Transient Performance Analysis Of Nonlinear Error Function Filter

The performance of adaptive filters includes steady-state performance and transient performance.The former studies the steady-state mean square error of the adaptive filter,and the latter studies the convergence speed and stability of the adaptive filter.The most important part of the adaptive filter is the adaptive algorithm.Many researchers have extended from the least mean square error algorithm to the least mean mixed norm algorithm,the least mean p-order algorithm,and the affine projection algorithm,which is to generalize the estimated error signal from linear to nonlinear,and to perform performance analysis of steady state on nonlinear algorithms.Not only they analyze the mean square error of each of the above algorithms in real form,but also analyze the mean square error of each of the above-mentioned algorithms in the complex form,and the selection of the noise signal is not limited.However,for the transient performance of the adaptive filter,many people analyze its real form,and its complex form is rarely analyzed,and the selection of noise signals is also limited.Therefore,it is necessary to propose a method to adapt to the adaptive algorithm under different noises for the analysis of transient performance of adaptive algorithms.The main contributions of the thesis are as following:(1)Based on the principle of separation hypothesis,the transient performance,mean performance and steady state performance of the adaptive filter with nonlinear estimation error function were studied by using Taylor expansion,complex Taylor expansion,Borel function and Price's Theorem.The theoretical value analysis was carried out,and the mean square deviation,mean and mean square performance expressions of adaptive algorithms with nonlinear error signals under complex and real valued were derived.Then,the theory and simulation MSD curses of each real adaptive algorithm under Gaussian noise and uniform distributed noise was compared.(2)Based on the work of the first part,the expression of the convergence performance of the adaptive filtering algorithm with nonlinear error signal were derived.Then the expression was applied to the least mean square algorithm,the least mean p-order algorithm,the least mean fourth algorithm,and the least mean mixed norm algorithm.The experimental results show that the convergence performance formulas of the above several algorithms are correct.(3)The transient performance of the improved sign algorithm was analyzed.The derivation methods of the transient performance expression of the sign algorithm in real and complex case was different:Borel function was used in real sign algorithm and Price's Theorem was used in complex case.Finally,the transient performance of new sign algorithms with different n-valued was simulated.The simulation results show that the theoretical derivation formula is correct.