  Random access is necessary in crowded scenarios due to the limitation of
pilot sequences and the intermittent pattern of device activity. Nowadays, most
of the related works are based on independent and identically distributed
(i.i.d.) channels. However, massive multiple-input multiple-output (MIMO)
channels are not always i.i.d. in realistic outdoor wireless propagation
environments. In this paper, a device grouping and pilot set allocation
algorithm is proposed for the uplink massive MIMO systems over spatially
correlated Rayleigh fading channels. Firstly, devices are divided into multiple
groups, and the channel covariance matrixes of devices within the same group
are approximately orthogonal. In each group, a dedicated pilot set is assigned.
Then active devices perform random pilot and data access process. The mean
square error of channel estimation (MSE-CE) and the spectral efficiency of this
scheme are derived, and the MSE-CE can be minimized when collision devices have
non-overlapping angle of arrival (AoA) intervals. Simulation results indicate
that the MSE-CE and spectral efficiency of this protocol are improved compared
with the traditional scheme. The MSE-CE of the proposed scheme is close to the
theoretical lower bound over a wide signal-to-noise ratio (SNR) region
especially for long pilot sequence. Furthermore, the MSE-CE performance gains
are significant in high SNR and strongly correlated scenarios.
