Adaptive Filtering With Reduced Computational Complexity Using SOPOT Arithmetic

Implementing
finite impulse response
(FIR) adaptive filters by employing the
sums of signed-powers-of-two
(SOPOT) arithmetic may lead to simpler hardware and consequently reduced power consumption. In this paper, one evaluates the effects of SOPOT arithmetic on the adaptive filter’s recursion algorithms. The filters’ coefficients and algorithms’ underlying variables are fully operated using SOPOT arithmetic in the whole iterative process. More specifically, one evaluates convergence rate, numerical stability, and accuracy since using few
signed-powers-of-two
(SPT) terms propagates numerical errors during the adaptive cycle that may impair the algorithm behavior. The SOPOT approximations are obtained through the technique known as
Matching Pursuits with Generalized Bit-Plane
(MPGBP) algorithm, with notable cost-performance trade-off and low computational complexity. Results are provided for the
Least-Mean-Squares
(LMS), the
Normalized Least-Mean-Squares
(NLMS) and the
Recursive-Least-Squares
(RLS) algorithms, considering adaptive filters employed for system identification and change detection.