  In this paper we propose a smoothing turbo equalizer based on the expectation
propagation (EP) algorithm with quite improved performance compared to the
Kalman smoother, at similar complexity. In scenarios where high-order
modulations or/and large memory channels are employed, the optimal BCJR
algorithm is computationally unfeasible. In this situation, low-cost but
suboptimal solutions, such as the linear minimum mean square error (LMMSE), are
commonly used. Recently, EP has been proposed as a tool to improve the Kalman
smoothing performance. In this paper we review these solutions to apply the EP
at the smoothing level, rather than at the forward and backwards stages. Also,
we better exploit the information coming from the channel decoder in the turbo
equalization schemes. With these improvements we reduce the computational
complexity, speed up convergence and outperform previous approaches. We
included some simulation results to show the robust behavior of the proposed
method regardless of the scenario, and its improvement in terms of performance
in comparison with other EP-based solutions in the literature.
