BEACON: an adaptive set-membership filtering technique with sparse updates

This paper deals with adaptive solutions to the so-called set-membership filtering (SMF) problem. The SMF methodology involves designing filters by imposing a deterministic constraint on the output error sequence. A set-membership decision feedback equalizer (SM-DFE) for equalization of a communications channel is derived, and connections with the minimum mean square error (MMSE) DFE are established. Further, an adaptive solution to the general SMF problem via a novel optimal bounding ellipsoid (OBE) algorithm called BEACON is presented. This algorithm features sparse updating, wherein it uses about 5-10% of the data to update the parameter estimates without any loss in mean-squared error performance, in comparison with the conventional recursive least-squares (RLS) algorithm. It is shown that the BEACON algorithm can also be derived as a solution to a certain constrained least-squares problem. Simulation results are presented for various adaptive signal processing examples, including estimation of a real communication channel. Further, it is shown that the algorithm can accurately track fast time variations in a nonstationary environment. This improvement is a result of incorporating an explicit test to check if an update is needed at every time instant as well as an optimal data-dependent assignment to the updating weights whenever an update is required.