We introduce a new sequential importance sampling(SIS) algorithm which propagates in time a Monte Carlo approximation of the posterior fixed-lag smoothing distribution of the symbols under doubly-selective channels. We perform an exact evaluation of the optimal importance distribution, at a reduced computational cost when compared to other optimal solutions proposed for the same state-space model. The method is applied as a soft input-soft output (SISO) blind equalizer in a turbo receiver framework and simulation results are obtained to show its outstanding BER performance.