  We consider large-scale fading precoding (LSFP), which is a two-layer
precoding scheme in the downlink of multi-cell massive MIMO (multiple-input
multiple-output) systems to suppress inter-cell interference. We obtain the
closed-form spectral efficiency (SE) with LSFP at the central network
controller and maximum ratio precoding at the base stations (BSs) using the
linear minimum mean-squared error or least squares channel estimators. The LSFP
weights are designed based on the long-term channel statistics and two
important performance metrics are optimized under the per-BS transmit power
constraints. These metrics are sum SE and proportional fairness, where the
resulting optimization problems are non-convex. Two efficient algorithms are
developed to solve these problems by using the weighted minimum mean-squared
error and the alternating direction method of multipliers methods. Moreover,
two partial LSFP schemes are proposed to reduce the fronthaul signaling
requirements. Simulations quantify the performance improvement of LSFP over
standard single-layer precoding schemes and identify the specific advantage of
each optimization problem.
