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CN112187382A - Noise power estimation method based on viscous hidden Markov model - Google Patents

Noise power estimation method based on viscous hidden Markov model Download PDF

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CN112187382A
CN112187382A CN202010856384.2A CN202010856384A CN112187382A CN 112187382 A CN112187382 A CN 112187382A CN 202010856384 A CN202010856384 A CN 202010856384A CN 112187382 A CN112187382 A CN 112187382A
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贾忠杰
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Abstract

本发明公开了一种基于粘性隐马尔可夫模型的噪声功率估计方法，其计算每个感知时隙对应的接收信号功率，作为隐马尔可夫模型中的观测数据；确定每个观测数据所对应的隐藏状态及属于各类隐藏状态的概率，确定状态转移概率矩阵；在隐马尔可夫模型中引入粘性因子，得到粘性隐马尔可夫模型；计算粘性隐马尔可夫模型中所有观测数据对应的隐藏状态在每次迭代下的聚类结果、状态转移概率矩阵在每次迭代下的值、均值和精度在每次迭代下的值；将均值在最后一次迭代下的值中每个元素的值作为对应一类隐藏状态的功率估计值，将最小功率估计值作为噪声功率的估计值；优点是其在接收信号中是否含有授权用户信号未知的情况下，能够快速、准确地估计出噪声功率。

Figure 202010856384

The invention discloses a noise power estimation method based on a viscous hidden Markov model, which calculates the received signal power corresponding to each sensing time slot as the observation data in the hidden Markov model; The hidden state and the probability of belonging to various hidden states are determined, and the state transition probability matrix is determined; the viscous factor is introduced into the hidden Markov model to obtain the viscous hidden Markov model; the viscous hidden Markov model is calculated. The clustering result of the hidden state under each iteration, the value of the state transition probability matrix under each iteration, the value of the mean and precision under each iteration; the value of each element in the value of the mean under the last iteration As the power estimation value corresponding to a class of hidden states, the minimum power estimation value is used as the estimation value of the noise power; the advantage is that it can quickly and accurately estimate the noise power when it is unknown whether the received signal contains an authorized user signal.

Figure 202010856384

Description

一种基于粘性隐马尔可夫模型的噪声功率估计方法A Noise Power Estimation Method Based on Viscous Hidden Markov Model

技术领域technical field

本发明涉及一种认知无线电中的噪声功率估计技术，尤其是涉及一种基于粘性隐马尔可夫模型的噪声功率估计方法。The present invention relates to a noise power estimation technology in cognitive radio, in particular to a noise power estimation method based on a viscous hidden Markov model.

背景技术Background technique

与第四代移动通信技术相比，第五代移动通信(5G)技术可将数据速率提高到10Gbit/s、将延迟降低到1毫秒、连接设备数量增加100倍。实现这些需求依赖大量的频谱资源，但是可用的频谱资源是有限的，且基本上已经被分配完了。为了解决无线网络频谱资源短缺的问题，目前业界的常见思路是引入认知无线电技术来提高频谱资源的利用率。与传统的时隙被单一用户授权占用的系统不同，无线网络通过认知无线电频谱感知技术可以从环境中智能地检测时隙占用情况，从而使认知用户能智能接入空闲的授权时隙。Compared with the fourth generation mobile communication technology, the fifth generation mobile communication (5G) technology can increase the data rate to 10Gbit/s, reduce the delay to 1 millisecond, and increase the number of connected devices by 100 times. The realization of these requirements relies on a large amount of spectrum resources, but the available spectrum resources are limited and have basically been allocated. In order to solve the problem of shortage of spectrum resources in wireless networks, a common idea in the industry is to introduce cognitive radio technology to improve the utilization of spectrum resources. Different from the traditional system in which the time slot is authorized to be occupied by a single user, the wireless network can intelligently detect the time slot occupancy from the environment through cognitive radio spectrum sensing technology, so that the cognitive user can intelligently access the idle authorized time slot.

为了能更好地进行频谱感知，很多文献中都是首先假定噪声功率已知，但实际情况中，噪声功率值其实是未知的，这样就需要有效地估计出噪声功率。但是，现有的噪声功率估计方案通常假定某一段时隙内授权用户信号一直处于不活跃状态，然后通过计算这段时隙内所有样本的平均功率来获得噪声功率的估计值。但实际中，授权用户信号的存在与否是未知的，这时的噪声功率估计性能便会严重下降。In order to perform better spectrum sensing, many literatures first assume that the noise power is known, but in practice, the noise power value is actually unknown, so it is necessary to estimate the noise power effectively. However, the existing noise power estimation scheme usually assumes that the authorized user signal is always inactive in a certain time slot, and then obtains the estimated value of the noise power by calculating the average power of all samples in this time slot. But in practice, the presence or absence of the authorized user signal is unknown, and the noise power estimation performance will be seriously degraded at this time.

发明内容SUMMARY OF THE INVENTION

本发明所要解决的技术问题是提供一种基于粘性隐马尔可夫模型的噪声功率估计方法，其在接收信号中是否含有授权用户信号未知的情况下，能够快速、准确地估计出噪声功率。The technical problem to be solved by the present invention is to provide a noise power estimation method based on a viscous hidden Markov model, which can quickly and accurately estimate the noise power when it is unknown whether the received signal contains an authorized user signal.

本发明解决上述技术问题所采用的技术方案为：一种基于粘性隐马尔可夫模型的噪声功率估计方法，其特征在于具体包括以下步骤：The technical solution adopted by the present invention to solve the above technical problems is: a noise power estimation method based on a viscous hidden Markov model, which is characterized in that it specifically includes the following steps:

步骤一：在认知无线电系统中，对连续的L个感知时隙内的信号进行采样，且对每个感知时隙内的信号进行等时间间隔地采样，共采样得到N个样本，将对第j个感知时隙内的信号进行采样得到的第n个样本记为rj(n)；然后计算每个感知时隙对应的接收信号功率，将第j个感知时隙对应的接收信号功率记为xj，即为对第j个感知时隙内的信号进行采样得到的所有样本的平均功率，

Figure BDA0002646559800000021
其中，L、N、j和n均为正整数，L＞1，100≤N≤1000，1≤j≤L，1≤n≤N，符号“||”为求模符号，xj服从高斯分布，即
Figure BDA0002646559800000022
Figure BDA0002646559800000023
表示噪声功率，
Figure BDA0002646559800000024
表示第j个感知时隙内授权用户的信号功率，
Figure BDA0002646559800000025
表示第j个感知时隙未被授权用户占用，
Figure BDA0002646559800000026
表示第j个感知时隙已被授权用户占用，
Figure BDA0002646559800000027
表示xj服从均值为
Figure BDA0002646559800000028
方差为
Figure BDA0002646559800000029
的高斯分布，
Figure BDA00026465598000000210
表示xj服从均值为
Figure BDA00026465598000000211
方差为
Figure BDA00026465598000000212
的高斯分布；Step 1: In the cognitive radio system, sample the signals in consecutive L sensing time slots, and sample the signals in each sensing time slot at equal time intervals, and obtain N samples in total. The n-th sample obtained by sampling the signal in the j-th sensing time slot is recorded as r j (n); then the received signal power corresponding to each sensing time slot is calculated, and the received signal power corresponding to the j-th sensing time slot is calculated. Denoted as x j , which is the average power of all samples obtained by sampling the signal in the jth sensing time slot,
Figure BDA0002646559800000021
Among them, L, N, j and n are all positive integers, L>1, 100≤N≤1000, 1≤j≤L, 1≤n≤N, the symbol "||" is the modulo symbol, and x j obeys the Gaussian distribution, that is
Figure BDA0002646559800000022
Figure BDA0002646559800000023
represents the noise power,
Figure BDA0002646559800000024
represents the signal power of the authorized user in the jth sensing time slot,
Figure BDA0002646559800000025
Indicates that the jth sensing time slot is not occupied by an authorized user,
Figure BDA0002646559800000026
Indicates that the jth sensing time slot has been occupied by an authorized user,
Figure BDA0002646559800000027
Indicates that x j obeys the mean
Figure BDA0002646559800000028
The variance is
Figure BDA0002646559800000029
the Gaussian distribution of ,
Figure BDA00026465598000000210
Indicates that x j obeys the mean
Figure BDA00026465598000000211
The variance is
Figure BDA00026465598000000212
the Gaussian distribution of ;

步骤二：将每个感知时隙对应的接收信号功率作为隐马尔可夫模型中的观测数据，即隐马尔可夫模型中的第j个观测数据为xj；然后确定隐马尔可夫模型中的每个观测数据所对应的一个隐藏状态，将xj对应的隐藏状态记为zj，zj的取值为区间[1,K]中的一个值，若zj的取值为1则认为xj属于第1类隐藏状态，若zj的取值为k则认为xj属于第k类隐藏状态，若zj的取值为K则认为xj属于第K类隐藏状态；接着计算隐马尔可夫模型中的每个观测数据属于各类隐藏状态的概率，将xj属于第k类隐藏状态的概率记为

Figure BDA00026465598000000213
最后计算隐马尔可夫模型中的状态转移概率矩阵，记为Q，
Figure BDA0002646559800000031
其中，K和k均为正整数，K表示隐马尔可夫模型中设定的隐藏状态的类别数，2≤K≤10，1≤k≤K，
Figure BDA0002646559800000032
表示xj服从的高斯分布的概率密度函数，其变量为xj、均值为μk、方差为
Figure BDA0002646559800000033
μk表示属于第k类隐藏状态的高斯分布的均值，τk表示属于第k类隐藏状态的高斯分布的精度即方差的倒数，Q1,1、Q1,2、Q1,k'、Q1,K对应表示Q中的第1行第1列的元素、第1行第2列的元素、第1行第k'列的元素、第1行第K列的元素，Q2,1、Q2,2、Q2,k'、Q2,K对应表示Q中的第2行第1列的元素、第2行第2列的元素、第2行第k'列的元素、第2行第K列的元素，Qk,1、Qk,2、Qk,k'、Qk,K对应表示Q中的第k行第1列的元素、第k行第2列的元素、第k行第k'列的元素、第k行第K列的元素，QK,1、QK,2、QK,k'、QK,K对应表示Q中的第K行第1列的元素、第K行第2列的元素、第K行第k'列的元素、第K行第K列的元素，1≤k'≤K，Qk,k'表示zj'-1＝k的条件下zj'＝k'的概率，2≤j'≤L，zj'-1表示隐马尔可夫模型中的第j'-1个观测数据xj'-1对应的隐藏状态，zj'表示隐马尔可夫模型中的第j'个观测数据xj'对应的隐藏状态；Step 2: The received signal power corresponding to each sensing time slot is used as the observation data in the hidden Markov model, that is, the jth observation data in the hidden Markov model is x j ; A hidden state corresponding to each observation data of , the hidden state corresponding to x j is recorded as z j , the value of z j is a value in the interval [1, K], if the value of z j is 1, then It is considered that x j belongs to the first hidden state, if the value of z j is k, it is considered that x j belongs to the k-th hidden state, and if the value of z j is K, it is considered that x j belongs to the K-th hidden state; then calculate The probability that each observation data in the hidden Markov model belongs to various hidden states, and the probability that x j belongs to the kth hidden state is recorded as
Figure BDA00026465598000000213
Finally, the state transition probability matrix in the hidden Markov model is calculated, denoted as Q,
Figure BDA0002646559800000031
Among them, K and k are both positive integers, K represents the number of categories of hidden states set in the hidden Markov model, 2≤K≤10, 1≤k≤K,
Figure BDA0002646559800000032
represents the probability density function of the Gaussian distribution that x j obeys, its variable is x j , the mean is μ k , and the variance is
Figure BDA0002646559800000033
μ k represents the mean value of the Gaussian distribution belonging to the k-th hidden state, τ k represents the accuracy of the Gaussian distribution belonging to the k-th hidden state, that is, the inverse of the variance, Q 1,1 , Q 1,2 , Q 1,k' , Q 1,K corresponds to the element in the 1st row and the 1st column of Q, the element in the 1st row and the 2nd column, the element in the 1st row and the k'th column, and the element in the 1st row and the Kth column, Q 2,1 , Q 2,2 , Q 2,k' , Q 2,K correspond to the elements in the second row and the first column of Q, the elements in the second row and the second column, the elements in the second row and the k'th column, and the Elements in row 2, column K, Q k,1 , Q k,2 , Q k,k' , Q k,K correspond to elements in row k and column 1 and elements in row k and column 2 in Q , the element of the kth row and the k'th column, the element of the kth row and the Kth column, Q K,1 , Q K,2 , Q K,k' , Q K,K correspond to the Kth row and the 1st row in Q The element of the column, the element of the Kth row and the 2nd column, the element of the Kth row and the k'th column, the element of the Kth row and the Kth column, 1≤k'≤K, Q k,k' means z j'-1 The probability of z j' = k' under the condition of =k, 2≤j'≤L, z j'-1 represents the hidden mark corresponding to the j'-1th observation data x j'-1 in the hidden Markov model state, z j' represents the hidden state corresponding to the j'th observation data x j' in the hidden Markov model;

步骤三：在隐马尔可夫模型中引入粘性因子，得到粘性隐马尔可夫模型；在粘性隐马尔可夫模型中，初始化属于每类隐藏状态的高斯分布的均值和精度，将μk的初始化值记为

Figure BDA0002646559800000034
将τk的初始化值记为
Figure BDA0002646559800000035
初始化状态转移概率矩阵Q，将Q的初始化值记为Q(0)，Q(0)中的每行中的所有元素的共轭先验分布服从狄利克雷分布，Q(0)中的第k行中的所有元素的共轭先验分布服从的狄利克雷分布为：
Figure BDA0002646559800000036
其中，
Figure BDA0002646559800000037
表示Q(0)中的第k行中的所有元素，Dir()表示狄利克雷分布，γ表示狄利克雷分布的参数，κ表示粘性因子，δ(k,1)表示两个参数分别为k和1的克罗内克函数，δ(k,k')表示两个参数分别为k和k'的克罗内克函数，δ(k,K)表示两个参数分别为k和K的克罗内克函数，
Figure BDA0002646559800000041
γ+κδ(k,1)表示共轭先验分布服从的狄利克雷分布的第1个元素，γ+κδ(k,k')表示共轭先验分布服从的狄利克雷分布的第k'个元素，γ+κδ(k,K)表示共轭先验分布服从的狄利克雷分布的第K个元素；Step 3: Introduce a viscous factor into the hidden Markov model to obtain a viscous hidden Markov model; in the viscous hidden Markov model, initialize the mean and precision of the Gaussian distribution belonging to each type of hidden state, and initialize μ k value as
Figure BDA0002646559800000034
Denote the initial value of τ k as
Figure BDA0002646559800000035
Initialize the state transition probability matrix Q, denote the initial value of Q as Q (0) , the conjugate prior distribution of all elements in each row in Q (0) obeys the Dirichlet distribution, the first in Q (0) The Dirichlet distribution of the conjugate prior distribution of all elements in row k is:
Figure BDA0002646559800000036
in,
Figure BDA0002646559800000037
represents all elements in the kth row in Q (0) , Dir() represents the Dirichlet distribution, γ represents the parameters of the Dirichlet distribution, κ represents the viscosity factor, and δ(k,1) represents the two parameters, respectively Kronecker function of k and 1, δ(k,k') represents the Kronecker function with two parameters k and k' respectively, δ(k,K) represents the two parameters of k and K respectively Kronecker function,
Figure BDA0002646559800000041
γ+κδ(k,1) represents the first element of the Dirichlet distribution obeyed by the conjugate prior distribution, and γ+κδ(k,k') denotes the kth element of the Dirichlet distribution obeyed by the conjugate prior distribution ' elements, γ+κδ(k, K) represents the Kth element of the Dirichlet distribution that the conjugate prior distribution obeys;

步骤四：令t表示迭代次数，t的初始值为1；令T表示设定的最大迭代次数，T≥3；Step 4: Let t represent the number of iterations, and the initial value of t is 1; let T represent the maximum number of iterations set, T≥3;

步骤五：计算粘性隐马尔可夫模型中的所有观测数据对应的隐藏状态在第t次迭代下的聚类结果，记为z(t)，

Figure BDA0002646559800000042
其中，
Figure BDA0002646559800000043
表示求使得p(z|x,Q(t-1),μ(t-1),τ(t-1))取最大值时变量z的值，z为粘性隐马尔可夫模型中的所有观测数据对应的隐藏状态构成的向量，z＝[z1,z2,…,zj,…,zL]，z1表示第1个观测数据x1对应的隐藏状态，z2表示第2个观测数据x2对应的隐藏状态，zL表示第L个观测数据xL对应的隐藏状态，x表示粘性隐马尔可夫模型中的所有观测数据构成的向量，x＝[x1,x2,…,xj,…,xL]，t＝1时Q(t-1)即为Q(0)，t≠1时Q(t-1)表示粘性隐马尔可夫模型中的状态转移概率矩阵Q在第t-1次迭代下的值，t＝1时μ(t-1)即为μ的初始值μ(0)，μ＝[μ1,…,μk…,μK]，μ1表示属于第1类隐藏状态的高斯分布的均值，μK表示属于第K类隐藏状态的高斯分布的均值，
Figure BDA0002646559800000044
Figure BDA0002646559800000045
表示μ1的初始化值，
Figure BDA0002646559800000046
表示μK的初始化值，t≠1时μ(t-1)表示μ在第t-1次迭代下的值，
Figure BDA0002646559800000047
Figure BDA0002646559800000048
表示μ1在第t-1次迭代下的值，
Figure BDA0002646559800000049
表示μk在第t-1次迭代下的值，
Figure BDA00026465598000000410
表示μK在第t-1次迭代下的值，t＝1时τ(t-1)即为τ的初始值τ(0)，τ＝[τ1,…,τk,…,τK]，τ1表示属于第1类隐藏状态的高斯分布的精度，τK表示属于第K类隐藏状态的高斯分布的精度，
Figure BDA00026465598000000411
Figure BDA00026465598000000412
表示τ1的初始化值，
Figure BDA00026465598000000413
表示τK的初始化值，t≠1时τ(t-1)表示τ在第t-1次迭代下的值，
Figure BDA00026465598000000414
Figure BDA00026465598000000415
表示τ1在第t-1次迭代下的值，
Figure BDA00026465598000000416
表示τk在第t-1次迭代下的值，
Figure BDA00026465598000000417
表示τK在第t-1次迭代下的值，p(z|x,Q(t-1),μ(t-1),τ(t-1))表示z的后验概率，根据贝叶斯定理得到
Figure BDA0002646559800000051
p(zj|x,Q(t-1),μ(t-1),τ(t-1))表示zj的后验概率，符号“∝”表示正比，xj+1表示第j+1个观测数据，xj+2表示第j+2个观测数据，p(zj,x1,x2,...,xj|Q(t-1),μ(t-1),τ(t-1))表示zj,x1,x2,...,xj的联合概率，p(xj+1,xj+2,...,xL|zj,Q(t-1),μ(t-1),τ(t-1))表示zj的条件下xj+1,xj+2,...,xL的联合概率，p(zj,x1,x2,...,xj|Q(t-1),μ(t-1),τ(t-1))和p(xj+1,xj+2,...,xL|zj,Q(t-1),μ(t-1),τ(t-1))通过前向后向算法计算得到，
Figure BDA0002646559800000052
Figure BDA0002646559800000053
表示z1在第t次迭代下的值，
Figure BDA0002646559800000054
表示z2在第t次迭代下的值，
Figure BDA0002646559800000055
为z(t)中的第j个元素，也即表示zj在第t次迭代下的值，
Figure BDA0002646559800000056
表示zL在第t次迭代下的值；Step 5: Calculate the clustering results of the hidden states corresponding to all observed data in the viscous hidden Markov model under the t-th iteration, denoted as z (t) ,
Figure BDA0002646559800000042
in,
Figure BDA0002646559800000043
Represents the value of the variable z when p(z|x,Q (t-1) , μ (t-1) ,τ (t-1) ) takes the maximum value, z is all the values in the viscous hidden Markov model The vector of hidden states corresponding to the observed data, z=[z 1 , z 2 ,…,z j ,…,z L ], z 1 represents the hidden state corresponding to the first observation data x 1 , and z 2 represents the second The hidden state corresponding to the observation data x 2 , z L represents the hidden state corresponding to the L-th observation data x L , x represents the vector formed by all the observation data in the viscous hidden Markov model, x=[x 1 , x 2 ,…,x j ,…,x L ], when t=1, Q (t-1) is Q (0) , and when t≠1, Q (t-1) represents the state transition in the viscous hidden Markov model The value of the probability matrix Q at the t-1th iteration, when t=1 μ (t-1) is the initial value μ (0) of μ, μ=[μ 1 ,…,μ k …,μ K ] , μ 1 represents the mean of the Gaussian distribution belonging to the first hidden state, μ K represents the mean of the Gaussian distribution belonging to the Kth hidden state,
Figure BDA0002646559800000044
Figure BDA0002646559800000045
represents the initialization value of μ 1 ,
Figure BDA0002646559800000046
represents the initialization value of μ K , when t≠1 μ (t-1) represents the value of μ at the t-1th iteration,
Figure BDA0002646559800000047
Figure BDA0002646559800000048
represents the value of μ 1 at the t-1th iteration,
Figure BDA0002646559800000049
represents the value of μ k at the t-1th iteration,
Figure BDA00026465598000000410
Represents the value of μ K at the t-1th iteration, when t=1, τ (t-1) is the initial value of τ τ (0) , τ=[τ 1 ,...,τ k ,...,τ K ], τ 1 represents the accuracy of the Gaussian distribution belonging to the first hidden state, τ K represents the accuracy of the Gaussian distribution belonging to the Kth hidden state,
Figure BDA00026465598000000411
Figure BDA00026465598000000412
represents the initialization value of τ 1 ,
Figure BDA00026465598000000413
represents the initialization value of τ K , when t≠1, τ (t-1) represents the value of τ at the t-1th iteration,
Figure BDA00026465598000000414
Figure BDA00026465598000000415
represents the value of τ 1 at the t-1th iteration,
Figure BDA00026465598000000416
represents the value of τ k at the t-1th iteration,
Figure BDA00026465598000000417
represents the value of τ K at the t-1th iteration, p(z|x,Q (t-1) ,μ (t-1) ,τ (t-1) ) represents the posterior probability of z, according to the Yeas' theorem gives
Figure BDA0002646559800000051
p(z j |x,Q (t-1) , μ (t-1) ,τ (t-1) ) represents the posterior probability of z j , the symbol “∝” represents the proportionality, and x j+1 represents the jth +1 observation data, x j+2 represents the j+2th observation data, p(z j ,x 1 ,x 2 ,...,x j |Q (t-1) ,μ (t-1) ,τ (t-1) ) represents the joint probability of z j ,x 1 ,x 2 ,...,x j , p(x j+1 ,x j+2 ,...,x L |z j , Q (t-1) , μ (t-1) , τ (t-1) ) represent the joint probability of x j+1 , x j+2 ,...,x L under the condition of z j , p(z j ,x 1 ,x 2 ,...,x j |Q (t-1) ,μ (t-1) ,τ (t-1) ) and p(x j+1 ,x j+2 ,. ..,x L |z j ,Q (t-1) ,μ (t-1) ,τ (t-1) ) are calculated by forward-backward algorithm,
Figure BDA0002646559800000052
Figure BDA0002646559800000053
represents the value of z 1 at the t-th iteration,
Figure BDA0002646559800000054
represents the value of z 2 at the t-th iteration,
Figure BDA0002646559800000055
is the j-th element in z (t) , that is, the value of z j under the t-th iteration,
Figure BDA0002646559800000056
represents the value of z L at the t-th iteration;

步骤六：计算粘性隐马尔可夫模型中的状态转移概率矩阵Q在第t次迭代下的值，记为Q(t)，Q(t)中的第k行中的所有元素的共轭先验分布服从的狄利克雷分布为：

Figure BDA0002646559800000057
Q(t)中的第k行中的所有元素的后验分布服从的狄利克雷分布为：
Figure BDA0002646559800000058
其中，
Figure BDA0002646559800000059
表示Q(t)中的第k行中的所有元素，
Figure BDA00026465598000000510
表示在第t次迭代下从第k类隐藏状态转移到第1类隐藏状态的观测数据的数量，
Figure BDA00026465598000000511
表示在第t次迭代下从第k类隐藏状态转移到第k'类隐藏状态的观测数据的数量，
Figure BDA00026465598000000512
表示在第t次迭代下从第k类隐藏状态转移到第K类隐藏状态的观测数据的数量，
Figure BDA00026465598000000513
表示后验分布服从的狄利克雷分布的第1个元素，
Figure BDA00026465598000000514
表示后验分布服从的狄利克雷分布的第k'个元素，
Figure BDA00026465598000000515
表示后验分布服从的狄利克雷分布的第K个元素；Step 6: Calculate the value of the state transition probability matrix Q in the viscous hidden Markov model under the t-th iteration, denoted as Q (t) , the conjugate first of all elements in the k-th row in Q (t) . The Dirichlet distribution obeyed by the test distribution is:
Figure BDA0002646559800000057
The posterior distribution of all elements in the kth row in Q (t) follows the Dirichlet distribution:
Figure BDA0002646559800000058
in,
Figure BDA0002646559800000059
represents all elements in the kth row in Q (t) ,
Figure BDA00026465598000000510
represents the number of observations transferred from the k-th hidden state to the 1-th hidden state at the t-th iteration,
Figure BDA00026465598000000511
represents the number of observations transferred from the kth hidden state to the k'th hidden state at the tth iteration,
Figure BDA00026465598000000512
represents the number of observations transferred from the k-th hidden state to the k-th hidden state at the t-th iteration,
Figure BDA00026465598000000513
represents the first element of the Dirichlet distribution that the posterior distribution obeys,
Figure BDA00026465598000000514
represents the k'th element of the Dirichlet distribution to which the posterior distribution obeys,
Figure BDA00026465598000000515
represents the Kth element of the Dirichlet distribution that the posterior distribution obeys;

步骤七：利用属于同一类隐藏状态的所有观测数据，根据贝叶斯定理，计算在x和z(t)确定后μ在第t次迭代下的值μ(t)和τ在第t次迭代下的值τ(t)的后验概率，记为

Figure BDA0002646559800000061
Figure BDA0002646559800000062
其中，μ(t)表示μ在第t次迭代下的值，
Figure BDA0002646559800000063
Figure BDA0002646559800000064
表示μ1在第t次迭代下的值，
Figure BDA0002646559800000065
表示μk在第t次迭代下的值，
Figure BDA0002646559800000066
表示μK在第t次迭代下的值，τ(t)表示τ在第t次迭代下的值，
Figure BDA0002646559800000067
Figure BDA0002646559800000068
表示τ1在第t次迭代下的值，
Figure BDA0002646559800000069
表示τk在第t次迭代下的值，
Figure BDA00026465598000000610
表示τK在第t次迭代下的值，
Figure BDA00026465598000000611
表示
Figure BDA00026465598000000612
服从的高斯分布的概率密度函数，其变量为
Figure BDA00026465598000000613
均值为
Figure BDA00026465598000000614
方差为
Figure BDA00026465598000000615
表示
Figure BDA00026465598000000616
服从的伽马分布的概率密度函数，其变量为
Figure BDA00026465598000000617
形状参数为
Figure BDA00026465598000000618
速率参数为
Figure BDA00026465598000000619
Figure BDA00026465598000000620
表示在第t次迭代下属于第k类隐藏状态的观测数据的数量，
Figure BDA00026465598000000621
表示在第t次迭代下属于第k类隐藏状态的所有观测数据的平均值，
Figure BDA00026465598000000622
表示在第t次迭代下属于第k类隐藏状态的第
Figure BDA00026465598000000623
个观测数据，η0、m0、a0和b0均为常数；Step 7: Using all observation data belonging to the same hidden state, according to Bayes' theorem, calculate the values of μ (t) and τ at the t-th iteration after x and z (t) are determined. The posterior probability of the value τ (t) under , denoted as
Figure BDA0002646559800000061
Figure BDA0002646559800000062
where μ (t) represents the value of μ at the t-th iteration,
Figure BDA0002646559800000063
Figure BDA0002646559800000064
represents the value of μ 1 at the t-th iteration,
Figure BDA0002646559800000065
represents the value of μ k at the t-th iteration,
Figure BDA0002646559800000066
represents the value of μ K at the t-th iteration, τ (t) represents the value of τ at the t-th iteration,
Figure BDA0002646559800000067
Figure BDA0002646559800000068
represents the value of τ 1 at the t-th iteration,
Figure BDA0002646559800000069
represents the value of τ k at the t-th iteration,
Figure BDA00026465598000000610
represents the value of τ K at the t-th iteration,
Figure BDA00026465598000000611
express
Figure BDA00026465598000000612
The probability density function of the Gaussian distribution subject to the variable
Figure BDA00026465598000000613
mean is
Figure BDA00026465598000000614
The variance is
Figure BDA00026465598000000615
express
Figure BDA00026465598000000616
Probability density function of the gamma distribution obeyed, whose variables are
Figure BDA00026465598000000617
The shape parameter is
Figure BDA00026465598000000618
The speed parameter is
Figure BDA00026465598000000619
Figure BDA00026465598000000620
represents the number of observations belonging to the k-th hidden state at the t-th iteration,
Figure BDA00026465598000000621
represents the mean of all observations belonging to the kth hidden state at the tth iteration,
Figure BDA00026465598000000622
represents the hidden state belonging to the kth class at the tth iteration
Figure BDA00026465598000000623
observation data, η 0 , m 0 , a 0 and b 0 are all constants;

步骤八：判断t＜T是否成立，如果成立，则令t＝t+1，然后返回步骤五继续迭代；如果不成立，则执行步骤九；其中，t＝t+1中的“＝”为赋值符号；Step 8: Determine whether t<T is established, if so, set t=t+1, and then return to step 5 to continue the iteration; if not, execute step 9; among them, "=" in t=t+1 is an assignment symbol;

步骤九：将μ(t)中的每个元素的值作为对应一类隐藏状态的功率估计值，即将μ(t)中的第k个元素的值作为第k类隐藏状态的功率估计值；然后将所有类隐藏状态的功率估计值中的最小功率估计值作为噪声功率的估计值，记为

Figure BDA0002646559800000072
Step 9: The value of each element in μ (t) is used as the power estimation value of the corresponding type of hidden state, that is, the value of the kth element in μ (t) is used as the power estimation value of the kth type of hidden state; Then the minimum power estimate among the power estimates of all classes of hidden states is used as the estimate of noise power, denoted as
Figure BDA0002646559800000072

与现有技术相比，本发明的优点在于：Compared with the prior art, the advantages of the present invention are:

1)本发明方法适用于对多感知时隙内的信号进行噪声功率估计，在对多感知时隙内的信号进行噪声功率估计中，本发明方法通过在相邻感知时隙之间增加粘性因子建立粘性隐马尔可夫模型，来增加相邻感知时隙的相关性，利用多感知时隙中相邻感知时隙的相关性进行功率估计，从而降低授权用户信号对噪声功率估计的影响，因此在相同条件下本发明方法能够有效降低噪声功率的估计误差。1) The method of the present invention is suitable for estimating the noise power of the signal in the multi-sensing time slot. In the noise power estimation of the signal in the multi-sensing time slot, the method of the present invention increases the viscosity factor between adjacent sensing time slots. A viscous hidden Markov model is established to increase the correlation of adjacent sensing time slots, and the correlation of adjacent sensing time slots in multi-sensing time slots is used for power estimation, thereby reducing the influence of authorized user signals on noise power estimation. Therefore, Under the same conditions, the method of the present invention can effectively reduce the estimation error of noise power.

2)本发明方法由于利用到多感知时隙中相邻感知时隙的相关性，因而不管感知时隙内是否存在授权用户信号，均能够对噪声功率进行估计，并具有良好的估计性能。2) Since the method of the present invention utilizes the correlation of adjacent sensing time slots in multiple sensing time slots, the noise power can be estimated regardless of whether there is an authorized user signal in the sensing time slot, and has good estimation performance.

3)本发明方法由于利用到粘性隐马尔可夫模型特有的对观测数据的有效聚类能力，可以实现快速收敛，因而具有较低的计算复杂度。3) The method of the present invention can achieve rapid convergence due to the effective clustering capability of the viscous hidden Markov model unique to the observation data, and thus has a lower computational complexity.

附图说明Description of drawings

图1为本发明方法的总体实现框图；Fig. 1 is the overall realization block diagram of the method of the present invention;

图2为使用本发明方法的均方误差随信噪比的变化曲线。FIG. 2 is a graph showing the variation of the mean square error with the signal-to-noise ratio using the method of the present invention.

具体实施方式Detailed ways

以下结合附图实施例对本发明作进一步详细描述。The present invention will be further described in detail below with reference to the embodiments of the accompanying drawings.

本发明提出的一种基于粘性隐马尔可夫模型的噪声功率估计方法，其总体实现框图如图1所示，其具体包括以下步骤：A noise power estimation method based on a viscous hidden Markov model proposed by the present invention, its overall implementation block diagram is shown in Figure 1, which specifically includes the following steps:

步骤一：在认知无线电系统中，对连续的L个感知时隙内的信号进行采样，且对每个感知时隙内的信号进行等时间间隔地采样，共采样得到N个样本，将对第j个感知时隙内的信号进行采样得到的第n个样本记为rj(n)；然后计算每个感知时隙对应的接收信号功率，将第j个感知时隙对应的接收信号功率记为xj，即为对第j个感知时隙内的信号进行采样得到的所有样本的平均功率，

Figure BDA0002646559800000071
其中，L、N、j和n均为正整数，L＞1，100≤N≤1000，1≤j≤L，1≤n≤N，符号“| |”为求模符号，N的取值太大(N＞1000)时采样的样本数量太多，会导致运算速度下降，因此只需确保N的取值充分大即可，当N充分大时，根据中心极限定理，xj服从高斯分布，即
Figure BDA0002646559800000081
Figure BDA0002646559800000082
表示噪声功率，
Figure BDA0002646559800000083
表示第j个感知时隙内授权用户的信号功率，
Figure BDA0002646559800000084
表示第j个感知时隙未被授权用户占用，
Figure BDA0002646559800000085
表示第j个感知时隙已被授权用户占用，
Figure BDA0002646559800000086
表示xj服从均值为
Figure BDA0002646559800000087
方差为
Figure BDA0002646559800000088
的高斯分布，
Figure BDA0002646559800000089
表示xj服从均值为
Figure BDA00026465598000000810
方差为
Figure BDA00026465598000000811
的高斯分布。Step 1: In the cognitive radio system, sample the signals in consecutive L sensing time slots, and sample the signals in each sensing time slot at equal time intervals, and obtain N samples in total. The n-th sample obtained by sampling the signal in the j-th sensing time slot is recorded as r j (n); then the received signal power corresponding to each sensing time slot is calculated, and the received signal power corresponding to the j-th sensing time slot is calculated. Denoted as x j , which is the average power of all samples obtained by sampling the signal in the jth sensing time slot,
Figure BDA0002646559800000071
Among them, L, N, j and n are all positive integers, L>1, 100≤N≤1000, 1≤j≤L, 1≤n≤N, the symbol "| |" is the modulo symbol, and the value of N When the value is too large (N>1000), the number of samples sampled is too large, which will reduce the operation speed. Therefore, it is only necessary to ensure that the value of N is sufficiently large. When N is sufficiently large, according to the central limit theorem, x j obeys the Gaussian distribution. ,Right now
Figure BDA0002646559800000081
Figure BDA0002646559800000082
represents the noise power,
Figure BDA0002646559800000083
represents the signal power of the authorized user in the jth sensing time slot,
Figure BDA0002646559800000084
Indicates that the jth sensing time slot is not occupied by an authorized user,
Figure BDA0002646559800000085
Indicates that the jth sensing time slot has been occupied by an authorized user,
Figure BDA0002646559800000086
Indicates that x j obeys the mean
Figure BDA0002646559800000087
The variance is
Figure BDA0002646559800000088
the Gaussian distribution of ,
Figure BDA0002646559800000089
Indicates that x j obeys the mean
Figure BDA00026465598000000810
The variance is
Figure BDA00026465598000000811
Gaussian distribution.

步骤二：将每个感知时隙对应的接收信号功率作为隐马尔可夫模型中的观测数据，即隐马尔可夫模型中的第j个观测数据为xj；然后确定隐马尔可夫模型中的每个观测数据所对应的一个隐藏状态，将xj对应的隐藏状态记为zj，zj的取值为区间[1,K]中的一个值，若zj的取值为1则认为xj属于第1类隐藏状态，若zj的取值为k则认为xj属于第k类隐藏状态，若zj的取值为K则认为xj属于第K类隐藏状态；接着计算隐马尔可夫模型中的每个观测数据属于各类隐藏状态的概率，将xj属于第k类隐藏状态(即zj＝k)的概率记为

Figure BDA00026465598000000812
最后计算隐马尔可夫模型中的状态转移概率矩阵，记为Q，
Figure BDA00026465598000000813
其中，K和k均为正整数，K表示隐马尔可夫模型中设定的隐藏状态的类别数，2≤K≤10，在本实施例中取K＝4，1≤k≤K，
Figure BDA00026465598000000814
表示xj服从的高斯分布的概率密度函数，其变量为xj、均值为μk、方差为
Figure BDA0002646559800000091
μk表示属于第k类隐藏状态的高斯分布的均值，τk表示属于第k类隐藏状态的高斯分布的精度即方差的倒数，Q1,1、Q1,2、Q1,k'、Q1,K对应表示Q中的第1行第1列的元素、第1行第2列的元素、第1行第k'列的元素、第1行第K列的元素，Q2,1、Q2,2、Q2,k'、Q2,K对应表示Q中的第2行第1列的元素、第2行第2列的元素、第2行第k'列的元素、第2行第K列的元素，Qk,1、Qk,2、Qk,k'、Qk,K对应表示Q中的第k行第1列的元素、第k行第2列的元素、第k行第k'列的元素、第k行第K列的元素，QK,1、QK,2、QK,k'、QK,K对应表示Q中的第K行第1列的元素、第K行第2列的元素、第K行第k'列的元素、第K行第K列的元素，1≤k'≤K，Qk,k'表示zj'-1＝k的条件下zj'＝k'的概率，2≤j'≤L，zj'-1表示隐马尔可夫模型中的第j'-1个观测数据xj'-1对应的隐藏状态，zj'表示隐马尔可夫模型中的第j'个观测数据xj'对应的隐藏状态。Step 2: The received signal power corresponding to each sensing time slot is used as the observation data in the hidden Markov model, that is, the jth observation data in the hidden Markov model is x j ; A hidden state corresponding to each observation data of , the hidden state corresponding to x j is recorded as z j , the value of z j is a value in the interval [1, K], if the value of z j is 1, then It is considered that x j belongs to the first hidden state, if the value of z j is k, it is considered that x j belongs to the k-th hidden state, and if the value of z j is K, it is considered that x j belongs to the K-th hidden state; then calculate The probability that each observation data in the hidden Markov model belongs to various hidden states, and the probability that x j belongs to the kth hidden state (that is, z j = k) is recorded as
Figure BDA00026465598000000812
Finally, the state transition probability matrix in the hidden Markov model is calculated, denoted as Q,
Figure BDA00026465598000000813
Among them, K and k are both positive integers, K represents the number of hidden state categories set in the hidden Markov model, 2≤K≤10, in this embodiment, K=4, 1≤k≤K,
Figure BDA00026465598000000814
represents the probability density function of the Gaussian distribution that x j obeys, its variable is x j , the mean is μ k , and the variance is
Figure BDA0002646559800000091
μ k represents the mean value of the Gaussian distribution belonging to the k-th hidden state, τ k represents the accuracy of the Gaussian distribution belonging to the k-th hidden state, that is, the inverse of the variance, Q 1,1 , Q 1,2 , Q 1,k' , Q 1,K corresponds to the element in the 1st row and the 1st column of Q, the element in the 1st row and the 2nd column, the element in the 1st row and the k'th column, and the element in the 1st row and the Kth column, Q 2,1 , Q 2,2 , Q 2,k' , Q 2,K correspond to the elements in the second row and the first column of Q, the elements in the second row and the second column, the elements in the second row and the k'th column, and the Elements in row 2, column K, Q k,1 , Q k,2 , Q k,k' , Q k,K correspond to elements in row k and column 1 and elements in row k and column 2 in Q , the element of the kth row and the k'th column, the element of the kth row and the Kth column, Q K,1 , Q K,2 , Q K,k' , Q K,K correspond to the Kth row and the 1st row in Q The element of the column, the element of the Kth row and the 2nd column, the element of the Kth row and the k'th column, the element of the Kth row and the Kth column, 1≤k'≤K, Q k,k' means z j'-1 The probability of z j' = k' under the condition of =k, 2≤j'≤L, z j'-1 represents the hidden mark corresponding to the j'-1th observation data x j'-1 in the hidden Markov model state, z j' represents the hidden state corresponding to the j'th observation data x j' in the hidden Markov model.

步骤三：在隐马尔可夫模型中引入粘性因子，得到粘性隐马尔可夫模型；在粘性隐马尔可夫模型中，初始化属于每类隐藏状态的高斯分布的均值和精度，将μk的初始化值记为

Figure BDA0002646559800000092
Figure BDA0002646559800000093
将τk的初始化值记为
Figure BDA0002646559800000094
Figure BDA0002646559800000095
初始化状态转移概率矩阵Q，将Q的初始化值记为Q(0)，Q(0)中的每行中的所有元素的共轭先验分布服从狄利克雷分布，Q(0)中的第k行中的所有元素的共轭先验分布服从的狄利克雷分布为：
Figure BDA0002646559800000096
其中，
Figure BDA0002646559800000097
表示Q(0)中的第k行中的所有元素，Dir()表示狄利克雷分布，γ表示狄利克雷分布的参数，在本实施例中取γ＝1，κ表示粘性因子，在本实施例中取κ＝50，δ(k,1)表示两个参数分别为k和1的克罗内克函数，δ(k,k')表示两个参数分别为k和k'的克罗内克函数，δ(k,K)表示两个参数分别为k和K的克罗内克函数，
Figure BDA0002646559800000098
γ+κδ(k,1)表示共轭先验分布服从的狄利克雷分布的第1个元素，γ+κδ(k,k')表示共轭先验分布服从的狄利克雷分布的第k'个元素，γ+κδ(k,K)表示共轭先验分布服从的狄利克雷分布的第K个元素。Step 3: Introduce a viscous factor into the hidden Markov model to obtain a viscous hidden Markov model; in the viscous hidden Markov model, initialize the mean and precision of the Gaussian distribution belonging to each type of hidden state, and initialize μ k value as
Figure BDA0002646559800000092
Figure BDA0002646559800000093
Denote the initial value of τ k as
Figure BDA0002646559800000094
Figure BDA0002646559800000095
Initialize the state transition probability matrix Q, denote the initial value of Q as Q (0) , the conjugate prior distribution of all elements in each row in Q (0) obeys the Dirichlet distribution, the first in Q (0) The Dirichlet distribution of the conjugate prior distribution of all elements in row k is:
Figure BDA0002646559800000096
in,
Figure BDA0002646559800000097
Represents all the elements in the kth row in Q (0) , Dir() represents the Dirichlet distribution, γ represents the parameters of the Dirichlet distribution, in this embodiment, γ=1, κ represents the viscosity factor, in this In the example, κ=50, δ(k, 1) represents the Kronecker function with two parameters k and 1 respectively, and δ(k, k') represents the Krone function with two parameters k and k' respectively Kronecker function, δ(k, K) represents the Kronecker function with two parameters k and K, respectively,
Figure BDA0002646559800000098
γ+κδ(k,1) represents the first element of the Dirichlet distribution obeyed by the conjugate prior distribution, and γ+κδ(k,k') denotes the kth element of the Dirichlet distribution obeyed by the conjugate prior distribution ' elements, γ+κδ(k, K) represents the Kth element of the Dirichlet distribution that the conjugate prior distribution obeys.

步骤四：令t表示迭代次数，t的初始值为1；令T表示设定的最大迭代次数，T≥3，在本实施例中取T＝100。Step 4: Let t represent the number of iterations, and the initial value of t is 1; let T represent the set maximum number of iterations, T≥3, and T=100 in this embodiment.

步骤五：计算粘性隐马尔可夫模型中的所有观测数据对应的隐藏状态在第t次迭代下的聚类结果，记为z(t)，

Figure BDA0002646559800000101
其中，
Figure BDA0002646559800000102
表示求使得p(z|x,Q(t-1),μ(t-1),τ(t-1))取最大值时变量z的值，z为粘性隐马尔可夫模型中的所有观测数据对应的隐藏状态构成的向量，z＝[z1,z2,…,zj,…,zL]，z1表示第1个观测数据x1对应的隐藏状态，z2表示第2个观测数据x2对应的隐藏状态，zL表示第L个观测数据xL对应的隐藏状态，x表示粘性隐马尔可夫模型中的所有观测数据构成的向量，x＝[x1,x2,…,xj,…,xL]，t＝1时Q(t-1)即为Q(0)，t≠1时Q(t-1)表示粘性隐马尔可夫模型中的状态转移概率矩阵Q在第t-1次迭代下的值，t＝1时μ(t-1)即为μ的初始值μ(0)，μ＝[μ1,…,μk…,μK]，μ1表示属于第1类隐藏状态的高斯分布的均值，μK表示属于第K类隐藏状态的高斯分布的均值，
Figure BDA0002646559800000103
Figure BDA0002646559800000104
表示μ1的初始化值，
Figure BDA0002646559800000105
表示μK的初始化值，t≠1时μ(t-1)表示μ在第t-1次迭代下的值，
Figure BDA0002646559800000106
Figure BDA0002646559800000107
表示μ1在第t-1次迭代下的值，
Figure BDA0002646559800000108
表示μk在第t-1次迭代下的值，
Figure BDA0002646559800000109
表示μK在第t-1次迭代下的值，t＝1时τ(t-1)即为τ的初始值τ(0)，τ＝[τ1,…,τk,…,τK]，τ1表示属于第1类隐藏状态的高斯分布的精度，τK表示属于第K类隐藏状态的高斯分布的精度，
Figure BDA00026465598000001010
Figure BDA00026465598000001011
表示τ1的初始化值，
Figure BDA00026465598000001012
表示τK的初始化值，t≠1时τ(t-1)表示τ在第t-1次迭代下的值，
Figure BDA00026465598000001013
Figure BDA00026465598000001014
表示τ1在第t-1次迭代下的值，
Figure BDA00026465598000001015
表示τk在第t-1次迭代下的值，
Figure BDA00026465598000001016
表示τK在第t-1次迭代下的值，p(z|x,Q(t-1),μ(t-1),τ(t-1))表示z的后验概率，根据贝叶斯定理得到
Figure BDA00026465598000001017
Step 5: Calculate the clustering results of the hidden states corresponding to all observed data in the viscous hidden Markov model under the t-th iteration, denoted as z (t) ,
Figure BDA0002646559800000101
in,
Figure BDA0002646559800000102
Represents the value of the variable z when p(z|x,Q (t-1) , μ (t-1) ,τ (t-1) ) takes the maximum value, z is all the values in the viscous hidden Markov model The vector of hidden states corresponding to the observed data, z=[z 1 , z 2 ,…,z j ,…,z L ], z 1 represents the hidden state corresponding to the first observation data x 1 , and z 2 represents the second The hidden state corresponding to the observation data x 2 , z L represents the hidden state corresponding to the L-th observation data x L , x represents the vector formed by all the observation data in the viscous hidden Markov model, x=[x 1 , x 2 ,…,x j ,…,x L ], when t=1, Q (t-1) is Q (0) , and when t≠1, Q (t-1) represents the state transition in the viscous hidden Markov model The value of the probability matrix Q at the t-1th iteration, when t=1 μ (t-1) is the initial value μ (0) of μ, μ=[μ 1 ,…,μ k …,μ K ] , μ 1 represents the mean of the Gaussian distribution belonging to the first hidden state, μ K represents the mean of the Gaussian distribution belonging to the Kth hidden state,
Figure BDA0002646559800000103
Figure BDA0002646559800000104
represents the initialization value of μ 1 ,
Figure BDA0002646559800000105
represents the initialization value of μ K , when t≠1 μ (t-1) represents the value of μ at the t-1th iteration,
Figure BDA0002646559800000106
Figure BDA0002646559800000107
represents the value of μ 1 at the t-1th iteration,
Figure BDA0002646559800000108
represents the value of μ k at the t-1th iteration,
Figure BDA0002646559800000109
Represents the value of μ K at the t-1th iteration, when t=1, τ (t-1) is the initial value of τ τ (0) , τ=[τ 1 ,...,τ k ,...,τ K ], τ 1 represents the accuracy of the Gaussian distribution belonging to the first hidden state, τ K represents the accuracy of the Gaussian distribution belonging to the Kth hidden state,
Figure BDA00026465598000001010
Figure BDA00026465598000001011
represents the initialization value of τ 1 ,
Figure BDA00026465598000001012
represents the initialization value of τ K , when t≠1, τ (t-1) represents the value of τ at the t-1th iteration,
Figure BDA00026465598000001013
Figure BDA00026465598000001014
represents the value of τ 1 at the t-1th iteration,
Figure BDA00026465598000001015
represents the value of τ k at the t-1th iteration,
Figure BDA00026465598000001016
represents the value of τ K at the t-1th iteration, p(z|x,Q (t-1) ,μ (t-1) ,τ (t-1) ) represents the posterior probability of z, according to the Yeas' theorem gives
Figure BDA00026465598000001017

p(zj|x,Q(t-1),μ(t-1),τ(t-1))表示zj的后验概率，符号“∝”表示正比，xj+1表示第j+1个观测数据，xj+2表示第j+2个观测数据，p(zj,x1,x2,...,xj|Q(t-1),μ(t-1),τ(t-1))表示zj,x1,x2,...,xj的联合概率，p(xj+1,xj+2,...,xL|zj,Q(t-1),μ(t-1),τ(t-1))表示zj的条件下xj+1,xj+2,...,xL的联合概率，p(zj,x1,x2,...,xj|Q(t-1),μ(t-1),τ(t-1))和p(xj+1,xj+2,...,xL|zj,Q(t-1),μ(t-1),τ(t-1))通过现有的前向后向算法计算得到，

Figure BDA0002646559800000111
Figure BDA0002646559800000112
表示z1在第t次迭代下的值，
Figure BDA0002646559800000113
表示z2在第t次迭代下的值，
Figure BDA0002646559800000114
为z(t)中的第j个元素，也即表示zj在第t次迭代下的值，
Figure BDA0002646559800000115
表示zL在第t次迭代下的值。p(z j |x,Q (t-1) , μ (t-1) ,τ (t-1) ) represents the posterior probability of z j , the symbol “∝” represents the proportionality, and x j+1 represents the jth +1 observation data, x j+2 represents the j+2th observation data, p(z j ,x 1 ,x 2 ,...,x j |Q (t-1) ,μ (t-1) ,τ (t-1) ) represents the joint probability of z j ,x 1 ,x 2 ,...,x j , p(x j+1 ,x j+2 ,...,x L |z j , Q (t-1) , μ (t-1) , τ (t-1) ) represent the joint probability of x j+1 , x j+2 ,...,x L under the condition of z j , p(z j ,x 1 ,x 2 ,...,x j |Q (t-1) ,μ (t-1) ,τ (t-1) ) and p(x j+1 ,x j+2 ,. ..,x L |z j ,Q (t-1) ,μ (t-1) ,τ (t-1) ) are calculated by the existing forward-backward algorithm,
Figure BDA0002646559800000111
Figure BDA0002646559800000112
represents the value of z 1 at the t-th iteration,
Figure BDA0002646559800000113
represents the value of z 2 at the t-th iteration,
Figure BDA0002646559800000114
is the j-th element in z (t) , that is, the value of z j under the t-th iteration,
Figure BDA0002646559800000115
represents the value of z L at the t-th iteration.

步骤六：计算粘性隐马尔可夫模型中的状态转移概率矩阵Q在第t次迭代下的值，记为Q(t)，Q(t)中的第k行中的所有元素的共轭先验分布服从的狄利克雷分布为：

Figure BDA0002646559800000116
Q(t)中的第k行中的所有元素的后验分布服从的狄利克雷分布为：
Figure BDA0002646559800000117
其中，
Figure BDA0002646559800000118
表示Q(t)中的第k行中的所有元素，
Figure BDA0002646559800000119
表示在第t次迭代下从第k类隐藏状态转移到第1类隐藏状态的观测数据的数量，
Figure BDA00026465598000001110
表示在第t次迭代下从第k类隐藏状态转移到第k'类隐藏状态的观测数据的数量，
Figure BDA00026465598000001111
表示在第t次迭代下从第k类隐藏状态转移到第K类隐藏状态的观测数据的数量，
Figure BDA00026465598000001112
表示后验分布服从的狄利克雷分布的第1个元素，
Figure BDA00026465598000001113
表示后验分布服从的狄利克雷分布的第k'个元素，
Figure BDA00026465598000001114
表示后验分布服从的狄利克雷分布的第K个元素。Step 6: Calculate the value of the state transition probability matrix Q in the viscous hidden Markov model under the t-th iteration, denoted as Q (t) , the conjugate first of all elements in the k-th row in Q (t) . The Dirichlet distribution obeyed by the test distribution is:
Figure BDA0002646559800000116
The posterior distribution of all elements in the kth row in Q (t) follows the Dirichlet distribution:
Figure BDA0002646559800000117
in,
Figure BDA0002646559800000118
represents all elements in the kth row in Q (t) ,
Figure BDA0002646559800000119
represents the number of observations transferred from the k-th hidden state to the 1-th hidden state at the t-th iteration,
Figure BDA00026465598000001110
represents the number of observations transferred from the kth hidden state to the k'th hidden state at the tth iteration,
Figure BDA00026465598000001111
represents the number of observations transferred from the k-th hidden state to the k-th hidden state at the t-th iteration,
Figure BDA00026465598000001112
represents the first element of the Dirichlet distribution that the posterior distribution obeys,
Figure BDA00026465598000001113
represents the k'th element of the Dirichlet distribution to which the posterior distribution obeys,
Figure BDA00026465598000001114
Represents the Kth element of the Dirichlet distribution to which the posterior distribution follows.

步骤七：利用属于同一类隐藏状态的所有观测数据，根据贝叶斯定理，计算在x和z(t)确定后μ在第t次迭代下的值μ(t)和τ在第t次迭代下的值τ(t)的后验概率，记为p(μ(t),τ(t)|x,z(t))，

Figure BDA0002646559800000121
其中，μ(t)表示μ在第t次迭代下的值，
Figure BDA0002646559800000122
Figure BDA0002646559800000123
表示μ1在第t次迭代下的值，
Figure BDA0002646559800000124
表示μk在第t次迭代下的值，
Figure BDA0002646559800000125
表示μK在第t次迭代下的值，τ(t)表示τ在第t次迭代下的值，
Figure BDA0002646559800000126
Figure BDA0002646559800000127
表示τ1在第t次迭代下的值，
Figure BDA0002646559800000128
表示τk在第t次迭代下的值，
Figure BDA0002646559800000129
表示τK在第t次迭代下的值，
Figure BDA00026465598000001210
表示
Figure BDA00026465598000001211
服从的高斯分布的概率密度函数，其变量为
Figure BDA00026465598000001212
均值为
Figure BDA00026465598000001213
方差为
Figure BDA00026465598000001214
表示
Figure BDA00026465598000001215
服从的伽马分布的概率密度函数，其变量为
Figure BDA00026465598000001216
形状参数为
Figure BDA00026465598000001217
速率参数为
Figure BDA00026465598000001218
Figure BDA00026465598000001219
表示在第t次迭代下属于第k类隐藏状态的观测数据的数量，
Figure BDA00026465598000001220
表示在第t次迭代下属于第k类隐藏状态的所有观测数据的平均值，
Figure BDA00026465598000001221
Figure BDA00026465598000001222
表示在第t次迭代下属于第k类隐藏状态的第
Figure BDA00026465598000001223
个观测数据，η0、m0、a0和b0均为常数，在本实施例中取η0＝1、m0＝1、a0＝1、b0＝1。Step 7: Using all observation data belonging to the same hidden state, according to Bayes' theorem, calculate the values of μ (t) and τ at the t-th iteration after x and z (t) are determined. The posterior probability of the value τ (t) under , denoted as p(μ (t) ,τ (t) |x,z (t) ),
Figure BDA0002646559800000121
where μ (t) represents the value of μ at the t-th iteration,
Figure BDA0002646559800000122
Figure BDA0002646559800000123
represents the value of μ 1 at the t-th iteration,
Figure BDA0002646559800000124
represents the value of μ k at the t-th iteration,
Figure BDA0002646559800000125
represents the value of μ K at the t-th iteration, τ (t) represents the value of τ at the t-th iteration,
Figure BDA0002646559800000126
Figure BDA0002646559800000127
represents the value of τ 1 at the t-th iteration,
Figure BDA0002646559800000128
represents the value of τ k at the t-th iteration,
Figure BDA0002646559800000129
represents the value of τ K at the t-th iteration,
Figure BDA00026465598000001210
express
Figure BDA00026465598000001211
The probability density function of the Gaussian distribution subject to the variable
Figure BDA00026465598000001212
mean is
Figure BDA00026465598000001213
The variance is
Figure BDA00026465598000001214
express
Figure BDA00026465598000001215
Probability density function of the gamma distribution obeyed, whose variables are
Figure BDA00026465598000001216
The shape parameter is
Figure BDA00026465598000001217
The speed parameter is
Figure BDA00026465598000001218
Figure BDA00026465598000001219
represents the number of observations belonging to the k-th hidden state at the t-th iteration,
Figure BDA00026465598000001220
represents the mean of all observations belonging to the kth hidden state at the tth iteration,
Figure BDA00026465598000001221
Figure BDA00026465598000001222
represents the hidden state belonging to the kth class at the tth iteration
Figure BDA00026465598000001223
For the observation data, η 0 , m 0 , a 0 and b 0 are all constants, and in this embodiment, η 0 =1, m 0 =1, a 0 =1, and b 0 =1.

步骤八：判断t＜T是否成立，如果成立，则令t＝t+1，然后返回步骤五继续迭代；如果不成立，则执行步骤九；其中，t＝t+1中的“＝”为赋值符号。Step 8: Determine whether t<T is established, if so, set t=t+1, and then return to step 5 to continue the iteration; if not, execute step 9; among them, "=" in t=t+1 is an assignment symbol.

步骤九：将μ(t)中的每个元素的值作为对应一类隐藏状态的功率估计值，即将μ(t)中的第k个元素的值作为第k类隐藏状态的功率估计值；然后将所有类隐藏状态的功率估计值中的最小功率估计值作为噪声功率的估计值，记为

Figure BDA00026465598000001224
Step 9: The value of each element in μ (t) is used as the power estimation value of the corresponding type of hidden state, that is, the value of the kth element in μ (t) is used as the power estimation value of the kth type of hidden state; Then the minimum power estimate among the power estimates of all classes of hidden states is used as the estimate of noise power, denoted as
Figure BDA00026465598000001224

通过以下仿真来进一步说明本发明方法的可行性和有效性。The feasibility and effectiveness of the method of the present invention are further illustrated by the following simulations.

图2给出了使用本发明方法的均方误差随信噪比的变化曲线。在仿真中，噪声功率为

Figure BDA0002646559800000131
最大迭代次数T＝100，m0、η0、a0、b0均取1，狄利克雷分布的参数γ＝1，粘性因子κ＝50，样本数量N＝1000，蒙特卡洛次数为1000。均方误差的计算公式为
Figure BDA0002646559800000132
Figure BDA0002646559800000133
表示噪声功率的估计值，
Figure BDA0002646559800000134
表示噪声功率，符号
Figure BDA0002646559800000135
表示求2-范数的平方符号。从图2中可以看出，均方误差随着信噪比的增大而下降，充分说明本发明方法确实是能够很好地估计出噪声功率。Figure 2 shows the variation curve of the mean square error with the signal-to-noise ratio using the method of the present invention. In the simulation, the noise power is
Figure BDA0002646559800000131
The maximum number of iterations T=100, m 0 , η 0 , a 0 , b 0 are all set to 1, the parameter of Dirichlet distribution γ=1, the viscosity factor κ=50, the number of samples N=1000, the number of Monte Carlo is 1000 . The formula for calculating the mean square error is
Figure BDA0002646559800000132
Figure BDA0002646559800000133
represents an estimate of the noise power,
Figure BDA0002646559800000134
represents the noise power, symbol
Figure BDA0002646559800000135
Indicates the square notation for finding the 2-norm. It can be seen from FIG. 2 that the mean square error decreases with the increase of the signal-to-noise ratio, which fully demonstrates that the method of the present invention can indeed estimate the noise power well.

Claims (1)

1. A noise power estimation method based on a viscous hidden Markov model is characterized by comprising the following steps:
the method comprises the following steps: in a cognitive radio system, signals in continuous L sensing time slots are sampled, the signals in each sensing time slot are sampled at equal time intervals, N samples are obtained through total sampling, and the nth sample obtained through sampling the signals in the jth sensing time slot is recorded as rj(n); then calculating the received signal power corresponding to each sensing time slot, and recording the received signal power corresponding to the jth sensing time slot as xjI.e. the average power of all samples obtained by sampling the signal in the jth sensing slot,
Figure FDA0002646559790000011
wherein L, N, j and N are positive integers, L is more than 1, N is more than or equal to 100 and less than or equal to 1000, j is more than or equal to 1 and less than or equal to L, N is more than or equal to 1 and less than or equal to N, the symbol "|" is a modulo symbol, x isjObeying a Gaussian distribution, i.e.
Figure FDA0002646559790000012
Figure FDA0002646559790000013
Which is indicative of the power of the noise,
Figure FDA0002646559790000014
indicating the signal power of the authorized user in the j-th sensing slot,
Figure FDA0002646559790000015
indicating that the jth sensing slot is not occupied by an authorized user,
Figure FDA0002646559790000016
indicating that the jth sensing slot is occupied by an authorized user,
Figure FDA0002646559790000017
denotes xjObey mean value of
Figure FDA0002646559790000018
Variance of
Figure FDA0002646559790000019
The distribution of the gaussian component of (a) is,
Figure FDA00026465597900000110
denotes xjObey mean value of
Figure FDA00026465597900000111
Variance of
Figure FDA00026465597900000112
(ii) a gaussian distribution of;
step two: taking the received signal power corresponding to each perception time slot as the observation data in the hidden Markov model, namely taking the jth observation data in the hidden Markov model as xj(ii) a Then determining a hidden state corresponding to each observation data in the hidden Markov model, and determining xjThe corresponding hidden state is noted as zj，zjIs the interval [1, K ]]Is a value of (a) if zjIf the value of (1) is xjBelongs to class 1 hidden state if zjIf k is the value of (a), x is considered to bejBelongs to class k hidden state if zjIf the value of (A) is K, then x is considered to bejBelong to class K hidden state; then calculating the probability of each observation data in the hidden Markov model belonging to various hidden states, and calculating the probability of each observation data in the hidden Markov modeljThe probability of belonging to class k hidden states is noted
Figure FDA00026465597900000113
Finally, calculating a state transition probability matrix in the hidden Markov model, and marking as Q,
Figure FDA0002646559790000021
wherein K and K are positive integers, K represents the number of classes of hidden states set in the hidden Markov model, K is more than or equal to 2 and less than or equal to 10, K is more than or equal to 1 and less than or equal to K,
Figure FDA0002646559790000022
denotes xjObeyed Gaussian distributed probability density function with variable xjMean value of μkVariance of
Figure FDA0002646559790000023
μkMean, τ, representing a Gaussian distribution belonging to class k hidden stateskExpressing the inverse of the variance, Q, which is the precision of the Gaussian distribution belonging to the kth class of hidden states1,1、Q1,2、Q1,k'、Q1,KCorresponding to the element in Q, which represents the 1 st row and 1 st column, the 1 st row and 2 nd column, the 1 st row and K' th column, and the 1 st row and K column2,1、Q2,2、Q2,k'、Q2,KCorresponding to the element in Q, which represents the 2 nd row, 1 st column, the 2 nd row, 2 nd column, the 2 nd row, K' th column and the 2 nd row, K columnk,1、Qk,2、Qk,k'、Qk,KCorresponding to the element of the kth row and the 1 st column, the element of the kth row and the 2 nd column, the element of the kth row and the kth' column and the element of the kth row and the kth column in Q, QK,1、QK,2、QK,k'、QK,KCorrespondingly represents the elements of the K-th row and the 1 st column, the K-th row and the 2 nd column, the K-th row and the K '-th column, the elements of the K-th row and the K-th column in Q, wherein K' is more than or equal to 1 and less than or equal to K, and Qk,k'Denotes zj'-1K under the condition of zj'K ', j' is 2. ltoreq. L, zj'-1Represents the j' -1 st observation data x in the hidden Markov modelj'-1Corresponding hidden state, zj'Representing the jth' observation x in a hidden Markov modelj'A corresponding hidden state;
step three: introducing a viscosity factor into the hidden Markov model to obtain a viscous hidden Markov model; in a viscous hidden Markov modelThe mean and precision of the Gaussian distribution belonging to each class of hidden states are initialized, mukIs recorded as
Figure FDA0002646559790000024
Will taukIs recorded as
Figure FDA0002646559790000025
Initializing the state transition probability matrix Q, and recording the initialization value of Q as Q(0)，Q(0)The conjugate prior distribution of all elements in each row in (a) obeys a dirichlet distribution, Q(0)The conjugate prior distribution of all elements in the k-th row in (a) obeys a dirichlet distribution of:
Figure FDA0002646559790000026
wherein,
Figure FDA0002646559790000027
represents Q(0)All elements in the K-th row of (a), Dir () representing a dirichlet distribution, γ representing a parameter of the dirichlet distribution, κ representing a viscosity factor, (K,1) representing a kronecker function with two parameters K and 1, respectively, (K, K ') representing a kronecker function with two parameters K and K', respectively, (K, K) representing a kronecker function with two parameters K and K, respectively,
Figure FDA0002646559790000031
γ + κ (K,1) denotes the 1 st element of the dirichlet distribution to which the conjugate-prior distribution obeys, γ + κ (K, K') denotes the kth element of the dirichlet distribution to which the conjugate-prior distribution obeys, and γ + κ (K, K) denotes the kth element of the dirichlet distribution to which the conjugate-prior distribution obeys;
step four: let t represent the number of iterations, the initial value of t is 1; let T represent the maximum iteration number set, T ≧ 3;
step five: calculating the clustering result of the hidden states corresponding to all the observed data in the viscous hidden Markov model under the t-th iteration, and recording as z(t)，
Figure FDA00026465597900000315
Wherein,
Figure FDA00026465597900000316
expression equation p (z | x, Q)(t-1),μ(t-1),τ(t-1)) Taking the value of a maximum value time variable z, wherein z is a vector formed by hidden states corresponding to all observation data in the viscous hidden Markov model, and z is [ z ═ z1,z2,…,zj,…,zL]，z1Represents the 1 st observation data x1Corresponding hidden state, z2Represents the 2 nd observation x2Corresponding hidden state, zLRepresents the L-th observed data xLCorresponding hidden states, x represents a vector of all observed data in the viscous hidden Markov model, x ═ x1,x2,…,xj,…,xL]When t is 1, Q(t-1)Is namely Q(0)Q when t is not equal to 1(t-1)Represents the value of the state transition probability matrix Q in the sticky hidden Markov model at the t-1 th iteration, when t is 1, mu(t-1)Is the initial value mu of mu(0)，μ＝[μ1,…,μk…,μK]，μ1Mean, μ, of a Gaussian distribution representing hidden states belonging to class 1KRepresents the mean of the gaussian distribution belonging to class K hidden states,
Figure FDA0002646559790000032
Figure FDA00026465597900000317
represents μ1The initial value of (a) is set,
Figure FDA0002646559790000033
represents μKWhen the initialization value of (1), t ≠ 1 μ(t-1)Represents the value of μ at the t-1 th iteration,
Figure FDA0002646559790000034
Figure FDA00026465597900000312
represents μ1At the value at the t-1 th iteration,
Figure FDA0002646559790000035
represents μkAt the value at the t-1 th iteration,
Figure FDA0002646559790000036
represents μKAt the t-1 th iteration, t is 1(t-1)I.e. the initial value tau of tau(0)，τ＝[τ1,…,τk,…,τK]，τ1Indicating the accuracy of the Gaussian distribution, τ, of hidden states belonging to class 1KIndicating the accuracy of the gaussian distribution belonging to class K hidden states,
Figure FDA0002646559790000037
Figure FDA00026465597900000313
denotes τ1The initial value of (a) is set,
Figure FDA0002646559790000038
denotes τKτ when t ≠ 1(t-1)Denotes the value of tau at the t-1 th iteration,
Figure FDA0002646559790000039
Figure FDA00026465597900000314
denotes τ1At the value at the t-1 th iteration,
Figure FDA00026465597900000310
denotes τkAt the value at the t-1 th iteration,
Figure FDA00026465597900000311
denotes τKValue at t-1 iteration, p (z | x, Q)(t-1),μ(t-1),τ(t-1)) The posterior probability of z is obtained according to Bayes theorem
Figure FDA0002646559790000041
p(zj|x,Q(t-1),μ(t-1),τ(t-1)) Denotes zjThe symbol ". alpha." indicates a direct ratio, xj+1Denotes the j +1 th observation, xj+2Denotes the j +2 th observation, p (z)j,x1,x2,...,xj|Q(t-1),μ(t-1),τ(t-1)) Denotes zj,x1,x2,...,xjJoint probability of p (x)j+1,xj+2,...,xL|zj,Q(t-1),μ(t-1),τ(t-1)) Denotes zjUnder the condition of (1) xj+1,xj+2,...,xLJoint probability of p (z)j,x1,x2,...,xj|Q(t-1),μ(t-1),τ(t-1)) And p (x)j+1,xj+2,...,xL|zj,Q(t-1),μ(t-1),τ(t-1)) Is calculated by a forward-backward algorithm,
Figure FDA0002646559790000042
Figure FDA00026465597900000415
denotes z1At the value at the t-th iteration,
Figure FDA0002646559790000043
denotes z2At the value at the t-th iteration,
Figure FDA0002646559790000044
is z(t)The j-th element in (1), i.e. representing zjAt the value at the t-th iteration,
Figure FDA0002646559790000045
denotes zLThe value at the t-th iteration;
step six: calculating the value of the state transition probability matrix Q in the viscous hidden Markov model under the t-th iteration and recording as Q(t)，Q(t)The conjugate prior distribution of all elements in the k-th row in (a) obeys a dirichlet distribution of:
Figure FDA0002646559790000046
Q(t)the posterior distribution of all elements in the k-th row of (a) obeys a dirichlet distribution of:
Figure FDA0002646559790000047
wherein,
Figure FDA0002646559790000048
represents Q(t)All of the elements in the k-th row in (a),
Figure FDA0002646559790000049
representing the amount of observation data that is transferred from the kth class of hidden states to the class 1 hidden states at the tth iteration,
Figure FDA00026465597900000410
representing the amount of observation data that is transferred from a hidden state of class k to a hidden state of class k' at the t-th iteration,
Figure FDA00026465597900000411
representing the amount of observation data that is transferred from a type K hidden state to a type K hidden state at the t-th iteration,
Figure FDA00026465597900000412
representing posterior distributed complianceThe 1 st element of the dirichlet distribution,
Figure FDA00026465597900000413
the k' th element of the dirichlet distribution to which the posterior distribution obeys,
Figure FDA00026465597900000414
a kth element representing a dirichlet distribution to which the posterior distribution obeys;
step seven: calculating the values in x and z according to Bayes theorem by using all observation data belonging to the same type of hidden state(t)Determining the value μ of μ at the t-th iteration(t)And the value of τ at the t-th iteration τ(t)The posterior probability of (d), is denoted as p (μ)(t),τ(t)|x,z(t))，p(μ(t),τ(t)|x,z(t))
Figure FDA0002646559790000051
Wherein, mu(t)Represents the value of μ at the t-th iteration,
Figure FDA0002646559790000053
Figure FDA00026465597900000525
represents μ1At the value at the t-th iteration,
Figure FDA0002646559790000054
represents μkAt the value at the t-th iteration,
Figure FDA0002646559790000055
represents μKValue at the t-th iteration, τ(t)Denotes the value of tau at the t-th iteration,
Figure FDA0002646559790000056
Figure FDA00026465597900000522
denotes τ1At the value at the t-th iteration,
Figure FDA0002646559790000057
denotes τkAt the value at the t-th iteration,
Figure FDA0002646559790000058
denotes τKAt the value at the t-th iteration,
Figure FDA0002646559790000059
to represent
Figure FDA00026465597900000510
Obeying a probability density function of a Gaussian distribution having a variable of
Figure FDA00026465597900000511
Mean value of
Figure FDA00026465597900000512
Variance of
Figure FDA00026465597900000523
Figure FDA00026465597900000513
To represent
Figure FDA00026465597900000514
A probability density function of the obeyed gamma distribution having the variable
Figure FDA00026465597900000515
The shape parameter is
Figure FDA00026465597900000516
A rate parameter of
Figure FDA00026465597900000517
Figure FDA00026465597900000518
Representing the number of observations that belong to the kth class of hidden states at the tth iteration,
Figure FDA00026465597900000519
represents the average of all observed data belonging to class k hidden states at the t-th iteration,
Figure FDA00026465597900000520
Figure FDA00026465597900000524
indicating hidden states belonging to class k at the t-th iteration
Figure FDA00026465597900000521
Individual observation data, η0、m0、a0And b0Are all constants;
step eight: judging whether T is greater than T, if so, making T equal to T +1, and then returning to the fifth step to continue iteration; if not, executing the step nine; wherein, t is in t +1, and is an assignment symbol;
step nine: mu to(t)As a power estimate for a class of hidden states, i.e. mu(t)The value of the kth element in (a) is used as the power estimation value of the kth hidden state; then, the minimum power estimation value in the power estimation values of all the classes of hidden states is taken as the estimation value of the noise power and is recorded as the estimation value
Figure FDA0002646559790000061
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