Signal space diversity (SSD) is a technique to obtain diversity without loss in spectral efficiency. Despite this, SSD has been minimally studied in multiuser scenarios. In this paper, SSD is operated in the uplink of orthogonal frequency division multiple access (OFDMA) cellular systems that exploit frequency diversity, use the optimum maximum-likelihood detector (MLD) and employ antenna arrays at the receivers. Thus, a multiuser multiple-input-multiple-output (MU-MIMO) system that works in presence of own-cell and co-cell interference (CCI) is taken into account. In order to diminish CCI, fractional frequency reuse (FFR) is used in the cellular system. For a feasible MLD implementation, a matrix structure of the received signals is obtained in order to use the sphere decoder algorithm. An exact closed-form expression to calculate the pairwise error probability between two multidimensional symbols is derived. From this, a bit error rate (BER) upper bound is found for single user scenarios. This BER expression is an accurate lower bound for high diversity orders in multiuser scenarios. The BER asymptotic analysis shows that our approach maintains the SSD multidimensional diversity, the spatial diversity of MIMO and the frequency diversity. This allows to overload the system by minimizing the BER and increasing the spectral efficiency, simultaneously. INDEX TERMSDiversity methods, MIMO, mobile communication, multiple access interference, OFDM. HENRY CARVAJAL MORA received the B.Sc. degree (Hons.) in electronics and telecommunications engineering from Armed Forces University-ESPE, Sangolquí, Ecuador, in 2009, and the M.Sc. and Ph.D. degrees in electrical engineering from the School of Electrical and Computer Engineering (FEEC), University of Campinas (UNICAMP), Brazil, in 2014 and 2018, respectively. In 2018, he was the Director of technology transfer area with the Education, Science, Technology, and Innovation Secretariat (SENESCYT), Ecuador. He is currently a Full Professor with the Universidad de Las Américas (UDLA), Quito, Ecuador. His research interests include diversity-combining systems, multiple access systems, multiuser detection, MIMO systems, and 5G communications systems. NATHALY OROZCO G. received the Electronic and Telecommunications Engineering degree from Armed Forces University-ESPE, Sangolquí, Ecuador, in 2011, and the M.Sc. and Ph.D. degrees in electrical engineering from the University of Campinas (UNICAMP), Brazil, in 2014 and 2018, respectively. She is currently a Full Professor with the Universidad de Las Américas (UDLA), Quito, Ecuador. Her research interests include digital communications with a specific emphasis on multiple access techniques, fading channels, MIMO, cognitive opportunistic wireless systems, and 5G technologies. PAULO CHILIGUANO T. received the B.Sc. degree in electrical engineering and telecommunications from Armed Forces University-ESPE, Sangolquí, Ecuador, in 2009, and the M.Sc. degree in sound and music computing from the School of Electronic Engineering and Computer Sci...