The block LMS algorithm and its FFT based fast implementation— new efficient realization using block floating point arithmetic

An efficient scheme is proposed for implementing the block LMS 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 block LMS algorithm.