Research On Blind Source Separation And Its Application In Blind Beamforming

In many signal processing cases,some necessary information is unknown.In such case,the blind signal processing(BSP)has to be used.Blind signal separation(BSS)is one of the blind signal processing problems.BSS is a challenging task since not only the potential variables are unknown,but also the way of signal mixed is unknown.Independent component analysis(ICA)is a technology based on statistics.Since its birth,ICA has attracted wide attention of the scholars at home and abroad,and its relative researches have made a large number of achievements,which have found utility in many applications such as speech signal processing,digital communications,image signal processing,and so on.So ICA has become almost synonymous with BSS.Nevertheless,there are a lot of problems still need to be further researched in BSS.Beamforming(i.e.spatial filtering)is an important task in array signal processing,which aims to extract the signal of interest(SOI),suppress the interference and noise,and improve the signal to interference plus noise ratio(SINR)of output.The direction-of-arrival(DOA)of signal has to be predicted before beamforming.It is well known that the errors of DOA estimation or the amplitude and phase of the array elements will lead to the steering vector mismatch,resulting in the decline of beamforming performance.Therefore,many effective adaptive methods,such as diagonal loading technique,are proposed.However,it is difficult to determine the diagonal loading level or constraint parameters,where more apriori information is required.Furthermore,it will affect the output performance when the parameter is too large or too small.Thus,the mismatch problem of steering vector still exists.In fact,beamforming can be considered as a special kind of BSS problem when the signal direction is unknown,so the ICA technique can be used to solve the problem.Based on the previous researches on ICA in the complex domain,the further research on this topic is provided in this thesis.Some new ideas and algorithms are proposed,and some results are applied to beamforming.The main contributions and contents are summarized as follows.Firstly,the complex fixed-point algorithm of BSS for noisy observation data is discussed.The classical noncircular FastICA(nc-FastICA)algorithm and the kurtosis maximization using fixed-point update(KM-F)algorithm adopt the standard ICA signal model without noise.When these algorithms are used to separate the noisy data in the low signal-to-noise Ratio(SNR)case,they can usually obtain a low performance,or even fail to separate the mixtures.So it is necessary to take the noise into consideration in ICA signal model.Based on the ICA model with noise,the following two contributions are made.1)The update rule of nc-FastICA is reformulated,resulting in a new fixed-point update rule,which extends the algorithm to a new one,namely mnc-FastICA.If the noise term disappears,the mnc-FastICA is reduced to the nc-FastICA.In addition,the stability condition of the cost function of mnc-FastICA is derived for a given nonlinearity.2)By applying pseudo-whitening to the observations,the KM-F algorithm is modified into a new one,namely mKM-F,and the stability condition of the kurtosis cost function is also analyzed.Simulation results show that both modified algorithms improve the separation performance significantly,especially in the case of low SNR.However,it is necessary to devote a general discussion on the stability condition of the cost function of mnc-FastICA.Secondly,the blind separation method for mixture with delays is studied.The Infomax(Information-maximization)method proposed by Torkkola is extended from the real domain to the complex domain,and the complex Infomax method is still applicable to real valued data.The complex nonlinear functions in the feedback network for unmixing are chosen in the both forms,i.e.Split-Complex and Fully-Complex,and two corresponding Infomax methods are obtained.The latter has a lower computational complexity.According to the principle of information maximization,the adaptive rule for each parameter of feedback network for unmixing is given in the complex Infomax method.A measure matrix is also constructed to measure the performance of the proposed algorithm.The effectiveness of the proposed algorithm is illustrated via simulations.Compared with the frequency domain methods,the complex Infomax method has a simpler iterative scheme,and is easy to implement.Additionally,unlike the frequency domain methods,it doesn't require signals pairing and equalization.Thirdly,under some assumptions including that the source is non-Gaussian,a new beamformer based on the mnc-FastICA algorithm is proposed,where the weight vector is constructed by the separation matrix obtained via the BSS.Since the observation direction of beam is not involved,the method avoids the steering vector mismatch caused by the inaccurate DOA estimation in methods such as diagonal loading sample matrix inversion(LSMI).The proposed method is insensitive to the steering vector mismatch caused by the amplitude and phase errors of array channels,and thus it is not necessary to calibrate the array.The output performance is better than other methods such as worst-case performance optimization(WCPO).For the case that the array is ideal or has only the amplitude and phase errors of the channels,the proposed method can be used to calibrate the amplitude and phase ambiguity caused by the BSS,where the special structure of array manifold matrix(i.e.,the elements of the first row of this matrix are all equal to 1)is fully utilized.In addition,the proposed method can be applied to an arbitrary array,including uniform linear array and non-uniform one.However,the number of non-Gaussian source is assumed to be no more than one in the proposed method,while WCPO and other methods are not limited by this assumption and have a wider scope of application.Finally,the power restoration of the SOI obtained from the blind separation of the array signals under strong interference is discussed.The fact,that in the previous contribution calibrating the amplitude and phase of signals by using the elements in first row of separation matrix may result in a large error,is pointed out.After analyzing its shortcomings,a new method is proposed to recover the SOI,where the waveform of the SOI is estimated via an ICA method and the power of the SOI estimated by principal component analysis(PCA)method is used to scale the waveform.In a strong interference environment,compared with the ICA method,the combination of PCA method and ICA method can restore the SOI more accurately.Simulation results indicate the effectiveness of the proposed method.It is also pointed out that,if the Amari index obtained by the ICA method is higher,the error of the signal amplitude and phase calibrated by using the first row of the separation matrix will be smaller.