Theoretical Design And Analysis Of Subband Adaptive Filter Algorithm In Different Number Domains

As one of the adaptive filtering algorithms,subband adaptive filtering algorithm has broad application prospects due to its structural characteristics and easy implementation.However,the study of subband adaptive filtering has been limited to linear systems and real domain.In order to make subband adaptive filtering have a broader application background and practicality,the main research work of this thesis includes the following two aspects:(1)In real domain,aiming at the environment of Gaussian impulsive noise and the nonlinear system,corresponding subband adaptive filtering algorithms are proposed to resist impulsive noise and identify the nonlinear system,respectively.(2)For complex-valued input and hypercomplex input,subband adaptive filtering algorithms are proposed,which can be used to process with complex-valued signals,and their performances are analyzed.The main contributions and innovations of this thesis are as follows:1 In order to improve the convergence performance of SSAF algorithm in impulse noise environment,two robust against impulse noise algorithms are proposed.One is to improve the performance of SSAF algorithm by minimizing the mean square deviation and designing a variable step size scheme.The other is to design a new cost function by using logarithmic function to improve the performance of the algorithm.Then the performance of the two algorithms is analyzed by energy conservation theorem.The simulation results verify the effectiveness of the two proposed algorithms.2 In order to make the subband adaptive filtering algorithm have the ability to identify the nonlinear system,a SAF-DNSAF algorithm by using spline interpolation and delayless subband structure is proposed.Based on the principle of energy conservation,the mean,mean square convergence conditions and steady state performance analysis of the proposed algorithm are given.In addition,in order to further reduce the computational complexity,the set-membership method is applied to the proposed SAF-DNSAF algorithm,the SAF-SMDNSAF algorithm is proposed and its performance is analyzed.The simulation results show that the two proposed algorithms have good performance.3 In order to solve the problem that subband adaptive filtering algorithm can not deal with non-circular complex signals,an ACNSAF algorithm is proposed based on augmented statistics,WL model and CR calculation,which can process both circular and non-circular complex signals.Based on the principle of energy conservation,the stability and mean square steady-state performance analysis of the proposed algorithm are given.The simulation results validate our theoretical analysis results.Besides,the QNSAF algorithm that can process hypercomplex signals is proposed by using GHR calculation containing the novel product and chain rules.Based on the principle of energy conservation,the convergence conditions of the proposed algorithm are given.The simulation results of hypercomplex system identification and one-step prediction show that the algorithm has good performance.In addition,the simulation results of actual three-dimensional and four-dimensional data signals show that the proposed algorithm has broad application prospects.4 To further improve the performance of ACNSAF algorithm,based on augmented statistics,WL model,distributed network and CR computation,a D-ACNSAF filtering algorithm is proposed.This algorithm perfectly inherits the advantages of ACNSAF algorithm and distributed adaptive network,that is,it can process both circular and non-circular complex signals and achieve better convergence performance.Based on the principle of space energy conservation,the mean stability and mean square steady-state performance of the algorithm are deduced.The simulation results of identification and prediction of complex system show that it has good performance.Besides,in order to resist complex attack in sensor networks,a secure diffusion augmented complex-valued normalized subband adaptive filtering algorithm is proposed,which can be divided into two parts.Firstly,reliable reference estimates are found by using ACNSAF algorithm without communication,then reliable reference estimates are used to detect the trusted neighbors of each node,and then D-ACNSAF algorithm is used to recombine the information from trusted neighbors.The theoretical analysis of the mean and mean square performance of the algorithm is given.The simulation results in different attack environments show that the proposed algorithm exhibits good performance.