The log-log LMS algorithm

This paper describes a new variant of the least-mean-squares (LMS) algorithm, with low computational complexity, for updating an adaptive filter. The reduction in complexity is obtained by using values of the input data and the output error, quantized to the nearest power of two, to compute the gradient. This eliminates the need for multipliers or shifters in the algorithm´s update section. The quantization itself is efficiently realizable in hardware. The filtering section is unchanged. Thus, this algorithm is similar to the sign based variants of the LMS algorithm. However, the complexity of the proposed algorithm is lower than that of the sign-error LMS algorithm, while its performance is superior to this algorithm. In particular, it is close to that of the regular LMS algorithm. The new algorithm also requires much lower area for ASIC implementation