CN101819782A

CN101819782A - Variable-step self-adaptive blind source separation method and blind source separation system

Info

Publication number: CN101819782A
Application number: CN201010121553A
Authority: CN
Inventors: 张天骐; 侯瑞玲; 代少升; 高翔云; 赵德芳; 杜小华; 庞统; 金翔
Original assignee: Chongqing University of Post and Telecommunications
Current assignee: Chongqing University of Post and Telecommunications
Priority date: 2010-03-10
Filing date: 2010-03-10
Publication date: 2010-09-01
Anticipated expiration: 2030-03-10
Also published as: CN101819782B

Abstract

The invention claims to protect a variable step size self-adaptive EASI blind source signal separation processing method, which belongs to the technical field of signal processing. This method estimates the global matrix that can reflect the separation accuracy by the minimum mean square error criterion to control the step size. Compared with the traditional EASI algorithm, this method overcomes the inherent contradiction of the traditional EASI algorithm's convergence speed and steady-state error. The mixed signal can be separated accurately, the convergence speed is improved, the steady-state error is reduced, and the stability is better at the same time. It has broad application prospects in wireless communication, radar, image, voice signal processing and other fields.

Description

A Variable Step Size Adaptive Blind Source Separation Method and Blind Source Separation System

技术领域technical field

本发明涉及信号处理技术领域，是一种盲源分离方法。The invention relates to the technical field of signal processing, and is a blind source separation method.

背景技术Background technique

在许多情况下，源信号是相互混合的，对观测信号进行处理的目的就是恢复出无法直接观测的各个原始源信号。盲源分离过程可描述为：通过寻找一个满秩线性变换矩阵，以便使输出的各个分量尽可能地相互独立，最大程度地逼近各个源信号。即建立目标函数以寻优来实现逼近。(参考文献：[1]Cardoso J F，Laheld B.Equivariant adaptive source separation[J].IEEETransaction on Signal Processing，44(12)：3017-3030，1996.)In many cases, the source signals are mixed with each other, and the purpose of processing the observed signals is to recover the original source signals that cannot be directly observed. The process of blind source separation can be described as: by looking for a full-rank linear transformation matrix, in order to make each component of the output as independent as possible, and to approximate each source signal to the greatest extent. That is, the objective function is established to optimize to achieve approximation. (References: [1] Cardoso J F, Laheld B. Equivariant adaptive source separation [J]. IEEE Transaction on Signal Processing, 44(12): 3017-3030, 1996.)

EASI(Equivariant Adaptive Source Separation，等变化自适应)算法是经典的自适应盲源分离算法，属于LMS(Least Mean Squares，最小均方误差)型算法。LMS型学习算法都存在一个步长的优选问题，步长是影响算法收敛速度和稳态性能的关键所在。若采用大的步长，则算法收敛快，但信号的分离精度(即稳态性能)差；而采用小的步长，则稳态性能好，但算法收敛慢。传统的EASI算法都采用固定步长，这就决定了传统的EASI算法存在收敛速度和稳态误差的内在矛盾。采用大的步长，信号分离精度得不到保证；若采用小的步长，收敛速度慢，会导致接收完所有混合信号后，信号未能得到成功分离。EASI (Equivariant Adaptive Source Separation) algorithm is a classic adaptive blind source separation algorithm, which belongs to the LMS (Least Mean Squares, minimum mean square error) algorithm. There is a step size optimization problem in all LMS learning algorithms, and the step size is the key to the algorithm's convergence speed and steady-state performance. If a large step size is used, the algorithm will converge quickly, but the separation accuracy of the signal (that is, the steady-state performance) will be poor; if a small step size is used, the steady-state performance will be good, but the algorithm will converge slowly. The traditional EASI algorithm adopts a fixed step size, which determines that the traditional EASI algorithm has an inherent contradiction between the convergence speed and the steady-state error. If a large step size is used, the signal separation accuracy cannot be guaranteed; if a small step size is used, the convergence speed will be slow, which will cause the signal to fail to be successfully separated after receiving all mixed signals.

发明内容Contents of the invention

本发明所要解决的技术问题是，提出一种变步长自适应盲源分离方法，解决在对盲源信号进行分离的过程中，LMS型算法存在的收敛速度和稳态误差这一矛盾。在信号处理过程中，可以有效地对混合信号进行分离，提高了收敛速度，降低了稳态误差，同时算法收敛的稳定性更好。The technical problem to be solved by the present invention is to propose a variable step size self-adaptive blind source separation method to solve the contradiction between convergence speed and steady-state error in the LMS algorithm during the process of separating blind source signals. In the signal processing process, the mixed signal can be effectively separated, the convergence speed is improved, the steady-state error is reduced, and the stability of the algorithm convergence is better at the same time.

本发明解决上述技术问题的技术方案是，在EASI算法的基础上，应用最小均方误差准则，估计系统的全局矩阵，由此得到算法性能指数(PI)的估计值，通过该估计值来控制系统的步长，在信号分离初期采用较大的步长，以加快算法的收敛速度，然后慢慢减小步长，提高算法的稳态误差。变步长自适应EASI盲源分离方法具体包括，n个独立同分布的未知源信号s(k)＝[s₁(k)，s₂(k)，…，s_n(k)]^T经过信道混合矩阵H的传输得到m个混合信号x(k)＝[x₁(k)，x₂(k)，…，x_m(k)]^T；对所有混合信号逐点更新分离矩阵W，可根据公式：W(k+1)＝W(k)+μ(k)[I-y(k)y^T(k)-g(y(k))y^T(k)+y(k)g^T(y(k))]W(k)对接收到的所有混合信号逐点更新分离矩阵W，所建立的分离矩阵随步长的变化而变化。将全部混合信号通过分离矩阵W，根据公式：y＝Wx将信号分离。在构建分离矩阵的过程中，根据性能指数的估计值

控制步长的大小，根据公式：

确定下一点信号送入时，更新分离矩阵W的步长，使步长随着

值的下降而不断减小。确定

值具体包括，利用最小均方误差准则

得到混合矩阵H的估计矩阵

；根据公式

获取全局传输矩阵的估计矩阵，根据全局传输矩阵

调用公式得到性能指数的估计值

，由此确定每次迭代所需的步长，并由分离矩阵更新模块构建分离矩阵。The technical solution of the present invention to solve the above-mentioned technical problems is that, on the basis of the EASI algorithm, the minimum mean square error criterion is applied to estimate the global matrix of the system, thereby obtaining the estimated value of the algorithm performance index (PI), and controlling the For the step size of the system, a larger step size is used in the early stage of signal separation to speed up the convergence speed of the algorithm, and then gradually reduce the step size to improve the steady-state error of the algorithm. The variable step size adaptive EASI blind source separation method specifically includes n independent and identically distributed unknown source signals s(k)=[s ₁ (k), s ₂ (k), ..., s _n (k)] ^T through The transmission of channel mixing matrix H obtains m mixed signals x(k)=[x ₁ (k), x ₂ (k), ..., x _m (k)] ^T ; update separation matrix W point by point for all mixed signals, According to the formula: W(k+1)=W(k)+μ(k)[Iy(k)y ^T (k)-g(y(k))y ^T (k)+y(k)g ^T (y(k))]W(k) update the separation matrix W point by point for all the mixed signals received, and the established separation matrix changes with the change of the step size. Pass all the mixed signals through the separation matrix W, and separate the signals according to the formula: y=Wx. In the process of constructing the separation matrix, according to the estimated value of the performance index

Control the size of the step size, according to the formula:

When it is determined that the next point signal is sent in, update the step size of the separation matrix W so that the step size follows

decrease in value. Sure

Values specifically include, using the minimum mean square error criterion

Get the estimated matrix of the mixing matrix H

;according to the formula

Obtain the estimated matrix of the global transmission matrix, according to the global transmission matrix

call formula Get an estimate of the performance index

, so as to determine the step size required for each iteration, and the separation matrix is constructed by the separation matrix update module.

本发明提出一种变步长自适应EASI盲源分离系统，包括分离矩阵更新模块、全局传输矩阵估计模块、性能指标估计模块、变步长模块。源信号s(k)经过信道混合矩阵的传输后得到m个混合信号x(k)＝[x₁(k)，x₂(k)，…，x_m(k)]^T；全局传输矩阵估计模块利用最小均方误差准则

得到混合矩阵H的估计矩阵

，调用公式

获取全局估计矩阵

；性能指标估计模块根据全局估计矩阵调用公式

得到性能指数的估计值，变步长模块根据

控制步长的大小，调用公式：

确定下一点信号的步长；分离矩阵更新模块利用步长根据公式：W(k+1)＝W(k)+μ(k)[I-y(k)y^T(k)-g(y(k))y^T(k)+y(k)g^T(y(k))]W(k)构建每一点信号的分离矩阵，所有信号接收完得到最终分离矩阵W，将全部混合信号通过分离矩阵W，获得相互独立的估计信号。The invention proposes a variable step size adaptive EASI blind source separation system, which includes a separation matrix update module, a global transmission matrix estimation module, a performance index estimation module, and a variable step size module. After the source signal s(k) is transmitted through the channel mixing matrix, m mixed signals x(k)=[x ₁ (k), x ₂ (k), ..., x _m (k)] ^T are obtained; the global transmission matrix is estimated The module utilizes the minimum mean square error criterion

Get the estimated matrix of the mixing matrix H

, calling the formula

Get the global estimate matrix

;Performance index estimation module according to the global estimation matrix call formula

Get an estimate of the performance index , the variable step size module according to

To control the size of the step size, call the formula:

Determine the step size of the next point signal; the separation matrix update module utilizes the step size according to the formula: W(k+1)=W(k)+μ(k)[Iy(k)y ^T (k)-g(y(k ))y ^T (k)+y(k)g ^T (y(k))]W(k) Construct the separation matrix of each point signal, after all the signals are received, the final separation matrix W is obtained, and all mixed signals pass through the separation matrix W, to obtain estimated signals independent of each other.

该盲源分离方法逐点接收信号，实时地调整步长，自适应地更新系统，可以将接收到的混合信号快速、有效地进行盲源分离，以恢复原始信号。该盲源分离算法提高了算法的收敛速度，降低了算法的稳态误差，提高了信号盲源分离精度和分离效果，并且提高了算法收敛的稳定性，操作的可实现性更强。相比已有的传统方法从收敛稳定性、误差、速度方面得到显著的提高。本发明所体现出来的优势，使其在无线通信、雷达、图像、语音信号处理等领域均有广泛的应用前景。The blind source separation method receives signals point by point, adjusts the step size in real time, and updates the system adaptively. It can quickly and effectively perform blind source separation on the received mixed signal to restore the original signal. The blind source separation algorithm improves the convergence speed of the algorithm, reduces the steady-state error of the algorithm, improves the signal blind source separation accuracy and separation effect, and improves the stability of the algorithm convergence, and the operation is more realizable. Compared with the existing traditional methods, it has been significantly improved in terms of convergence stability, error and speed. The advantages embodied by the invention make it have wide application prospects in the fields of wireless communication, radar, image, voice signal processing and the like.

附图说明Description of drawings

图1本发明变步长自适应算法处理框图Fig. 1 variable step size adaptive algorithm processing block diagram of the present invention

图2本发明变步长自适应算法流程图Fig. 2 variable step size self-adaptive algorithm flow chart of the present invention

图3待分离的源信号波形Figure 3 Source signal waveform to be separated

图4本发明变步长自适应算法分离性能指标(PI)分布柱状图Fig. 4 variable step size adaptive algorithm separation performance index (PI) distribution histogram of the present invention

图5传统方法分离性能指标(PI)分布柱状图Fig. 5 Histogram of separation performance index (PI) distribution by traditional method

图6传统方法和本发明变步长自适应算法分离性能指标(PI)比较的变化曲线The variation curve of Fig. 6 traditional method and the variable step size self-adaptive algorithm separation performance index (PI) comparison of the present invention

具体实施方式Detailed ways

传统的EASI算法在提出的多数ICA方法中，学习规则都是代价函数或对比函数的梯度下降算法。典型的代价函数具有J(W)＝E{ρ(y)}的形式，其中ρ是某个标量函数，并且通常会有若干额外的约束，E{·}表示求期望。这里y＝Wx，假设W是方阵且可逆。函数ρ及x的概率密度决定了对比函数J(W)的形式。In the traditional EASI algorithm, in most of the ICA methods proposed, the learning rules are the gradient descent algorithm of the cost function or the comparison function. A typical cost function has the form of J(W)=E{ρ(y)}, where ρ is a scalar function, and there are usually several additional constraints, and E{·} represents expectation. Here y=Wx, assuming that W is a square matrix and invertible. The probability density of the function ρ and x determines the form of the contrast function J(W).

$\frac{&PartialD; &PartialD; J J ((W W))}{&PartialD; &PartialD; W W} = = E E. {{((\frac{&PartialD; &PartialD; ρ ρ ((y the y))}{&PartialD; &PartialD; y the y})) {x x}^{T T}}} = = E E. {{g g ((y the y)) {x x}^{T T}}} = = E E. {{g g ((y the y)) {y the y}^{T T}}} {(({W W}^{T T}))}^{- - 11} - - - - - - ((11))$

式中，g(y)是ρ(y)的梯度。通过引入自然梯度求矩阵的逆(W^T)^-1，自然梯度通过对矩阵梯度式(1)右乘W^TW得到，即为E{g(y)y^T}W。随之，极小化代价函数J(W)的随机梯度算法为：where g(y) is the gradient of ρ(y). By introducing the natural gradient to find the inverse of the matrix (W ^T ) ^-1 , the natural gradient is obtained by right-multiplying the matrix gradient formula (1) by W ^T W, which is E{g(y)y ^T }W. Then, the stochastic gradient algorithm for minimizing the cost function J(W) is:

ΔW＝-μg(y)y^TW (2)ΔW＝-μg(y)y ^T W (2)

其中，μ为迭代步长。Among them, μ is the iteration step size.

要考虑混合向量x的白化过程，首先对x做线性变换z＝Qx，使z_i为单位方差和零协方差：E{zz^T}＝I(I为单位方阵)。用如下的修正规则To consider the whitening process of the mixed vector x, first do a linear transformation z=Qx on x, so that z _i is unit variance and zero covariance: E{zz ^T }=I (I is a unit square matrix). with the following correction rules

ΔQ＝μ(I-zz^T)Q (3)ΔQ=μ(I-zz ^T )Q (3)

使用白化后的向量代替原始向量，即z＝QHs，易见矩阵QH为正交矩阵。所以它的逆，即分离矩阵也是正交的，用B来表示这个正交的分离矩阵。然而，如果每一步迭代中要保留B的正交性，B的每步更新就必须满足特定的约束。参照式(2)，得到B的更新序列：B←B+DB，其中D＝-μg(y)y^T。更新矩阵的正交条件为：(B+DB)(B+DB)^T＝I+D+D^T+DD^T＝I，式中做了BB^T＝I的代换。假设D很小，一阶近似给出条件：D＝-D^T或D应为反对称的。将这个条件用于相对梯度学习规则上，有Use the whitened vector instead of the original vector, ie z=QHs, it is easy to see that the matrix QH is an orthogonal matrix. So its inverse, that is, the separation matrix is also orthogonal, and B is used to represent this orthogonal separation matrix. However, each update of B must satisfy certain constraints if the orthogonality of B is to be preserved at each iteration. Referring to formula (2), the update sequence of B is obtained: B←B+DB, where D=-μg(y)y ^T . The orthogonal condition for updating the matrix is: (B+DB)(B+DB) ^T =I+D+D ^T +DD ^T =I, where BB ^T =I is replaced. Assuming D is small, a first order approximation gives the condition: D=-D ^T or D should be antisymmetric. Applying this condition to the relative gradient learning rule, we have

ΔB＝-μ[g(y)y^T-yg^T(y)]B (4)ΔB＝-μ[g(y)y ^T -yg ^T (y)]B (4)

式中，y＝Bz。In the formula, y=Bz.

将(3)和(4)这两式合成一个针对全局系统分离矩阵的统一规则。因为y＝Bz＝BQx，这个全局矩阵为W＝BQ。假设两个规则使用一样的迭代步长，一阶近似给出：Combine (3) and (4) into a unified rule for the separation matrix of the global system. Since y=Bz=BQx, this global matrix is W=BQ. Assuming the same iteration step size is used for both rules, a first-order approximation gives:

ΔW＝ΔBQ+BΔQΔW=ΔBQ+BΔQ

＝-μ[g(y)y^T-yg^T(y)]BQ+μ[BQ-Bzz^TB^TBQ] (5)＝-μ[g(y)y ^T -yg ^T (y)]BQ+μ[BQ-Bzz ^T B ^T BQ] (5)

＝μ[I-yy^T-g(y)y^T+yg^T(y)]W＝μ[I-yy ^T -g(y)y ^T +yg ^T (y)]W

这就是EASI算法。它具有将白化和分离联合起来的良好性质。This is the EASI algorithm. It has the nice property of uniting whitening and separation.

由式(5)可以看出，步长μ的作用是控制分离矩阵中因迭代所更新的元素的幅度，因此步长的选择对提高信号分离的性能是非常重要的。最优步长的选取是一个比较难解决的问题。对于时变信号，要使算法跟得上其变化速度，则必须要有一个大的步长来加速算法的收敛速度。当采用固定步长时，为了使算法达到收敛，其选值又要求非常小，从而无法达到收敛速度和稳态误差的最佳统一。为了解决这个难题，本发明利用最小均方误差准则，提出了一种新的步长自适应的EASI算法。It can be seen from formula (5) that the function of the step size μ is to control the magnitude of elements updated by iteration in the separation matrix, so the selection of the step size is very important to improve the performance of signal separation. The selection of the optimal step size is a difficult problem to solve. For time-varying signals, to make the algorithm keep up with its changing speed, it is necessary to have a large step size to accelerate the convergence speed of the algorithm. When using a fixed step size, in order to achieve convergence of the algorithm, its selection value is required to be very small, so that the best unity of convergence speed and steady-state error cannot be achieved. In order to solve this difficult problem, the present invention uses the minimum mean square error criterion to propose a new step size adaptive EASI algorithm.

根据本信号点的分离矩阵W(k)、步长μ(k)、输出的估计信号y(k)、由y(k)定义的非线性函数g(y(k))调用上述公式获得下一点信号的分离矩阵W(k+1)。其中，y(k)＝W(k)x(k)。According to the separation matrix W(k) of this signal point, the step size μ(k), the output estimated signal y(k), and the nonlinear function g(y(k)) defined by y(k) call the above formula to obtain the following Separation matrix W(k+1) of one point signal. Among them, y(k)=W(k)x(k).

建立如下变步长算法公式：Establish the following variable step size algorithm formula:

$\{\begin{matrix} W W ((k k + + 11)) = = W W ((k k)) + + μ μ ((k k)) [[I I - - y the y ((k k)) {y the y}^{T T} ((k k)) - - g g ((y the y ((k k)))) {y the y}^{T T} ((k k)) + + y the y ((k k)) {g g}^{T T} ((y the y ((k k))))]] W W ((k k)) \\ y the y ((k k)) = = W W ((k k)) x x ((k k)) \end{matrix} - - - - - - ((66))$

通过对传统的固定步长自适应EASI盲源分离算法改进，得到如式(6)的变步长自适应EASI盲源分离算法。其中，W(k)为算法通过第k点混合信号后得到的分离矩阵，W(k+1)为在W(k)的基础上，通过第k+1点混合信号后得到的分离矩阵；y(k)是第k点混合信号通过第k次更新后的分离矩阵得到的估计信号；这样，当接收完所有混合信号后，我们得到最终的分离矩阵W。μ(k)为变步长，其大小可根据性能指数的估计值来控制。By improving the traditional fixed-step-size adaptive EASI blind source separation algorithm, a variable-step-size adaptive EASI blind source separation algorithm as shown in formula (6) is obtained. Wherein, W(k) is the separation matrix obtained after the algorithm passes the k-th point mixed signal, and W(k+1) is the separation matrix obtained after passing the k+1 point mixed signal on the basis of W(k); y(k) is the estimated signal obtained by passing the k-th point mixed signal through the k-th updated separation matrix; in this way, after receiving all the mixed signals, we get the final separation matrix W. μ(k) is a variable step size, and its size can be controlled according to the estimated value of the performance index.

下面分析μ(k)的具体确定方法。The specific determination method of μ(k) is analyzed below.

在分析算法性能的时候，通常用性能指数PI(Performance Index)来估计，PI由下式确定：When analyzing the performance of the algorithm, it is usually estimated by the performance index PI (Performance Index), and the PI is determined by the following formula:

$PI P.I. ((k k)) = = \underset{i i}{Σ Σ} {{((\underset{j j}{Σ Σ} \frac{| | {G G}_{k k} ((i i,, j j)) | |}{{max max}_{j j} ((| | {G G}_{k k} ((i i,, j j)) | |))} - - 11)) + + ((\underset{j j}{Σ Σ} \frac{| | {G G}_{k k} ((j j,, i i))}{{max max}_{j j} ((| | {G G}_{k k} ((j j,, i i)) | |))} - - 11))}} - - - - - - ((77))$

其中，G_k(i，j)＝W(k)H为全局传输矩阵。理想情况下，G_k应该是各行各列只有一个非零元素的矩阵，为准单位阵。如果G_k是准单位阵，分离系统能够完全将源信号分离，分离后的信号除了在排序顺序不同和信号幅度上有伸缩之外，其信号特征与源信号是完全一样的。因此，性能指标PI(k)表征了G_k与准单位阵的近似程度。分离出的信号与源信号波形完全相同时PI(k)＝0。Wherein, G _k (i, j)=W(k)H is the global transmission matrix. Ideally, G _k should be a matrix with only one non-zero element in each row and column, which is a quasi-identity matrix. If G _k is a quasi-unit matrix, the separation system can completely separate the source signal, and the signal characteristics of the separated signal are exactly the same as the source signal except for the different order of sorting and the expansion and contraction of the signal amplitude. Therefore, the performance index PI(k) characterizes the degree of approximation of G _k to the quasi-identity matrix. When the separated signal is exactly the same as the source signal waveform, PI(k)=0.

分析可知，分离精度决定了性能指数PI(k)的大小，而PI(k)反映了分离信号和源信号的相似程度。随着分离精度的提高，PI(k)逐渐减小。在信号分离初期，应采用较大步长提高收敛速度，然后步长应逐渐减小以降低稳态误差。因此，我们可以在这两者之间建立一定的关系，通过PI(k)来控制步长μ(k)。然而，实际应用中PI(k)是未知的。PI(k)取决于全局传输矩阵G_k，G_k(i，j)＝W(k)H。所以，要想得到PI(k)的估计值

，我们首先就是得到混合矩阵H的估计矩阵 The analysis shows that the separation accuracy determines the size of the performance index PI(k), and PI(k) reflects the similarity between the separated signal and the source signal. As the separation precision increases, PI(k) decreases gradually. In the early stage of signal separation, a larger step size should be used to increase the convergence speed, and then the step size should be gradually reduced to reduce the steady-state error. Therefore, we can establish a certain relationship between the two, and control the step size μ(k) through PI(k). However, PI(k) is unknown in practical applications. PI(k) depends on the global transmission matrix G _k , G _k (i, j)=W(k)H. So, to get an estimate of PI(k)

, we first get the estimated matrix of the mixing matrix H

利用最小均方误差准则：Using the minimum mean square error criterion:

$min min ((E E. {{| | | | x x - - \overset{^^}{H h} y the y | | {| |}^{22}}})) - - - - - - ((88))$

用普通的随机梯度下降实时学习算法使式(8)极小化，得到混合矩阵的估计矩阵

Using ordinary stochastic gradient descent real-time learning algorithm to minimize Equation (8), the estimated matrix of the mixing matrix is obtained

$Δ Δ \overset{^^}{H h} ((k k)) = = \overset{^^}{H h} ((k k + + 11)) - - \overset{^^}{H h} ((k k)) = = - - η η ((k k)) \frac{&PartialD; &PartialD; {| | | | x x ((k k)) - - \overset{^^}{H h} y the y ((k k)) | | | |}^{22}}{&PartialD; &PartialD; \overset{^^}{H h}}$

$= = - - η η ((k k)) \frac{&PartialD; &PartialD; [[{((x x ((k k)) - - \overset{^^}{H h} y the y ((k k))))}^{T T} ((x x ((k k)) - - \overset{^^}{H h} y the y ((k k))))]]}{&PartialD; &PartialD; \overset{^^}{H h}} - - - - - - ((99))$

$= = 22 η η ((k k)) [[x x ((k k)) - - \overset{^^}{H h} y the y ((k k))]] {y the y}^{T T} ((k k))$

令λ(k)＝2η(k)，λ(k)为迭代步长。可得估计矩阵

的迭代公式如下：Let λ(k)=2η(k), λ(k) is the iteration step size. Estimated matrix can be obtained

The iteration formula of is as follows:

$\overset{^^}{H h} ((k k + + 11)) = = \overset{^^}{H h} ((k k)) + + λ λ ((k k)) [[x x ((k k)) - - \overset{^^}{H h} ((k k)) y the y ((k k))]] {y the y}^{T T} ((k k)) - - - - - - ((1010))$

因此，进一步可得到全局传输矩阵的估计矩阵：Therefore, the estimated matrix of the global transmission matrix can be further obtained:

${\overset{^^}{G G}}_{k k} = = W W ((k k)) \overset{^^}{H h} ((k k)) - - - - - - ((1111))$

利用

，根据下式确定性能指数PI的估计值

use

, to determine the estimated value of the performance index PI according to the following formula

$\overset{^^}{P P} I I ((k k)) = = \underset{i i}{Σ Σ} {{((\underset{j j}{Σ Σ} \frac{| | {\overset{^^}{G G}}_{k k} ((i i,, j j)) | |}{{max max}_{j j} ((| | {\overset{^^}{G G}}_{k k} ((i i,, j j)) | |))} - - 11)) + + ((\underset{j j}{Σ Σ} \frac{| | {\overset{^^}{G G}}_{k k} ((j j,, i i)) | |}{{max max}_{j j} ((| | {\overset{^^}{G G}}_{k k} ((j j,, i i)) | |))} - - 11))}} - - - - - - ((1212))$

根据以上分析，用

来控制步长的大小，即使步长随着值的下降而不断减小。由此，变步长确定如下：According to the above analysis, the

to control the size of the step size, even if the step size varies with decrease in value. Therefore, the variable step size is determined as follows:

$μ μ ((k k)) = = α α ((11 - - {e e}^{- - β β \cdot &Center Dot; \overset{^^}{P P} I I ((k k))})) - - - - - - ((1313))$

其中，α、β为经验常数，0＜α＜1，0＜β＜1。

的求解过程也与步长有关，由步长对信号分离收敛过程的影响特性，我们可以用μ(k)来代替λ(k)。Among them, α and β are empirical constants, 0<α<1, 0<β<1.

The solution process of is also related to the step size. According to the influence characteristics of the step size on the signal separation and convergence process, we can use μ(k) to replace λ(k).

以上重点描述了通过估计性能指数PI的值来，把变步长表示为时间变量的函数。也可通过其他方式确定变步长，如根据信号不同的分离状态，将步长取为不同的表达形式；根据步长梯度的不同求取方法，将步长取为不同的表达形式；根据模糊控制理论，将模糊控制器作为步长的调节因子。The above description focuses on expressing the variable step size as a function of the time variable by estimating the value of the performance index PI. The variable step size can also be determined in other ways, such as taking different expression forms of the step size according to different separation states of the signal; taking different expression forms of the step size according to different calculation methods of the step gradient; according to the fuzzy Control theory, the fuzzy controller is used as the adjustment factor of the step size.

下面结合附图和实例，对本发明的实施作进一步详细说明，但本发明的实施方式并不仅限于此。The implementation of the present invention will be described in further detail below in conjunction with the accompanying drawings and examples, but the implementation of the present invention is not limited thereto.

如图1所示为本发明变步长自适应算法处理示意框图。FIG. 1 is a schematic block diagram of variable step size adaptive algorithm processing in the present invention.

对逐点接收到的观测信号，运用变步长自适应算法进行学习。对分离矩阵权值W进行调节，逐点更新算法的步长μ，为下一次调节W的权值做准备。然后接收下一点的数据重复如上步骤，直到接收完所有观测信号。For the observed signals received point by point, the variable step size adaptive algorithm is used for learning. Adjust the weight W of the separation matrix, update the step size μ of the algorithm point by point, and prepare for the next adjustment of the weight W. Then receive the data of the next point and repeat the above steps until all observation signals are received.

假设有n个独立同分布的信号s(k)＝[s₁(k)，s₂(k)，…，s_n(k)]^T，(i＝1～n，k＝1～L)。经过信道混合矩阵H的传输后得到m个观测信号(混合信号)x(k)＝[x₁(k)，x₂(k)，…，x_m(k)]^T，(i＝1～n，k＝1～L)。其中s(k)、H、x(k)分别表示源信号、混合矩阵和混合信号，并假设m≥n(本发明中，设m＝n)，各个源信号之间相互统计独立。那么可建立盲源分离问题的信号混合模型，这种模型中混合信号表示为：x(k)＝Hs(k)。Suppose there are n independent and identically distributed signals s(k)=[s ₁ (k), s ₂ (k), ..., s _n (k)] ^T , (i=1~n, k=1~L) . After the transmission of the channel mixing matrix H, m observation signals (mixed signals) x(k)=[x ₁ (k), x ₂ (k),..., x _m (k)] ^T , (i=1～ n, k=1~L). Wherein s(k), H, x(k) represent source signal, mixing matrix and mixed signal respectively, and it is assumed that m≥n (in the present invention, m=n), each source signal is statistically independent from each other. Then the signal mixing model of the blind source separation problem can be established, and the mixed signal in this model is expressed as: x(k)=Hs(k).

在实际接收信号x(k)中，由于独立分量s_j(k)不能被直接观测到，具有隐藏特性，因此也成为“隐藏变量”。由于混合矩阵H也是未知矩阵，盲源分离问题唯一可利用的信息只有传感器检测到的观测信号向量x(k)。In the actual received signal x(k), since the independent component s _j (k) cannot be directly observed and has hidden characteristics, it also becomes a "hidden variable". Since the mixing matrix H is also an unknown matrix, the only available information for the blind source separation problem is the observed signal vector x(k) detected by the sensor.

在上述变步长基础上，根据式(6)更新分离矩阵W，使x(k)通过W(k)时的输出为源信号x(k)的估计y(k)，y(k)＝W(k)x(k)。同时，根据式(10)和式(13)更新下一次迭代所需步长。且y＝Wx＝WHs＝ΛPs，当Λ为一可逆对角阵，P为任一置换阵时，y＝[y₁，y₂，…，y_n]^T的各分量相互独立，源信号得以分离。On the basis of the above variable step size, update the separation matrix W according to formula (6), so that the output when x(k) passes through W(k) is the estimated y(k) of the source signal x(k), y(k)= W(k)x(k). At the same time, update the step size required for the next iteration according to formula (10) and formula (13). And y=Wx=WHs=ΛPs, when Λ is a reversible diagonal matrix and P is any permutation matrix, the components of y=[y ₁ , y ₂ ,…,y _n ] ^T are independent of each other, and the source signal can be separate.

如图2所示为对盲源信号进行分离的流程示意图，具体包括如下步骤：步骤1：根据信号长度L初始化μ，初始化W＝0.5I，

初始化时各元素在区间[-1，1]随机产生，并选取恰当的非线性函数g(y)。其中g(y)的选取可根据信号峭度的正负来确定。当信号的峭度小于零(亚高斯信号)时，选取的非线性函数一般为当信号的峭度大于零(超高斯信号)时，选取的非线性函数一般为g(y_i)＝tanh(y_i)。As shown in Figure 2, it is a schematic flow diagram of separating blind source signals, which specifically includes the following steps: Step 1: Initialize μ according to the signal length L, initialize W=0.5I,

During initialization, each element is randomly generated in the interval [-1, 1], and an appropriate nonlinear function g(y) is selected. The selection of g(y) can be determined according to the positive or negative of the signal kurtosis. When the kurtosis of the signal is less than zero (sub-Gaussian signal), the selected nonlinear function is generally When the kurtosis of the signal is greater than zero (super-Gaussian signal), the selected nonlinear function is generally g(y _i )=tanh(y _i ).

步骤2：逐点实时接收观察信号，对接收到的混合信号逐点进行迭代，更新分离矩阵W。具体步骤为：观察信号通过分离矩阵W获得估计值，即根据y(k)＝W(k)x(k)，得到源信号x(k)的估计信号y(k)；调用公式W(k+1)＝W(k)+μ(k)[I-y(k)y^T(k)-g(y(k))y^T(k)+y(k)g^T(y(k))]W(k)对接收到的混合信号逐点更新分离矩阵W。Step 2: Receive the observation signal point by point in real time, iterate the received mixed signal point by point, and update the separation matrix W. The specific steps are: the observed signal obtains the estimated value through the separation matrix W, that is, according to y(k)=W(k)x(k), the estimated signal y(k) of the source signal x(k) is obtained; the formula W(k) is called +1)=W(k)+μ(k)[Iy(k)y ^T (k)-g(y(k))y ^T (k)+y(k)g ^T (y(k))] W(k) updates the separation matrix W point by point for the received mixed signal.

步骤3：在更新分离矩阵的过程中，利用本时刻接收到的观察信号，根据

控制步长μ(k)的大小，使步长随着

值的下降而不断减小。具体步骤为：在步骤2的基础上，调用式(10)和式(11)，分别计算混合矩阵的估计矩阵和全局传输矩阵的估计矩阵

；根据

，调用式(12)计算性能指数估计值

；根据，调用式(13)计算μ(k)，为下一次分离矩阵W的更新做准备。Step 3: In the process of updating the separation matrix, use the observation signal received at this moment, according to

Control the size of the step size μ(k), so that the step size follows

decrease in value. The specific steps are: on the basis of step 2, call formula (10) and formula (11) to calculate the estimated matrix of the mixing matrix respectively and the estimated matrix of the global transmission matrix

;according to

, call (12) to calculate the performance index estimate

;according to , call equation (13) to calculate μ(k), and prepare for the next update of separation matrix W.

接收下一时刻的信号，针对每一点接收的信号循环执行步骤2和步骤3。The signal at the next moment is received, and step 2 and step 3 are executed cyclically for the signal received at each point.

步骤4：接收完所有混合信号，由步骤2获得最终分离矩阵W。将全部观测信号x通过最终获得的分离矩阵W，得到相互独立的估计信号y＝Wx。Step 4: After receiving all the mixed signals, the final separation matrix W is obtained from Step 2. Pass all the observed signals x through the finally obtained separation matrix W to obtain mutually independent estimated signals y=Wx.

接下来对图3所示的5个源信号(m＝5)按上述分析进行仿真实验，它们分别是符号信号、正弦信号、FM信号、AM信号和[-1，1]均匀分布的随机噪声信号。仿真中，混合信号H的各元素在区间[-1，1]随机产生，非线性函数选为

改进的变步长自适应算法中α＝0.1，β＝0.001。初始化μ＝0.0005，W＝0.5I，

初始化时各元素在区间[-1，1]随机产生。为了进行比较，同时也用传统算法来分离信号，选择能得到好的分离效果的固定步长0.0005。Next, carry out the simulation experiment on the five source signals (m=5) shown in Figure 3 according to the above analysis, they are symbol signal, sinusoidal signal, FM signal, AM signal and [-1, 1] uniformly distributed random noise Signal. In the simulation, each element of the mixed signal H is randomly generated in the interval [-1, 1], and the nonlinear function is selected as

In the improved variable step size adaptive algorithm, α=0.1, β=0.001. Initialize μ=0.0005, W=0.5I,

Each element is randomly generated in the interval [-1, 1] during initialization. For comparison, the traditional algorithm is also used to separate the signal, and a fixed step size of 0.0005 is selected to obtain a good separation effect.

为了更客观的评价分离信号与源信号近似的程度，我们对上述5个信号做500次Monte Carlo仿真，图4是本发明变步长自适应算法分离性能指标(PI)分布柱状图，可以看出，PI值基本全部分布在[0，0.6]之间，并且随着PI值的增大，分布次数逐渐越少。图5是传统方法分离性能指标(PI)分布柱状图，可以看出PI值分布不稳定，分布范围为[0.4，1.8]，PI值普遍较大。In order to more objectively evaluate the degree of approximation between the separation signal and the source signal, we do 500 Monte Carlo simulations for the above five signals. Fig. 4 is a histogram of the separation performance index (PI) distribution of the variable step size adaptive algorithm of the present invention, which can be seen It can be seen that the PI values are basically all distributed between [0, 0.6], and as the PI value increases, the number of distributions gradually decreases. Figure 5 is a histogram of the distribution of the separation performance index (PI) of the traditional method. It can be seen that the distribution of the PI value is unstable, the distribution range is [0.4, 1.8], and the PI value is generally large.

因此，本发明降低了算法的稳态误差，提高了信号盲源分离的精度，提高了分离信号效果。算法收敛的稳定性更好，操作的可实现性更强。Therefore, the invention reduces the steady-state error of the algorithm, improves the accuracy of signal blind source separation, and improves the signal separation effect. The stability of algorithm convergence is better, and the achievability of operation is stronger.

本发明通过另一组实验来验证改进的变步长自适应算法在收敛速度上的优势。我们使传统算法在达到与改进的变步长自适应算法相似的稳态误差的情况下，比较两者的收敛速度。假设源信号数m＝8，它们分别是符号信号、正弦信号、FM信号、AM信号、2ASK信号、4PSK信号、8FSK信号和[-1，1]均匀分布的随机噪声信号。做500次蒙特卡罗仿真，每次仿真源信号的起点不同。仿真中，混合信号H的各元素在区间[-1，1]随机产生，非线性函数选为

初始化μ＝0.0005，W＝0.5I，

初始化时各元素在区间[-1，1]随机产生。为了进行比较，同时也用传统算法来分离信号，固定步长选为0.0003。The present invention verifies the advantages of the improved variable step size self-adaptive algorithm in terms of convergence speed through another group of experiments. We compare the convergence speed of the traditional algorithm while achieving a similar steady-state error to the improved variable step-size adaptive algorithm. Assuming that the number of source signals is m=8, they are symbol signals, sinusoidal signals, FM signals, AM signals, 2ASK signals, 4PSK signals, 8FSK signals and [-1, 1] uniformly distributed random noise signals. Do 500 Monte Carlo simulations, and the starting point of each simulation source signal is different. In the simulation, each element of the mixed signal H is randomly generated in the interval [-1, 1], and the nonlinear function is selected as

Initialize μ=0.0005, W=0.5I,

Each element is randomly generated in the interval [-1, 1] during initialization. For comparison, the traditional algorithm was also used to separate the signals, with a fixed step size of 0.0003 chosen.

仿真结果如图6，可以看出，当两种算法收敛后的性能指标PI值基本相同时，改进的变步长自适应算法的只需要7000次左右就可以收敛，而固定步长算法则需要迭代15000次以上。收敛速度提高了两倍多。The simulation results are shown in Figure 6. It can be seen that when the performance index PI values of the two algorithms after convergence are basically the same, the improved variable step size adaptive algorithm only needs about 7000 times to converge, while the fixed step size algorithm needs Iterate over 15000 times. The convergence speed is more than doubled.

因此，本发明变步长自适应算法在满足实时处理要求的同时，极大地提高了算法的收敛速度。Therefore, the variable step size self-adaptive algorithm of the present invention greatly improves the convergence speed of the algorithm while meeting the requirements of real-time processing.

Claims

1. a variable-step self-adaptive blind source separation method is characterized in that, n unknown source signal s (k)=[s ₁(k), s ₂(k) ..., s _n(k)] ^TObtain m mixed signal x (k)=[x after the transmission through channel hybrid matrix H ₁(k), x ₂(k) ..., x _m(k)] ^TAccording to the estimated signal y (k) of the separation matrix W (k) of this signaling point, step size mu (k), output, by the nonlinear function g (y (k)) of y (k) definition, call formula W (k+1)=W (k)+μ (k) [I-y (k) y ^T(k)-g (y (k)) y ^T(k)+y (k) g ^T(y (k))] W (k) obtains down the separation matrix W (k+1) of some signals, and separation matrix is upgraded in all mixed signal pointwises, and whole mixed signals by final separation matrix W, are obtained separate estimated signal.

2. blind source separation method according to claim 1 is characterized in that, in the process of upgrading separation matrix, according to the estimated value of performance index

The size of control variable step, call formula: Determine the step-length of next iteration, make step-length in iterative process along with

The decline of value and constantly reducing.

3. blind source separation method according to claim 1 is characterized in that, wherein choosing according to the positive and negative of signal kurtosis of g (y) come to be determined, when the kurtosis of signal less than zero the time, the nonlinear function of choosing is g (y (k))=(y (k)) ³When the kurtosis of signal greater than zero the time, the nonlinear function of choosing is g (y (k))=tanh (y (k)).

4. blind source signal separation method according to claim 2 is characterized in that, determines Value specifically comprises, utilizes minimum mean square error criterion Obtain the estimated matrix of hybrid matrix H

Call formula

Obtain the estimated matrix of global transmission matrix, according to overall estimated matrix

Call formula Obtain the estimated value of performance index

5. variable-step self-adaptive blind source piece-rate system, it is characterized in that, comprise that separation matrix update module, global transmission matrix estimation module, performance index estimation module, variable step module obtain m mixed signal x (k)=[x after the transmission of source signal s (k) through the channel hybrid matrix ₁(k), x ₂(k) ..., x _m(k)] ^TThe global transmission matrix estimation module is utilized minimum mean square error criterion Obtain the estimated matrix of hybrid matrix H

Call formula

Obtain overall estimated matrix The performance index estimation module is according to overall estimated matrix Call formula

Obtain the estimated value of performance index

Variable step module basis The size of control step-length, call formula:

Determine the step-length of some signals down; The separation matrix update module utilizes step-length according to formula: W (k+1)=W (k)+μ (k) [I-y (k) y ^T(k)-g (y (k)) y ^T(k)+y (k) g ^T(y (k))] W (k) makes up the separation matrix of every bit signal, and all signals are received and are obtained final separation matrix W, and whole mixed signals by separation matrix W, are obtained separate estimated signal.