High speed RLS using scaled tangent rotations (STAR)

The QR decomposition based recursive least-squares (RLS) adaptive filtering algorithm (referred to as QRD-RLS) has a processing speed limitation. Fine-grain pipelining of the recursive loops within the cells using look-ahead techniques requires large hardward increase. In this paper, a new scaled tangent rotation (STAR) is used instead of the usual Givens rotations. The scaled tangent rotation (STAR) RLS algorithm (referred to as STAR-RLS) is designed such that fine-grain pipelining can be accomplished very easily. The scaled tangent rotations are not exactly orthogonal transformations but tend to become orthogonal asymptotically. Simulation results show that the algorithm performance is similar to that of the QRD-RLS algorithm. The STAR-RLS algorithm can be mapped onto a systolic array. The computational complexity and inter cell communications are considerably lower than the QRD-RLS algorithm and the square-root free techniques. An interesting aspect of the STAR-RLS systolic array is that the a priori estimation error can be obtained directly as the output of the last internal cell, without any extra computation.