CN103795481A

CN103795481A - Cooperative spectrum sensing method based on free probability theory

Info

Publication number: CN103795481A
Application number: CN201410042029.6A
Authority: CN
Inventors: 王磊; 薛海涛; 周亮; 郑宝玉; 孟庆民
Original assignee: Nanjing Post and Telecommunication University
Current assignee: Nanjing Post and Telecommunication University
Priority date: 2014-01-28
Filing date: 2014-01-28
Publication date: 2014-05-14
Anticipated expiration: 2034-01-28
Also published as: CN103795481B

Abstract

The invention discloses a cooperative spectrum sensing method based on a free probability theory. The cooperative spectrum sensing method is suitable for an MIMO communication environment and includes the steps that received signals of a plurality of antennas of all auxiliary base stations are sampled, and sampled signals are processed in a centralized mode; according to noise variance of all the received sampled signals and channels, by means of the asymptotic freedom characteristic and the Wishart distribution characteristic of a random matrix, the average received signal power (img file=' DDA0000463198220000011. TIF' wi=' 64' he=' 54' /) of all receiving antennas is solved by the adoption of a free deconvolution algorithm, and namely statistics are detected; according to target false alarm probability pf, a detection threshold value tau is calculated by using MonteCarlo simulation under the condition that only noise exsits; finally (img file=' DDA0000463198220000012. TIF' wi=' 41' he=' 54' /) is compared with tau to judge whether a main base station sends signals or not. The accurate receiving power can be obtained through the received signals of the auxiliary base stations, and moreover the spectrum sensing performance can be improved effectively particularly under the condition of a low signal to noise ratio and small samples.

Description

cooperative spectrum sensing method based on free probability theory

Technical Field

The invention relates to the technical field of computer communication of cognitive radio spectrum sensing, in particular to a cooperative spectrum sensing method based on a free probability theory.

Background

Under the fixed spectrum allocation mode commonly adopted in all countries at present, the utilization rate of most authorized frequency bands is low, and great waste of wireless spectrum resources is caused. On the other hand, with the rapid development of the wireless communication industry, the available wireless spectrum resources are increasingly scarce. How to meet the explosive growth of wireless spectrum demand has become a common problem facing global mobile communications. Therefore, cognitive radio has received a great deal of attention in recent years from both academic and industrial fields as one of the effective ways to alleviate the problem of shortage of wireless spectrum resources. The basic idea of cognitive radio is spectrum multiplexing or spectrum sharing, which allows cognitive users to communicate using the primary user frequency band when the band is idle. In order to do this, the cognitive user needs to perform spectrum sensing frequently, that is, detect whether the master user is using the frequency band. Once the primary user reuses the frequency band, the cognitive user must detect the primary user with a high detection probability and quickly exit the frequency band within a specified time. The spectrum sensing technology is the core and the foundation of the cognitive radio technology and becomes a hot spot of current research. Currently, research in this field has been greatly advanced, and various research institutes or individuals have intensively studied it from various aspects of spectrum sensing, have preliminarily established a theoretical framework of spectrum sensing, and have been applied to corresponding international standards. For example, the IEEE802.22 standard is the first international standard that explicitly employs spectrum sensing, which specifies that fixed wireless local area networks and televisions operate in the same frequency band, and that idle television bands can be automatically detected and utilized to improve spectral efficiency.

The existing spectrum sensing method mainly includes Energy Detection (ED), Matched Filter Detection (MFD), Cyclostationary Feature Detection (CFD), interference temperature Detection, and various multi-node cooperation detections evolved from the foregoing. The multi-node cooperative detection is mainly used for overcoming the influence of wireless communication fading and shadow so as to prevent the hidden terminal problem. Recently, another scholars have proposed schemes based on Random Matrix Theory (RMT), such as MME algorithm. Unlike previous studies in this field, this type of scheme does not require knowledge of the noise statistics and variance, but only with respect to the maximum and minimum eigenvalues of the random matrix.

The spectrum sensing methods have advantages and disadvantages and applicable conditions, but have a problem that the performance of the spectrum sensing methods still cannot meet the practical requirement under the conditions of low signal-to-noise ratio and small samples. Therefore, finding a high-performance spectrum sensing method has become an urgent problem to be solved.

In the last 80 th century, under the pioneering work of Voiculescu, the free probability theory has developed into a complete research field. The free probability theory is an important branch of the random matrix theory, is a powerful tool for describing the asymptotic characteristic of the random matrix, establishes a strong relation between two random matrices and their sum or product matrices, and can be used for a digital communication system modeled by the random matrix. In recent years, it has been applied to the field of spectrum sensing to further improve performance at low signal-to-noise ratios, which essentially separates the true signal power matrix from the sample covariance matrix containing the signal and noise powers. The present invention can solve the above problems well.

Disclosure of Invention

The invention aims to provide a cooperative spectrum sensing method based on a free probability theory, which is suitable for an MIMO communication environment, can obtain accurate receiving power from a receiving signal of a secondary base station, and solves the problem of lower spectrum sensing performance under the conditions of low signal-to-noise ratio and small sample.

The technical scheme adopted by the invention for solving the technical problems is as follows: in fig. 1 of the model of the cooperative spectrum sensing system to which the present invention is directed, K secondary base stations BS distributed at different geographical locations₁,BS₂,…,BS_KAnd the cooperative sensing channel is used for judging whether the main base station is transmitting signals.The main base station and each secondary base station are respectively provided with N_tAnd N_rAnd antennas between which is a MIMO rayleigh fading channel. The cooperative spectrum sensing method based on the free probability theory comprises the following specific steps:

1. and sampling the received signals of the multiple antennas of each secondary base station, and performing centralized processing on the sampled signals. The sampling rate is 1/T_sThen the k-th receiver outputs a sampled signal at time n ofK is 1,2, …, K. The sampled signals collected at time n by all the receiving antennas are then

Wherein (·)^ΗRepresents a conjugate transpose;

2. according to the noise variance of all received sampling signals and channels, by means of the asymptotic free characteristic and Wishart distribution characteristic of the random matrix, KN is solved by adopting an algorithm based on free deconvolution_rAverage received signal power of each antenna

I.e., the detection statistics. The method comprises the following specific steps:

(1) inputting: receiving sampling signals { y (n), n ═ 1,2, …, M_SAnd channel noise variance σ². Wherein M is_SIs the total number of samples of the received signal;

(2) calculating a sample covariance matrix for a received sampled signal

And its eigenvalue { lambda_i,i＝1,2,…,KNr}；

(3) Computing

K order moment of

And

k order moment of

(4) Computing

The method comprises the following steps:

①

②

(5) computing

The method comprises the following steps:

①

<math> <mrow> <msubsup> <mi>α</mi> <mi>k</mi> <mi>ν</mi> </msubsup> <mo>=</mo> <mi>momcum</mi> <mrow> <mo>(</mo> <mo>{</mo> <msubsup> <mi>m</mi> <mi>k</mi> <mi>ν</mi> </msubsup> <mo>}</mo> <mo>)</mo> </mrow> </mrow> </math>

②

<math> <mrow> <msubsup> <mi>α</mi> <mi>k</mi> <msub> <mi>μ</mi> <mrow> <msup> <mi>σ</mi> <mn>2</mn> </msup> <mi>I</mi> </mrow> </msub> </msubsup> <mo>=</mo> <mi>momcum</mi> <mrow> <mo>(</mo> <mo>{</mo> <msup> <mrow> <mo>(</mo> <msup> <mi>σ</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mi>k</mi> </msup> <mo>}</mo> <mo>)</mo> </mrow> </mrow> </math>

③

④

<math> <mrow> <mo>{</mo> <msubsup> <mi>m</mi> <mi>k</mi> <mi>η</mi> </msubsup> <mo>}</mo> <mo>=</mo> <mi>cummom</mi> <mrow> <mo>(</mo> <mo>{</mo> <msubsup> <mi>α</mi> <mi>k</mi> <mi>η</mi> </msubsup> <mo>}</mo> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

(6) computingThe method comprises the following steps:

①

<math> <mrow> <mo>{</mo> <msub> <mi>ρ</mi> <mi>k</mi> </msub> <mo>}</mo> <mo>=</mo> <mi>momcum</mi> <mrow> <mo>(</mo> <mo>{</mo> <mfrac> <msub> <mi>KN</mi> <mi>r</mi> </msub> <msub> <mi>N</mi> <mi>t</mi> </msub> </mfrac> <mo>·</mo> <msubsup> <mi>m</mi> <mi>k</mi> <mi>η</mi> </msubsup> <mo>}</mo> <mo>)</mo> </mrow> </mrow> </math>

②

(7)

i.e. mu_PFirst moment of (d).

The symbol explanation in the above steps:

and

respectively representing free addition deconvolution operator and free multiplication in free probability theoryA normal deconvolution operator;

and mu_PRespectively represent matricesσ²The extreme probability distribution of I (I is the identity matrix) and P;and

correspond to

Law mu_cC taking respectively

And

the momcumm and cummomm are obtained according to a moment-cumulant formula of the distribution mu, the input of the momcumm is a moment sequence, the output of the momcumm is a cumulant sequence, the input of the cummomm is a cumulant sequence, and the output of the cummomm is a moment sequence.

3. According to target false alarm probability p_fThe detection threshold τ is calculated using Monte Carlo simulation in the presence of noise only. Step 2 is first performed to obtain noise samples only

After many such simulations, the calculation

Mean value of (theta)_PSum variance

Approximately satisfying a gaussian distribution. Then according to the target false alarm probability p_fCalculating a threshold τ = υ_PQ^-1(p_f)+θ_PWherein Q is^-1(. cndot.) is an inverse Q-function,

4. will be provided with

And tau, and determining whether the main base station is transmitting signals. When in useWhen the master base station is transmitting a signal; when in use

At this time, the main base station does not transmit a signal.

Has the advantages that:

1. in the MIMO communication environment, the invention adopts the algorithm based on free deconvolution to calculate the detection statistic, uses MonteCarlo simulation to obtain the detection threshold value, realizes the spectrum sensing, and can obtain accurate receiving power from the receiving signal of the secondary base station.

2. The invention can effectively improve the spectrum sensing performance, especially under the conditions of low signal-to-noise ratio and small samples.

Drawings

Fig. 1 is a diagram of a cooperative spectrum sensing system model according to the present invention.

FIG. 2 is a flow chart of the method of the present invention.

FIG. 3 is a graph of the results of Monte Carlo simulations in the presence of noise only

Is normalized to the histogram.

Fig. 4 is a diagram illustrating comparison of perceptual performance between the method of the present invention and a detection method based on feature values.

Detailed Description

The invention is described in further detail below with reference to the figures and examples.

Example 1

As shown in FIG. 1, K secondary base stations BS distributed at different geographical locations₁,BS₂,…,BS_KAnd the cooperative sensing channel is used for judging whether the main base station is transmitting signals. The main base station and each secondary base station are respectively provided with N_tAnd N_rAnd antennas between which is a MIMO rayleigh fading channel. When the main base station transmits signals, the sampling rate is 1/T_sThe sampled signal output by the kth receiver at time nCan be expressed as

y_{k} (n) = \sqrt{\frac{P_{k}}{N_{t}}} H_{k} s (n) + v_{k} (n), k = 1 . . . k - - - (1)

Wherein,

is a transmitted symbol vector at time n, the elements of which satisfy zero mean independent equal distribution, and the variance is 1;is a MIMO channel matrix between the transmitter and the kth receiver, whose elements are complex Gaussian variables with mean 0 and variance 1, i.e. obeying N_c(0,1)；P_kIs the received signal power of each antenna of the kth receiver;

is the complex gaussian noise vector at the kth receiver,

all secondary base stations perceive the same frequency band and their received signals are centrally processed. The following symbols are defined:

the received signal model (1) can also be written as

y (n) = P^{\frac{1}{2}} Hs (n) + v (n) - - - (2)

The spectrum sensing problem is therefore the following binary hypothesis testing problem

y (n) = \{\begin{matrix} v (n), & H_{0} \\ x (n) + v (n), & H_{1} \end{matrix} - - - (3)

Wherein

Η₀Denotes that no signal is sent by the main BS, h₁Indicating that the master BS is transmitting a signal. In the present invention, we propose a new spectrum sensing method based on the free probability theory, whose basic idea is to estimate the distribution of the elements of the diagonal matrix P, so that the average received signal power can be estimated

By mixing

H by comparison with a threshold value of τ₀H and H₁Make a decision in between, that is if

H is H₁Otherwise is H₀。

In this connection, it is possible to use,solving by free probability theory

Is a simple and easy method. The mathematical background of the free probability theory is:

let A_NIs an NxN-dimensional Hermitian matrix with only real eigenvalues, and the eigenvalue set is lambda_i(A_N) I 1,2, …, an empirical probability distribution over N of

Where 1 (-) is an indicator function. Of interest to us is the limiting spectral distribution μ at N → ∞_AIt is composed of

Unique description, where Ε [ · ] denotes expectation, tr (·) denotes the traces of the matrix.

In particular, if the elements of the N M matrix H satisfy a zero-mean independent homodistribution with a variance of 1/M, A is when N, M → ∞ and N/M → c_N＝HH^ΗLimit spectral distribution mu_cIs that

Law, its density function is

Wherein (z)⁺＝max{0,z}，

In particular, mu_cAn asymptotic eigenvalue distribution of the Wishart matrix is described, where the elements of H satisfy an independent homodistribution, subject to

If two random matrices A are given_N、B_NTheir limiting probability distributions are respectively μ_A、μ_BWe wish to be based on μ_AAnd mu_BObtaining A_N+B_NAnd A_NBN_{Is/are as follows}A limit probability distribution. To this end we introduce a concept similar to "independence" in classical probability theory, called "progressive freedom", to compute these distributions. When A is_NAnd B_NWhen the asymptotic free is satisfied, A_N+B_NCan be determined from the limiting probability distribution of_AAnd mu_BIs obtained by free addition convolution, expressed as

A_NB_NCan be determined from the limiting probability distribution of_AAnd mu_BIs obtained by free multiplicative convolution, denoted asIn other words, when A_NAnd B_NWhen the asymptotic free is satisfied, A_N+B_NAnd A_NB_NCan be represented by A_NAnd B_NThe moment of (2) is obtained.

Both the free-add and multiplicative convolutions are interchangeable, i.e.

And

and defineDeconvoluted for free addition, i.e. if

Then

Analogously, defineDeconvolution for free multiplication, i.e. if

Then

A_NAnd B_NThe conditions for meeting the asymptotic freedom are very abstract. However, we know that two independent co-distributed gaussian matrices, two independent co-distributed Hermitian matrices, one independent co-distributed gaussian or Hermitian matrix and one definite diagonal matrix are asymptotically free.

Then, using free probability theory to solve

The specific theoretical basis and method are as follows:

A. limit distribution mu of the power matrix P_P

Suppose M_SSamples y (1), …, y (M) of a received signal_S) For sensing the spectrum. The covariance matrix of the samples of the received signal is

When the master base station is transmitting, there is y (n) ═ x (n) + v (n). The sample covariance matrix of the signal components x (n) is

For the signal-Gaussian noise model, the two sample covariance matrices are described above using free probability theory

Andsatisfies the following equation

Wherein

c = \frac{{KN}_{r}}{M_{S}} - - - (11)

On the other hand, the covariance matrix of the signal components x (n) obtained from equation (4) is

Definition of

Z is KN_r×M_SDimension matrix with elements satisfying zero mean value independent distribution and variance of 1/M_S. Obtained by using formula (9)

Or

I.e., Wishart distribution characteristics. It is noteworthy that ZZ^ΗThe elements of (1) satisfy zero mean value independent same distribution, and the variance is 1; HH (Hilbert-Huang) with high hydrogen storage capacity^ΗThe Wishart matrix has elements meeting zero mean value independent same distribution and variance of 1. Thus is in

Their corresponding limit distributions under the law are

Andfrom formulae (12) and (13), we obtain

Substituting equation (14) into equation (10) yields a limit distribution of the signal power matrix P of

B、μ_PNumerical calculation process of

In the formula (15), the reaction mixture is,μ_Pincludes an

Free-add deconvolution of

Law mu_cBoth of which can be efficiently implemented by the moment-cumulant method described below.

1) Calculation and

free-addition deconvolution of (c): the R-transform of the probability distribution μ is defined as

WhereinIs the nth order cumulative amount of μ. The importance of R-transform is due to the additive nature of free-add convolution, i.e.

Equivalent to the cumulative amount being additive under free-add convolution, i.e.

The moments and the cumulative quantities of the distribution μ are related as follows:

wherein coef_n(. represents z)ⁿThe coefficient of (a). From equation (19), we can derive the cumulative quantity sequence

Obtaining a sequence of moments

And vice versa. Defining a function momcum, taking a moment sequence as an input quantity and taking a cumulant sequence as an output quantity; the function cummom takes the cumulant series as input and the moment series as output.

To obtain

First, we calculate the sample covariance matrix in equation (8)

Characteristic value of

Then calculating the moment

On the other hand, σ²The characteristic values of I are all sigma². Thus, it is possible to provide

Has a moment of

2) Calculation of the sum of_cDeconvolution by free multiplication of (1):

and mu_AThe moments of (c) have the following relationship:

wherein

Comparing equations (22) and (19) shows that equation (22) is a moment-cumulant equation, except that the cumulant is represented by

Alternative, moment isAnd (6) replacing. Thus, using the function momcum, the input is

The corresponding output is

To calculate

The moment of (c).

After performing the free multiplication and addition deconvolution in equation (15), we get μ_PMoment of

As mentioned earlier, the decision rule for spectrum sensing is based on the average received power

Is estimated, i.e. mu_PA first moment of (i.e.

Thus, we can conclude that the computation is based on free deconvolution

Comprises the following steps:

(1) inputting: receiving sampling signals { y (n), n ═ 1,2, …, M_SAnd channel noise variance σ²；

(2) Calculating the sample covariance matrix in equation (8)

And its eigenvalue { lambda_i,i＝1,2,…,KN_r}；

(3) Calculating moments in equation (20)And moments in formula (21)

(4) Computing

The method comprises the following steps:

①

②

(5) computing

The method comprises the following steps:

①

②

③

④

(6) computing

The method comprises the following steps:

①

②

(7)

next, for the selection of the detection threshold τ, it is common to satisfy the target false alarm probability p_fThat is to say

But in H₀In this case, the result of the algorithm based on free deconvolution introduced above

There is no analytical expression for the probability distribution. We then used Monte Carlo simulations to obtain H₀Under the circumstances

As shown in fig. 3, the validated histogram approximates a gaussian distribution. Thus, in the case of only noise samples, we can use the estimated noise variance and perform a free deconvolution-based algorithm to obtainWe run many such simulations and then compute themMean value of (theta)_PSum variance

To obtain

Then the target false alarm probability p_fHas a detection threshold of

τ=υ_PQ^-1(p_f)+θ_P(23) Wherein Q^-1(. cndot.) is an inverse Q-function,

finally, will

And tau, and determining whether the main base station is transmitting signals. When in use

When the master base station is transmitting a signal; when in use

At this time, the main base station does not transmit a signal.

To better describe the effect of the present invention, it will be further demonstrated by the following simulation examples:

1. simulation parameter setting

A MIMO Rayleigh fading channel is arranged between the main base station and each secondary base station. The secondary base stations are distributed over different geographical locations, so P_kAre different from each other. Further averaging

Wherein

2. Simulation method

The existing detection method based on characteristic values and the method of the invention.

Introduction of a detection method based on a characteristic value: eigenvalue based detection methods do not require noise variance and utilize the asymptotic property of the maximum to minimum eigenvalue ratio of the sample covariance matrix. Specifically, it first calculates the sample covariance matrix in equation (8)

And its characteristic valueThen compare

And threshold τ_EVIf, if

Then is H₁Otherwise is H₀. The threshold value is calculated by the formula

Wherein

Is an inverse Tracy-Widom second cumulative distribution function. In our simulation

3. Simulation result

As shown in fig. 4, the method of the present invention compares the spectrum sensing performance with the detection method based on the feature value. It can be seen that the performance of the inventive method is superior to the eigenvalue based method at all SNR values and total number of samples, especially at low signal-to-noise ratios and small samples.

Example 2

As shown in fig. 2, the present invention provides a cooperative spectrum sensing method based on the free probability theory, which is suitable for the MIMO communication environment, and specifically includes the following steps:

step 1: sampling received signals of a plurality of antennas of each secondary base station, and carrying out centralized processing on the sampled signals;

step 2: solving the average received signal power of all receiving antennas by adopting an algorithm based on free deconvolution by means of the asymptotic free characteristic and the Wishart distribution characteristic of a random matrix according to the noise variance of all the received sampling signals and channels

I.e., the detection statistic;

and step 3: according to target false alarm probability p_fCalculating a detection threshold tau under the condition that only noise exists by applying Monte Carlo simulation;

and 4, step 4: will be provided with

At this time, the main base station does not transmit a signal.

Step 1 in the method of the present invention comprises:

k secondary base stations BS distributed in different geographical positions₁,BS₂,…,BS_KAnd the cooperative sensing channel is used for judging whether the main base station is transmitting signals. The main base station and each secondary base station are respectively provided with N_tAnd N_rAnd antennas between which is a MIMO rayleigh fading channel. The sampling rate is 1/T_sThen the k-th receiver outputs a sampled signal at time n of

K is 1,2, …, K. The sampled signals collected at time n by all the receiving antennas are then

Wherein (·)^ΗRepresenting a conjugate transpose.

Step 2 in the method of the invention comprises:

(2) calculating a sample covariance matrix for a received sampled signal

And its eigenvalue { lambda_i,i＝1,2,…,KN_r}；

(3) Computing

K order moment of

And

k order moment of

(4) Computing

The method comprises the following steps:

①

②

(5) computing

The method comprises the following steps:

①

②

③

④

(6) computing

The method comprises the following steps:

①

②

(7)

i.e. mu_PFirst moment of (d).

The symbol explanation in the above steps:

and

respectively representing a free addition deconvolution operator and a free multiplication deconvolution operator in a free probability theory;

and mu_PRespectively represent matrices

σ²The extreme probability distribution of I (I is the identity matrix) and P;

and

correspond toLaw mu_cC taking respectively

And

Step 3 in the method of the present invention comprises:

step 2 is first performed to obtain noise samples only

After many such simulations, the calculation

Mean value of (theta)_PSum variance

Claims

1. A cooperative spectrum sensing method based on a free probability theory is characterized by comprising the following steps:

I.e., the detection statistic;

and 4, step 4: will be provided withComparing with tau to judge whether the main base station is transmitting signal; when in use

When the master base station is transmitting a signal; when in use

At this time, the main base station does not transmit a signal.

2. The cooperative spectrum sensing method based on the free probability theory as claimed in claim 1, wherein step 1 of the method comprises:

k secondary base stations BS distributed in different geographical positions₁,BS₂,…,BS_KThe cooperative sensing channel is used for judging whether the main base station is transmitting signals; the main base station and each secondary base station are respectively provided with N_tAnd N_rAntennas between which is a MIMO rayleigh fading channel; the sampling rate is 1/T_sThen the k-th receiver outputs a sampled signal at time n of

K is 1,2, …, K; the sampled signals collected at time n by all the receiving antennas are thenWherein (·)^ΗRepresenting a conjugate transpose.

3. The cooperative spectrum sensing method based on the free probability theory as claimed in claim 1, wherein step 2 of the method comprises:

(1) inputting: receiving sampling signals { y (n), n ═ 1,2, …, M_SAnd channel noise variance σ²Wherein M is_SIs the total number of samples of the received signal;

(2) calculating a sample covariance matrix for a received sampled signal

And its eigenvalue { lambda_i,i＝1,2,…,KN_r}；

(3) Computing

K order moment ofAnd

k order moment of

(4) Computing

The method comprises the following steps:

①

②

(5) computing

The method comprises the following steps:

①

②

③

④

(6) computingThe method comprises the following steps:

①

②

(7)

i.e. mu_PThe first moment of (d);

the symbol explanation in the above steps:

and

and mu_PRespectively represent matrices

σ²The extreme probability distribution of I (I is the identity matrix) and P;

and

correspond to

Law mu_cC taking respectively

And

momcumm and cummomm are obtained according to a moment-cumulant formula of distribution mu, the input of momcumm is a moment sequence, the output is a cumulant sequence, the input of cummomm is a cumulant sequence, and the output isIs a sequence of moments.

4. The cooperative spectrum sensing method based on the free probability theory as claimed in claim 1, wherein step 3 of the method comprises:

step 2 is first performed to obtain noise samples only

After many such simulations, the calculation

Mean value of (theta)_PSum varianceApproximately satisfying a Gaussian distribution, and then based on a target false alarm probability p_fCalculating a threshold τ = υ_PQ^-1(p_f)+θ_PWherein Q is^-1(. cndot.) is an inverse Q-function,

5. the cooperative spectrum sensing method based on the free probability theory as claimed in claim 1, wherein: the method is applicable to a MIMO communication environment.