This paper considers a multiuser multiple-input multiple-output (MU-MIMO) non orthogonal multiple access (NOMA) communication scenario with one base station and two users. As a potential precoding scheme, the generalized singular value decomposition (GSVD) can be adopted in MU-MIMO- NOMA systems and has been proved to have high spectral efficiency. The power consumption at the access point (AP) should be as low as possible, making single-carrier (SC) schemes, such as single carrier with frequency-domain equalization (SC- FDE), particularly interesting. In this work, we first introduce a general uplink framework channel for GSVD based MU-MIMO- NOMA system. Then, by taking advantage of GSVD properties, we propose a novel receiver based on minimum mean square error (MMSE) equalizer offering a balanced trade-off between performance and computational complexity.