MSE Analysis of a Multi-Loop LMS Pseudo-Random Noise Canceler for Mixed-Signal Circuit Calibration

Abstract

This paper applies new analytical techniques to evaluate the stability and mean-square error (MSE) convergence of a multi-loop LMS pseudo-random noise canceller which applies to a variety of known mixed-signal circuit calibration techniques. To the authors’ knowledge, it is the first published MSE analysis of any multi-loop LMS system, and, unlike most published MSE analyses of single-loop LMS systems, it does not make any simplifying assumptions. The analysis proves that the noise canceler can be made unconditionally stable by design, and provides guidance on how to choose design parameters to achieve a desired level of noise cancellation.