The logarithmic number system for strength reduction in adaptive filtering

An important technique for reducing power consumption in VLSI systems is strength reduction, the substitution of a less-costly operation such as a shift, for a more-costly operation such a multiplication. Using a logarithmic number representation provides several opportunities for strength reductions; in particular, multiplication is performed as the fixed-point addition of logarithms, and extracting a square root is implemented via a shift. These reductions occur transparently at the hardware level; consequently relatively little algorithmic modification is required, and they are readily applicable to adaptive filtering. For performing Givens rotations in the QR decomposition recursive least squares adaptive filter, logarithmic arithmetic is shown to compare favorably to other strength reduction techniques, such as CORDIC arithmetic, in terms of switched capacitance and numerical accuracy.