Proportionate Adaptation and Partial Updates in Constrained Adaptive Filters

Adaptive filters that are designed or assumed to be sparse typically make use of either proportionate adaptation (PA) or partial updates (PU). In this paper, we study the use of both techniques for adaptive filters operating under a constraint. In particular, we focus on the adaptive minimum mean squared error channel shortening equalizer (MMSE CSE), which is a pair of adaptive filters, one of which has a unit norm constraint. The MMSE CSE is often used to reduce the complexity of maximum likelihood sequence detection or to mitigate multipath in multicarrier systems. Each iteration of the algorithm involves adapting the channel shortener, adapting the target impulse response, and enforcing the constraint via a projection. We will show that there are additional design considerations that must be made in order to apply PA and PU techniques to the adaptive MMSE CSE. Simulation results will be provided to illustrate the design tradeoffs.