Research On Complex-valued Adaptive Filters And Networks For Second-order Noncircular Signals

Complex-valued adaptive filters are widely used in channel equalization,stereo echo cancellation,power system frequency estimation,interference cancellation,and so on.In addition,distributed signal processing has become a research hotspot in the field of signal processing in recent years because a single adaptive filter has a low processing efficiency is unable to run in parallel.This thesis studies complex-valued adaptive filters and distributed network,mainly including:Accelerate the convergence rate of the partial-update augmented complex-valued least mean square(PU-ACLMS)filter.Duo to its simple structure and easy implementation,the augmented complex-valued least mean square(ACLMS)filter is one of the most popular augmented complex-valued adaptive filters,but its computational complexity increases with the increase of filter weights,which greatly restricts its application in practical problems.In order to reduce the computational complexity of the ACLMS filter,a selective PU-ACLMS(SEL-PU-ACLMS)filter is proposed based on the modulus of the input signal amplitude.Compared with the sequential PU-ACLMS(SEQ-PU-ACLMS)and the stochastic PU-ACLMS(STO-PU-ACLMS)filters,the SEL-PU-ACLMS filter can obtain a faster convergence rate with a comparable computational complexity.In addition,the double integral is used for the first time to solve the values of two proportional coefficients,based on which the performance of the filter is analyzed comprehensively.Accelerate the convergence rate of the least stochastic entropy(LSE)filter and the diffusion LSE(DLSE)network.For noncircular measurement noise,the LSE filter and the DLSE network can obtain a low steady-state misalignment.However,when the input signal is noncircular,the convergence rate of the LSE filter and the DLSE network will decay,and this attenuation will increase with the increase of the noncircularity of input signal.In this thesis,the reason of this problem is analyzed,and an improved LSE(ILSE)filter and an improved DLSE(IDLSE)network are proposed based on the combination strategy to accelerate the convergence rate of the LSE filter and the DLSE network for noncircular input signals.Furthermore,to predict the stochastic behavior of the ILSE filter and the DILSE network,a comprehensive performance analysis is performed.Improve the convergence performance of the diffusion augmented complex-valued adaptive network.As a typical combination method of widely linear model and distributed estimation,the diffusion ACLMS(DACLMS)adaptive network has attracted extensive attention.In this thesis,the error kurtosis is used as the local cost function and the diffusion augmented complex-valued least mean kurtosis(DACLMK)adaptive network is proposed to yields a better convergence performance than the DACLMS adaptive network.Moreover,a comprehensive theoretical performance analysis is also performed to predict the stochastic behavior of the network.The performance of the adaptive filter and the network is tested through experiments,and the accuracy of theoretical performance analysis is also verified by experiments.The research results shown in this thesis provide theoretical basis and methodological guidance for the design of complex-valued adaptive filters and networks.