  To support machine-type communication (MTC), massive multiple-input
multiple-output (MIMO) has been considered for grant-free random access. In
general, the performance of grant-free random access with massive MIMO is
limited by the number of preambles and the number of active devices. In
particular, when there are a number of active devices transmitting data packets
simultaneously, the signal-to-interference-plus-noise ratio (SINR) cannot be
high enough for successful decoding. In this paper, in order to improve
performance, we consider immediate re-transmissions for an active device that
has a low SINR although it does not experience preamble collision to exploit
re-transmission diversity (RTD) gain. To see the performance of the proposed
approach, we perform throughput analysis with certain approximations and
assumption. Since the proposed approach can be unstable due to immediate
re-transmissions, conditions for stable systems are also studied. Simulations
are carried out and it is shown that analysis results reasonably match
simulation results.
