  In this paper, we study grant-free random access with massive multiple input
multiple output (MIMO) systems. We first show that the performance of massive
MIMO based grant-free random access is mainly decided by the probability of
preamble collision. The implication of this is that although the number of
antennas can be arbitrarily large, the (average) number of successful packet
transmissions can be limited by the number of preambles. Then, we propose an
approach to preamble collision reduction without increasing the number of
preambles using the notion of superpositioned preambles (S-preambles). Since
the channel estimation for conjugate beamforming can be carried out when unused
S-preambles are known, a simple approach is derived to detect unused
S-preambles and its performance is analyzed for a special case (superpositions
with 2 preambles). Based on analysis and simulation results, it is confirmed
that the proposed approach with S-preambles can increase the success
probability with the same spectral efficiency as the conventional approach.
