  Grant-free random access (RA) with massive MIMO is a promising RA technique
for massive access with low signaling overhead. In the grant-free RA with
massive MIMO, preamble length has a critical impact on the performance of the
system. In this paper, the optimal preamble length is investigated to maximize
spectral efficiency (SE) of the grant-free RA with massive MIMO, where effects
of the preamble length on the preamble collision and preamble overhead as well
as channel estimation accuracy are taken into account. Simulation results agree
well with our analyses and confirm the existence of optimal preamble length for
SE maximization in the grant-free RA with massive MIMO. Moreover, properties of
the optimal preamble length with respect to system parameters are revealed.
Compared to the granted access, it is shown that longer preamble length is
required for SE maximization in the grant-free RA.
