Study Of Proportionate Adaptive Filtering Algorithms With Reused Coefficients

The convergence rate and steady-state misalignment of different adaptive filteringalgorithms differ from each other. The convergence rate determines the time cost by theadaptive filter to approximate the unknown system, while the steady-state misalignmentdetermines the accuracy obtained by the adaptive filter to approximate the unknownsystem. With certain degree of convergence rate, the classical normalized least meansquare (NLMS) algorithm and affine projection algorithm (APA) show relatively largesteady-state misalignment, and the larger the measurement noise, the larger the steady-statemisalignment. Recently, Hyeonwoo Cho et al. have proposed the NLMS and APA-basedreusing coefficient (RC) algorithms (i.e., NLMS-RC and APA-RC) to reduce steady-statemisalignment. In many applications, the unknown systems to be estimate may be sparse. Ifthe NLMS-RC or APA-RC algorithm is used to estimate such systems, its convergence rateis slow. In order to solve this problem, this thesis incorporates the concept of proportionateadaption into NLMS-RC and APA-RC algorithms and proposes a proportionate NLMS-RC(PNLMS-RC) algorithm and a proportionate APA-RC (PAPA-RC) algorithm. In order toincrease the initial convergence rate, this thesis also employs the idea of variable order ofreusing coefficient in the PNLMS-RC and PAPA-RC algorithms. Simulation results showthat the algorithms proposed in this thesis have good convergence performance.