  Massive MIMO systems, where the base stations are equipped with hundreds of
antenna elements, are an attractive way to attain unprecedented spectral
efficiency in future wireless networks. In the "classical" massive MIMO
setting, the terminals are assumed fully loaded and a main impairment to the
performance comes from the inter-cell pilot contamination, i.e., interference
from terminals in neighboring cells using the same pilots as in the home cell.
However, when the terminals are active intermittently, it is viable to avoid
inter-cell contamination by pre-allocation of pilots, while same-cell terminals
use random access to select the allocated pilot sequences. This leads to the
problem of intra-cell pilot contamination. We propose a framework for random
access in massive MIMO networks and derive new uplink sum rate expressions that
take intra-cell pilot collisions, intermittent terminal activity, and
interference into account. We use these expressions to optimize the terminal
activation probability and pilot length.
