In this paper, we address the resource allocation (RA) problem for uplink single input multiple output (SIMO) single carrier frequency division multiple access (SC-FDMA). A novel RA algorithm for joint user scheduling and resource block allocation is presented. Particularly, with the aim of improving the spectral efficiency (SE) and reducing the computational complexity, a sub-optimal power projection method based on users' spatial correlation is employed, which chooses the users for each RB. A parametric multiple access channel (MAC) model is used for modelling the receive antenna correlation at the base station. Our simulation results show that the proposed scheme improves the the SE considerably, while keeping the complexity at an acceptable level. We also investigate the variation of different system design parameters, i.e., RB size, number of receive antenna, etc, on the SIMO SC-FDMA uplink SE, to shed insight on the role of these parameters in system SE optimization.