Annihilation-reordering look-ahead pipelined CORDIC-based RLS adaptive filters and their application to adaptive beamforming

Abstract

The novel annihilation-reordering look-ahead technique is proposed as an attractive technique for pipelining of Givens rotation (or CORDIC)-based adaptive filters. Unlike the existing relaxed look-ahead, the annihilation-reordering look-ahead does not depend on the statistical properties of the input samples. It is an exact look-ahead based on CORDIC arithmetic, which is known to be numerically stable. The conventional look-ahead is based on multiply-add arithmetic. The annihilation-reordering 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 complexities are also studied and compared. The annihilation-reordering look-ahead is employed to develop fine-grain pipelined QR decomposition-based RLS adaptive filters. Both QRD-RLS and inverse QRD-RLS 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 pipelined CORDIC-based RLS adaptive filters are then employed to develop high-speed linear constraint minimum variance (LCMV) adaptive beamforming algorithms. Both QR decomposition-based minimum variance distortionless response (MVDR) realization and generalized sidelobe canceller (GSC) realization are presented. The complexity of the pipelined architectures are analyzed and compared. The proposed architectures can be operated at arbitrarily high sample rate and consist of only Givens rotations, which can be scheduled onto CORDIC arithmetic-based processors.