Efficient implementation of rotation operations for high performance QRD-RLS filtering

In this paper we present practical techniques for implementing Givens rotations based on the well-known CORDIC algorithm. Rotations are the basic operation in many high performance adaptive filtering schemes as well as numerous other advanced signal processing algorithms relying on matrix decompositions. To improve the efficiency of these methods, we propose to use “approximate rotations”, whereby only a few (i.e. r≪b, where b is the operand word length) elementary angles of the original CORDIC sequence are applied, so as to reduce the total number of required shift add operations. This seamingly rather ad hoc and heuristic procedure constitutes a representative example of a very useful design concept termed “approximate signal processing” recently introduced and formally exposed by S.H. Nawab et al. (1997), concerning the trade-off between system performance and implementation complexity, i.e. between accuracy and resources. This is a subject of increasing importance with respect to the efficient realization of demanding signal processing tasks. We present the application of the described rotation schemes to QRD-RLS filtering in wireless communications, specifically high speed channel equalization and beamforming, i.e. for intersymbol and co-channel/interuser interference suppression, respectively. It is shown via computer simulations that the convergence behavior of the scheme using approximate Givens rotations is insensitive to the value of r, and that the misadjustment error decreases as r is increased, opening zip possibilities for “incremental refinement” strategies