  Grant-free massive access is an important technique for supporting massive
machine-type communications (mMTC) for Internet-of-Things (IoT). Two important
features in grant-free massive access are low-complexity devices and
short-packet data transmission, making the traditional performance metric,
achievable rate, unsuitable in this case. In this letter, we investigate
grant-free massive access in a massive multiple-input multiple-output (MIMO)
system. We consider random access control, and adopt approximate message
passing (AMP) for user activity detection and channel estimation in the pilot
transmission phase and small phase-shift-keying (PSK) modulation in the data
transmission phase. We propose a more reasonable performance metric, namely
successful symbol transmission rate (SSTR), for grant-free massive access. We
obtain closed-form approximate expressions for the asymptotic SSTR in the cases
of maximal ratio combining (MRC) and zero forcing (ZF) beamforming at the base
station (BS), respectively. We also maximize the asymptotic SSTR with respect
to the access parameter and pilot length.
