Effect of finite wordlength on the performance of an adaptive filter equipped with the signed regressor algorithm

The signed variants of the least mean square (LMS) algorithm have become appealing in the domain of high speed data communications. However, published analyses of these variants deal only with infinite precision implementation of the algorithms. The paper provides a roundoff error analysis of the signed regressor algorithm (SRA). An expression is derived for the steady state mean square error (MSE) of the algorithm. The derived expression is found to be in a good agreement with computer simulation results. It is found that the performance of the SRA is more affected by the wordlength assigned to the filter coefficients than the wordlength assigned to data. An expression is derived for the step size that minimizes the MSE. Finally the paper provides design issues that may reduce the effect of roundoff errors on the performance of the algorithm