Pipelining extended givens rotation RLS adaptive filters

In this paper, we propose a new pipelining extended Givens Rotation Recursive Least Square (PEGR-RLS) architecture using look-ahead technique. The square-root-free forms of QRD-RLS are also difficult to pipeline. The PEGR-RLS algorithm (referred to as Scaled Tangent Rotation, STAR-RLS) is designed such that fine-grain pipelining can be accomplished with little hardware overhead. Similar to STAR-RLS, this algorithm is not exactly orthogonal transformations but tends to become orthogonal asymptotically. This algorithm also preserves the desired properties of the STAR-RLS algorithm. Specifically, it can be pipelined at very low forgetting factor by using extended look-ahead. Simulation results are presented to compare the performance of the STAR-RLS, QRD-RLS, and LMS algorithms.

[1]  T. Kailath,et al.  A state-space approach to adaptive RLS filtering , 1994, IEEE Signal Processing Magazine.

[2]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[3]  Keshab K. Parhi,et al.  Pipeline interleaving and parallelism in recursive digital filters. I. Pipelining using scattered look-ahead and decomposition , 1989, IEEE Trans. Acoust. Speech Signal Process..

[4]  Keshab K. Parhi,et al.  Hybrid annihilation transformation (HAT) for pipelining QRD-based least-square adaptive filters , 2001 .

[5]  G. J. Borse,et al.  Numerical Methods with MATLAB: A Resource for Scientists and Engineers , 1996 .

[6]  H. T. Kung,et al.  Systolic Arrays for (VLSI). , 1978 .

[7]  Keshab K. Parhi,et al.  Pipeline interleaving and parallelism in recursive digital filters. II. Pipelined incremental block filtering , 1989, IEEE Trans. Acoust. Speech Signal Process..

[8]  Fuyun Ling.  Givens rotation based least squares lattice and related algorithms , 1991, IEEE Trans. Signal Process..

[9]  K. J. Ray Liu,et al.  A unified square-root-free approach for QRD-based recursive-least-squares estimation , 1993, IEEE Trans. Signal Process..

[10]  W. E. Gentleman.  Least Squares Computations by Givens Transformations Without Square Roots , 1973 .

[11]  Keshab K. Parhi,et al.  Pipelined RLS adaptive filtering using scaled tangent rotations (STAR) , 1996, IEEE Trans. Signal Process..

[12]  Edward A. Lee,et al.  Least squares computation at arbitrarily high speeds , 1987, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[13]  Keshab K. Parhi,et al.  Annihilation-reordering look-ahead pipelined CORDIC-based RLS adaptive filters and their application to adaptive beamforming , 2000, IEEE Trans. Signal Process..