We introduce a novel sequential importance sampling (SIS) algorithm for the blind equalization of doubly selective channels. Our algorithm propagates a Monte Carlo (MC) approximation of the posterior fixed-lag smoothing distribution of the symbols. As we shall see, it is possible to sample particles from the optimal importance distribution and to update the smoothing importance weights accordingly. We next apply the developed method as a SISO (Soft Input Soft Output) equalizer in a turbo receiver framework. The performance evaluation of our algorithm is carried out under different fading scenarios, and the results are compared with a soft iterative channel estimation scheme available in the literature