An Efficient Implementation of the Sign LMS Algorithm Using Block Floating Point Format
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Research Article An Efficient Implementation of the Sign LMS Algorithm Using Block Floating Point Format Mrityunjoy Chakraborty,1 Rafiahamed Shaik,1 and Moon Ho Lee2 1 Department 2 Department
of Electronics and Electrical Communication Engineering, Indian Institute of Technology, Kharagpur 721302, India of Information and Communication, Chonbuk National University, Chonju 561756, South Korea
Received 11 July 2005; Revised 31 August 2006; Accepted 24 November 2006 Recommended by Roger Woods An efficient scheme is presented for implementing the sign LMS algorithm in block floating point format, which 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. It also employs a scaled representation for the stepsize that has a time-varying mantissa and also a time-varying exponent. Using these and an upper bound on the step-size mantissa, 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. Separate update relations are also worked out for the step size mantissa. The proposed scheme employs mostly fixed-point-based operations, and thus achieves considerable speedup over its floatingpoint-based counterpart. Copyright © 2007 Hindawi Publishing Corporation. All rights reserved.
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INTRODUCTION
Sufficient signal-to-quantization noise ratio over a large dynamic range is a desirable feature of modern day digital signal processing systems. While the floating point (FP) data format is ideally suited to achieve this due to normalized data representation, the accompanying high processing cost restricts its usage in many applications. This is specially true for resource-constrained contexts like batteryoperated low power devices, where custom implementations on FPGA/ASIC are the primary mode of realization. In such contexts, the block floating point (BFP) format provides a viable alternative to the FP scheme. In BFP, a common exponent is assigned to a group of variables. As a result, computations involving these variables can be carried out in simple fixed point (FxP) like manner, while presence of the exponent provides an FP-like high dynamic range. Over years, the BFP format has been used by several researchers for efficient realization of many signal processing systems and algorithms. These include various forms of fixed coefficient digital filters (see [1–6]), adaptive filters (see [7, 8]), and unitary transforms (see [9–11]) on one hand and several audio data transmission standards like NICAM (stereophonic sound system for PAL TV standard), the audio part of MUSE (Japanese HDTV standard), and DSR (German digital satellite radio system) on the other. Of the vari-
ous systems studied, adaptive filters pose special challenges to their implementation using the BFP arithmetic. This is mainly because (i) unlike a fixed coefficient
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