Turbo Equalization/Estimation of Doubly Selective Channels using Basis Expansion and Tree Search

For turbo reception of coded transmissions over unknown doubly selective channels, such as time-varying ISI channels or frequency-varying ICI channels, we propose several soft noncoherent equalizers based on basis expansion (BE) channel modeling and tree-search, as a departure from traditional designs based on autoregressive (AR) channel modeling and/or trellis processing. By “noncoherent,” we mean an equalizer that operates in the absence of channel state information. We begin by deriving the optimal BE-based soft noncoherent equalizer, whose complexity is shown to be impractical. We then propose a nearoptimal approximation, based on soft tree-search and leveraging a fast recursive metric update, whose per-symbol complexity is only quadratic in the number of BE coefficients. Finally, we propose a different approach to soft noncoherent equalization that results from an application of the space-alternating generalized expectation-maximization (SAGE) algorithm. Using a tree-search-based practical implementation, the per-symbol complexity of this latter scheme is, for the multicarrier case, only linear in the number of BE coefficients. Numerical experiments demonstrate coded bit error rates near genie-aided bounds, as well as robustness to Doppler-spread mismatch.