  In this letter, we introduce a novel pilot design approach that minimizes the
total mean square errors of the minimum mean square error estimators of all
base stations (BSs) subject to the transmit power constraints of individual
users in the network, while tackling the pilot contamination in multi-cell
Massive MIMO systems. First, we decompose the original non-convex problem into
distributed optimization sub-problems at individual BSs, where each BS can
optimize its own pilot signals given the knowledge of pilot signals from the
remaining BSs. We then introduce a successive optimization approach to
transform each optimization sub-problem into a linear matrix inequality (LMI)
form, which is convex and can be solved by available optimization packages.
Simulation results confirm the fast convergence of the proposed approach and
prevails a benchmark scheme in terms of providing higher accuracy.
