Logarithmic quantization in the least mean squares algorithm

In this paper, we introduce a framework for adaptive filtering techniques with simplified recursion. The simplification is mainly carried out by rounding the full-precision error information of the recursion to their closest power-of-two values. A new method for power-of-two quantization is proposed in this study. The method uses companded delta modulation structure to perform the quantization. The proposed structure shows a performance that is comparable to that of full precision adaptive filters. Convergence analysis of this structure is included and closed-form expressions for the error statistics are derived. Furthermore, an efficient method for implementing the new structure is presented where only simple shift and loop operations are required. (c) 2007 Elsevier Inc. All rights reserved.