Adaptive filters with individual adaptation of parameters

Conventional gradient-type adaptive filters use the fixed convergence factor
\mu
which is normally chosen to be the same for all the filter parameters. In this paper, we propose to use individual convergence factors which are optimally tailored to adapt individual filter parameters. Furthermore, we propose to adjust the individual convergence factors in real time so that their values are kept optimum for a new set of input variables. We call this approach "individual" adaptation as opposed to the conventional fixed "group" adaptation using the same fixed
\mu
for all the filter parameters. Computer simulation results show that the individual adaptation approach yields much better filters than the conventional fixed group adaptation approach. Optimization of individual time-varying convergence factors leads to a constraint which may be satisfied by several different algorithms. We propose and investigate here two algorithms satisfying the above constraint: individual adaptation (IA) and homogeneous adaptation (HA). The HA algorithm turns out to have the general form as some well known gradient algorithms that normalize the step size which were previously obtained either intuitively or using involved derivations. Both IA and HA are shown to provide much better performance than the conventional "group" adaptation. However, for several simulations, IA provides better performance than HA, at the expense of increased computation.