CN103795481A - Cooperative spectrum sensing method based on free probability theory - Google Patents

Cooperative spectrum sensing method based on free probability theory Download PDF

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CN103795481A
CN103795481A CN201410042029.6A CN201410042029A CN103795481A CN 103795481 A CN103795481 A CN 103795481A CN 201410042029 A CN201410042029 A CN 201410042029A CN 103795481 A CN103795481 A CN 103795481A
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王磊
薛海涛
周亮
郑宝玉
孟庆民
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Nanjing Post and Telecommunication University
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Abstract

本发明公开了一种基于自由概率理论的协作频谱感知方法,该方法适用于MIMO通信环境,首先对各个次基站的多个天线的接收信号进行采样,采样信号将进行集中处理;接着根据所有接收采样信号和信道的噪声方差,借助于随机矩阵的渐近自由特性和Wishart分布特性,采用基于自由解卷积的算法求解所有接收天线的平均接收信号功率也就是检测统计量;然后依据目标虚警概率pf,运用Monte Carlo仿真在仅有噪声存在的情况下计算检测阈值τ;最后将和τ进行比较,判断主基站是否在发送信号。该发明能够从次基站的接收信号中获得准确的接收功率,而且可以有效地提高频谱感知性能,尤其是在低信噪比和小样本情况下。

The invention discloses a cooperative spectrum sensing method based on free probability theory. The method is suitable for MIMO communication environment. Firstly, the received signals of multiple antennas of each secondary base station are sampled, and the sampled signals are processed centrally; then, according to all received The noise variance of the sampling signal and the channel, with the help of the asymptotic free characteristics of the random matrix and the Wishart distribution characteristics, uses the algorithm based on free deconvolution to solve the average received signal power of all receiving antennas That is, the detection statistic; then, according to the target false alarm probability p f , use Monte Carlo simulation to calculate the detection threshold τ under the condition that only noise exists; finally, the Compared with τ, it is judged whether the main base station is sending a signal. The invention can obtain accurate received power from the received signal of the secondary base station, and can effectively improve the spectrum sensing performance, especially in the case of low signal-to-noise ratio and small sample.

Description

一种基于自由概率理论的协作频谱感知方法A Cooperative Spectrum Sensing Method Based on Free Probability Theory

技术领域technical field

本发明涉及认知无线电频谱感知的计算机通信技术领域,特别涉及一种基于自由概率理论的协作频谱感知方法。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 free probability theory.

背景技术Background technique

在目前各国普遍采用的频谱固定分配方式下,大部分授权频段使用率很低,已造成无线频谱资源的很大浪费。而另一方面,随着无线通信产业的快速发展,可用无线频谱资源日益匮乏。如何满足爆炸式增长的无线频谱需求已成为全球移动通信面临的一个共同问题。因此,认知无线电作为缓解无线频谱资源紧缺问题的有效途径之一,近些年来受到了学术界和产业界广泛关注。认知无线电的基本思想是频谱复用或频谱共享,它允许认知用户在主用户频段空闲时,利用该频段通信。为了做到这一点,认知用户需要频繁地进行频谱感知,即检测主用户是否正在使用该频段。一旦主用户重新使用该频段,认知用户必须以很高的检测概率检测到主用户,并在规定的时间内迅速退出该频段。频谱感知技术作为认知无线电技术的核心和基础,成为当前研究的热点。目前,该领域的研究已经取得了较大的进展,各个研究机构或个人从频谱感知的多个方面对其进行了深入的研究,初步建立了频谱感知的理论框架,且已经应用到相应的国际标准中。如IEEE802.22标准是第一个明确采用频谱感知的国际标准,它规定固定无线区域网络和电视工作于相同的频段,可自动检测和利用空闲的电视频段,以提高频谱效率。Under the current spectrum fixed allocation method commonly adopted by various countries, the utilization rate of most licensed frequency bands is very low, which has caused a great waste of wireless spectrum resources. On the other hand, with the rapid development of the wireless communication industry, available wireless spectrum resources are increasingly scarce. How to meet the explosive growth of wireless spectrum demand has become a common problem faced by global mobile communications. Therefore, cognitive radio, as one of the effective ways to alleviate the shortage of wireless spectrum resources, has attracted extensive attention from academia and industry in recent years. The basic idea of cognitive radio is spectrum reuse or spectrum sharing, which allows cognitive users to use the frequency band for communication when the primary user frequency band is idle. In order to do this, cognitive users need to frequently perform spectrum sensing, that is, to detect whether the primary user is using the frequency band. Once the primary user re-uses the frequency band, the cognitive user must detect the primary user with a high detection probability and exit the frequency band quickly within a specified time. As the core and basis of cognitive radio technology, spectrum sensing technology has become a hot research topic. At present, research in this field has made great progress. Various research institutions or individuals have conducted in-depth research on spectrum sensing from multiple aspects, and initially established a theoretical framework for spectrum sensing, which has been applied to the corresponding international standard. For example, the IEEE802.22 standard is the first international standard that explicitly adopts spectrum sensing. It stipulates that fixed wireless area networks and TVs work in the same frequency band, and can automatically detect and utilize idle TV bands to improve spectrum efficiency.

现有的频谱感知方法主要有能量检测(Energy Detection,ED)、匹配滤波检测(MatchedFilter Detection,MFD)、循环平稳特征检测(Cyclostationary Feature Detection,CFD)、干扰温度检测等以及由此演变而来的各种多节点协作检测。采用多节点协作检测主要是为了克服无线通信衰落和阴影的影响,以防出现隐终端问题。最近,又有学者提出了基于随机矩阵理论(Random Matrix Theory,RMT)的方案,如MME算法。与该领域先前的研究不同,这类方案不需要知道噪声统计量和方差,仅仅与随机矩阵的最大和最小特征值有关。The existing spectrum sensing methods mainly include energy detection (Energy Detection, ED), matched filter detection (Matched Filter Detection, MFD), cyclostationary feature detection (Cyclostationary Feature Detection, CFD), interference temperature detection, etc. Various multi-node cooperative detection. The main purpose of using multi-node cooperative detection is to overcome the influence of wireless communication fading and shadows, and to prevent hidden terminal problems. Recently, some scholars have proposed a scheme based on Random Matrix Theory (RMT), such as the MME algorithm. Unlike previous work in this area, such schemes do not require knowledge of the noise statistics and variance, only the largest and smallest eigenvalues of the random matrix.

上述频谱感知方法各有优缺点和适用条件,但是共同存在一个问题,即在低信噪比和小样本的情况下,它们的性能仍不能满足实际需求。因此,寻找一种高性能频谱感知方法已经成为一个亟待解决的问题。The above spectrum sensing methods have their own advantages and disadvantages and applicable conditions, but there is a problem in common, that is, their performance cannot meet the actual needs in the case 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.

上世纪80年代,在Voiculescu的开创性工作下,自由概率理论已发展成为一个完整的研究领域。自由概率理论作为随机矩阵理论的一个重要分支,是描述随机矩阵渐近特性的有力工具,在两个随机矩阵与它们的和或乘积矩阵之间建立了强大的联系,可以用于以随机矩阵建模的数字通信系统。近年来,它被运用到频谱感知领域,以进一步提高在低信噪比情况下的性能,其实质上是从包含信号和噪声功率的样本协方差矩阵中分离出真正的信号功率矩阵。而本发明能够很好地解决上面的问题。In the 1980s, under the pioneering work of Voiculescu, free probability theory developed into an entire research field. As an important branch of random matrix theory, free probability theory is a powerful tool to describe the asymptotic properties of random matrices. It establishes a strong connection between two random matrices and their sum or product matrices, which can be used to construct Modular digital communication system. In recent years, it has been applied to the field of spectrum sensing to further improve the performance in the case of low signal-to-noise ratio, which essentially separates the real signal power matrix from the sample covariance matrix containing signal and noise power. And the present invention can well solve the above problems.

发明内容Contents of the invention

本发明目的在于提供一种基于自由概率理论的协作频谱感知方法,该方法适用于MIMO通信环境,能够从次基站的接收信号中获得准确的接收功率,并且解决在低信噪比和小样本情况下频谱感知性能较低的问题。The purpose of the present invention is to provide a cooperative spectrum sensing method based on free probability theory, which is suitable for MIMO communication environment, can obtain accurate received power from the received signal of the secondary base station, and solve the problem of low signal-to-noise ratio and small sample The problem of low spectrum sensing performance.

本发明解决其技术问题所采取的技术方案是:在本发明所针对的协作频谱感知系统模型的图1中,K个分布在不同地理位置上的次基站BS1,BS2,…,BSK协作感知信道,判断主基站是否在发送信号。主基站和每个次基站分别配备Nt和Nr个天线,在它们之间是MIMO瑞利衰落信道。基于自由概率理论的协作频谱感知方法的具体步骤为:The technical solution adopted by the present invention to solve the technical problem is: in Fig. 1 of the cooperative spectrum sensing system model targeted by the present invention, K secondary base stations BS 1 , BS 2 ,..., BS K distributed in different geographic locations Cooperate to sense the channel, and judge whether the main base station is sending a signal. The primary base station and each secondary base station are equipped with N t and N r antennas respectively, and there is a MIMO Rayleigh fading channel between them. The specific steps of the collaborative spectrum sensing method based on free probability theory are as follows:

1、对各个次基站的多个天线的接收信号进行采样,采样信号将进行集中处理。采样速率为1/Ts,则第k个接收机在时刻n输出的采样信号为k=1,2,…,K。那么所有接收天线在时刻n集中起来的采样信号为

Figure BDA0000463198200000022
其中(·)Η表示共轭转置;1. The received signals of multiple antennas of each sub-base station are sampled, and the sampled signals are processed centrally. The sampling rate is 1/T s , then the sampling signal output by the kth receiver at time n is k=1,2,...,K. Then the sampled signal collected by all receiving antennas at time n is
Figure BDA0000463198200000022
Wherein ( ) Η represents conjugated transposition;

2、根据所有接收采样信号和信道的噪声方差,借助于随机矩阵的渐近自由特性和Wishart分布特性,采用基于自由解卷积的算法求解KNr个天线的平均接收信号功率

Figure BDA0000463198200000029
也就是检测统计量。具体步骤为:2. According to the noise variance of all received sampling signals and channels, with the help of the asymptotic free characteristics of the random matrix and the Wishart distribution characteristics, an algorithm based on free deconvolution is used to solve the average received signal power of KN r antennas
Figure BDA0000463198200000029
That is the detection statistic. The specific steps are:

(1)输入:接收采样信号{y(n),n=1,2,…,MS}和信道噪声方差σ2。其中MS为接收信号的总样本数;(1) Input: receive sampling signals {y(n), n=1, 2, ..., M S } and channel noise variance σ 2 . Where M S is the total number of samples of the received signal;

(2)计算接收采样信号的样本协方差矩阵

Figure BDA0000463198200000023
和它的特征值{λi,i=1,2,…,KNr};(2) Calculate the sample covariance matrix of the received sampling signal
Figure BDA0000463198200000023
And its eigenvalue {λ i , i=1,2,...,KNr};

(3)计算

Figure BDA00004631982000000210
的k阶矩
Figure BDA0000463198200000024
Figure BDA0000463198200000025
的k阶矩
Figure BDA0000463198200000026
(3) calculation
Figure BDA00004631982000000210
k-order moment
Figure BDA0000463198200000024
and
Figure BDA0000463198200000025
k-order moment
Figure BDA0000463198200000026

(4)计算

Figure BDA0000463198200000027
步骤如下:(4) calculation
Figure BDA0000463198200000027
Proceed as follows:

Figure BDA0000463198200000028
Figure BDA0000463198200000028

{ m k ν = γ k / ( KN r M S ) } ; { m k ν = γ k / ( KN r m S ) } ;

(5)计算

Figure BDA0000463198200000032
步骤如下:(5) calculation
Figure BDA0000463198200000032
Proceed as follows:

α k ν = momcum ( { m k ν } ) α k ν = mom cum ( { m k ν } )

α k μ σ 2 I = momcum ( { ( σ 2 ) k } ) α k μ σ 2 I = mom cum ( { ( σ 2 ) k } )

{ α k η = α k ν - α k μ σ 2 I } { α k η = α k ν - α k μ σ 2 I }

{ m k η } = cummom ( { α k η } ) ; { m k η } = cummom ( { α k η } ) ;

(6)计算步骤如下:(6) calculation Proceed as follows:

{ ρ k } = momcum ( { KN r N t · m k η } ) { ρ k } = mom cum ( { KN r N t · m k η } )

{ m k P = ρ k / ( KN r N t ) } ; { m k P = ρ k / ( KN r N t ) } ;

(7)

Figure BDA00004631982000000310
也就是μP的一阶矩。(7)
Figure BDA00004631982000000310
That is, the first moment of μ P.

上述步骤里的符号解释:

Figure BDA00004631982000000311
Figure BDA00004631982000000312
分别表示自由概率理论中的自由加法解卷积算子和自由乘法解卷积算子;
Figure BDA00004631982000000327
和μP分别表示矩阵σ2I(I为单位矩阵)和P的极限概率分布;
Figure BDA00004631982000000315
对应于
Figure BDA00004631982000000316
律μc,c分别取
Figure BDA00004631982000000317
Figure BDA00004631982000000318
momcum和cummom是根据分布μ的矩-累积量公式得到的,momcum的输入为矩序列,输出为累积量序列,cummom的输入为累积量序列,输出为矩序列。Explanation of symbols in the above steps:
Figure BDA00004631982000000311
and
Figure BDA00004631982000000312
represent the free additive deconvolution operator and the free multiplicative deconvolution operator in the free probability theory, respectively;
Figure BDA00004631982000000327
and μ P respectively denote the matrix σ 2 I (I is the identity matrix) and the limiting probability distribution of P; and
Figure BDA00004631982000000315
corresponds to
Figure BDA00004631982000000316
Law μ c , c respectively take
Figure BDA00004631982000000317
and
Figure BDA00004631982000000318
Momcum and cummom are obtained according to the moment-cumulant formula of the distribution μ. The input of momcum is a moment sequence and the output is a cumulant sequence, and the input of cummom is a cumulant sequence and the output is a moment sequence.

3、依据目标虚警概率pf,运用Monte Carlo仿真在仅有噪声存在的情况下计算检测阈值τ。首先在只有噪声样本的情况下执行步骤2来获得

Figure BDA00004631982000000319
经过很多次这样的仿真后计算
Figure BDA00004631982000000320
的均值θP和方差
Figure BDA00004631982000000321
近似满足高斯分布。然后依据目标虚警概率pf,计算阈值τ=υPQ-1(pf)+θP,其中Q-1(·)为逆Q-函数, 3. According to the target false alarm probability p f , Monte Carlo simulation is used to calculate the detection threshold τ under the condition that only noise exists. First perform step 2 with only noise samples to obtain
Figure BDA00004631982000000319
After many such simulations, the calculation
Figure BDA00004631982000000320
The mean θ P and variance of
Figure BDA00004631982000000321
approximately satisfy a Gaussian distribution. Then according to the target false alarm probability p f , calculate the threshold τ=υ P Q -1 (p f )+θ P , where Q -1 (·) is the inverse Q-function,

4、将

Figure BDA00004631982000000324
和τ进行比较,判断主基站是否在发送信号。当时,主基站在发送信号;当
Figure BDA00004631982000000326
时,主基站没有发送信号。4. will
Figure BDA00004631982000000324
Compared with τ, it is judged whether the main base station is sending a signal. when When , the master base station is sending signals; when
Figure BDA00004631982000000326
, the main base station does not send a signal.

有益效果:Beneficial effect:

1、本发明在MIMO通信环境下,采用基于自由解卷积的算法计算检测统计量,使用MonteCarlo仿真获得检测阈值,实现频谱感知,并且能够从次基站的接收信号中获得准确的接收功率。1. In the MIMO communication environment, the present invention uses an algorithm based on free deconvolution to calculate detection statistics, uses Monte Carlo simulation to obtain detection thresholds, realizes spectrum sensing, and can obtain accurate received power from received signals of secondary base stations.

2、本发明可以有效地提高频谱感知性能,尤其是在低信噪比和小样本情况下。2. The present invention can effectively improve the performance of spectrum perception, especially in the case of low signal-to-noise ratio and small samples.

附图说明Description of drawings

图1为本发明的协作频谱感知系统模型图。FIG. 1 is a model diagram of the cooperative spectrum sensing system of the present invention.

图2为本发明的方法流程图。Fig. 2 is a flow chart of the method of the present invention.

图3为运用Monte Carlo仿真在仅有噪声存在的情况下得到的

Figure BDA0000463198200000048
的归一化直方图。Figure 3 is obtained by using Monte Carlo simulation in the presence of only noise
Figure BDA0000463198200000048
The normalized histogram of .

图4为本发明的方法和基于特征值的检测方法的感知性能比较示意图。FIG. 4 is a schematic diagram of the comparison of perceptual performance between the method of the present invention and the detection method based on eigenvalues.

具体实施方式Detailed ways

下面结合附图和实施例对本发明作进一步详细描述。The present invention will be described in further detail below in conjunction with the accompanying drawings and embodiments.

实施例1Example 1

如图1所示,K个分布在不同地理位置上的次基站BS1,BS2,…,BSK协作感知信道,判断主基站是否在发送信号。主基站和每个次基站分别配备Nt和Nr个天线,在它们之间是MIMO瑞利衰落信道。当主基站发送信号时,采样速率为1/Ts,则第k个接收机在时刻n输出的采样信号可表示为As shown in FIG. 1 , K secondary base stations BS 1 , BS 2 , ..., BS K distributed in different geographical locations cooperate to sense the channel, and judge whether the primary base station is sending signals. The primary base station and each secondary base station are equipped with N t and N r antennas respectively, and there is a MIMO Rayleigh fading channel between them. When the main base station sends a signal, the sampling rate is 1/T s , then the sampling signal output by the kth receiver at time n can be expressed as

ythe y kk (( nno )) == PP kk NN tt Hh kk sthe s (( nno )) ++ vv kk (( nno )) ,, kk == 11 .. .. .. kk -- -- -- (( 11 ))

其中,

Figure BDA0000463198200000043
是在时刻n的发送符号矢量,其元素满足零均值独立同分布,方差为1;是在发射机和第k个接收机之间的MIMO信道矩阵,它的元素是均值为0,方差为1的复高斯变量,即服从Nc(0,1);Pk是第k个接收机的每个天线的接收信号功率;
Figure BDA0000463198200000045
是在第k个接收机上的复高斯噪声矢量,
Figure BDA0000463198200000046
in,
Figure BDA0000463198200000043
is the transmitted symbol vector at time n, whose elements satisfy the zero-mean independent and identical distribution, and the variance is 1; Is the MIMO channel matrix between the transmitter and the kth receiver, and its elements are complex Gaussian variables with mean value 0 and variance 1, that is, subject to N c (0,1); P k is the kth receiver The received signal power of each antenna of the machine;
Figure BDA0000463198200000045
is the complex Gaussian noise vector at the kth receiver,
Figure BDA0000463198200000046

所有次基站感知相同的频带,它们的接收信号进行集中处理。定义下列符号:All secondary base stations sense the same frequency band and their received signals are processed collectively. Define the following symbols:

Figure BDA0000463198200000047
Figure BDA0000463198200000047

Figure BDA0000463198200000051
Figure BDA0000463198200000051

Figure BDA0000463198200000052
Figure BDA0000463198200000052

Figure BDA0000463198200000053
Figure BDA0000463198200000053

接收信号模型(1)也可以写成The received signal model (1) can also be written as

ythe y (( nno )) == PP 11 22 HsHs (( nno )) ++ vv (( nno )) -- -- -- (( 22 ))

因此频谱感知问题就是下列二元假设检验问题The spectrum sensing problem is therefore the following binary hypothesis testing problem

ythe y (( nno )) == vv (( nno )) ,, Hh 00 xx (( nno )) ++ vv (( nno )) ,, Hh 11 -- -- -- (( 33 ))

其中in

xx (( nno )) == ΔΔ PP 11 22 HsHs (( nno )) -- -- -- (( 44 ))

Η0表示主BS没有发送信号,Η1表示主BS在发送信号。在本发明中,我们提出一种基于自由概率理论的新频谱感知方法,其基本思想是估计对角矩阵P的元素的分布,从而可以估计平均接收信号功率

Figure BDA0000463198200000057
通过将
Figure BDA0000463198200000058
与阈值τ进行比较,在Η0和Η1之间做出判决,也就是如果
Figure BDA0000463198200000059
为Η1,否则为Η0。H 0 means that the master BS is not sending a signal, and H 1 means that the master BS is sending a signal. In this invention, we propose a new spectrum sensing method based on free probability theory, the basic idea of which is to estimate the distribution of the elements of the diagonal matrix P, so that the average received signal power can be estimated
Figure BDA0000463198200000057
by putting
Figure BDA0000463198200000058
Compared with the threshold τ, a decision is made between H 0 and H 1 , that is, if
Figure BDA0000463198200000059
is H 1 , otherwise it is H 0 .

在这里,用自由概率理论求解

Figure BDA00004631982000000510
是一种简单易行的办法。自由概率理论的数学背景为:Here, using free probability theory to solve
Figure BDA00004631982000000510
It is a simple and easy way. The mathematical background of free probability theory is:

令AN为只有实特征值的N×N维Hermitian矩阵,在它的特征值集合λi(AN),i=1,2,…,N上的经验概率分布为Let A N be an N×N-dimensional Hermitian matrix with only real eigenvalues, and the empirical probability distribution on its eigenvalue set λ i (A N ), i=1,2,...,N is

μμ AA NN (( xx )) == 11 NN ΣΣ ii == 11 NN 11 (( λλ ii (( AA NN )) ≤≤ xx )) -- -- -- (( 55 ))

其中1(·)是指示函数。我们感兴趣的是在N→∞时的极限谱分布μA,它由矩where 1(·) is an indicator function. We are interested in the limiting spectral distribution μ A at N→∞, which is given by the moment

唯一描述,其中Ε[·]表示期望,tr(·)表示矩阵的迹。Unique description, where Ε[·] represents the expectation, and tr(·) represents the trace of the matrix.

特别地,如果N×M矩阵H的元素满足零均值独立同分布,方差为1/M,则当N,M→∞且N/M→c时,AN=HHΗ的极限谱分布μc

Figure BDA0000463198200000062
律,它的密度函数为In particular, if the elements of the N×M matrix H satisfy the zero-mean independent and identical distribution, and the variance is 1/M, then when N,M→∞ and N/M→c, A N =HH H 's limiting spectral distribution μ c yes
Figure BDA0000463198200000062
law, its density function is

ff μμ cc (( xx )) == (( 11 -- 11 cc )) ++ δδ (( xx )) ++ 11 22 πcxπcx (( xx -- aa )) ++ (( bb -- xx )) ++ -- -- -- (( 77 ))

其中(z)+=max{0,z},

Figure BDA0000463198200000064
Figure BDA0000463198200000065
特别地,μc描述了Wishart矩阵的渐近特征值分布,这里H的元素满足独立同分布,服从于
Figure BDA0000463198200000066
where (z) + = max{0,z},
Figure BDA0000463198200000064
Figure BDA0000463198200000065
In particular, μ c describes the asymptotic eigenvalue distribution of the Wishart matrix, where the elements of H satisfy independent and identical distribution, obeying
Figure BDA0000463198200000066

若给定两个随机矩阵AN、BN,它们的极限概率分布分别为μA、μB,我们希望根据μA和μB获得AN+BN和ANBN极限概率分布。为此我们引入一个类似于经典概率论中“独立”的概念,称之为“渐进自由”,来计算这些分布。当AN和BN满足渐近自由时,AN+BN的极限概率分布可由μA与μB的自由加法卷积得到,表示为

Figure BDA0000463198200000067
ANBN的极限概率分布可由μA与μB的自由乘法卷积得到,表示为换句话说,当AN和BN满足渐近自由时,AN+BN和ANBN的矩可由AN和BN的矩求得。If two random matrices A N and B N are given, and their limit probability distributions are μ A and μ B respectively, we hope to obtain the limit probability distributions of A N + B N and A N BN according to μ A and μ B. To this end, we introduce a concept similar to "independence" in classical probability theory, called "asymptotic freedom", to calculate these distributions. When A N and B N satisfy asymptotic freedom, the limit probability distribution of A N + B N can be obtained by the free additive convolution of μ A and μ B , expressed as
Figure BDA0000463198200000067
The limit probability distribution of A N B N can be obtained by the free multiplication convolution of μ A and μ B , expressed as In other words, when A N and B N satisfy asymptotic freedom, the moments of A N + B N and A N B N can be obtained from the moments of A N and B N.

自由加法和乘法卷积都是可交换的,也就是

Figure BDA0000463198200000069
Figure BDA00004631982000000610
并且定义为自由加法解卷积,即如果
Figure BDA00004631982000000612
那么
Figure BDA00004631982000000613
类似地,定义为自由乘法解卷积,即如果
Figure BDA00004631982000000615
那么
Figure BDA00004631982000000616
Both free additive and multiplicative convolutions are commutative, that is,
Figure BDA0000463198200000069
and
Figure BDA00004631982000000610
and define Deconvolution for free addition, i.e. if
Figure BDA00004631982000000612
So
Figure BDA00004631982000000613
Similarly, define deconvolution for free multiplication, that is, if
Figure BDA00004631982000000615
So
Figure BDA00004631982000000616

AN和BN满足渐近自由的条件是非常抽象的。但是,我们知道两个独立同分布高斯矩阵、两个独立同分布Hermitian矩阵、一个独立同分布高斯或Hermitian矩阵和一个确定对角矩阵是渐进自由的。The conditions for A N and B N to be asymptotically free are very abstract. However, we know that two IID Gaussian matrices, two IID Hermitian matrices, an IID Gaussian or Hermitian matrix, and a definite diagonal matrix are asymptotically free.

那么,运用自由概率理论求解

Figure BDA00004631982000000617
的具体理论依据与方法为:Then, using free probability theory to solve
Figure BDA00004631982000000617
The specific theoretical basis and method are as follows:

A、功率矩阵P的极限分布μP A. Limit distribution μ P of power matrix P

假设MS个接收信号的样本y(1),…,y(MS)用于感知频谱。接收信号的样本协方差矩阵为Assume M S samples y(1),...,y(M S ) of the received signal are used for sensing the spectrum. The sample covariance matrix of the received signal is

Figure BDA00004631982000000618
Figure BDA00004631982000000618

当主基站在发送信号时,有y(n)=x(n)+v(n)。信号分量x(n)的样本协方差矩阵为When the master base station is sending a signal, there is y(n)=x(n)+v(n). The sample covariance matrix of the signal component x(n) is

ΣΣ ^^ == 11 Mm SS ΣΣ nno == 11 Mm SS xx (( nno )) xx (( nno )) Hh -- -- -- (( 99 ))

对于信号-高斯噪声模型,使用自由概率理论,上述的两个样本协方差矩阵

Figure BDA0000463198200000072
满足以下等式For the signal-Gaussian noise model, using free probability theory, the above two sample covariance matrices
Figure BDA0000463198200000072
and satisfy the following equation

Figure BDA0000463198200000074
Figure BDA0000463198200000074

其中in

cc == KNKN rr Mm SS -- -- -- (( 1111 ))

另一方面,由式(4)得到信号分量x(n)的协方差矩阵为On the other hand, the covariance matrix of the signal component x(n) obtained from formula (4) is

ΣΣ == EE. {{ xx (( nno )) xx (( nno )) Hh }} == PP 11 22 HHHH Hh PP 11 22 -- -- -- (( 1212 ))

定义

Figure BDA0000463198200000077
Z是KNr×MS维矩阵,它的元素满足零均值独立同分布,方差为1/MS。使用式(9)得到definition
Figure BDA0000463198200000077
Z is a KN r ×M S dimensional matrix, its elements satisfy zero-mean independent and identical distribution, and the variance is 1/M S . Using formula (9) to get

ZZ H = Σ - 1 2 Σ ^ Σ - 1 2 Σ ^ = Σ 1 2 ZZ H Σ 1 2 - - - ( 13 ) ZZ h = Σ - 1 2 Σ ^ Σ - 1 2 or Σ ^ = Σ 1 2 ZZ h Σ 1 2 - - - ( 13 )

也就是Wishart分布特性。值得注意的是,ZZΗ的元素满足零均值独立同分布,方差为1;HHΗ是Wishart矩阵,它的元素也满足零均值独立同分布,方差为1。因此在

Figure BDA0000463198200000079
律下它们对应的极限分布为
Figure BDA00004631982000000710
由式(12)和(13),我们得到That is, the Wishart distribution characteristic. It is worth noting that the elements of ZZ Η satisfy the zero-mean independent and identical distribution, and the variance is 1; HH Η is a Wishart matrix, and its elements also satisfy the zero-mean independent and identical distribution, and the variance is 1. Thus, in
Figure BDA0000463198200000079
Their corresponding limiting distributions under the law are
Figure BDA00004631982000000710
and From equations (12) and (13), we get

将式(14)代入到式(10)中,得到信号功率矩阵P的极限分布为Substituting Equation (14) into Equation (10), the limiting distribution of the signal power matrix P is obtained as

Figure BDA00004631982000000713
Figure BDA00004631982000000713

B、μP的数值计算过程B. Numerical calculation process of μ P

在式(15)中,μP的表达式包括一个与

Figure BDA00004631982000000714
的自由加法解卷积以及两个与
Figure BDA00004631982000000715
律μc的自由乘法解卷积,它们都可以由下文介绍的矩-累积量方法有效地实现。In Equation (15), the expression of μ P includes a and
Figure BDA00004631982000000714
Additive-free deconvolution of and two AND
Figure BDA00004631982000000715
The free multiplicative deconvolution of the law μ c can be efficiently realized by the moment-cumulant method described below.

1)计算与

Figure BDA00004631982000000716
的自由加法解卷积:概率分布μ的R-变换定义为1) Calculate with
Figure BDA00004631982000000716
Additive-free deconvolution of : The R-transform of the probability distribution μ is defined as

RR μμ (( zz )) == ΣΣ nno αα nno μμ zz nno -- -- -- (( 1616 ))

其中是μ的n阶累积量。R-变换的重要性体现在自由加法卷积的相加性,也就是in is the nth order cumulant of μ. The importance of the R-transform is reflected in the additive nature of the free additive convolution, that is

相当于在自由加法卷积下累积量是加性的,即It is equivalent to the cumulant under the free additive convolution is additive, that is,

Figure BDA0000463198200000084
Figure BDA0000463198200000084

分布μ的矩和累积量的关系如下:The relationship between the moment and the cumulant of the distribution μ is as follows:

mm kk μμ == ΣΣ nno ≤≤ kk αα nno μμ coefcoef kk -- nno (( (( 11 ++ mm 11 μμ zz ++ mm 22 μμ zz 22 ++ .. .. .. )) nno )) -- -- -- (( 1919 ))

其中coefn(·)表示zn的系数。由式(19)知,我们可以从累积量序列

Figure BDA0000463198200000086
得到矩序列
Figure BDA0000463198200000087
反之亦然。定义函数momcum以矩序列为输入量,累积量序列为输出量;函数cummom以累积量序列为输入量,矩序列为输出量。where coef n (·) represents the coefficient of z n . From formula (19), we can get from the cumulant sequence
Figure BDA0000463198200000086
get sequence of moments
Figure BDA0000463198200000087
vice versa. The definition function momcum takes moment series as input and cumulant series as output; function cummom takes cumulant series as input and moment series as output.

为了获得

Figure BDA0000463198200000088
的矩,我们首先计算式(8)中的样本协方差矩阵
Figure BDA0000463198200000089
的特征值
Figure BDA00004631982000000822
接着计算矩in order to achieve
Figure BDA0000463198200000088
Moments of , we first calculate the sample covariance matrix in equation (8)
Figure BDA0000463198200000089
The eigenvalues of
Figure BDA00004631982000000822
Then calculate the moments

Figure BDA00004631982000000810
Figure BDA00004631982000000810

另一方面,σ2I的特征值都是σ2。因此

Figure BDA00004631982000000811
的矩为On the other hand, the eigenvalues of σ 2 I are all σ 2 . therefore
Figure BDA00004631982000000811
The moment of

mm kk μμ σσ 22 II == (( σσ 22 )) kk -- -- -- (( 21twenty one ))

2)计算与μc的自由乘法解卷积:

Figure BDA00004631982000000813
和μA的矩有如下关系:2) Compute the free multiplicative deconvolution with μ c :
Figure BDA00004631982000000813
and the moment of μ A have the following relationship:

Figure BDA00004631982000000814
Figure BDA00004631982000000814

其中in

ZZ (( zz )) == (( 11 ++ cc ·&Center Dot; mm 11 μμ AA zz ++ cc ·&Center Dot; mm 22 μμ AA zz 22 ++ .. .. .. )) nno

比较式(22)和(19)后发现,式(22)就是矩-累积量公式,只不过累积量由

Figure BDA00004631982000000816
替换,矩由替换。因此,使用函数momcum,其输入量为
Figure BDA00004631982000000818
相应的输出量为
Figure BDA00004631982000000819
来计算
Figure BDA00004631982000000820
的矩。Comparing formulas (22) and (19), it is found that formula (22) is the moment-cumulant formula, but the cumulant is given by
Figure BDA00004631982000000816
replace the moment by replace. Therefore, using the function momcum, its input is
Figure BDA00004631982000000818
The corresponding output is
Figure BDA00004631982000000819
to calculate
Figure BDA00004631982000000820
moment.

执行完式(15)中的自由乘法和加法解卷积后,我们得到μP的矩

Figure BDA00004631982000000821
如前所述,频谱感知的判决规则是基于平均接收功率
Figure BDA0000463198200000091
的估计,也就是μP的一阶矩,即
Figure BDA0000463198200000092
因此,我们可以总结出基于自由解卷积计算
Figure BDA0000463198200000093
的步骤为:After performing free multiplication and additive deconvolution in (15), we obtain the moment of μ P
Figure BDA00004631982000000821
As mentioned earlier, the decision rule for spectrum sensing is based on the average received power
Figure BDA0000463198200000091
The estimate of , which is the first moment of μ P , is
Figure BDA0000463198200000092
Therefore, we can conclude that based on the free deconvolution computation
Figure BDA0000463198200000093
The steps are:

(1)输入:接收采样信号{y(n),n=1,2,…,MS}和信道噪声方差σ2(1) Input: receive sampling signal {y(n), n=1, 2,..., M S } and channel noise variance σ 2 ;

(2)计算式(8)中的样本协方差矩阵

Figure BDA0000463198200000094
和它的特征值{λi,i=1,2,…,KNr};(2) Calculate the sample covariance matrix in formula (8)
Figure BDA0000463198200000094
and its eigenvalue {λ i , i=1,2,...,KN r };

(3)计算式(20)中的矩和式(21)中的矩

Figure BDA00004631982000000921
(3) Calculate the moment in formula (20) and the moments in (21)
Figure BDA00004631982000000921

(4)计算

Figure BDA0000463198200000096
步骤如下:(4) calculation
Figure BDA0000463198200000096
Proceed as follows:

Figure BDA0000463198200000097
Figure BDA0000463198200000097

{ m k ν = γ k / ( KN r M S ) } ; { m k ν = γ k / ( KN r m S ) } ;

(5)计算

Figure BDA0000463198200000099
步骤如下:(5) calculation
Figure BDA0000463198200000099
Proceed as follows:

α k ν = momcum ( { m k ν } ) α k ν = mom cum ( { m k ν } )

α k μ σ 2 I = momcum ( { ( σ 2 ) k } ) α k μ σ 2 I = mom cum ( { ( σ 2 ) k } )

{ α k η = α k ν - α k μ σ 2 I } { α k η = α k ν - α k μ σ 2 I }

{ m k η } = cummom ( { α k η } ) ; { m k η } = cummom ( { α k η } ) ;

(6)计算

Figure BDA00004631982000000914
步骤如下:(6) calculation
Figure BDA00004631982000000914
Proceed as follows:

{ ρ k } = momcum ( { KN r N t · m k η } ) { ρ k } = mom cum ( { KN r N t · m k η } )

{ m k P = ρ k / ( KN r N t ) } ; { m k P = ρ k / ( KN r N t ) } ;

(7)

Figure BDA00004631982000000917
(7)
Figure BDA00004631982000000917

接下来,对于检测阈值τ的选择,通常是要满足目标虚警概率pf,也就是

Figure BDA00004631982000000918
但是在Η0情况下,由上面介绍的基于自由解卷积的算法得到的
Figure BDA00004631982000000919
没有概率分布的解析表达式。于是我们采用Monte Carlo仿真来获得在Η0情况下
Figure BDA00004631982000000920
的直方图,如图3所示,经验证直方图近似于高斯分布。因此,在只有噪声样本的情况下,我们可以使用估计的噪声方差并且执行基于自由解卷积的算法来获得我们运行很多次这样的仿真,然后以此计算的均值θP和方差
Figure BDA0000463198200000103
得到
Figure BDA0000463198200000104
则目标虚警概率pf的检测阈值为Next, for the selection of the detection threshold τ, it is usually necessary to satisfy the target false alarm probability p f , that is
Figure BDA00004631982000000918
But in the case of Η 0 , obtained by the algorithm based on free deconvolution introduced above
Figure BDA00004631982000000919
There is no analytical expression for the probability distribution. So we use Monte Carlo simulation to obtain in the case of Η 0
Figure BDA00004631982000000920
The histogram of , as shown in Figure 3, has been verified that the histogram approximates a Gaussian distribution. Therefore, in the case of only noisy samples, we can use the estimated noise variance and perform a free deconvolution based algorithm to obtain We run this simulation many times, and then calculate The mean θ P and variance of
Figure BDA0000463198200000103
get
Figure BDA0000463198200000104
Then the detection threshold of target false alarm probability p f is

τ=υPQ-1(pf)+θP    (23)其中Q-1(·)为逆Q-函数,

Figure BDA0000463198200000105
τ=υ P Q -1 (p f )+θ P (23) where Q -1 ( ) is the inverse Q-function,
Figure BDA0000463198200000105

最后,将

Figure BDA0000463198200000106
和τ进行比较,判断主基站是否在发送信号。当
Figure BDA0000463198200000107
时,主基站在发送信号;当
Figure BDA0000463198200000108
时,主基站没有发送信号。Finally, the
Figure BDA0000463198200000106
Compared with τ, it is judged whether the main base station is sending a signal. when
Figure BDA0000463198200000107
When , the master base station is sending signals; when
Figure BDA0000463198200000108
, the main base station does not send a signal.

为了更好地描述本发明的效果,将通过下面的仿真实例进一步证明:In order to better describe the effect of the present invention, it will be further proved by the following simulation examples:

1、仿真参数设置1. Simulation parameter setting

Figure BDA0000463198200000109
Figure BDA0000463198200000109

主基站和每个次基站之间都为MIMO瑞利衰落信道。次基站分布在不同的地理位置上,因此Pk各不相同。另外平均

Figure BDA00004631982000001010
其中
Figure BDA00004631982000001011
There is a MIMO Rayleigh fading channel between the primary base station and each secondary base station. The secondary base stations are distributed in different geographical locations, so Pk is different. Also average
Figure BDA00004631982000001010
in
Figure BDA00004631982000001011

2、仿真方法2. Simulation method

现有的基于特征值的检测方法和本发明方法。Existing detection methods based on eigenvalues and the method of the present invention.

基于特征值的检测方法介绍:基于特征值的检测方法不需要噪声方差,它利用样本协方差矩阵的最大与最小特征值比值的渐近特性。确切地说,它首先计算式(8)中的样本协方差矩阵

Figure BDA00004631982000001012
和它的特征值然后比较
Figure BDA00004631982000001013
和阈值τEV,如果
Figure BDA00004631982000001014
则为Η1,否则为Η0。阈值计算公式为 τ EV = ( KN r + M S KN r - M S ) 2 ( 1 + ( KN r + M S ) - 2 / 3 ( KN r M S ) 1 / 6 F TW 2 - 1 ( 1 - p f ) ) , 其中
Figure BDA00004631982000001016
为逆Tracy-Widom第二累计分布函数。在我们的仿真中
Figure BDA00004631982000001017
Introduction to eigenvalue-based detection methods: The eigenvalue-based detection method does not require noise variance, and it uses the asymptotic characteristics of the ratio of the largest and smallest eigenvalues of the sample covariance matrix. To be precise, it first computes the sample covariance matrix in equation (8)
Figure BDA00004631982000001012
and its eigenvalues then compare
Figure BDA00004631982000001013
and threshold τ EV , if
Figure BDA00004631982000001014
Then it is Η 1 , otherwise it is Η 0 . The threshold calculation formula is τ EV = ( KN r + m S KN r - m S ) 2 ( 1 + ( KN r + m S ) - 2 / 3 ( KN r m S ) 1 / 6 f TW 2 - 1 ( 1 - p f ) ) , in
Figure BDA00004631982000001016
is the inverse Tracy-Widom second cumulative distribution function. In our simulation
Figure BDA00004631982000001017

3、仿真结果3. Simulation results

如图4所示,本发明方法与基于特征值的检测方法进行频谱感知性能比较。可以看出本发明方法在所有的SNR值和总样本数下的性能都优于基于特征值的方法,尤其是在低信噪比和小样本情况下。As shown in FIG. 4 , the spectrum sensing performance is compared between the method of the present invention and the detection method based on eigenvalues. It can be seen that the performance of the method of the present invention is better than the method based on eigenvalues under all SNR values and total number of samples, especially in the case of low signal-to-noise ratio and small samples.

实施例2Example 2

如图2所示,本发明提供了一种基于自由概率理论的协作频谱感知方法,该方法适用于MIMO通信环境中,具体包括如下步骤:As shown in Figure 2, the present invention provides a cooperative spectrum sensing method based on free probability theory, which is suitable for MIMO communication environments, and specifically includes the following steps:

步骤1:对各个次基站的多个天线的接收信号进行采样,采样信号将进行集中处理;Step 1: Sampling the received signals of multiple antennas of each secondary base station, and the sampled signals will be processed centrally;

步骤2:根据所有接收采样信号和信道的噪声方差,借助于随机矩阵的渐近自由特性和Wishart分布特性,采用基于自由解卷积的算法求解所有接收天线的平均接收信号功率

Figure BDA00004631982000001112
也就是检测统计量;Step 2: According to the noise variance of all received sampling signals and channels, with the help of the asymptotic free characteristics of the random matrix and the Wishart distribution characteristics, the algorithm based on free deconvolution is used to solve the average received signal power of all receiving antennas
Figure BDA00004631982000001112
That is, the detection statistic;

步骤3:依据目标虚警概率pf,运用Monte Carlo仿真在仅有噪声存在的情况下计算检测阈值τ;Step 3: According to the target false alarm probability p f , use Monte Carlo simulation to calculate the detection threshold τ under the condition that only noise exists;

步骤4:将

Figure BDA0000463198200000111
和τ进行比较,判断主基站是否在发送信号。当时,主基站在发送信号;当
Figure BDA0000463198200000113
时,主基站没有发送信号。Step 4: Put
Figure BDA0000463198200000111
Compared with τ, it is judged whether the main base station is sending a signal. when When , the master base station is sending signals; when
Figure BDA0000463198200000113
, the main base station does not send a signal.

本发明所述方法中的步骤1包含:Step 1 in the method of the present invention comprises:

K个分布在不同地理位置上的次基站BS1,BS2,…,BSK协作感知信道,判断主基站是否在发送信号。主基站和每个次基站分别配备Nt和Nr个天线,在它们之间是MIMO瑞利衰落信道。采样速率为1/Ts,则第k个接收机在时刻n输出的采样信号为

Figure BDA0000463198200000114
k=1,2,…,K。那么所有接收天线在时刻n集中起来的采样信号为
Figure BDA0000463198200000115
其中(·)Η表示共轭转置。K secondary base stations BS 1 , BS 2 , ..., BS K distributed in different geographical locations cooperate to sense the channel, and determine whether the primary base station is sending signals. The primary base station and each secondary base station are equipped with N t and N r antennas respectively, and there is a MIMO Rayleigh fading channel between them. The sampling rate is 1/T s , then the sampling signal output by the kth receiver at time n is
Figure BDA0000463198200000114
k=1,2,...,K. Then the sampled signal collected by all receiving antennas at time n is
Figure BDA0000463198200000115
Wherein (·) Η represents conjugate transposition.

本发明所述方法中的步骤2包括:Step 2 in the method of the present invention comprises:

(1)输入:接收采样信号{y(n),n=1,2,…,MS}和信道噪声方差σ2。其中MS为接收信号的总样本数;(1) Input: receive sampling signals {y(n), n=1, 2, ..., M S } and channel noise variance σ 2 . Where M S is the total number of samples of the received signal;

(2)计算接收采样信号的样本协方差矩阵

Figure BDA0000463198200000116
和它的特征值{λi,i=1,2,…,KNr};(2) Calculate the sample covariance matrix of the received sampling signal
Figure BDA0000463198200000116
and its eigenvalue {λ i , i=1,2,...,KN r };

(3)计算

Figure BDA0000463198200000117
的k阶矩
Figure BDA0000463198200000118
Figure BDA0000463198200000119
的k阶矩
Figure BDA00004631982000001110
(3) calculation
Figure BDA0000463198200000117
k-order moment
Figure BDA0000463198200000118
and
Figure BDA0000463198200000119
k-order moment
Figure BDA00004631982000001110

(4)计算

Figure BDA00004631982000001111
步骤如下:(4) calculation
Figure BDA00004631982000001111
Proceed as follows:

Figure BDA0000463198200000121
Figure BDA0000463198200000121

{ m k ν = γ k / ( KN r M S ) } ; { m k ν = γ k / ( KN r m S ) } ;

(5)计算

Figure BDA0000463198200000123
步骤如下:(5) calculation
Figure BDA0000463198200000123
Proceed as follows:

α k ν = momcum ( { m k ν } ) α k ν = mom cum ( { m k ν } )

α k μ σ 2 I = momcum ( { ( σ 2 ) k } ) α k μ σ 2 I = mom cum ( { ( σ 2 ) k } )

{ α k η = α k ν - α k μ σ 2 I } { α k η = α k ν - α k μ σ 2 I }

{ m k η } = cummom ( { α k η } ) ; { m k η } = cummom ( { α k η } ) ;

(6)计算

Figure BDA0000463198200000128
步骤如下:(6) calculation
Figure BDA0000463198200000128
Proceed as follows:

{ ρ k } = momcum ( { KN r N t · m k η } ) { ρ k } = mom cum ( { KN r N t · m k η } )

{ m k P = ρ k / ( KN r N t ) } ; { m k P = ρ k / ( KN r N t ) } ;

(7)

Figure BDA00004631982000001211
也就是μP的一阶矩。(7)
Figure BDA00004631982000001211
That is, the first moment of μ P.

上述步骤里的符号解释:

Figure BDA00004631982000001212
Figure BDA00004631982000001213
分别表示自由概率理论中的自由加法解卷积算子和自由乘法解卷积算子;
Figure BDA00004631982000001214
和μP分别表示矩阵
Figure BDA00004631982000001215
σ2I(I为单位矩阵)和P的极限概率分布;
Figure BDA00004631982000001216
Figure BDA00004631982000001217
对应于律μc,c分别取
Figure BDA00004631982000001219
Figure BDA00004631982000001220
momcum和cummom是根据分布μ的矩-累积量公式得到的,momcum的输入为矩序列,输出为累积量序列,cummom的输入为累积量序列,输出为矩序列。Explanation of symbols in the above steps:
Figure BDA00004631982000001212
and
Figure BDA00004631982000001213
represent the free additive deconvolution operator and the free multiplicative deconvolution operator in the free probability theory, respectively;
Figure BDA00004631982000001214
and μ P respectively denote the matrix
Figure BDA00004631982000001215
σ 2 I (I is the identity matrix) and the limiting probability distribution of P;
Figure BDA00004631982000001216
and
Figure BDA00004631982000001217
corresponds to Law μ c , c respectively take
Figure BDA00004631982000001219
and
Figure BDA00004631982000001220
Momcum and cummom are obtained according to the moment-cumulant formula of the distribution μ. The input of momcum is a moment sequence and the output is a cumulant sequence, and the input of cummom is a cumulant sequence and the output is a moment sequence.

本发明所述方法中的步骤3包含:Step 3 in the method of the present invention comprises:

首先在只有噪声样本的情况下执行步骤2来获得

Figure BDA00004631982000001221
经过很多次这样的仿真后计算
Figure BDA00004631982000001222
的均值θP和方差
Figure BDA00004631982000001223
Figure BDA00004631982000001224
近似满足高斯分布。然后依据目标虚警概率pf,计算阈值τ=υPQ-1(pf)+θP,其中Q-1(·)为逆Q-函数,
Figure BDA00004631982000001225
First perform step 2 with only noise samples to obtain
Figure BDA00004631982000001221
After many such simulations, the calculation
Figure BDA00004631982000001222
The mean θ P and variance of
Figure BDA00004631982000001223
Figure BDA00004631982000001224
approximately satisfy a Gaussian distribution. Then according to the target false alarm probability p f , calculate the threshold τ=υ P Q -1 (p f )+θ P , where Q -1 (·) is the inverse Q-function,
Figure BDA00004631982000001225

Claims (5)

1.一种基于自由概率理论的协作频谱感知方法,其特征在于,所述方法包括如下步骤:1. A collaborative spectrum sensing method based on free probability theory, characterized in that, the method comprises the steps of: 步骤1:对各个次基站的多个天线的接收信号进行采样,采样信号将进行集中处理;Step 1: Sampling the received signals of multiple antennas of each secondary base station, and the sampled signals will be processed centrally; 步骤2:根据所有接收采样信号和信道的噪声方差,借助于随机矩阵的渐近自由特性和Wishart分布特性,采用基于自由解卷积的算法求解所有接收天线的平均接收信号功率
Figure FDA00004631981900000111
也就是检测统计量;
Step 2: According to the noise variance of all received sampling signals and channels, with the help of the asymptotic free characteristics of the random matrix and the Wishart distribution characteristics, the algorithm based on free deconvolution is used to solve the average received signal power of all receiving antennas
Figure FDA00004631981900000111
That is, the detection statistic;
步骤3:依据目标虚警概率pf,运用Monte Carlo仿真在仅有噪声存在的情况下计算检测阈值τ;Step 3: According to the target false alarm probability p f , use Monte Carlo simulation to calculate the detection threshold τ under the condition that only noise exists; 步骤4:将和τ进行比较,判断主基站是否在发送信号;当
Figure FDA0000463198190000012
时,主基站在发送信号;当
Figure FDA0000463198190000013
时,主基站没有发送信号。
Step 4: Put Compare with τ to judge whether the main base station is sending a signal; when
Figure FDA0000463198190000012
When , the main base station is sending signals; when
Figure FDA0000463198190000013
, the main base station does not send a signal.
2.根据权利要求1所述的一种基于自由概率理论的协作频谱感知方法,其特征在于,所述方法中的步骤1包含:2. A kind of collaborative spectrum sensing method based on free probability theory according to claim 1, is characterized in that, step 1 in the described method comprises: K个分布在不同地理位置上的次基站BS1,BS2,…,BSK协作感知信道,判断主基站是否在发送信号;主基站和每个次基站分别配备Nt和Nr个天线,在它们之间是MIMO瑞利衰落信道;采样速率为1/Ts,则第k个接收机在时刻n输出的采样信号为
Figure FDA0000463198190000014
k=1,2,…,K;那么所有接收天线在时刻n集中起来的采样信号为其中(·)Η表示共轭转置。
K secondary base stations BS 1 , BS 2 ,...,BS K distributed in different geographic locations cooperate to sense the channel, and judge whether the primary base station is sending signals; the primary base station and each secondary base station are equipped with N t and N r antennas respectively, Between them is a MIMO Rayleigh fading channel; the sampling rate is 1/T s , then the sampling signal output by the kth receiver at time n is
Figure FDA0000463198190000014
k=1,2,...,K; then the sampled signals collected by all receiving antennas at time n are Wherein (·) Η represents conjugate transposition.
3.根据权利要求1所述的一种基于自由概率理论的协作频谱感知方法,其特征在于,所述方法中的步骤2包括:3. A kind of collaborative spectrum sensing method based on free probability theory according to claim 1, is characterized in that, step 2 in the described method comprises: (1)输入:接收采样信号{y(n),n=1,2,…,MS}和信道噪声方差σ2,其中MS为接收信号的总样本数;(1) Input: receive sampling signal {y(n),n=1,2,...,M S } and channel noise variance σ 2 , where M S is the total number of samples of the received signal; (2)计算接收采样信号的样本协方差矩阵
Figure FDA0000463198190000016
和它的特征值{λi,i=1,2,…,KNr};
(2) Calculate the sample covariance matrix of the received sampling signal
Figure FDA0000463198190000016
and its eigenvalue {λ i , i=1,2,...,KN r };
(3)计算
Figure FDA00004631981900000112
的k阶矩
Figure FDA0000463198190000018
的k阶矩
Figure FDA0000463198190000019
(3) calculation
Figure FDA00004631981900000112
k-order moment and
Figure FDA0000463198190000018
k-order moment
Figure FDA0000463198190000019
(4)计算
Figure FDA00004631981900000110
步骤如下:
(4) calculation
Figure FDA00004631981900000110
Proceed as follows:
{ m k ν = γ k / ( KN r M S ) } ; { m k ν = γ k / ( KN r m S ) } ; (5)计算
Figure FDA0000463198190000023
步骤如下:
(5) calculation
Figure FDA0000463198190000023
Proceed as follows:
α k ν = momcum ( { m k ν } ) α k ν = mom cum ( { m k ν } ) α k μ σ 2 I = momcum ( { ( σ 2 ) k } ) α k μ σ 2 I = mom cum ( { ( σ 2 ) k } ) { α k η = α k ν - α k μ σ 2 I } { α k η = α k ν - α k μ σ 2 I } { m k η } = cummom ( { α k η } ) ; { m k η } = cummom ( { α k η } ) ; (6)计算步骤如下:(6) calculation Proceed as follows: { ρ k } = momcum ( { KN r N t · m k η } ) { ρ k } = mom cum ( { KN r N t · m k η } ) { m k P = ρ k / ( KN r N t ) } ; { m k P = ρ k / ( KN r N t ) } ; (7)
Figure FDA00004631981900000211
也就是μP的一阶矩;
(7)
Figure FDA00004631981900000211
That is, the first moment of μ P ;
上述步骤里的符号解释:
Figure FDA00004631981900000212
Figure FDA00004631981900000213
分别表示自由概率理论中的自由加法解卷积算子和自由乘法解卷积算子;
Figure FDA00004631981900000214
和μP分别表示矩阵
Figure FDA00004631981900000215
σ2I(I为单位矩阵)和P的极限概率分布;
Figure FDA00004631981900000216
Figure FDA00004631981900000217
对应于
Figure FDA00004631981900000218
律μc,c分别取
Figure FDA00004631981900000219
Figure FDA00004631981900000220
momcum和cummom是根据分布μ的矩-累积量公式得到的,momcum的输入为矩序列,输出为累积量序列,cummom的输入为累积量序列,输出为矩序列。
Explanation of symbols in the above steps:
Figure FDA00004631981900000212
and
Figure FDA00004631981900000213
represent the free additive deconvolution operator and the free multiplicative deconvolution operator in the free probability theory, respectively;
Figure FDA00004631981900000214
and μ P respectively denote the matrix
Figure FDA00004631981900000215
σ 2 I (I is the identity matrix) and the limiting probability distribution of P;
Figure FDA00004631981900000216
and
Figure FDA00004631981900000217
corresponds to
Figure FDA00004631981900000218
Law μ c , c respectively take
Figure FDA00004631981900000219
and
Figure FDA00004631981900000220
Momcum and cummom are obtained according to the moment-cumulant formula of the distribution μ. The input of momcum is a moment sequence and the output is a cumulant sequence, and the input of cummom is a cumulant sequence and the output is a moment sequence.
4.根据权利要求1所述的一种基于自由概率理论的协作频谱感知方法,其特征在于,所述方法中的步骤3包含:4. A kind of collaborative spectrum sensing method based on free probability theory according to claim 1, is characterized in that, step 3 in the described method comprises: 首先在只有噪声样本的情况下执行步骤2来获得
Figure FDA00004631981900000221
经过很多次这样的仿真后计算
Figure FDA00004631981900000222
的均值θP和方差近似满足高斯分布,然后依据目标虚警概率pf,计算阈值τ=υPQ-1(pf)+θP,其中Q-1(·)为逆Q-函数,
Figure FDA00004631981900000224
First perform step 2 with only noise samples to obtain
Figure FDA00004631981900000221
After many such simulations, the calculation
Figure FDA00004631981900000222
The mean θ P and variance of Approximately satisfy the Gaussian distribution, and then calculate the threshold τ=υ P Q -1 (p f )+θ P according to the target false alarm probability p f , where Q -1 (·) is the inverse Q-function,
Figure FDA00004631981900000224
5.根据权利要求1所述的一种基于自由概率理论的协作频谱感知方法,其特征在于:所述方法适用于MIMO通信环境中。5. A cooperative spectrum sensing method based on free probability theory according to claim 1, characterized in that: said method is applicable to a MIMO communication environment.
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