Underdetermined Blind Source Separation Algorithm And Applied Research In The Field Of Electromagnetic

In the electromagnetic environment and electromagnetic interference test process,the number of the received signal may be less than the number of source signals,as the number of source signals is unknown and the number of the received signals is small because of limited test resources.It is difficult to extract communication signal parameters from the mixed signals directly or locate and analyse the interference source.Generally,the mixed signals should be separated at first.Currently,using many sophisticated algorithms for BSS,the mixed signals can be separated with only observed signals needed based on some assumptions.However,these algorithms are mostly suitable for the overdetermined or positive definite condition that the number of mixed signals is bigger than that of source signals.Therefore,UBSS(Underdetermined Blind Source Separation)which is more suitable for real situation will be studied in this paper.Using typical communication signal in electromagnetic environment and harmonic interference as study object,based on the assumption of the sparsity of signals,the underdetermined problem is transformed to overdetermined or positive definite problem to separate the mixed signals.Details are as follows:For the application object in this paper,typical signal in electromagnetic field,the sparsity of several typical communication signals and electromagnetic interference test signals are analysed.Typical communication signals include FM signal,AM signal,frequency hopping signals,Ultra-Wideband signals.Electromagnetic interference test signal is harmonic interference caused by crystal oscillator.Before analyzing typical electromagnetic signals,theoretical knowledge related to sparsity of signal is introduced at first,and several time-frequency analyzing algorithms are introduced to separate the signal.After the time-frequency analysis of typical electromagnetic signals,these signals are divided into two categories:One conforms to sparsity just in time domain or in frequency domain,the other conforms to sparsity in time frequency domain.Further study of algorithms for this two type of signals are conducted.The underdetermined blind source separation based on Hough-Windowed and modify subspace projection is proposed in the case of that sparse signals in time domain or frequency domain.Firstly,find the single source area by calculating the ratio of observed sampling points.Then an algorithm based on Hough-Windowed was introduced to estimate the number of sources and mixing matrix.Finally separate the mixing signals by using modify subspace projection.The simulation results indicate that the proposed method can separate signals which is sparse in time domain or frequency domain successfully,estimate the mixing matrix with higher accuracy and separate the mixing signals with higher gain compared with other conventional algorithms.For sparse signals in time frequency domain,an algorithm of UBSS based on decomposition and clustering of characteristic function and weighted minimum l1 norm is proposed.First of all,fourth-order cumulant of the mixed signal is calculated.Using the characteristic that fourth-order cumulant is insensitive to Gaussian Noise,the number of the dominant source signals in different searching domains is estimated to separate the mixed signal,and then,sampling points whose eigenvalue is one are collected as single-source dominate interval.And then,estimate the mixing matrix by clustering the principal eigenvectors of the covariance matrixes corresponding to the single source area without knowing the number of sources.Accuracy and robustness of this algorithm are both improved,because of not clustering the observed signals directly.Finally,with the number of the dominant source signals based on fourth-order cumulant,by searching the second best solutions which are closest to minimum l1 norm solution,and then the weighted sum of these best solutions and minimum l1 norm solution is taken as the estimation of the sources.This method reduced the request for the sparsity of signals.The experimental results show the effectiveness of the algorithm.Using the harmonic interference of the electromagnetic interference as study object,study is conducted in the case of two mixing signals because of the lack of electromagnetic interference test results considering wide test bandwidth,long time consuming and limited resources.An algorithm of unconstrained gradient descent is proposed.First,the electromagnetic interference signals are preprocessed to remove the impact of magnitude and improve the sparsity of signals.After that,the mixing matrix is estimated using Hough Windowing.And then,the constrained separation problem is transformed to unconstrained optimization problem,and the initial value,step value,termination condition are proposed.Interior-point method and angle difference sorting method are proposed to improve the selection criteria of the mixing matrix column vector in minimum angle method.Experimental results demonstrate that the accuracy of unconstrained separation algorithm is identical to the shortest path algorithm and minimunm l1 norm,but the efficiency of the former is higher than the latter two.In addition,many electromagnetic interference test data are stored as images which are difficult to process.Therefore,a pixel-coordinate method is proposed,further expanding the scope of the algorithm.