  We introduce a low complexity approach to iterative equalization and
decoding, or "turbo equalization", that uses clustered models to better match
the nonlinear relationship that exists between likelihood information from a
channel decoder and the symbol estimates that arise in soft-input channel
equalization. The introduced clustered turbo equalizer uses piecewise linear
models to capture the nonlinear dependency of the linear minimum mean square
error (MMSE) symbol estimate on the symbol likelihoods produced by the channel
decoder and maintains a computational complexity that is only linear in the
channel memory. By partitioning the space of likelihood information from the
decoder, based on either hard or soft clustering, and using locally-linear
adaptive equalizers within each clustered region, the performance gap between
the linear MMSE equalizer and low-complexity, LMS-based linear turbo equalizers
can be dramatically narrowed.
