CN106169945A - A kind of cooperative frequency spectrum sensing method of difference based on minimax eigenvalue - Google Patents

Abstract

The present invention relates to the cooperative frequency spectrum sensing method of a kind of difference based on minimax eigenvalue, including: the cognitive user receiving terminal signal to receiving carries out stochastical sampling and calculates reception signal matrix；It is calculated sample covariance matrix by receiving signal matrix, and it is carried out Eigenvalues Decomposition；Select the eigenvalue of maximum difference with minimal eigenvalue as detection statistic；Calculate the threshold value in the presence of authorized user；Detection statistic is compared with threshold value, it is judged that whether primary user exists；If statistic is more than or equal to threshold value, showing that primary user exists, otherwise primary user does not exists, in order to cognitive user accesses frequency range.The present invention is using the difference of minimax eigenvalue as detection statistic, and its distribution function is the regularity of distribution based on minimal eigenvalue, and the threshold value obtained will be more accurate.In the case of many cognitive user collaborative sensing, it is possible to ensure higher accuracy of detection, simultaneously required for sampled point less, reduce the complexity of system.

Description

A kind of cooperative frequency spectrum sensing method of difference based on minimax eigenvalue

Technical field

The invention belongs to cognitive radio technology field, particularly to a kind of for cognitive radio system based on maximum The cooperative frequency spectrum sensing method of the difference of minimal eigenvalue.

Background technology

Along with the quick growth of radio communication service, it is becoming tight radio spectrum resources day.Owing to existing frequency spectrum uses solely The method of salary distribution accounted for, only primary user just can use mandate frequency spectrum, though primary user be in other users of idle condition also without Method uses this frequency range.In order to improve this phenomenon, cognitive radio the most just arises at the historic moment, as the frequency spectrum share skill of a kind of intelligence Art, can detect the idle frequency range that primary user is not used by, and allows other users to access in the case of not affecting primary user, thus Improve the utilization rate of frequency spectrum.

Frequency spectrum perception technology is the key technology of cognitive radio.Conventional frequency spectrum perception technology includes energy measuring side Method, matched filtering detection method and cyclostationary characteristic detection method.Owing to energy measuring realizes simple, it is not necessary to know that primary user believes Number any priori so that energy measuring becomes one of most common detection method.But due to effect of noise, to micro- Testing of Feeble Signals ability is poor, it is to be appreciated that noise variance when setting thresholding, and in actual environment, noise variance is time-varying, no Determine.Matched filtering detection is the detection method of a kind of best performance, but the prior information of necessary known primary user, to not With the transmitter signal of type, need to design different matched filtering devices, add the complexity of system.Cyclostationary characteristic is examined Surveying anti-noise strong, detection performance is good, but computationally intensive, and the detection time is long, reduces the accuracy of system.

Shortcomings in view of above classic algorithm.In recent years, Random Matrices Theory (RMT) is gradually applied to frequency spectrum Perception field, many outstanding algorithms are suggested the most in succession, including minimax eigenvalue algorithm (MME), energy-minimal eigenvalue Algorithm (EME), ratio (AGM) algorithm of geometric average and arithmetic mean of instantaneous value of eigenvalue based on covariance.These algorithms have Imitate avoids the impact that incorrect noise brings, but mostly uses the Asymptotic solution regularity of distribution, obtained threshold expression Need to improve further.

Summary of the invention

It is an object of the invention to overcome the shortcoming of prior art with not enough, it is provided that in a kind of cognitive radio system based on The cooperative frequency spectrum sensing method of the difference of minimax eigenvalue.This method based on new statistic, by minimax eigenvalue it Difference is as detection statistic；The threshold value expression formula used is that the regularity of distribution based on minimal eigenvalue is calculated, The distribution function of little eigenvalue is not based on asymptotic hypothesis.The threshold value expression formula of derivation gained is to use based on false-alarm probability and cooperation The function of amount, can judge whether primary user exists in the case of low sample number more accurately, has both improve system Performance reduce again the complexity of system.

The purpose of the present invention is achieved through the following technical solutions:

(1) M cognitive user is to same primary user's cooperation detection, and the signal that each cognitive user receives carries out n times and adopts Sample, then can form reception signal matrix Y of M × N.

(2) according to above-mentioned reception signal matrix Y, sample covariance matrix is calculatedWherein Y^HFor signal The E Mite transposed matrix of matrix Y.

(3) sample covariance matrix is calculatedEigenvalue, and select eigenvalue of maximum λ therein_maxWith minimal eigenvalue λ_minDifference as detection statistic Γ.

(4) theory of algorithm basis one

For normalized sample covariance matrixThe probability density function of minimal eigenvalue can To be expressed as:

In formula:

$C={\[\underset{m=1}{\overset{M}{\Π}}(N-m)!(M-m)!\]}^{-1}$

M_λBeing the matrix on one (M-1) × (M-1) rank, the element in matrix can be expressed as:

Γ () expression incomplete Gamma function in formula:

R_YThe distribution function of ' (N) minimal eigenvalue can be expressed as:

$F_{min}\left(\mathrm{\λ}\right)={\∫}_{-\mathrm{\∞}}^{\mathrm{\λ}}{f}_{min}\left(t\right)dt={\∫}_0^{\mathrm{\λ}}{f}_{min}\left(t\right)dt$

(5) theory of algorithm basis two

If the element in random matrix X meets zero-mean independent same distribution, variance is σ²/ N, then as M → ∞, N → ∞, and During M/N=β, XX^HESD the most necessarily converge to M-P rule, its probability density function is:

$f_{\mathrm{\β}}\left(x\right)={(1-{\mathrm{\β}}^{-1})}^{+}\mathrm{\δ}\left(x\right)+\frac{\sqrt{{(x-{\mathrm{\η}}_1)}^{+}{({\mathrm{\η}}_2-x)}^{+}}}{2\mathrm{\π}\mathrm{\β}x}$

In formula:It is respectively minimal eigenvalue and the convergence of eigenvalue of maximum Value, i.e. λ ∈ [η₁,η₂], σ²For variance, (a)⁺It is that to remove the greater, δ (x) in 0 and a be unit impulse function.

(6) according to theory of algorithm basis two, the eigenvalue of maximum convergency value of covariance matrix can be expressed asAccording to given false-alarm probability value, decision threshold expression formula can be derived:

So,WhereinRepresent F_minThe inverse function of (t), σ²It it is noise variance.If When noise is known, directly it is updated in threshold expression；If during without knowledge of noise covariance, by minimal eigenvalue to noise side Difference is estimated in real time, and noise variance estimation obtained substitutes in threshold expression, utilizes minimal eigenvalue to estimate to make an uproar to reduce The error that sound variance is brought, noise variance expression formula can be expressed as

(7) detection statistic Γ obtained is compared with decision threshold γ, when detection statistic is more than or equal to judgement During thresholding, i.e. Γ >=γ, show that current spectral resource is taken by primary user, cognitive user can not utilize this frequency spectrum resource.Work as inspection When surveying statistic less than decision threshold, i.e. Γ ＜ γ, it is believed that current spectral resource is idle, and cognitive user can utilize this frequency spectrum to provide Source.

The present invention has such advantages as relative to prior art and effect:

(1) it is required in the case of sampled point is very many realizing based on random matrix frequency spectrum perception algorithm in the past, and this The algorithm that invention is proposed need not substantial amounts of sampled point, reduces the complexity of calculating and designs the one-tenth needed for detector This.

(2) conventional random matrix frequency spectrum perception algorithm is many due to the sampled point needed, and the detection distribution function of employing is big Being all the distribution theory using big dimension asymptotic, the threshold expression calculated is accurate not, reduces the detection to primary user Accuracy.The detection distribution function that the present invention provides is not based on the regularity of distribution in the case of tieing up greatly, but according to sampled point relatively The regularity of distribution of minimal eigenvalue time few, its probability density function is not based on asymptotic it is assumed that the threshold expression of derivation gained is Function based on false-alarm probability, under Small Sample Size, its superiority is verified.

Accompanying drawing explanation

Fig. 1 is the FB(flow block) of the frequency spectrum sensing method of the present invention；

Fig. 2 is the relation comparison diagram between the present invention and the detection probability-signal to noise ratio of other two kinds of algorithms.

Detailed description of the invention

Below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention do not limit In this.

Embodiment content is as follows:

Fig. 1 is a kind of based on minimal eigenvalue the cooperative frequency spectrum sensing method flow chart of the present embodiment

Step 1, calculates and receives signal matrix Y:

M cognitive user, to primary user's cooperation detection, carries out sampling and obtains signal X, each cognition the signal received User is respectively to the signal sampling n times received.

The signal matrix of M cognitive user sampling n times can be expressed as Y=[y₁y₂…y_M]^T

Wherein y₁Represent the one-dimensional vector that first cognitive user sampling n times is formed.

Step 2, according to receiving signal matrix Y, calculates sample covariance matrix

${\hat{R}}_y\stackrel{\mathrm{\Δ}}{=}\frac{1}{N}\underset{n=0}{\overset{N-1}{\Σ}}y\left(n\right)y^H\left(n\right)=\frac{1}{N}{\mathrm{YY}}^H,$

Wherein, ()^HThe E Mite transposition of representing matrix.

Step 3, calculates sample covarianceEigenvalue λ₁,λ₂,…,λ_M, wherein λ_iThe i-th being covariance matrix is special Value indicative, wherein M is the number of cognitive user, selects the poor λ of eigenvalue of maximum and minimal eigenvalue_max-λ_minAs statistic Γ.

Step 4, the situation that primary user's signal is detected by single cognitive user, can be with the dualism hypothesis in statistics Model represents, it is assumed that H₀Represent that primary user does not exists, H₁Represent that authorized user exists, calculate the judgement in the presence of primary user Threshold gamma.

Step 5, solves distribution function expression formula.For normalized sample covariance matrix The probability density function of minimal eigenvalue can be expressed as:

In formula:

$C={\[\underset{m=1}{\overset{M}{\Π}}(N-m)!(M-m)!\]}^{-1}$

M_λBeing the matrix on one (M-1) × (M-1) rank, the element in matrix can be expressed as:

Γ () expression incomplete Gamma function in formula:

R_YThe distribution function of ' (N) minimal eigenvalue can be expressed as:

$F_{min}\left(\mathrm{\λ}\right)={\∫}_{-\mathrm{\∞}}^{\mathrm{\λ}}{f}_{min}\left(t\right)dt={\∫}_0^{\mathrm{\λ}}{f}_{min}\left(t\right)dt$

Step 6, random matrix eigenvalue of maximum asymptotic distribuion rule.If it is only that the element in random matrix X meets zero-mean Vertical with distribution, variance is σ²/ N, then as M → ∞, N → ∞, and during M/N=β, XX^HESD the most necessarily converge to M-P rule, it Probability density function be:

$f_{\mathrm{\β}}\left(x\right)={(1-{\mathrm{\β}}^{-1})}^{+}\mathrm{\δ}\left(x\right)+\frac{\sqrt{{(x-{\mathrm{\η}}_1)}^{+}{({\mathrm{\η}}_2-x)}^{+}}}{2\mathrm{\π}\mathrm{\β}x}$

In formula:It is respectively minimal eigenvalue and the convergence of eigenvalue of maximum Value, i.e. λ ∈ [η₁,η₂], σ²For variance, (a)⁺It is that to remove the greater, δ (x) in 0 and a be unit impulse function.

So, the eigenvalue of maximum convergency value of covariance matrix can be expressed as

Step 7, solves the expression formula of threshold value.

So,WhereinRepresent F_minThe inverse function of (t), σ²It it is noise variance.If When noise is known, directly it is updated in threshold expression；If during without knowledge of noise covariance, by minimal eigenvalue to noise side Difference is estimated in real time, and noise variance estimation obtained substitutes in threshold expression, utilizes minimal eigenvalue to estimate to make an uproar to reduce The error that sound variance is brought, noise variance expression formula can be expressed as

Step 8, it is judged that whether primary user exists, if statistic Γ is more than or equal to threshold gamma, represents that primary user exists； Otherwise, primary user does not exists.

Step 9, Fig. 2 is minimax eigenvalue (MME), average energy and minimal eigenvalue (ED-ME) and the present invention Relation curve comparison diagram between detection probability and the signal to noise ratio of the difference (DMM) of minimax eigenvalue.The present embodiment uses Being Monte Carlo simulation, the signal of primary user's transmitter is BPSK modulated signal, and parameter involved in simulation process has signal Sample frequency f_sBeing 1, sampling number N is 150, and the number of cooperative cognitive user is 4, false-alarm probability P_fIt is 0.1.Simulation result Showing that inventive algorithm (DMM) is better than MME algorithm and EME algorithm in the environment of identical, particularly when low signal-to-noise ratio, DMM calculates Method is substantially better than MME algorithm and EME algorithm.

Above-described embodiment is the present invention preferably embodiment, but embodiments of the present invention are not by above-described embodiment Limit, the change made under other any spirit without departing from the present invention and principle, modify, substitute, combine, simplify, All should be the substitute mode of equivalence, within being included in protection scope of the present invention.

Claims (1)

1. a cooperative frequency spectrum sensing method based on minimal eigenvalue, it is characterised in that comprise the following steps:

Step 1, calculates and receives signal matrix Y:

M cognitive user, to primary user's cooperation detection, carries out sampling and obtains signal X, each cognitive user the signal received Respectively to the signal sampling n times received,

The signal matrix of M cognitive user sampling n times can be expressed as Y=[y₁ y₂ … y_M]^T

Wherein y₁Represent the one-dimensional vector that first cognitive user sampling n times is formed；

Step 2, according to receiving signal matrix Y, calculates sample covariance matrix

${\hat{R}}_y\stackrel{\mathrm{\Δ}}{=}\frac{1}{N}\underset{n=0}{\overset{N-1}{\Σ}}y\left(n\right)y^H\left(n\right)=\frac{1}{N}{\mathrm{YY}}^H,$

Wherein, ()^HThe E Mite transposition of representing matrix；

Step 3, calculates sample covarianceEigenvalue λ₁,λ₂,…,λ_M, wherein λ_iIt is the ith feature value of covariance matrix, Wherein M is the number of cognitive user, selects the poor λ of eigenvalue of maximum and minimal eigenvalue_max-λ_minAs statistic Γ；

Step 4, the situation that primary user's signal is detected by single cognitive user, can be with the dualism hypothesis model in statistics Represent, it is assumed that H₀Represent that primary user does not exists, H₁Represent that authorized user exists, calculate the decision threshold in the presence of primary user γ；

Step 5, solves distribution function expression formula:

For normalized sample covariance matrixThe probability density function of minimal eigenvalue can be with table It is shown as:

In formula:

$C={\[\underset{m=1}{\overset{M}{\Π}}(N-m)!(M-m)!\]}^{-1}$

M_λBeing the matrix on one (M-1) × (M-1) rank, the element in matrix can be expressed as:

Γ () expression incomplete Gamma function in formula:

R′_Y(N) distribution function of minimal eigenvalue can be expressed as:

$F_{min}\left(\mathrm{\λ}\right)={\∫}_{-\mathrm{\∞}}^{\mathrm{\λ}}{f}_{min}\left(t\right)dt={\∫}_0^{\mathrm{\λ}}{f}_{min}\left(t\right)dt;$

Step 6, random matrix eigenvalue of maximum asymptotic distribuion rule:

If the element in random matrix X meets zero-mean independent same distribution, variance is σ²/ N, then as M → ∞, N → ∞, and M/N= During β, XX^HESD the most necessarily converge to M-P rule, its probability density function is:

$f_{\mathrm{\β}}\left(x\right)={(1-{\mathrm{\β}}^{-1})}^{+}\mathrm{\δ}\left(x\right)+\frac{\sqrt{{(x-{\mathrm{\η}}_1)}^{+}{({\mathrm{\η}}_2-x)}^{+}}}{2\mathrm{\π}\mathrm{\β}x}$

In formula:It is respectively minimal eigenvalue and the convergency value of eigenvalue of maximum, i.e. λ∈[η₁,η₂], σ²For variance, (a)+it is in 0 and a, to remove the greater, δ (x) is unit impulse function,

So, the eigenvalue of maximum convergency value of covariance matrix can be expressed as

Step 7, solves the expression formula of threshold value:

So,WhereinRepresent F_minThe inverse function of (t), σ²It is noise variance, if noise is When knowing, directly it is updated in threshold expression；If during without knowledge of noise covariance, real-time to noise variance by minimal eigenvalue Estimating, noise variance estimation obtained substitutes in threshold expression, utilizes minimal eigenvalue to estimate noise variance to reduce The error brought, noise variance expression formula can be expressed as

Step 8, it is judged that whether primary user exists, if statistic Γ is more than or equal to threshold gamma, represents that primary user exists；No Then, primary user does not exists.