  Massive machine-type communications (mMTC) is a crucial scenario to support
booming Internet of Things (IoTs) applications. In mMTC, although a large
number of devices are registered to an access point (AP), very few of them are
active with uplink short packet transmission at the same time, which requires
novel design of protocols and receivers to enable efficient data transmission
and accurate multi-user detection (MUD). Aiming at this problem, grant-free
non-orthogonal multiple access (GF-NOMA) protocol is proposed. In GF-NOMA,
active devices can directly transmit their preambles and data symbols
altogether within one time frame, without grant from the AP. Compressive
sensing (CS)-based receivers are adopted for non-orthogonal preambles
(NOP)-based MUD, and successive interference cancellation is exploited to
decode the superimposed data signals. In this paper, we model, analyze, and
optimize the CS-based GF-MONA mMTC system via stochastic geometry (SG), from an
aspect of network deployment. Based on the SG network model, we first analyze
the success probability as well as the channel estimation error of the CS-based
MUD in the preamble phase and then analyze the average aggregate data rate in
the data phase. As IoT applications highly demands low energy consumption, low
infrastructure cost, and flexible deployment, we optimize the energy efficiency
and AP coverage efficiency of GF-NOMA via numerical methods. The validity of
our analysis is verified via Monte Carlo simulations. Simulation results also
show that CS-based GF-NOMA with NOP yields better MUD and data rate
performances than contention-based GF-NOMA with orthogonal preambles and
CS-based grant-free orthogonal multiple access.
