In this paper, a new filter-bank multi-carrier(FBMC) receiver targeted at short prototype filters (PFs) is presented. In addition to the typical advantages of FBMC modulation such as improved frequency containment and support of relaxed synchronization, the proposed receiver enables accurate one-tap equalization of the signal despite the use of a short PF, while significantly reducing the complexity by merging the equalization and the standard FBMC receiver. An adapted frame structure is proposed that occupies the same radio resources as a 4G/LTE orthogonal frequency-division multiplexing (OFDM) frame while providing a similar data rate. Moreover, this frame structure is shown to readily support block-based Alamouti-coded multiple-input multiple-output transmissions. Simulation results show that the proposed FBMC receiver can outperform an OFDM system on 4G/LTE channel models in both single antenna and Alamouti configurations, while having a better robustness to synchronization errors than a frequency-spread FBMC receiver.