Conventional spatial modulation (SM) is typically considered for transmission in the downlink of small-scale MIMO systems, where a single one of a set of antenna elements (AEs) is activated for implicitly conveying extra bits. By contrast, inspired by the compelling benefits of large-scale MIMO (LS- MIMO) systems, here we propose a LS-SM-MIMO scheme for the uplink (UL), where each user having multiple AEs but only a single radio frequency (RF) chain invokes SM for increasing the UL-throughput. At the same time, by relying on hundreds of AEs but a small number of RF chains, the base station (BS) can simultaneously serve multiple users whilst reducing the power consumption. Due to the large number of AEs of the UL-users and the comparably small number of RF chains at the BS, the UL multi-user signal detection becomes a challenging large-scale under-determined problem. To solve this problem, we propose a joint SM transmission scheme and a carefully designed structured compressive sensing (SCS)-based multi-user detector (MUD) to be used at the users and BS, respectively. Additionally, the cyclic- prefix single-carrier (CPSC) is used to combat the multipath channels, and a simple receive AE selection is used for the improved performance over correlated Rayleigh-fading MIMO channels. We demonstrate that the aggregate SM signal consisting of SM signals of multiple UL-users in one CPSC block appears the distributed sparsity. Moreover, due to the joint SM transmission scheme, aggregate SM signals in the same transmission group exhibit the group sparsity. By exploiting these intrinsically sparse features, the proposed SCS-based MUD can reliably detect the resultant SM signals with low complexity. Simulation results demonstrate that the proposed SCS-based MUD achieves a better signal detection performance than its counterparts even with higher UL-throughtput.