Roundoff error analysis of the tracking performance of the block LMS algorithm

The paper is concerned with analyzing the roundoff error effect on the tracking performance of the block least mean square (BLMS) algorithm when used in the adaptive identification of a time-varying plant. Rounding quantization is assumed. Expressions are derived for the steady state mean square error, steady state mean square weight deviation, and the corresponding optimum step sizes. It is found that the mean square error and the mean square weight deviation are decreasing functions of both the filter coefficients wordlength and the algorithm block size. Expressions for minimum and maximum block lengths are derived. The performance of the BLMS is compared to that of the conventional LMS algorithm. It is found that the BLMS possesses a higher resistance to roundoff errors than the LMS algorithm. The theoretical results of the paper are validated by computer simulations