Forgetting factor selection in RLS decision-directed tracking of doubly-selective channels

We consider a decision-directed tracking approach to doubly-selective channel estimation exploiting the complex exponential basis expansion model (CE-BEM). The time-varying nature of the channel is well captured by the CE-BEM while the time-variations of the (unknown) BEM coefficients are likely much slower than those of the channel. We track the BEM coefficients via the exponentially-weighted recursive least-squares (RLS) algorithm, aided by symbol decisions from a decision-feedback equalizer (DFE). Such a scheme was recently presented in a conference paper by the authors. In this paper we investigate selection of the forgetting factor in the RLS algorithm. We show that its selection depends upon how often the BEM coefficients are updated and we provide simple guidelines for its choice. Simulation examples demonstrate superior performance of the proposed decision-directed scheme over an existing subblock-wise channel tracking scheme.