In this work, a new precoded filter bank system based on the pruned discrete Fourier transform spread filter-bank multicarrier (Pruned DFTs FBMC) modulation is proposed. The new scheme utilizes only the double rate transmission idea combined with a data allocation strategy, without the use of Offset Quadrature Amplitude Modulation (OQAM). In addition, we introduce an iterative equalizer in order to obtain better performance, work with larger filter overlap factors and consequently a better spectral localization. The whole system analysis is presented in a new matrix structure in order to make the precoding stage clearer.