  Grant-free sparse code multiple access (GF-SCMA) is considered to be a
promising multiple access candidate for future wireless networks. In this
paper, we focus on characterizing the performance of uplink GF-SCMA schemes in
a network with ubiquitous connections, such as the Internet of Things (IoT)
networks. To provide a tractable approach to evaluate the performance of
GF-SCMA, we first develop a theoretical model taking into account the property
of multi-user detection (MUD) in the SCMA system. We then analyze the error
rate performance of GF-SCMA in the case of codebook collision to investigate
the reliability of GF-SCMA when reusing codebook in massive IoT networks. For
performance evaluation, accurate approximations for both success probability
and average symbol error probability (ASEP) are derived. To elaborate further,
we utilize the analytical results to discuss the impact of codeword sparse
degree in GFSCMA. After that, we conduct a comparative study between SCMA and
its variant, dense code multiple access (DCMA), with GF transmission to offer
insights into the effectiveness of these two schemes. This facilitates the
GF-SCMA system design in practical implementation. Simulation results show that
denser codebooks can help to support more UEs and increase the reliability of
data transmission in a GF-SCMA network. Moreover, a higher success probability
can be achieved by GFSCMA with denser UE deployment at low detection thresholds
since SCMA can achieve overloading gain.
