High speed least square adaptive filter design using ART and HAT

In this paper, annihilation reordering transformation (ART) for pipelining QR decomposition based recursive least square adaptive filters is fully developed and rigorous mathematical proof of ART is given. A novel transformation, referred to as hybrid annihilation transformation (HAT), for pipelining both the QR decomposition based recursive least square adaptive filters and QR decomposition based single/multi-channel least square lattice adaptive filters is presented. HAT does not introduce any approximation in the entire filtering process. Therefore, it causes no performance degradation no matter how deep the filter is pipelined. It allows a linear speedup of the throughput rate by a linear increase of hardware complexity.