Steady State Analysis of Convex Combination of Affine Projection Adaptive Filters

The aim of the study is to propose an adaptive algorithm using convex combinational approach to have both fast convergence and less steady state error simultaneously. For this purpose, we have used two affine projection adaptive filters with complementary nature (both in step size and projection order) as the component filters. The first component filter has high projection order and large step size which makes it to have fast convergence at the cost of more steady state error. The second component filter has slow convergence and less steady state error due to the selection of small step size and projection order. Both are combined using convex combiner so as to have best final output with fast convergence and less steady state error. Each of the component filters are updated using their own error signals and stochastic gradient approach is used to update the convex combiner so as to have minimum overall error. By using energy conservation argument, analytical treatment of the combination stage is made in stationary environment. It is found that during initial stage the proposed scheme converges to the fast filter which has good convergence later it converges to either of the two (whichever has less steady state error) and towards the end, the final output converges to slow filter which is superior in lesser steady state error. Experimental results proved that the proposed algorithm has adopted the best features of the component filters.