Pipelined RLS adaptive filtering using scaled tangent rotations (STAR)

The QR decomposition-based recursive least-squares (RLS) adaptive filtering algorithm (referred to as QRD-RLS) is very popular because it has good numerical properties and can be mapped onto a systolic array. However, in this architecture, pipelining of the operations within the systolic array cells is difficult. Pipelining would be necessary to operate at high speeds or to reduce the power dissipation in a VLSI implementation. Pipelining QRD-RLS using look-ahead techniques leads to a large hardware overhead. The square-root free forms of QRD-RLS are also difficult to pipeline. In this paper, a new scaled tangent rotation (STAR) is used instead of the Givens rotations used in QRD-RLS. The STAR-based RLS algorithm (referred to as STAR-RLS) is designed such that fine-grain pipelining can be accomplished with little hardware overhead The scaled tangent rotations are not exactly orthogonal transformations but tend to become orthogonal asymptotically. The STAR-RLS algorithm is square-root free and has less complexity and lower intercell communication than the QRD-RLS algorithm. The properties of the STAR-RLS algorithm, such as stability, numerical property, and dynamic range, are examined with and without pipelining and compared with those of QRD-RLS. Simulation results are presented to compare the performance of STAR-RLS and QRD-RLS algorithms