A Block-Floating-Point-Based Realization of the Block LMS Algorithm

An efficient scheme is proposed for implementing the block LMS (BLMS) algorithm in a block-floating-point framework that permits processing of data over a wide dynamic range at a processor complexity and cost as low as that of a fixed-point processor. The proposed scheme adopts appropriate formats for representing the filter coefficients and the data. Using these and a new upper bound on the step size, update relations for the filter weight mantissas and exponent are developed, taking care so that neither overflow occurs, nor are quantities which are already very small multiplied directly. It is further shown how the mantissas of the filter coefficients and also the filter output can be evaluated faster by suitably modifying the approach of the fast BLMS algorithm.