On convergence properties of subspace trackers based on orthogonal iteration

This paper studies convergence properties of subspace trackers using orthogonal iteration. In the context of blind estimation of a time-varying channel, orthogonal iteration and its variants have been widely considered for tracking the channel parameters by updating the eigendecomposition of an exponentially weighted correlation matrix. While it is well known that orthogonal iteration converges exponentially with arbitrary initial conditions, orthogonal-iteration-based subspace trackers can only inherit these merits when the channels considered undergo extremely slow time-variations. In this paper, we generalize the traditional (i.e. fixed subspace) convergence analysis of the orthogonal iteration to include non-stationary situations as well. We use the results to investigate the convergence behavior of subspace trackers based on orthogonal iteration under slow, moderate and rapid time-variations of the underlying subspace. In the latter case, we expose a fundamental limitation of the orthogonal iteration, i.e. practical limit on subspace variations to ensure effective tracking.