<title>Adaptive lattice filters for block RLS based on QR decomposition</title>

Abstract

ABSTRACTRecently, the QR decomposition (QRD) method has been extensively used in the recursive least squares (RLS)adaptive filtering problems. And the least squares lattice (LSL) algorithm has been rederived based on the QRD method. On the other hand, in order to increase the throughput in the general RLS, a triangular systolic array for blockprocessing based on the QRD method with Householder transformations has been derived. In this paper, we derive anadaptive FIR lattice filter structure for block processing based on QRD with Householder transformations. 1. INTRODUCTION Recently, the QR decomposition (QRD) method has been extensively used in the recursive least squares (RLS)adaptive filtering problems. Originally the method based on the Givens rotations has been applied to the general RLSadaptive filtering problem where the input signals have no special structures and the resulting algorithm is efficientlyimplemented on a triangular systolic array.If the input signals are delayed versions of one common signal, then it is called the adaptive FIR (finite impulseresponse) filtering problem, and the data matrix has a Toeplitz structure. For this problem, there are several so calledfast algorithms which require O(p) computations per iteration where p is the number of the input signals or delays.