  Pilot contamination is known to be one of the main impairments for massive
MIMO multi-cell communications. Inspired by the concept of fractional frequency
reuse and by recent contributions on pilot reutilization among non-adjacent
cells, we propose a new pilot allocation scheme to mitigate this effect. The
key idea is to allow users in neighboring cells that are closest to their base
stations to reuse the same pilot sequences. Focusing on the uplink, we obtain
expressions for the overall spectral efficiency per cell for different linear
combining techniques at the base station and use them to obtain both the
optimal pilot reuse parameters and the optimal number of scheduled users.
Numerical results show a remarkable improvement in terms of spectral efficiency
with respect to the existing techniques.
