We consider resource allocation in the 3GPP Long Term Evolution (LTE) cellular uplink, which will be the most widely deployed next generation cellular uplink. The key features of the 3GPP LTE uplink (UL) are that it is based on a modified form of the orthogonal frequency division multiplexing based multiple acess (OFDMA), which enables channel dependent frequency selective scheduling, and that it allows for multi-user (MU) scheduling wherein multiple users can be assigned the same time-frequency resource. In addition to the considerable spectral efficiency improvements that are possible by exploiting these two features, the LTE UL allows for transmit antenna selection together with the possibility of employing advanced receivers at the base-station, which promise further gains. However, several practical constraints that seek to maintain a low signaling overhead, are also imposed. In this paper, we show that the resulting resource allocation problem is APX-hard and then propose a local ratio test (LRT) based constant-factor deterministic polynomial-time approximation algorithm which can accommodate all the practical constraints. Detailed evaluations reveal that the proposed algorithm together with its proposed enhancements offers significant gains.