  Pilot contamination is a limiting factor in multicell massive multiple-input
multiple-output (MIMO) systems because it can severely impair channel
estimation. Prior works have suggested coordinating pilot design across cells
in order to reduce the channel estimation error caused by pilot contamination.
In this paper, we propose a method for coordinated pilot design using
fractional programming to minimize the weighted mean squared-error (MSE) in
channel estimation. In particular, we apply the recently proposed quadratic
transform to the MSE expression which allows the effect of pilot contamination
to be decoupled. The resulting problem reformulation enables the pilots to be
optimized in closed form if they can be designed arbitrarily. When the pilots
are restricted to a given set of orthogonal sequences, pilot optimization
reduces to an assignment problem which can be solved by weighted bipartite
matching. Furthermore, we consider the max-min fairness of data rates with
orthogonal pilots and obtain an extension of the proposed method to correlated
Rayleigh fading. Finally, simulations demonstrate the advantage of the proposed
(orthogonal and nonorthogonal) pilot designs as compared with state-of-the-art
methods in combating pilot contamination.
