On pipelined implementations of QRD-RLS adaptive filters

This chapter discusses the pipelined systolic implementations pipelined implementation of QR-decomposition-based recursive least-squares (QRD-RLS) adaptive filters. Theannihilation-reording look-ahead technique is presented as an attractive technique for pipelining of Givens rotation (or CO-ordinate Rotation DIgital Computer (CORDIC)) based adaptive filters. It is an exact look-ahead and is based on CORDIC arithmetic, CORDIC!arithmetic which is known to be numerically stable. The conventional look-ahead is based on multiply-add arithmetic. The annihilation-reording look-ahead technique transforms an orthogonal sequential adaptive filtering algorithm into an equivalent orthogonal concurrent one by creating additional concurrency in the algorithm. Parallelism in the transformed algorithm is explored, and different implementation styles including pipelining, block processing, and incremental block processing are presented. Their complexity are also studied and compared. The annihilation-reording look-ahead is employed to develop fine-grain pipelined QRD-RLS adaptive filters. fine-grain pipelining Both implicit and explicit weight extraction algorithms are considered. The proposed pipelined architectures can be operated at arbitrarily high sample rate without degrading the filter convergence behavior. Stability under finite-precision arithmetic are studied and proved for the proposed architectures. The complexity of the pipelined architectures are analyzed and compared.