  For the Internet of Things (IoT), there might be a large number of devices to
be connected to the Internet through wireless technologies. In general, IoT
devices would have various constraints due to limited processing capability,
memory, energy source, and so on, and it is desirable to employ efficient
wireless transmission schemes, especially for uplink transmissions. For
example, orthogonal frequency division multiplexing (OFDM) with index
modulation (IM) or OFDM-IM can be considered for IoT devices due to its energy
efficiency. In this paper, we study a different IM scheme for a single-carrier
(SC) system, which is referred to as SCIM. While SCIM is similar to OFDM-IM in
terms of energy efficiency, SCIM may be better suited for IoT uplink because it
has a low peak-to-average power ratio (PAPR) and does not require inverse fast
Fourier transform (FFT) at devices compared to OFDM-IM. We also consider
precoding for SCIM and generalize it to multiple access channel so that
multiple IoT devices can share the same radio resource block. To detect
precoded SCIM signals, low-complexity detectors are derived. For a better
performance, based on variational inference that is widely used in machine
learning, we consider a detector that provides an approximate solution to an
optimal detection.
