  Massive MIMO opens up new avenues for enabling highly efficient random access
(RA) by offering abundance of spatial degrees of freedom. In this paper, we
investigate the grant-free RA with massive MIMO and derive the analytic
expressions of success probability of the grant-free RA for conjugate
beamforming and zero-forcing beamforming techniques.With the derived analytic
expressions, we further shed light on the impact of system parameters on the
success probability. Simulation results verify the accuracy of the analyses. It
is confirmed that the grant-free RA with massive MIMO is an attractive RA
technique with low signaling overhead that could simultaneously accommodate a
number of RA users, which is multiple times the number of RA channels, with
close-to-one success probability. In addition, when the number of antennas in
massive MIMO is sufficiently large, we show that the number of orthogonal
preambles would dominate the success probability.
