High-speed RLS adaptive filters

Recursive least-squares (RLS) is an adaptive filtering algorithm which has a very fast convergence and hence it has a number of applications in signal processing and communications. The QR decomposition based RLS (or QRD-RLS) algorithm is a popular way of implementing RLS since it is known to have very good numerical properties. The use of Givens rotations technique in QRD-RLS results in a recursive solution. The QRD-RLS algorithm is not suitable for high-speed applications since it is difficult to pipeline it. The aim of this thesis is to develop a high-speed RLS algorithm.

We have developed a new rotation technique, referred to as the scaled tangent rotations (STAR), which can be used in place of the Givens rotations. The resulting algorithm, referred to as STAR-RLS, can be pipelined with very little hardware overhead. The pipelined algorithm is referred to as PSTAR-RLS. Efficient pipelined architectures are developed and the stability and dynamic range properties are studied.

A comprehensive finite-precision analysis of QRD-RLS algorithm has not been done before. We next do an analytical performance analysis of STAR-RLS, PSTAR-RLS and QRD-RLS. Both fixed-point and floating-point implementations are considered. Simulation results are in good agreement with the theoretical predictions.

To demonstrate the practicality of our architecture, we have designed a 1.2 $\mu$ VLSI chip for a 4-tap STAR-RLS adaptive filter. This bit level pipelined chip is expected to operate at over 100 MHz. Redundant number system based arithmetic operators were used in this chip.