Gradient-Descent Adaptive Filtering Using Gradient Adaptive Step-Size

At the heart of most adaptive filtering techniques lies an iterative statistical optimisation process. These techniques typically depend on adaptation gains, which are scalar parameters that must reside within a region determined by the input signal statistics to achieve convergence. This manuscript revisits the paradigm of determining near-optimal adaptation gains in adaptive learning and filtering techniques. The adaptation gain is considered as a matrix that is learned from the relation between input signal and filtering error. The matrix formulation allows adequate degrees of freedom for near-optimal adaptation, while the learning procedure allows the adaption gain to be formulated even in cases where the statistics of the input signal are not precisely known.