Adaptive Estimation and Equalization of Doubly-selective Fading Channels using Basis Expansion Models

Abstract

Wireless channels, due to multipath propagation and Doppler spread, are characterized by frequency- and time-selectivity, so-called doubly-selective wireless channels. In this dissertation, we concentrate on adaptive channel estimation and equalization for communications systems over doubly selective channels, exploiting basis expansion models (BEM). Since the time-varying nature of the channel is well captured in the complex exponential basis expansion model (CE-BEM) by the known exponential basis functions, the time variations of the (unknown) BEM coefficients are likely much slower than those of the channel and thus more convenient to track.

First, a subblock-wise channel estimation based on CE-BEM is considered, where we track the BEM coefficients using time-multiplexed (TM) periodic training symbols. Assuming the BEM coefficients follow a first-order AR model, Kalman filtering is used to track the BEM coefficients. This first-order AR assumption, however, is not necessarily true and possibly incurs significant modeling errors in estimation. We then seek adaptive channel estimation schemes with no \textit{a priori} model for the BEM coefficients using recursive least-square (RLS) algorithm with finite memory.

Next, taking the performance of BEM-based approach into account, we investigate an adaptive soft-in soft-out turbo equalization for coded communication systems, exploiting CE-BEM for the overall channel variations and AR model for the BEM coefficients. We extend an existing turbo equalization approach based on symbol-wise AR modeling of channels to channels based on CE-BEM.

Based on the subblock-wise approach, we also propose a decision-directed tracking based on BEM, where we track the BEM coefficients using the information symbol decisions of a decision feedback equalizer (DFE) as virtual training. The time gap between symbol decisions and required channel estimates, arising from the decision-directed tracking, is bridged by CE-BEM-based channel prediction using the estimated BEM coefficients. We also adopt an exponentially-weighted (EW) RLS algorithm for our BEM-based decision-directed tracking scheme. Decision-directed tracking requires fewer training symbols compared to the training-based tracking, for the same performance.

The contribution of the proposed BEM-based channel estimation and equalization schemes is that we track the BEM coefficients in CE-BEM, not the channel taps directly, based on the subblock-wise approach and then generate the time-varying channels via CE-BEM. Simulation examples illustrate the superior performance of our approach over several existing doubly-selective channel estimators.

Finally, we extend all the proposed channel estimation and equalization approaches to multiple-input multiple-output (MIMO) systems.