CN112087275B - Cooperative spectrum sensing method based on birth and death process and viscous hidden Markov model - Google Patents

Abstract

The invention discloses a cooperative spectrum sensing method based on a birth and death process and a viscous hidden Markov model, which takes the corresponding received signal power of each cognitive user in each channel as the observation data of the hidden Markov model, and then determines the hidden state of the observation data, the probability of various hidden states and a state transition probability matrix; introducing a viscosity factor to obtain a viscous hidden Markov model; calculating a clustering result of a hidden state of the observation data under each iteration, updating the clustering result and the category number of the hidden state through a birth and death process, and calculating a state transition probability matrix, a mean vector and a precision matrix; after iteration is finished, calculating the power estimation value of each cognitive user in each channel according to the channel power estimation values of various hidden states and the values of the hidden states in the last iteration, and comparing the power estimation values with a threshold value to determine whether the channel of one cognitive user is occupied by an authorized user; the method has the advantages that the spectrum sensing is carried out on a plurality of cognitive users, and the spectrum sensing performance is good.

Description

Cooperative spectrum sensing method based on birth and death process and viscous hidden Markov model

Technical Field

The invention relates to a multi-cognitive user spectrum sensing technology in cognitive radio, in particular to a cooperative spectrum sensing method based on a life-saving process and a viscous hidden Markov model.

Background

Compared with the fourth generation mobile communication technology, the fifth generation mobile communication (5G) technology can increase the data rate to 10Gbit/s, reduce the delay to 1 millisecond, and increase the number of connected devices by 100 times. Achieving these demands relies on a large amount of spectrum resources, but the available spectrum resources are limited and have been substantially allocated. In order to solve the problem of the shortage of spectrum resources of a wireless network, a common idea in the industry at present is to introduce a cognitive radio technology to improve the utilization rate of the spectrum resources. Different from a traditional system in which a frequency band is authorized and occupied by a single user, the wireless network can intelligently detect the frequency band occupation situation from the environment through the cognitive radio spectrum sensing technology, so that the cognitive user can intelligently access the idle authorized frequency band.

In recent years, various spectrum sensing methods have been proposed. Non-cooperative spectrum sensing methods such as energy detection and matched filter detection are used only, and independent decisions are made by the methods according to detection information of other nearby cognitive users; these methods are easily disturbed by the environment, making wrong decisions and making the perception performance unsatisfactory. In order to solve the technical problems of the non-cooperative spectrum sensing method, a cooperative spectrum sensing concept is introduced, and spatial diversity is used so that cognitive users can cooperate and exchange sensing information in a dynamic wireless environment. However, the existing cooperative spectrum sensing scheme often uses hard decision (i.e. the cognitive users only send the local decision result to the fusion center for global decision), and it does not consider more sensing information (such as sample average power information) of each cognitive user and malicious user interference that may exist in the scene, so that the spectrum sensing performance is generally not ideal.

Disclosure of Invention

The technical problem to be solved by the invention is to provide a cooperative spectrum sensing method based on a birth and death process and a viscous hidden Markov model, which is used for sending sample average power information obtained by a plurality of cognitive users from a channel to a fusion center for fusion judgment, thereby realizing spectrum sensing of the cognitive users at a plurality of spatial positions and having good spectrum sensing performance.

The technical scheme adopted by the invention for solving the technical problems is as follows: a cooperative spectrum sensing method based on a birth and death process and a viscous hidden Markov model is characterized by comprising the following steps:

the method comprises the following steps: the method comprises the steps that J cognitive users and L channels exist in a cognitive radio system, each cognitive user samples signals in each channel for N times at equal time intervals, the signals in one channel are sampled by one cognitive user to obtain N samples, the nth sample obtained by sampling the signals in the ith channel by the jth cognitive user is recorded as the nth sample

Then, calculating the corresponding received signal power of each cognitive user in each channel, and recording the corresponding received signal power of the jth cognitive user in the ith channel as

If the j cognitive user is not a malicious user, then

I.e. the average power of all samples obtained by sampling the signal in the ith channel by the jth cognitive user,

and when N is more than or equal to 100 and less than or equal to 1000 according to the central limit theorem,

obeying a gaussian distribution:

if the j cognitive user is a malicious user, according to the central limit theorem when N is more than or equal to 100 and less than or equal to 1000,

obeying a gaussian distribution:

wherein J, L, N, J, i and N are positive integers, J is more than 1, L is more than 1, N is more than or equal to 100 and less than or equal to 1000, J is more than or equal to 1 and less than or equal to J, i is more than or equal to 1 and less than or equal to L, N is more than or equal to 1 and less than or equal to N, the symbol "" is a modulo symbol,

which is indicative of the power of the noise,

indicating the signal power of the authorized user received by the j cognitive user in the i channel,

indicating that the ith channel is not occupied by an authorized user,

indicating that the ith channel has been occupied by an authorized user,

to represent

Obey mean value of

Covariance of

The distribution of the gaussian component of (a) is,

to represent

Obey mean value of

Covariance of

The gaussian distribution of (c), PM denotes the interference power,

to represent

Obey mean value of

Covariance of

The distribution of the gaussian component of (a) is,

to represent

Obey mean value of

Covariance of

(ii) a gaussian distribution of;

step two: taking a vector formed by the received signal power corresponding to each cognitive user in all channels as one observation datum in a hidden Markov model, taking a vector formed by the received signal power corresponding to the jth cognitive user in all channels as the jth observation datum in the hidden Markov model, and marking as x_j，

Then determining a hidden state corresponding to each observation data in the hidden Markov model, and determining x_jThe corresponding hidden state is recorded as z_j，z_jIs the interval [1, K ]]Is a value of (a) if z_jIf the value of (1) is x_jBelongs to class 1 hidden state if z_jIf k is the value of (a), x is considered to be_jBelongs to class k hidden state if z_jIf the value of (A) is K, then x is considered to be_jBelong to class K hidden state; then calculating the probability of each observation data in the hidden Markov model belonging to various hidden states, and calculating the probability of each observation data in the hidden Markov model_jThe probability of belonging to class k hidden states is noted

Finally, calculating a state transition probability matrix in the hidden Markov model, and marking as Q,

wherein the content of the first and second substances,

indicating the corresponding received signal power of the j-th cognitive user in the 1 st channel,

represents the corresponding received signal power of the j cognitive user in the L channel, K and K are positive integers, K represents the category number of the hidden state set in the hidden Markov model, K is more than or equal to 2 and less than or equal to 10, K is more than or equal to 1 and less than or equal to K,

denotes x_jObeyed Gaussian distributed probability density function with variable x_jMean vector of μ_kThe covariance matrix is

μ_kA mean vector representing a gaussian distribution belonging to class k hidden states,

covariance matrix, Lambda, representing a Gaussian distribution belonging to class k hidden states_kInverse of a covariance matrix, Q, which is a precision matrix representing a Gaussian distribution belonging to class k hidden states_1,1、Q_1,2、Q_1,k'、Q_1,KCorresponding to the element in Q, which represents the 1 st row and 1 st column, the 1 st row and 2 nd column, the 1 st row and K' th column, and the 1 st row and K column_2,1、Q_2,2、Q_2,k'、Q_2,KCorresponding to the element in Q, which represents the 2 nd row, 1 st column, the 2 nd row, 2 nd column, the 2 nd row, K' th column and the 2 nd row, K column_k,1、Q_k,2、Q_k,k'、Q_k,KCorresponding to the element of the kth row and the 1 st column, the element of the kth row and the 2 nd column, the element of the kth row and the kth' column and the element of the kth row and the kth column in Q, Q_K,1、Q_K,2、Q_K,k'、Q_K,KElements in line K, line 1, line K, line 2, line K, line K', line Q,Elements in the K-th row and the K-th column, K' is more than or equal to 1 and less than or equal to K, Q_k,k'Denotes z_j'-1K under the condition of z_j'J' is not less than 2 and not more than J, z_j'-1Represents the j' -1 st observation data x in the hidden Markov model_j'-1Corresponding hidden state, z_j'Representing the jth' observation x in a hidden Markov model_j'The corresponding hidden state;

step three: introducing a viscosity factor into the hidden Markov model to obtain a viscous hidden Markov model; in the viscous hidden Markov model, the mean vector and precision matrix of Gaussian distribution belonging to each class of hidden state are initialized, and mu is calculated_kIs recorded as

Will be Λ_kIs recorded as

I is an L-order identity matrix; initializing the class number K of the hidden state, and recording the initialization value of K as K⁽⁰⁾，K⁽⁰⁾Is the interval [2,10]Any positive integer within; initializing the state transition probability matrix Q, and recording the initialization value of Q as Q⁽⁰⁾，Q⁽⁰⁾The conjugate prior distribution of all elements in each row in (a) obeys a dirichlet distribution, Q⁽⁰⁾K of (1)⁽⁰⁾The conjugate prior distribution of all elements in a row obeys a dirichlet distribution of:

wherein the content of the first and second substances,

represents Q⁽⁰⁾K of (1)⁽⁰⁾All elements in the row, Dir () represent dirichlet distribution, γ represents the parameters of dirichlet distribution, κ represents the viscosity factor, δ (k)⁽⁰⁾1) two parameters are respectively k⁽⁰⁾And 1 Crohn's linerFunction, δ (k)⁽⁰⁾,k'⁽⁰⁾) Denotes that the two parameters are respectively k⁽⁰⁾And k'⁽⁰⁾Kronecker function of (d), δ (k)⁽⁰⁾,K⁽⁰⁾) Denotes that the two parameters are respectively k⁽⁰⁾And K⁽⁰⁾The function of the kronecker function of (c),

γ+κδ(k⁽⁰⁾1) denotes the 1 st element of the Dirichlet distribution, to which the conjugate prior distribution is subjected, γ + κ δ (k)⁽⁰⁾,k'⁽⁰⁾) Denotes the k 'of the Dirichlet distribution to which the conjugate prior distribution obeys here'⁽⁰⁾Element, γ + κ δ (k)⁽⁰⁾,K⁽⁰⁾) Kth of Dirichlet distribution representing the conjugate prior distribution obeyed herein⁽⁰⁾Element, 1. ltoreq. k⁽⁰⁾≤K⁽⁰⁾，1≤k'⁽⁰⁾≤K⁽⁰⁾；

Step four: let t represent the number of iterations, the initial value of t is 1; let t_maxIndicates the set maximum number of iterations, t_max≥3；

Step five: calculating the hidden state clustering result corresponding to all observation data in the viscous hidden Markov model under the t-th iteration, and recording as z^(t)，

Wherein the content of the first and second substances,

expression makes p (z | X, Q)^(t-1),μ^(t-1),Λ^(t-1)) Taking the value of a maximum value time variable z, wherein z is a vector formed by hidden states corresponding to all observation data in the viscous hidden Markov model, and z is [ z ═ z₁,z₂,…,z_j,…,z_J]，z₁Represents the 1 st observation x₁Corresponding hidden state, z₂Represents the 2 nd observation x₂Corresponding hidden state, z_JRepresents the J-th observed data x_JCorresponding hidden states, X representing all observation data in a viscous hidden Markov modelMatrix, X ═ X₁,x₂,…,x_j,…,x_J]When t is 1, Q^(t-1)Is namely Q⁽⁰⁾Q when t is not equal to 1^(t-1)Represents the value of the state transition probability matrix Q in the sticky hidden Markov model at the t-1 th iteration, when t is 1, mu^(t-1)Is the initial value mu of mu⁽⁰⁾，μ＝[μ₁,μ₂,…,μ_K]，μ₁Mean vector, μ, representing a Gaussian distribution belonging to class 1 hidden states₂Mean vector, μ, representing a Gaussian distribution belonging to class 2 hidden states_KA mean vector representing a gaussian distribution belonging to class K hidden states,

represents μ₁The initial value of (a) is set,

represents μ₂The initial value of (a) is set,

indicates belonging to the K⁽⁰⁾Mean vector of Gaussian distribution of hidden-state-like

When the initialization value of (1), t ≠ 1 μ^(t-1)Represents the value of μ at the t-1 th iteration,

represents μ₁At the value at the t-1 th iteration,

represents μ₂At the value at the t-1 th iteration,

is indicated as belonging to the K^(t-1)Mean vector of Gaussian distribution of hidden-state-like

Value at the t-1 th iteration, t 1 time Λ^(t-1)I.e. the initial value Λ of the set Λ⁽⁰⁾，Λ＝{Λ₁,Λ₂,…,Λ_K}，Λ₁Precision matrix, Λ, representing a gaussian distribution belonging to class 1 hidden states₂Precision matrix, Λ, representing a gaussian distribution belonging to class 2 hidden states_KA precision matrix representing a gaussian distribution belonging to class K hidden states,

is represented by₁The initial value of (a) is set,

is represented by₂The initial value of (a) is set,

indicates belonging to the K⁽⁰⁾Accuracy matrix of Gaussian distribution of class hidden state

When t ≠ 1, Λ^(t-1)Representing the value of the set a at the t-1 st iteration,

is represented by₁At the value at the t-1 th iteration,

is represented by₂At the value at the t-1 th iteration,

indicates belonging to the K^(t-1)Accuracy matrix of Gaussian distribution of class hidden state

At the value at the t-1 th iteration,k when t is 1^(t-1)Is the initial value K of K⁽⁰⁾K when t ≠ 1^(t-1)Denotes the value of K at the t-1 iteration, p (z | X, Q)^(t-1),μ^(t-1),Λ^(t-1)) The posterior probability of z is obtained according to Bayes theorem

p(z_j|X,Q^(t-1),μ^(t-1),Λ^(t-1)) Denotes z_jThe symbol ". alpha." indicates a direct ratio, x_j+1Denotes the j +1 th observation, x_j+2Denotes the j +2 th observation, p (z)_j,x₁,x₂,...,x_j|Q^(t-1),μ^(t-1),Λ^(t-1)) Denotes z_j,x₁,x₂,...,x_jJoint probability of p (x)_j+1,x_j+2,...,x_J|z_j,Q^(t-1),μ^(t-1),Λ^(t-1)) Denotes z_jUnder the condition of (1) x_j+1,x_j+2,...,x_JJoint probability of p (z)_j,x₁,x₂,...,x_j|Q^(t-1),μ^(t-1),Λ^(t-1)) And p (x)_j+1,x_j+2,...,x_J|z_j,Q^(t-1),μ^(t-1),Λ^(t-1)) Calculating by a forward and backward algorithm;

step six: updating z by a birth-kill process^(t)Further, the value K of the class number K of the hidden state in the viscous hidden Markov model at the t-th iteration is calculated^(t)The specific process is as follows:

1) statistics z^(t)Median value equal to interval [1, K^(t-1)]Total number of elements of each value in, will z^(t)Median value equal to k^(t-1)Total number of elements of (1) is recorded as

2) Press 1, …, k^(t-1),…,K^(t-1)Num is arranged from small to large₁To

Obtaining a statistical number arrangement sequence;

3) if the statistical number sequence has only one value of 0 and K: (^t-1) Not equal to 2, assume that the 0 value corresponds to the interval [1, K-^{(t -1)}]K in (1)^(t-1)Then z will be^(t)Median value is respectively equal to (k +1)^(t-1)To K^(t-1)All the values of z are reduced by 1, and the updated z is obtained^(t)Is newly recorded as z^*(t)And order K^(t)＝K^(t-1)-1, performing step seven again; if the statistical number is only one 0 value and K in the permutation sequence^(t-1)If 2, or the statistical number array sequence has a plurality of 0 values, executing step 4); if there is no 0 value in the statistical number permutation sequence and K is^(t-1)If < 10, randomly generating a starting value from 1 to J, and recording the starting value as J_minFrom J_minRandomly generating an end value of J, and recording the end value as J_maxWill z^(t)In (1)

Are all set to K^(t-1)+1, z to be updated^(t)Is newly recorded as z^*(t)And order K^(t)＝K^(t-1)+1, then executing step seven; if the statistical number array sequence is other than the four cases, keeping z^(t)Without change, will z^(t)Is newly recorded as z^*(t)And order K^(t)＝K^(t-1)Then, the seventh step is executed;

4) when the ω -th value in the statistical number permutation sequence is J, the 1 st to ω -1 th and the ω +1 th to Kth^(t-1)Values are all 0 i.e. z^(t)Is equal to ω, randomly generating a starting value from 1 to J, denoted as J'_minFrom J'_minTo J an end value, denoted J ', is randomly generated'_maxWill z^(t)In (1)

All are set to 2, z^(t)In (1)

And

all the values of (a) are set to 1, and z after updating is carried out^(t)Is newly recorded as z^*(t)And order K^(t)Step seven is executed again when the value is 2; when the statistical number array sequence has a plurality of 0 values and any non-0 value is not J, executing step 5);

5) let 0 have xi, for the 1 st 0 value and the 2 nd 0 value, assume that the 1 st 0 value corresponds to the interval [1, K^(t-1)]K in (1)^(t-1)And the 2 nd 0 value corresponding interval [1, K ]^(t-1)]Middle (k + upsilon)^(t-1)Then z will be^(t)Median value is respectively equal to (k +1)^(t-1)To (k + upsilon-1)^(t-1)All the values of (a) minus 1; for the 2 nd 0 value and the 3 rd 0 value, assume that the 2 nd 0 value corresponds to the interval [1, K^{(t -1)}]Middle (k + upsilon)^(t-1)And the 3 rd 0 value corresponding interval [1, K ]^(t-1)]In (1)

Then z will be^(t)Median value is respectively equal to (k + upsilon +1)^(t-1)To (k + zeta-1)^(t-1)All the values of (a) minus 2; by analogy, for the xi-1 0 values and the xi 0 values, suppose that the xi-1 0 values correspond to the interval [1, K^(t-1)]In

The xi 0 value corresponds to the interval [1, K ]^(t-1)]Middle (k + ρ)^(t-1)Then z will be^(t)Median values are respectively equal to

To (k + rho-1)^(t-1)All the values of the elements of (1) are decremented by ξ -1; then z is mixed^(t)Median value is equal to (k + ρ +1)^(t-1)To K^(t-1)All the values of (1) are decremented; will updated z^(t)Is newly recorded as z^*(t)And order K^(t)＝K^(t-1)ξ, then step seven is performed;

above, k^(t-1)Is the interval [1, K^(t-1)]K of (1)^(t-1)Value, Num₁Denotes z^(t)The total number of elements whose median value is equal to 1,

denotes z^(t)Median value equal to K^(t-1)The total number of the elements (1 ≤ omega ≤ K^(t-1)，1≤J_min≤J_max≤J，

Corresponding to represents z^(t)J in (1)_minElement, item J_min+1 element, …, J_max1 is not more than J'_min≤J'_max≤J，

Corresponding to represents z^(t)J 'of (1)'_minElement, J'_min+1 elements, …, J'_maxThe number of the elements is one,

corresponding to represents z^(t)The 1 st element, the 2 nd element, …, the J'_min-1 element of the group consisting of,

corresponding to represents z^(t)J 'of (1)'_max+1 elements, J'_max+2 elements, …, J element, 1 < xi < K^(t-1)，

K^(t)＝K^(t-1)Wherein "═ is an assigned symbol,

denotes z₁The value after the birth and death process at the t-th iteration,

denotes z₂The value after the birth and death process at the t-th iteration,

denotes z_jThe value after the birth and death process at the t-th iteration,

denotes z_JThe value after the birth and death process under the t-th iteration;

step seven: calculating the value of the state transition probability matrix Q in the viscous hidden Markov model at the t-th iteration, and recording as Q^(t)，Q^(t)K of (1)^(t)The conjugate prior distribution of all elements in a row obeys a dirichlet distribution of:

Q^(t)k of (1)^(t)The posterior distribution of all elements in a row obeys a dirichlet distribution of:

wherein k is more than or equal to 1^(t)≤K^(t)，1≤k'^(t)≤K^(t)，

Represents Q^(t)K of (1)^(t)All of the elements in the row are,

denotes the time from kth (k) after the birth and death process at the t-th iteration^t) The amount of observation data that class hidden state transitions to class 1 hidden state,

representing the k-th iteration after the birth and death process^(t)Class hidden State transition to kth'^(t)The number of observations of the class hidden state,

representing the k-th iteration after the birth and death process^(t)Class hidden state transition to Kth^(t)Number of observations like hidden states, δ (k)^(t)1) two parameters are respectively k^(t)And a Crohn's function of 1, δ (k)^(t),k'^(t)) Denotes that the two parameters are respectively k^(t)And k'^(t)Kronecker function of (d), δ (k)^(t),K^(t)) Denotes that the two parameters are respectively k^(t)And K^(t)The function of the kronecker function of (c),

γ+κδ(k^(t)1) denotes the 1 st element of the Dirichlet distribution, γ + κ δ (k), to which the conjugate prior distribution here follows^(t),k'^(t)) Denotes the k 'of the Dirichlet distribution to which the conjugate prior distribution obeys here'^(t)Element, γ + κ δ (k)^(t),K^(t)) Kth of Dirichlet distribution representing the conjugate prior distribution obeyed herein^(t)The number of the elements is one,

representing the 1 st element of the dirichlet distribution to which the posterior distribution here obeys,

denotes the k 'of the Dirichlet distribution to which the posterior distribution is subjected'^(t)The number of the elements is one,

k < th > of a Dirichlet distribution representing the posterior distribution obeyed by the distribution here^(t)An element;

step eight: all the observation data belonging to the same kind of hidden state are utilized, according to Bayes' theorem,calculated at X and z^*(t)Determining the value μ of μ at the t-th iteration^(t)And Λ value of Λ at the t-th iteration^(t)A posterior probability of (D), is recorded as

Wherein, mu^(t)Represents the value of μ at the t-th iteration,

represents μ₁At the value at the t-th iteration,

indicates belonging to the k-th^(t)Mean vector of Gaussian distribution of hidden-state-like

At the value at the t-th iteration,

indicates belonging to the K^(t)Mean vector of Gaussian distribution of hidden-state-like

Value at the t-th iteration, Λ^(t)Denotes the value of a at the t-th iteration,

is given by₁At the value at the t-th iteration,

indicates belonging to the k-th^(t)Accuracy matrix of Gaussian distribution of class hidden state

At the value at the t-th iteration,

indicates belonging to the K^(t)Gaussian distribution of class hidden statesIs measured in a precision matrix

At the value at the t-th iteration,

to represent

Obeying a probability density function of a Gaussian distribution having a variable of

Mean vector of

The covariance matrix is

Represent

Obeying a probability density function of a Weisset distribution having the variables

The scale matrix is

Degree of freedom of

Symbol "()^T"is a transposed symbol that is used to identify,

indicates that the signal belongs to the kth after the birth and death process under the t-th iteration^(t)The number of observations of the class hidden state,

indicates that the signal belongs to the kth after the birth and death process under the t-th iteration^(t)The average of all observed data for the class hidden state,

indicates that the signal belongs to the kth after the birth and death process under the t-th iteration^(t)Class i hidden state

Individual observation data, η₀、m₀、W₀、ν₀Are all constants;

step nine: judging t < t_maxIf yes, making t equal to t +1, and then returning to the fifth step to continue iteration; if not, executing step ten; wherein, t is in t +1, and is an assignment symbol;

step ten: mu to^(t)The value of each column element in the (b) is used as the power estimation value of L channels corresponding to a type of hidden state, namely mu^(t)K of (1)^(t)The value of the column element being the kth^(t)Power estimation values of L channels of similar hidden state, specifically, mu^(t)K of (1)^(t)The value of the ith element in the column element is taken as the k^(t)Power estimation value of ith channel of similar hiding state; then, calculating the power estimation value of each cognitive user in each channel according to the power estimation value of L channels of each type of hidden state and the value of the hidden state corresponding to each observation data after the extinction process under the t-th iteration, and recording the power estimation value of the j-th cognitive user in all channels as beta_jIf, if

Then beta is_jIs equal to kth^(t)The power estimates for the L channels that resemble the hidden state,

then comparing the power estimation value of each cognitive user in each channel with a threshold value, and comparing the power estimation value of each cognitive user in each channel with the threshold value

If it is not

If the number of the channels is smaller than the threshold value, the ith channel at the jth cognitive user is considered to be not occupied by the authorized user, and the ith channel is used as an available channel; if it is used

If the channel number is larger than or equal to the threshold value, the ith channel at the jth cognitive user is considered to be occupied by an authorized user and cannot be used by the cognitive user; wherein the content of the first and second substances,

indicating the power estimated value of the j cognitive user in the 1 st channel if

Then

Is equal to kth^(t)The power estimate of the 1 st channel like the hidden state,

indicating the power estimated value of the j cognitive user in the i channel if

Then the

Is equal to kth^(t)Of class hidden stateThe power estimate for the ith channel,

indicating the power estimated value of the jth cognitive user in the Lth channel if

Then

Is equal to kth^(t)The threshold value of the power estimated value of the L-th channel of the similar hidden state is calculated according to the given false alarm probability.

Compared with the prior art, the invention has the advantages that:

1) the method is suitable for performing cooperative spectrum sensing on signals obtained by a plurality of cognitive users from a channel, and in the cooperative spectrum sensing process, the sample average power information obtained by the plurality of cognitive users from the channel is sent to a fusion center for fusion judgment, so that spectrum sensing on the cognitive users at a plurality of spatial positions is realized.

2) The method of the invention builds a viscous hidden Markov model by adding viscous factors between adjacent cognitive users to increase the channel state correlation between the adjacent cognitive users, and because the channel state correlation between the adjacent cognitive users in the multi-cognitive users is used for detecting the frequency spectrum of the multi-cognitive users, the method of the invention can fully improve the frequency spectrum utilization rate of all channels under the same condition.

3) The method of the invention utilizes the channel state correlation between adjacent cognitive users in the plurality of cognitive users, thereby effectively reducing the influence of environmental interference, resisting the attack of malicious users on the cognitive radio network, simultaneously carrying out spectrum sensing on the plurality of cognitive users and having good detection performance.

4) The method of the invention utilizes the specific effective clustering capability of the viscous hidden Markov model to the observed data, thereby realizing rapid convergence and having lower computational complexity.

5) The method of the invention can automatically adjust the category total number of the frequency spectrum state because of utilizing the birth and death process, thereby enabling the algorithm to be more flexible.

Drawings

FIG. 1 is a block diagram of an overall implementation of the method of the present invention;

fig. 2 shows ROC curves when the number of malicious users is 5 and the interference power of the malicious users is 0dBm, 10dBm, and 20dBm, respectively.

Detailed Description

The invention is described in further detail below with reference to the following examples of the drawings.

The invention provides a cooperative spectrum sensing method based on a birth and death process and a viscous hidden Markov model, the overall implementation block diagram of which is shown in figure 1, and the cooperative spectrum sensing method comprises the following steps:

the method comprises the following steps: the method comprises the steps that J cognitive users and L channels exist in a cognitive radio system, each cognitive user samples signals in each channel for N times at equal time intervals, the signals in one channel are sampled by one cognitive user to obtain N samples, the nth sample obtained by sampling the signals in the ith channel by the jth cognitive user is recorded as the nth sample

Then, calculating the corresponding received signal power of each cognitive user in each channel, and recording the corresponding received signal power of the jth cognitive user in the ith channel as

If the j cognitive user is not a malicious user, then

I.e. the average power of all samples obtained by sampling the signal in the ith channel by the jth cognitive user,

and when N is more than or equal to 100 and less than or equal to 1000 according to the central limit theorem,

obeying a gaussian distribution:

if the j cognitive user is a malicious user, according to the central limit theorem when N is more than or equal to 100 and less than or equal to 1000,

obeying a gaussian distribution:

wherein J, L, N, J, i and N are positive integers, J is more than 1, L is more than 1, N is more than or equal to 100 and less than or equal to 1000, and when the value of N is too large (N is more than 1000), too many samples are sampled, which can cause the reduction of the operation speed, therefore, only the value of N is required to be ensured to be sufficiently large, when N is sufficiently large, according to the central limit theorem,

obeying Gaussian distribution, J is more than or equal to 1 and less than or equal to J, i is more than or equal to 1 and less than or equal to L, N is more than or equal to 1 and less than or equal to N, the symbol "|" is a modulo symbol,

which is indicative of the power of the noise,

indicating the signal power of the authorized user received by the j cognitive user in the i channel,

indicating that the ith channel is not occupied by an authorized user,

indicating that the ith channel has been occupied by an authorized user,

to represent

Obey mean value of

Covariance of

The distribution of the gaussian component of (a) is,

to represent

Obey mean value of

Covariance of

The gaussian distribution of (c), PM, represents the interference power, and if a cognitive user is not a malicious user, there is no interference power,

to represent

Obey mean value of

Covariance of

The distribution of the gaussian component of (a) is,

to represent

Obey mean value of

Assisting partyThe difference is

A gaussian distribution of (a).

Step two: taking a vector formed by the received signal power corresponding to each cognitive user in all channels as one observation datum in a hidden Markov model, taking a vector formed by the received signal power corresponding to the jth cognitive user in all channels as the jth observation datum in the hidden Markov model, and marking as x_j，

Then determining a hidden state corresponding to each observation data in the hidden Markov model, and determining x_jThe corresponding hidden state is recorded as z_j，z_jIs the interval [1, K ]]Is a value of (a) if z_jIf the value of (1) is x_jBelongs to class 1 hidden state if z_jIf k is the value of (a), x is considered to be_jBelongs to class k hidden state if z_jIf the value of (A) is K, then x is considered to be_jBelong to class K hidden state; then calculating the probability of each observation data in the hidden Markov model belonging to various hidden states, and calculating the probability of each observation data in the hidden Markov model_jThe probability of belonging to class k hidden states is noted

Finally, calculating a state transition probability matrix in the hidden Markov model, and marking as Q,

wherein the content of the first and second substances,

indicating the corresponding received signal power of the j-th cognitive user in the 1 st channel,

representing the corresponding received signal power of the j cognitive user in the L channel, wherein K and K are positive integers, and K represents the setting in a hidden Markov modelThe number of classes of hidden states is more than or equal to 2 and less than or equal to 10, and more than or equal to 1 and less than or equal to K,

denotes x_jObeyed Gaussian distributed probability density function with variable x_jMean vector of μ_kThe covariance matrix is

μ_kA mean vector representing a gaussian distribution belonging to class k hidden states,

covariance matrix, Lambda, representing a Gaussian distribution belonging to class k hidden states_kInverse of a covariance matrix, Q, which is a precision matrix representing a Gaussian distribution belonging to class k hidden states_1,1、Q_1,2、Q_1,k'、Q_1,KCorresponding to the element in Q, which represents the 1 st row and 1 st column, the 1 st row and 2 nd column, the 1 st row and K' th column, and the 1 st row and K column_2,1、Q_2,2、Q_2,k'、Q_2,KCorresponding to the element in Q, which represents the 2 nd row, 1 st column, the 2 nd row, 2 nd column, the 2 nd row, K' th column and the 2 nd row, K column_k,1、Q_k,2、Q_k,k'、Q_k,KCorresponding to the element of the kth row and the 1 st column, the element of the kth row and the 2 nd column, the element of the kth row and the kth' column and the element of the kth row and the kth column in Q, Q_K,1、Q_K,2、Q_K,k'、Q_K,KCorrespondingly represents the elements of the K-th row and the 1 st column, the K-th row and the 2 nd column, the K-th row and the K '-th column, the elements of the K-th row and the K-th column in Q, wherein K' is more than or equal to 1 and less than or equal to K, and Q_k,k'Denotes z_j'-1K under the condition of z_j'J' is not less than 2 and not more than J, z_j'-1Represents the j' -1 st observation data x in the hidden Markov model_j'-1Corresponding hidden state, z_j'Representing the jth' observation x in a hidden Markov model_j'The corresponding hidden state.

Step three: introducing a viscosity factor into the hidden Markov model to obtainTo a sticky hidden markov model; in the viscous hidden Markov model, the mean vector and precision matrix of Gaussian distribution belonging to each class of hidden state are initialized, and mu is calculated_kIs recorded as

Will be Λ_kIs recorded as

I is an L-order identity matrix; initializing the class number K of the hidden state, and recording the initialization value of K as K⁽⁰⁾，K⁽⁰⁾Is the interval [2,10]Within any positive integer, e.g. K⁽⁰⁾A value of 4; initializing the state transition probability matrix Q, and recording the initialization value of Q as Q⁽⁰⁾，Q⁽⁰⁾The conjugate prior distribution of all elements in each row in (a) obeys a dirichlet distribution, Q⁽⁰⁾K of (1)⁽⁰⁾The conjugate prior distribution of all elements in a row obeys a dirichlet distribution of:

wherein the content of the first and second substances,

represents Q⁽⁰⁾K of (1)⁽⁰⁾All elements in the row, Dir () represent dirichlet distribution, γ represents the parameters of dirichlet distribution, κ represents the viscosity factor, δ (k)⁽⁰⁾1) two parameters are respectively k⁽⁰⁾And a Crohn's function of 1, δ (k)⁽⁰⁾,k'⁽⁰⁾) Denotes that two parameters are respectively k⁽⁰⁾And k'⁽⁰⁾Kronecker function of (d), δ (k)⁽⁰⁾,K⁽⁰⁾) Denotes that the two parameters are respectively k⁽⁰⁾And K⁽⁰⁾The function of the kronecker function of (c),

γ+κδ(k⁽⁰⁾1) denotes the 1 st element of the Dirichlet distribution, γ + κ δ (k), to which the conjugate prior distribution here follows⁽⁰⁾,k'⁽⁰⁾) Denotes the conjugate prior score hereKth of cloth-compliant Dirichlet distribution'⁽⁰⁾Element, γ + κ δ (k)⁽⁰⁾,K⁽⁰⁾) Kth of Dirichlet distribution representing the conjugate prior distribution obeyed herein⁽⁰⁾Element, 1. ltoreq. k⁽⁰⁾≤K⁽⁰⁾，1≤k'⁽⁰⁾≤K⁽⁰⁾。

Step four: let t represent the number of iterations, the initial value of t is 1; let t_maxIndicates the set maximum number of iterations, t_maxNot less than 3, in this example, t is taken_max＝100。

Step five: calculating the hidden state clustering result corresponding to all observation data in the viscous hidden Markov model under the t-th iteration, and recording as z^(t)，

Wherein the content of the first and second substances,

expression makes p (z | X, Q)^(t-1),μ^(t-1),Λ^(t-1)) Taking the value of a maximum value time variable z, wherein z is a vector formed by hidden states corresponding to all observation data in the viscous hidden Markov model, and z is [ z ═ z₁,z₂,…,z_j,…,z_J]，z₁Represents the 1 st observation data x₁Corresponding hidden state, z₂Represents the 2 nd observation x₂Corresponding hidden state, z_JRepresents the J-th observed data x_JCorresponding hidden states, X represents a matrix formed by all observation data in the viscous hidden Markov model, and X is [ X [ ]₁,x₂,…,x_j,…,x_J]When t is 1, Q^(t-1)Is namely Q⁽⁰⁾Q when t is not equal to 1^(t-1)Represents the value of the state transition probability matrix Q in the sticky hidden Markov model at the t-1 th iteration, when t is 1, mu^(t-1)Is the initial value mu of mu⁽⁰⁾，μ＝[μ₁,μ₂,…,μ_K]，μ₁Mean vector, μ, representing a Gaussian distribution belonging to class 1 hidden states₂Representing a Gaussian distribution belonging to hidden states of class 2Mean vector, μ_KA mean vector representing a gaussian distribution belonging to class K hidden states,

represents μ₁The initial value of (a) is set,

represents μ₂The initial value of (a) is set,

indicates belonging to the K⁽⁰⁾Mean vector of Gaussian distribution of hidden-state-like

When the initialization value of (1), t ≠ 1 μ^(t-1)Representing the value of mu at the t-1 iteration,

represents mu₁At the value at the t-1 th iteration,

represents μ₂At the value at the t-1 th iteration,

indicates belonging to the K^(t-1)Mean vector of Gaussian distribution of hidden-state-like

Value at the t-1 th iteration, t 1 time Λ^(t-1)I.e. the initial value Λ of the set Λ⁽⁰⁾，Λ＝{Λ₁,Λ₂,…,Λ_K}，Λ₁Precision matrix, Λ, representing a gaussian distribution belonging to class 1 hidden states₂Precision matrix, Λ, representing a gaussian distribution belonging to class 2 hidden states_KA precision matrix representing a gaussian distribution belonging to class K hidden states,

is represented by₁The initial value of (a) is set,

is represented by₂The initial value of (a) is set,

indicates belonging to the K⁽⁰⁾Accuracy matrix of gaussian distribution of class hidden state

When t ≠ 1, Λ^(t-1)Representing the value of the set a at the t-1 st iteration,

is represented by₁At the value at the t-1 th iteration,

is represented by₂At the value at the t-1 th iteration,

indicates belonging to the K^(t-1)Accuracy matrix of Gaussian distribution of class hidden state

Value at the t-1 th iteration, K when t is 1^(t-1)Is the initial value K of K⁽⁰⁾K when t ≠ 1^(t-1)Denotes the value of K at the t-1 iteration, p (z | X, Q)^(t-1),μ^(t-1),Λ^(t-1)) The posterior probability of z is obtained according to Bayes theorem

p(z_j|X,Q^(t-1),μ^(t-1),Λ^(t-1)) Denotes z_jA posteriori ofProbability, symbol ". alpha." indicates a direct ratio, x_j+1Denotes the j +1 th observation, x_j+2Denotes the j +2 th observation, p (z)_j,x₁,x₂,...,x_j|Q^(t-1),μ^(t-1),Λ^(t-1)) Denotes z_j,x₁,x₂,...,x_jJoint probability of p (x)_j+1,x_j+2,...,x_J|z_j,Q^(t-1),μ^(t-1),Λ^(t-1)) Denotes z_jUnder the condition of (1) x_j+1,x_j+2,...,x_JJoint probability of p (z)_j,x₁,x₂,...,x_j|Q^(t-1),μ^(t-1),Λ^(t-1)) And p (x)_j+1,x_j+2,...,x_J|z_j,Q^(t-1),μ^(t-1),Λ^(t-1)) Calculated by the existing forward and backward algorithm.

Step six: updating z by a birth-kill process^(t)Further, the value K of the class number K of the hidden state in the viscous hidden Markov model at the t-th iteration is calculated^(t)The specific process comprises the following steps:

1) statistics z^(t)Median value equal to interval [1, K ]^(t-1)]Total number of elements of each value in, will z^(t)Median value equal to k^(t-1)Total number of elements of (1) is recorded as

2) Press 1, …, k^(t-1),…,K^(t-1)Num is arranged from small to large₁To

And obtaining a statistical number array sequence.

3) If the statistical number is only one 0 value in the permutation sequence and K is^(t-1)Not equal to 2, assume that the 0 value corresponds to the interval [1, K-^{(t -1)}]K in (1)^(t-1)Then z will be^(t)Median value is respectively equal to (k +1)^(t-1)To K^(t-1)All the values of z are reduced by 1, and the updated z is obtained^(t)To resumeIs denoted by z^*(t)And order K^(t)＝K^(t-1)-1, performing step seven again; if the statistical number is only one 0 value and K in the permutation sequence^(t-1)If 2, or the statistical number array sequence has a plurality of 0 values, executing step 4); if there is no 0 value in the statistical number permutation sequence and K is^(t-1)If < 10, randomly generating a starting value from 1 to J, and recording the starting value as J_minFrom J_minRandomly generating an end value of J, and recording the end value as J_maxWill z^(t)In (1)

Are all set to K^(t-1)+1, z to be updated^(t)Is newly recorded as z^*(t)And order K^(t)＝K^(t-1)+1, then executing step seven; if the statistical number array sequence is other than the four cases, keeping z^(t)Without change, will z^(t)Is newly recorded as z^*(t)And order K^(t)＝K^(t-1)And then step seven is executed.

4) When the ω -th value in the statistical number permutation sequence is J, the 1 st to ω -1 th and the ω +1 th to Kth^(t-1)Values are all 0 i.e. z^(t)Is equal to ω, randomly generating a starting value from 1 to J, denoted as J'_minFrom J'_minTo J an end value, denoted J ', is randomly generated'_maxWill z^(t)In (1)

All are set to 2, z^(t)In (1)

And

all of which are set to 1, and the updated z^(t)Is re-noted as z^*(t)And order K^(t)Step seven is executed again when the value is 2; and when the statistical number array sequence has a plurality of 0 values and any non-0 value is not J, executing the step 5).

5) Let 0 have xi, for the 1 st 0 value and the 2 nd 0 value, assume that the 1 st 0 value corresponds to the interval [1, K^(t-1)]K in (1)^(t-1)And the 2 nd 0 th value corresponds to the interval [1, K^(t-1)]Middle (k + upsilon)^(t-1)Then z will be^(t)Median value is respectively equal to (k +1)^(t-1)To (k + upsilon-1)^(t-1)All the values of (a) minus 1; for the 2 nd 0 value and the 3 rd 0 value, assume that the 2 nd 0 value corresponds to the interval [1, K^{(t -1)}]Middle (k + upsilon)^(t-1)And the 3 rd 0 value corresponding interval [1, K ]^(t-1)]In (1)

Then z will be^(t)Median value is respectively equal to (k + upsilon +1)^(t-1)To

All the values of (a) minus 2; by analogy, for the xi-1 0 values and the xi 0 values, suppose that the xi-1 0 values correspond to the interval [1, K^(t-1)]In (1)

The xi 0 value corresponds to the interval [1, K ]^(t-1)]Middle (k + ρ)^(t-1)Then z will be^(t)Median values are respectively equal to

To (k + rho-1)^(t-1)All the values of the elements of (1) are decremented by ξ -1; then z is mixed^(t)Median value is equal to (k + ρ +1)^(t-1)To K^(t-1)All the values of (1) are decremented; will updated z^(t)Is newly recorded as z^*(t)And order K^(t)＝K^(t-1)ξ, then step seven is performed.

Above, k^(t-1)Is the interval [1, K^(t-1)]K of (1)^(t-1)Value, Num₁Denotes z^(t)The total number of elements whose median value is equal to 1,

denotes z^(t)Median value equal to K^(t-1)The total number of the elements (1 ≤ omega ≤ K^(t-1)，1≤J_min≤J_max≤J，

Corresponding to represents z^(t)J in (1)_minElement, item J_min+1 element, …, J_max1 is not more than J'_min≤J'_max≤J，

Corresponding to represents z^(t)J 'of (1)'_minElement, J'_min+1 elements, …, J'_maxThe number of the elements is one,

corresponding to represents z^(t)The 1 st element, the 2 nd element, …, the J'_min-1 element of the group consisting of,

corresponding to represents z^(t)J 'of (1)'_max+1 elements, J'_max+2 elements, …, J element, 1 < xi < K^(t-1)，

K^(t)＝K^(t-1)Wherein "is an assigned symbol,

denotes z₁The value after the birth and death process at the t-th iteration,

denotes z₂The value after the birth and death process at the t-th iteration,

denotes z_jThe value after the birth and death process at the t-th iteration,

denotes z_JThe value after the birth and death process at the t-th iteration.

The process updates z again^(t)The process is a life-kill process.

Step seven: calculating the value of the state transition probability matrix Q in the viscous hidden Markov model at the t-th iteration, and recording as Q^(t)，Q^(t)K of (1)^(t)The conjugate prior distribution of all elements in a row obeys a dirichlet distribution of:

Q^(t)k of (1)^(t)The posterior distribution of all elements in a row obeys a dirichlet distribution of:

wherein k is more than or equal to 1^(t)≤K^(t)，1≤k'^(t)≤K^(t)，

Represents Q^(t)K (f) of (1)^(t)All of the elements in the row are,

representing the k-th iteration after the birth and death process^(t)The amount of observation data that class hidden state transitions to class 1 hidden state,

representing the k-th iteration after the birth and death process^(t)Class hidden State transition to kth'^(t)The number of observations of the class hidden state,

to representAfter the birth and death process under the t iteration, from the kth^(t)Class hidden state transition to Kth^(t)Number of observations like hidden states, δ (k)^(t)1) two parameters are respectively k^(t)And a Crohn's function of 1, δ (k)^(t),k'^(t)) Denotes that the two parameters are respectively k^(t)And k'^(t)Crohn's function of (d), δ (k)^(t),K^(t)) Denotes that the two parameters are respectively k^(t)And K^(t)The function of the kronecker function of (c),

γ+κδ(k^(t)1) denotes the 1 st element of the Dirichlet distribution, γ + κ δ (k), to which the conjugate prior distribution here follows^(t),k'^(t)) Denotes the k 'of the Dirichlet distribution to which the conjugate prior distribution obeys here'^(t)Element, γ + κ δ (k)^(t),K^(t)) Kth of Dirichlet distribution representing the conjugate prior distribution obeyed herein^(t)The number of the elements is one,

representing the 1 st element of the dirichlet distribution to which the posterior distribution here obeys,

denotes the k 'of the Dirichlet distribution to which the posterior distribution is subjected'^(t)The number of the elements is one,

k < th > of a Dirichlet distribution representing the posterior distribution obeyed by the distribution here^(t)And (4) each element.

Step eight: calculating the values in X and z according to Bayes theorem by using all observation data belonging to the same type of hidden state^*(t)Determining the value μ of μ at the t-th iteration^(t)And Λ value of Λ at the t-th iteration^(t)A posterior probability of (D), is recorded as

Wherein，μ^(t)Represents the value of μ at the t-th iteration,

represents μ₁At the value at the t-th iteration,

indicates belonging to the k-th^(t)Mean vector of Gaussian distribution of hidden-state-like

At the value at the t-th iteration,

indicates belonging to the K^(t)Mean vector of Gaussian distribution of hidden-state-like

Value at the t-th iteration, Λ^(t)Denotes the value of a at the t-th iteration,

is represented by₁At the value at the t-th iteration,

indicates belonging to the k-th^(t)Accuracy matrix of Gaussian distribution of class hidden state

At the value at the t-th iteration,

indicates belonging to the K^(t)Accuracy matrix of gaussian distribution of class hidden state

At the value at the t-th iteration,

to represent

Obeying a probability density function of a Gaussian distribution having a variable of

Mean vector of

The covariance matrix is

To represent

Obeying a probability density function of a Weisset distribution having the variables

The scale matrix is

Degree of freedom of

Symbol "()^T"is a transposed symbol that is used to identify,

indicates that the signal belongs to the kth after the birth and death process under the t-th iteration^(t)The number of observations of the class hidden state,

indicates that the signal belongs to the kth after the birth and death process under the t-th iteration^(t)The average of all observed data for the class hidden state,

indicates that the signal belongs to the kth after the birth and death process under the t-th iteration^(t)Class i hidden state

Individual observation data, η₀、m₀、W₀、ν₀Are all constants, in this example take η₀＝1、

W₀＝I、ν₀＝1。

Step nine: judging t < t_maxIf yes, making t equal to t +1, and then returning to the fifth step to continue iteration; if not, executing step ten; wherein, t + t is an assignment symbol.

Step ten: mu to^(t)The value of each column element in the (b) is used as the power estimation value of L channels corresponding to a type of hidden state, namely mu^(t)K of (1)^(t)The value of the column element being the kth^(t)Power estimation values of L channels of similar hidden state, specifically, mu^(t)K of (1)^(t)The value of the ith element in the column element is taken as the k^(t)Power estimation value of ith channel of similar hiding state; then, calculating the power estimation value of each cognitive user in each channel according to the power estimation value of L channels of each type of hidden state and the value of the hidden state corresponding to each observation data after the extinction process under the t-th iteration, and recording the power estimation value of the j-th cognitive user in all channels as beta_jIf, if

Then beta is_jIs equal to kth^(t)Power estimation values of L channels in similar hidden state，

Then comparing the power estimation value of each cognitive user in each channel with a threshold value, and comparing the power estimation value of each cognitive user in each channel with the threshold value

If it is not

If the number of the channels is smaller than the threshold value, the ith channel at the jth cognitive user is considered to be not occupied by the authorized user, and the ith channel is used as an available channel; if it is not

If the channel number is larger than or equal to the threshold value, the ith channel at the jth cognitive user is considered to be occupied by the authorized user and cannot be used by the cognitive user; wherein the content of the first and second substances,

indicating the power estimated value of the j cognitive user in the 1 st channel if

Then

Is equal to kth^(t)The power estimate of the 1 st channel like the hidden state,

indicating the power estimated value of the j cognitive user in the i channel if

Then

Is equal to kth^(t)The power estimate for the ith channel like the hidden state,

indicating the power estimated value of the jth cognitive user in the Lth channel if

Then

Is equal to kth^(t)The threshold value of the power estimation value of the lth channel in the concealment-like state is calculated according to a given false alarm probability, which is 0.1 in this embodiment. In practice, the threshold value can also be set to 2.1521 directly, and the value is obtained through a large number of experiments.

The feasibility and effectiveness of the method of the invention is further illustrated by the following simulations.

In the simulation, the noise power is

Supposing that the ith channel is occupied by the authorized user, the signal power of the authorized user received by the jth cognitive user in the ith channel is

Wherein, P_tranFor authorized users transmitting power, P_tran＝10log₁₀30dBm，

Representing the path loss of authorized user signal power received from the transmission to the jth cognitive user,

the distance between the j cognitive user and the authorized user occupying the i channel is represented, the unit is km, and the maximum iteration time t_max＝100，η₀＝1，

W₀＝I， ν ₀1, 1 for the dirichlet distribution parameter y,the viscosity factor k is 50, the number of samples N is 100, and the monte carlo number is 1000.

Fig. 2 shows ROC curves when the number of malicious users is 5 and the interference power of the malicious users is 0dBm, 10dBm, and 20dBm, respectively. As can be seen from fig. 2, the method of the present invention can perform spectrum sensing on multiple cognitive users under different malicious user interference power conditions, and has good detection performance, which fully illustrates that the method of the present invention can well improve the detection probability of spectrum sensing of multiple cognitive users.

Claims (1)

1. A cooperative spectrum sensing method based on a birth and death process and a viscous hidden Markov model is characterized by comprising the following steps:

the method comprises the following steps: the method comprises the steps that J cognitive users and L channels exist in a cognitive radio system, each cognitive user samples signals in each channel for N times at equal time intervals, the signals in one channel are sampled by one cognitive user to obtain N samples, the nth sample obtained by sampling the signals in the ith channel by the jth cognitive user is recorded as the nth sample

Then, calculating the corresponding received signal power of each cognitive user in each channel, and recording the corresponding received signal power of the jth cognitive user in the ith channel as

If the j cognitive user is not a malicious user, determining that the cognitive user is a malicious user

I.e. the average power of all samples obtained by sampling the signal in the ith channel by the jth cognitive user,

and when N is more than or equal to 100 and less than or equal to 1000 according to the central limit theorem,

obeying a gaussian distribution:

if the j cognitive user is a malicious user, according to the central limit theorem when N is more than or equal to 100 and less than or equal to 1000,

obeying a gaussian distribution:

wherein J, L, N, J, i and N are positive integers, J is more than 1, L is more than 1, N is more than or equal to 100 and less than or equal to 1000, J is more than or equal to 1 and less than or equal to J, i is more than or equal to 1 and less than or equal to L, N is more than or equal to 1 and less than or equal to N, the symbol "|" is a modulo symbol,

which is indicative of the power of the noise,

indicating the signal power of the authorized user received by the j cognitive user in the i channel,

indicating that the ith channel is not occupied by an authorized user,

indicating that the ith channel has been occupied by an authorized user,

to represent

Obey mean value of

Has a covariance of

The distribution of the gaussian component of (a) is,

to represent

Obey mean value of

Covariance of

PM, the interference power,

to represent

Obey mean value of

Covariance of

The distribution of the gaussian component of (a) is,

to represent

Obey mean value of

Covariance of

(ii) a gaussian distribution of;

step two: taking a vector formed by the received signal power corresponding to each cognitive user in all channels as one observation datum in a hidden Markov model, taking a vector formed by the received signal power corresponding to the jth cognitive user in all channels as the jth observation datum in the hidden Markov model, and marking as x_j，

Then determining a hidden state corresponding to each observation data in the hidden Markov model, and determining x_jThe corresponding hidden state is recorded as z_j，z_jIs the interval [1, K ]]Is a value of (a) if z_jIf the value of (1) is x_jBelongs to class 1 hidden state if z_jIf k is the value of (a), x is considered to be_jBelongs to class k hidden state if z_jIf the value of (A) is K, then x is considered to be_jBelong to class K hidden state; then calculating the probability of each observation data in the hidden Markov model belonging to various hidden states, and calculating the probability of each observation data in the hidden Markov model_jThe probability of belonging to class k hidden states is noted

Finally, calculating a state transition probability matrix in the hidden Markov model, and marking as Q,

wherein the content of the first and second substances,

indicating the corresponding received signal power of the j-th cognitive user in the 1 st channel,

representing the corresponding received signal power of the j cognitive user in the L channel, wherein K and K are positive integers, K represents the number of categories of hidden states set in a hidden Markov model, and 2 is less than or equal toK≤10，1≤k≤K，

Denotes x_jObeyed Gaussian distributed probability density function with variable x_jMean vector of μ_kThe covariance matrix is

μ_kA mean vector representing the gaussian distribution belonging to the kth class of hidden states,

covariance matrix, Lambda, representing a Gaussian distribution belonging to class k hidden states_kInverse of a covariance matrix, Q, which is a precision matrix representing a Gaussian distribution belonging to class k hidden states_1,1、Q_1,2、Q_1,k'、Q_1,KCorresponding to the element in Q, which represents the 1 st row and 1 st column, the 1 st row and 2 nd column, the 1 st row and K' th column, and the 1 st row and K column_2,1、Q_2,2、Q_2,k'、Q_2,KCorresponding to the elements in the 2 nd row, 1 st column, the 2 nd row, 2 nd column, the 2 nd row, K' th column in Q, Q_k,1、Q_k,2、Q_k,k'、Q_k,KCorresponding to the element of the kth row and the 1 st column, the element of the kth row and the 2 nd column, the element of the kth row and the kth' column and the element of the kth row and the kth column in Q, Q_K,1、Q_K,2、Q_K,k'、Q_K,KCorrespondingly represents the elements of the K-th row and the 1 st column, the K-th row and the 2 nd column, the K-th row and the K '-th column, the elements of the K-th row and the K-th column in Q, wherein K' is more than or equal to 1 and less than or equal to K, and Q_k,k'Denotes z_j'-1K under the condition of z_j'J' is not less than 2 and not more than J, z_j'-1Represents the j' -1 st observation data x in the hidden Markov model_j'-1Corresponding hidden state, z_j'Representing the jth' observation x in a hidden Markov model_j'The corresponding hidden state;

step three: a viscosity factor is introduced in the hidden markov model,obtaining a viscous hidden Markov model; in the viscous hidden Markov model, the mean vector and precision matrix of Gaussian distribution belonging to each class of hidden state are initialized, and mu is calculated_kIs recorded as

Will be Λ_kIs recorded as

I is an L-order identity matrix; initializing the class number K of the hidden state, and recording the initialization value of K as K⁽⁰⁾，K⁽⁰⁾Is the interval [2,10]Any positive integer within; initializing the state transition probability matrix Q, and recording the initialization value of Q as Q⁽⁰⁾，Q⁽⁰⁾The conjugate prior distribution of all elements in each row in (a) obeys a dirichlet distribution, Q⁽⁰⁾K of (1)⁽⁰⁾The conjugate prior distribution of all elements in a row obeys a dirichlet distribution of:

wherein the content of the first and second substances,

represents Q⁽⁰⁾K of (1)⁽⁰⁾All elements in the row, Dir () represent dirichlet distribution, γ represents the parameters of dirichlet distribution, κ represents the viscosity factor, δ (k)⁽⁰⁾1) two parameters are respectively k⁽⁰⁾And a Crohn's function of 1, δ (k)⁽⁰⁾,k'⁽⁰⁾) Denotes that the two parameters are respectively k⁽⁰⁾And k'⁽⁰⁾Crohn's function of (d), δ (k)⁽⁰⁾,K⁽⁰⁾) Denotes that the two parameters are respectively k⁽⁰⁾And K⁽⁰⁾Kronecker function of，

γ+κδ(k⁽⁰⁾1) denotes the 1 st element of the Dirichlet distribution, to which the conjugate prior distribution is subjected, γ + κ δ (k)⁽⁰⁾,k'⁽⁰⁾) Denotes the k 'of the Dirichlet distribution to which the conjugate prior distribution obeys here'⁽⁰⁾Element, γ + κ δ (k)⁽⁰⁾,K⁽⁰⁾) Kth of Dirichlet distribution representing the conjugate prior distribution obeyed herein⁽⁰⁾Element, 1. ltoreq. k⁽⁰⁾≤K⁽⁰⁾，1≤k'⁽⁰⁾≤K⁽⁰⁾；

Step four: let t represent the number of iterations, the initial value of t is 1; let t_maxIndicates the set maximum number of iterations, t_max≥3；

Step five: calculating the hidden state clustering result corresponding to all observation data in the viscous hidden Markov model under the t-th iteration, and recording as z^(t)，

Wherein the content of the first and second substances,

expression makes p (z | X, Q)^(t-1),μ^(t-1),Λ^(t-1)) Taking the value of a maximum value time variable z, wherein z is a vector formed by hidden states corresponding to all observation data in the viscous hidden Markov model, and z is [ z ═ z₁,z₂,…,z_j,…,z_J]，z₁Represents the 1 st observation data x₁Corresponding hidden state, z₂Represents the 2 nd observation x₂Corresponding hidden state, z_JRepresents the J-th observed data x_JCorresponding hidden states, X represents a matrix formed by all observation data in the viscous hidden Markov model, and X is [ X [ ]₁,x₂,…,x_j,…,x_J]When t is 1, Q^(t-1)Is namely Q⁽⁰⁾Q when t is not equal to 1^(t-1)Representing state transition probabilities in a sticky hidden Markov modelThe value of the matrix Q at the t-1 th iteration, μ when t is 1^(t-1)Is the initial value mu of mu⁽⁰⁾，μ＝[μ₁,μ₂,…,μ_K]，μ₁Mean vector, μ, representing a Gaussian distribution belonging to class 1 hidden states₂Mean vector, μ, representing a Gaussian distribution belonging to class 2 hidden states_KA mean vector representing a gaussian distribution belonging to class K hidden states,

represents μ₁The initial value of (a) is set,

represents μ₂The initial value of (a) is set,

indicates belonging to the K⁽⁰⁾Mean vector of Gaussian distribution of hidden-state-like

When the initialization value of (1), t ≠ 1 μ^(t-1)Represents the value of μ at the t-1 th iteration,

represents μ₁At the value at the t-1 th iteration,

represents μ₂At the value at the t-1 th iteration,

indicates belonging to the K^(t-1)Mean vector of Gaussian distribution of hidden-state-like

Value at t-1 iteration, Λ at t ═ 1^(t-1)I.e. the initial value Λ of the set Λ⁽⁰⁾，Λ＝{Λ₁,Λ₂,…,Λ_K}，Λ₁Precision matrix, Λ, representing a gaussian distribution belonging to class 1 hidden states₂Precision matrix, Λ, representing a gaussian distribution belonging to class 2 hidden states_KA precision matrix representing a gaussian distribution belonging to class K hidden states,

is represented by₁The initial value of (a) is set,

is represented by₂The initial value of (a) is set,

indicates belonging to the K⁽⁰⁾Accuracy matrix of Gaussian distribution of class hidden state

When t ≠ 1, Λ^(t-1)Representing the value of the set a at the t-1 st iteration,

is represented by₁At the value at the t-1 th iteration,

is given by₂At the value at the t-1 th iteration,

indicates belonging to the K^(t-1)Accuracy matrix of Gaussian distribution of class hidden state

Value at the t-1 th iteration, K when t is 1^(t-1)Is the initial value K of K⁽⁰⁾K when t ≠ 1^(t-1)Denotes the value of K at the t-1 iteration, p (z | X, Q)^(t-1),μ^(t-1),Λ^(t-1)) The posterior probability of z is obtained according to Bayes theorem

p(z_j|X,Q^(t-1),μ^(t-1),Λ^(t-1)) Denotes z_jThe symbol ". alpha." indicates a direct ratio, x_j+1Denotes the j +1 th observation, x_j+2Denotes the j +2 th observation, p (z)_j,x₁,x₂,...,x_j|Q^(t-1),μ^(t-1),Λ^(t-1)) Denotes z_j,x₁,x₂,...,x_jJoint probability of p (x)_j+1,x_j+2,...,x_J|z_j,Q^(t-1),μ^(t-1),Λ^(t-1)) Denotes z_jUnder the condition of (1) x_j+1,x_j+2,...,x_JJoint probability of p (z)_j,x₁,x₂,...,x_j|Q^(t-1),μ^(t-1),Λ^(t-1)) And p (x)_j+1,x_j+2,...,x_J|z_j,Q^(t-1),μ^(t-1),Λ^(t-1)) Calculating by a forward and backward algorithm;

step six: updating z by a birth-kill process^(t)Further, the value K of the class number K of the hidden state in the viscous hidden Markov model at the t-th iteration is calculated^(t)The specific process is as follows:

1) statistics z^(t)Median value, etcIn the interval [1, K^(t-1)]Total number of elements of each value in, will z^(t)Median value equal to k^(t-1)Total number of elements of (1) is recorded as

2) According to 1, …, k^(t-1),…,K^(t-1)Num is arranged from small to large₁To

Obtaining a statistical number arrangement sequence;

3) if the statistical number is only one 0 value and K in the permutation sequence^(t-1)Not equal to 2, assume that the 0 value corresponds to the interval [1, K-^(t-1)]K in (1)^(t-1)Then z will be^(t)Median value is respectively equal to (k +1)^(t-1)To K^(t-1)All the values of z are reduced by 1, and the updated z is obtained^(t)Is newly recorded as z^*(t)And order K^(t)＝K^(t-1)-1, performing step seven again; if the statistical number is only one 0 value and K in the permutation sequence^(t-1)If 2, or the statistical number array sequence has a plurality of 0 values, executing step 4); if there is no 0 value in the statistical number permutation sequence and K is^(t-1)If < 10, randomly generating a starting value from 1 to J, and recording the starting value as J_minFrom J_minRandomly generating a termination value in J, denoted as J_maxWill z^(t)In (1)

Are all set to K^(t-1)+1, z to be updated^(t)Is newly recorded as z^*(t)And order K^(t)＝K^(t-1)+1, then executing step seven; if the statistical number array sequence is other than the four cases, keeping z^(t)Without change, will z^(t)Is newly recorded as z^*(t)And order K^(t)＝K^(t-1)Then, the seventh step is executed;

4) when the ω -th value in the statistical number permutation sequence is J and the 1 st to ω -1 st andomega +1 to Kth^(t-1)Values are all 0 i.e. z^(t)Is equal to ω, randomly generating a starting value from 1 to J, denoted as J'_minFrom J'_minTo J an end value, denoted J ', is randomly generated'_maxWill z^(t)In

All are set to 2, z^(t)In (1)

And

all the values of (a) are set to 1, and z after updating is carried out^(t)Is re-noted as z^*(t)And order K^(t)Step seven is executed again when the value is 2; when the statistical number array sequence has a plurality of 0 values and any non-0 value is not J, executing step 5);

5) let 0 have xi, for the 1 st 0 value and the 2 nd 0 value, assume that the 1 st 0 value corresponds to the interval [1, K^(t-1)]K in (1)^(t-1)And the 2 nd 0 th value corresponds to the interval [1, K^(t-1)]Middle (k + upsilon)^(t-1)Then z will be^(t)Median value is respectively equal to (k +1)^(t-1)To (k + upsilon-1)^(t-1)All the values of (a) minus 1; for the 2 nd 0 value and the 3 rd 0 value, assume that the 2 nd 0 value corresponds to the interval [1, K^(t-1)]Middle (k + upsilon)^(t-1)And the 3 rd 0 value corresponding interval [1, K ]^(t-1)]In (1)

Then z will be^(t)Median value is respectively equal to (k + upsilon +1)^(t-1)To

All the values of (a) minus 2; by analogy, for the xi-1 0 values and the xi 0 values, suppose that the xi-1 0 values correspond to the interval [1, K^(t-1)]Middle (k + theta)^(t-1)And the xi 0 value corresponding areaM 1, K^(t-1)]Middle (k + ρ)^(t-1)Then z will be^(t)Median value is equal to (k + theta +1)^(t-1)To (k + rho-1)^(t-1)All the values of the elements of (1) are decremented by ξ -1; then z is mixed^(t)Median value is equal to (k + ρ +1)^(t-1)To K^(t-1)All the values of (1) are decremented; will updated z^(t)Is newly recorded as z^*(t)And order K^(t)＝K^(t-1)ξ, then step seven is performed;

above, k^(t-1)Is the interval [1, K^(t-1)]K of (1)^(t-1)Value, Num₁Denotes z^(t)The total number of elements whose median value is equal to 1,

denotes z^(t)Median value equal to K^(t-1)The total number of the elements (1 ≤ omega ≤ K^(t-1)，1≤J_min≤J_max≤J，

Corresponding to represents z^(t)J in (1)_minElement, item J_min+1 element, …, J_max1 is not more than J'_min≤J'_max≤J，

Corresponding to represents z^(t)J 'of (1)'_minElement, J'_min+1 elements, …, J'_maxThe number of the elements is one,

corresponding to represents z^(t)The 1 st element, the 2 nd element, …, the J'_min-1 element of the group consisting of,

corresponding to represents z^(t)J 'of (1)'_max+1 elements, J'_max+2 elements, …, J element, 1 < xi < K^(t-1)，

K^(t)＝K^(t-1)Wherein "═ is an assigned symbol,

denotes z₁The value after the birth and death process at the t-th iteration,

denotes z₂The value after the birth and death process at the t-th iteration,

denotes z_jThe value after the birth and death process at the t-th iteration,

denotes z_JThe value after the birth and death process under the t-th iteration;

step seven: calculating the value of the state transition probability matrix Q in the viscous hidden Markov model at the t-th iteration, and recording as Q^(t)，Q^(t)K of (1)^(t)The conjugate prior distribution of all elements in a row obeys a dirichlet distribution of:

Q^(t)k of (1)^(t)The posterior distribution of all elements in a row obeys a dirichlet distribution of:

(ii) a Wherein k is more than or equal to 1^(t)≤K^(t)，1≤k'^(t)≤K^(t)，

Represents Q^(t)K of (1)^(t)All of the elements in the row are,

representing the k-th iteration after the birth and death process^(t)The amount of observation data that class hidden state transitions to class 1 hidden state,

representing the k-th iteration after the birth and death process^(t)Transition of quasi-hidden state to kth'^(t)The number of observations of the class hidden state,

representing the k-th iteration after the birth and death process^(t)Class hidden state transition to Kth^(t)Number of observations like hidden states, δ (k)^(t)1) two parameters are respectively k^(t)And a Crohn's function of 1, δ (k)^(t),k'^(t)) Denotes that two parameters are respectively k^(t)And k'^(t)Kronecker function of (d), δ (k)^(t),K^(t)) Denotes that the two parameters are respectively k^(t)And K^(t)The function of the kronecker function of (c),

γ+κδ(k^(t)1) denotes the 1 st element of the Dirichlet distribution, γ + κ δ (k), to which the conjugate prior distribution here follows^(t),k'^(t)) Denotes the k 'of the Dirichlet distribution to which the conjugate prior distribution obeys here'^(t)Element, γ + κ δ (k)^(t),K^(t)) Kth of Dirichlet distribution representing the conjugate prior distribution obeyed herein^(t)The number of the elements is one,

is shown hereThe posterior distribution of (a) obeys the 1 st element of the dirichlet distribution,

denotes the k 'of the Dirichlet distribution to which the posterior distribution is subjected'^(t)The number of the elements is one,

k < th > of a Dirichlet distribution representing the posterior distribution obeyed by the distribution here^(t)An element;

step eight: calculating the values in X and z according to Bayes theorem by using all observation data belonging to the same type of hidden state^*(t)Determining the value μ of post μ at the t-th iteration^(t)And Λ value of Λ at the t-th iteration^(t)The posterior probability of (d), is denoted as p (μ)^(t),Λ^(t)|X,z^*(t))，

Wherein, mu^(t)Represents the value of μ at the t-th iteration,

represents μ₁At the value at the t-th iteration,

indicates belonging to the k-th^(t)Mean vector of Gaussian distribution of hidden-state-like

At the value at the t-th iteration,

indicates belonging to the K^(t)Mean vector of Gaussian distribution of hidden-state-like

Value at the t-th iteration, Λ^(t)Denotes the value of a at the t-th iteration,

is represented by₁At the value at the t-th iteration,

indicates belonging to the k-th^(t)Accuracy matrix of Gaussian distribution of class hidden state

At the value at the t-th iteration,

indicates belonging to the K^(t)Accuracy matrix of Gaussian distribution of class hidden state

At the value at the t-th iteration,

to represent

Obeying a probability density function of a Gaussian distribution having a variable of

Mean vector of

The covariance matrix is

To represent

Obeying a probability density function of a Weisset distribution having the variables

The scale matrix is

Degree of freedom of

Symbol "()^T"is a transposed symbol that is used to identify,

indicates that the signal belongs to the kth after the birth and death process under the t-th iteration^(t)The number of observations of the class hidden state,

indicates that the signal belongs to the kth after the birth and death process under the t-th iteration^(t)The average of all observed data for the class hidden state,

indicates that the signal belongs to the kth after the birth and death process under the t-th iteration^(t)Class i hidden state

Individual observation data, η₀、m₀、W₀、ν₀Are all constants;

step nine: judging t < t_maxIf yes, making t equal to t +1, and then returning to the fifth step to continue iteration; if not, executing step ten; wherein, t is in t +1, and is an assignment symbol;

step ten: mu is to be^(t)The value of each column of elements in the table is used as the power estimation value of L channels corresponding to a type of hidden state, namely mu^(t)K of (1)^(t)The value of the column element being the kth^(t)Power estimation values of L channels of similar hidden state, specifically, mu^(t)K of (1)^(t)The value of the ith element in the column element is taken as the k^(t)Power estimation value of ith channel of similar hiding state; then, calculating the power estimation value of each cognitive user in each channel according to the power estimation value of L channels of each type of hidden state and the value of the hidden state corresponding to each observation data after the extinction process under the t-th iteration, and recording the power estimation value of the j-th cognitive user in all channels as beta_jIf, if

Then beta is_jIs equal to kth^(t)The power estimates for the L channels that resemble the hidden state,

then comparing the power estimation value of each cognitive user in each channel with a threshold value, and comparing the power estimation value of each cognitive user in each channel with the threshold value

If it is not

If the current channel is smaller than the threshold value, the ith channel at the jth cognitive user is considered not occupied by the authorized user, and the ith channel is used as an available channel; if it is not

If the channel number is larger than or equal to the threshold value, the ith channel at the jth cognitive user is considered to be occupied by the authorized user and cannot be used by the cognitive user; wherein the content of the first and second substances,

indicating the power estimated value of the j cognitive user in the 1 st channel if

Then

Is equal to kth^(t)The power estimate of the 1 st channel like the hidden state,

indicating the power estimated value of the j cognitive user in the i channel if

Then

Is equal to kth^(t)The power estimate for the ith channel like the hidden state,

indicating the power estimated value of the jth cognitive user in the Lth channel if

Then

Is equal to kth^(t)The power estimation value of the L-th channel of the similar hidden state and the threshold value are calculated according to the given false alarm probability.

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