A low complexity realization of the sign-LMS algorithm

The sign-LMS algorithm is a popular adaptive filter that requires only addition/subtraction but no multiplication in the weight update loop. To reduce the complexity of multiplication that arises in the filtering part of the sign-LMS algorithm, a special radix-4 format is presented in this paper to represent each filter coefficient. The chosen format guarantees sufficient sparsity which in turn reduces the multiplicative complexity as no partial product needs to be computed when the multiplicand is a binary zero. Care, is, however taken to ensure that the weight update process generates the updated weight also in the same chosen radix-4 format, which is ensured by developing an algorithm for adding a 2's complement number with a number given in the adopted radix-4 format.