The NLMS algorithm in block floating-point format

We present a novel scheme to implement the normalized least mean square algorithm in block floating-point (BFP) format, which permits processing of data over a wide dynamic range, at a cost significantly less than that of a floating-point processor. Appropriate BFP formats for both the data and the filter coefficients are adopted. Care is taken so that the chosen formats remain invariant to interblock transition and weight-updating operation, respectively. Care is also taken to prevent overflow during filtering, as well as weight-updating processes, by using a dynamic scaling of the data and a slightly reduced range for the step size control parameter, with the latter having negligible effect on convergence speed.