrated, the invention has the advantages of less number of detected users, less number of sampling points, low complexity, high accuracy of detection threshold, and better detection performance than the prior cooperative detection scheme of the ratio of the maximum characteristic value to the minimum characteristic value and the cooperative detection scheme based on the ratio of the maximum characteristic value to the matrix trace, and can be better applied in practice.

Claims

1. A Cooperation spectrum detection method based on Cholesky matrix decomposition comprises the following steps:

(2) each detection user collects the number of the frequency band according to the frequency band to be observedAccording to which x is obtained_i(N), wherein N ═ 1.., N; 1, M, N are the number of sampling points of each detection user, M is the number of detection users, and each detection user will collect data x_i(n) uploading to a processing center;

X = [\begin{matrix} x_{1} (1) & x_{1} (2) & . . . & x_{1} (N) \\ x_{2} (1) & x_{2} (2) & . . . & x_{2} (N) \\ . & . & . & . \\ . & . & . & . \\ . & . & . & . \\ x_{M} (1) & x_{M} (2) & . . . & x_{M} (N) \end{matrix}],

the covariance matrix is:

R_{x} = \frac{1}{N} {XX}^{H},

wherein (·)^HTranspose for Heimiian;

(3.3) processing center to normalized covariance matrix R'_xPerforming Cholesky decomposition to obtain a decomposed upper triangular matrix, namely:

R'_x＝L^TL，

where L is an upper triangular matrix, which is represented as:

L = [\begin{matrix} l_{11} & l_{12} & . . . & l_{1 M} \\ 0 & l_{22} & . . . & l_{2 M} \\ . & . & . & . \\ . & . & . & . \\ . & . & . & . \\ 0 & 0 & . . . & l_{MM} \end{matrix}],

Wherein,andrespectively, the maximum eigenvalue ζ in step (3.4)₁And minimum eigenvalue ζ_MThe average value of (a) of (b),andrespectively, maximum eigenvalue ζ₁And minimum eigenvalue ζ_MVariance of (P)_faThe false alarm probability is represented by a value range of (0,1) -¹(. h) is the inverse of the cumulative quantity distribution function of the standard normal distribution, (. phi.);

2. The method of claim 1, wherein the processing center pairs normalized covariance matrix R 'of step (3.3)'_xCholesky decomposition was performed as follows:

wherein R is_ij'is a normalized covariance matrix R'_xI-th row and j-column of (1), i 1_ijThe ith row and j column elements of the upper triangular matrix L are i 1.

3. The Cholesky matrix decomposition-based cooperative spectrum detection method as claimed in claim 1, wherein the maximum eigenvalue ζ in step (4)₁Mean value ofMaximum eigenvalue ζ₁Variance of (2)Minimum eigenvalue ζ_MMean value ofMinimum eigenvalue ζ_MVariance of (2)Respectively, as follows:

wherein,represents the maximum eigenvalue ζ₁Is expressed as:

<math> <mrow> <msub> <mi>F</mi> <msub> <mi>ζ</mi> <mn>1</mn> </msub> </msub> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>Π</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <msup> <mi>y</mi> <mn>2</mn> </msup> </msubsup> <mfrac> <mrow> <msup> <mi>x</mi> <mfrac> <mrow> <mi>N</mi> <mo>-</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> </msup> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <mi>x</mi> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> <mrow> <msup> <mn>2</mn> <mfrac> <mrow> <mi>N</mi> <mo>-</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> <mtext></mtext> </msup> <mi>Γ</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>N</mi> <mo>-</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>dx</mi> <mo>,</mo> </mrow> </math>

represents the minimum eigenvalue ζ_MIs expressed as:

<math> <mrow> <msub> <mi>F</mi> <msub> <mi>ζ</mi> <mi>M</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>-</mo> <munderover> <mi>Π</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msubsup> <mo>&Integral;</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> <mrow> <mo>+</mo> <mo>∞</mo> </mrow> </msubsup> <mfrac> <mrow> <msup> <mi>x</mi> <mfrac> <mrow> <mi>N</mi> <mo>-</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> </msup> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <mi>x</mi> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> <mrow> <msup> <mn>2</mn> <mfrac> <mrow> <mi>N</mi> <mo>-</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> </msup> <mi>Γ</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>N</mi> <mo>-</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>dx</mi> <mo>,</mo> </mrow> </math>

wherein, N is the number of sampling points of each detection user, M is the number of detection users, and gamma (·) is a gamma function.

4. The cooperative spectrum detection method based on Cholesky matrix decomposition according to claim 1, wherein the cumulative quantity distribution function Φ () of the standard normal distribution in step (4) is represented as follows:

wherein the value of the independent variable x is (- ∞, + ∞).