  Despite being the subject of a growing body of research, non-orthogonal
multiple access has failed to garner sufficient support to be included in
modern standards. One of the more promising approaches to non-orthogonal
multiple access is sparse code multiple access, which seeks to utilize
non-orthogonal, sparse spreading codes to share bandwidth among users more
efficiently than traditional orthogonal methods. Nearly all of the studies
regarding sparse code multiple access assume synchronization at the receiver,
which may not always be a practical assumption. In this work, we aim to bring
this promising technology closer to a practical realization by dropping the
assumption of synchronization. We therefore propose a compressed sensing-based
delay estimation technique developed specifically for an uplink sparse code
multiple access system. The proposed technique can be used with nearly all of
the numerous decoding algorithms proposed in the existing literature, including
the popular message passing approach. Furthermore, we derive a theoretical
bound regarding the recovery performance of the proposed technique, and use
simulations to demonstrate its viability in a practical uplink system.
