A New Block-based NLMS Algorithm and Its Realization in Block Floating Point Format

Authors: Abhijit Mitra

Abstract:

we propose a new normalized LMS (NLMS) algorithm, which gives satisfactory performance in certain applications in comaprison with con-ventional NLMS recursion. This new algorithm can be treated as a block based simplification of NLMS algorithm with significantly reduced number of multi¬ply and accumulate as well as division operations. It is also shown that such a recursion can be easily implemented in block floating point (BFP) arithmetic, treating the implementational issues much efficiently. In particular, the core challenges of a BFP realization to such adaptive filters are mainly considered in this regard. A global upper bound on the step size control parameter of the new algorithm due to BFP implementation is also proposed to prevent overflow in filtering as well as weight updating operations jointly.

Keywords: Adaptive algorithm, Block floating point arithmetic, Implementation issues, Normalized least mean square methods

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1077914

References:

[1] S. Haykin, Adaptive Filter Theory, 4th ed. Englewood Cliffs, NJ: Prentice-Hall, 2001.
[2] N. J. Bershad, "Analysis of the Normalized LMS Algorithm with Gaussian Inputs," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP- 34, no. 4, pp. 793-806, April 1986.
[3] G. C. Goodwin and K. S. Sin, Adaptive Filtering, Prediction and Control. Englewood Cliffs, NJ: Prentice-Hall, 1984.
[4] R. Nitzberg, "Application of the Normalized LMS Algorithm to MSLC," IEEE Trans. Aerospace and Electronic Syst., vol. AES-21, no. 1, pp. 79-91, Jan. 1985.
[5] A. Mitra and M. Chakraborty, "The NLMS Algorithm in Block-Floating- Point Format," IEEE Signal Processing Letters, vol. 11, no. 3, pp. 301- 304, March 2004.
[6] K. R. Ralev and P. H. Bauer, "Realization of Block Floating Point Digital Filters and Application to Block Implementations," IEEE Trans. Signal Processing, vol. 47, no. 4, pp. 1076-1086, April 1999.
[7] K. Kallioja¨rvi and J. Astola, "Roundoff Errors in Block-Floating-Point Systems," IEEE Trans. Signal Processing, vol. 44, no. 4, pp. 783-790, April 1996.
[8] A. Erickson and B. Fagin, "Calculating FHT in Hardware," IEEE Trans. Signal Processing, vol. 40, pp. 1341-1353, June 1992.
[9] S. Sridharan and D. Williamson, "Implementation of high order direct form digital filter structures," IEEE Trans. Circuits Syst., vol. CAS-33, pp. 818-822, Aug. 1986.
[10] F. J. Taylor, "Block Floating Point Distributed Filters," IEEE Trans. Circuits Syst., vol. CAS-31, pp. 300-304, Mar. 1984.
[11] R. D. Koilpillai, S. Chennakeshu and R. L. Toy, "Low Complexity Equal- izers for U.S. Digital Cellular System," in Proc. IEEE VTC, May 1992. pp. 744-747.