Research On Adaptive Filters Under Nonnegative Constrains

Nonnegative constraints are often involved in the field of signal processing.The nonnegative least mean square(NNLMS)algorithm enriches adaptive filtering methods under conditional constraints.However,when estimating sparse unknown systems by using the NNLMS algorithm,the convergence speed is not fast,the robustness is not strong,and the steady-state mean-square deviation(MSD)is not small.In this thesis,by using a general approximation approach of the l₀-norm in the cost function for developing the NNLMS algorithm,an l₀-norm nonnegative least mean square(l₀-NNLMS)algorithm is proposed to improve convergence speed.Meanwhile,by using a sign function and a logarithmic function as the cost functions,respectively,an l₀-norm sign-sign nonnegative least mean square(l₀-SSNNLMS)algorithm and an l₀-norm nonnegative least logarithmic absolute difference(l₀-NNLLAD)algorithm are presented to improve robustness against impulsive interference.Moreover,the mean weights and mean square error of the l₀-NNLMS are analyzed,which provide theoretical supports for the performance of the l₀-NNLMS algorithm.Finally,by extending the l₀-NNLMS algorithm to distributed networks,a l₀-norm diffusion nonnegative least-mean square(l₀-DNNLMS)algorithm is proposed,which has small MSD due to the cooperation between adjacent nodes in networks.