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.