Convergence analysis of constrained joint adaptation in recording channels

Partial response (PR) equalization employing the linearly constrained least-mean-square (LCLMS) adaptive algorithm is widely used for jointly designing equalizer and PR target in recording channels. However, there is no literature on its convergence analysis. Further, existing analyses of the least-mean-square (LMS) algorithm assume that the input signals are jointly Gaussian, an assumption that is invalid for PR equalization with binary input. In this paper, we present a novel method to analyze the convergence of the LCLMS algorithm, without the Gaussian assumption. Our approach accommodates distinct step sizes for equalizer and PR target. It is shown that the step-size range required to guarantee stability of LCLMS with binary data is larger than that with Gaussian data. The analytical results are corroborated by extensive simulation studies.