  This paper presents an energy-efficient downlink precoding scheme with the
objective of maximizing system energy efficiency in a multi-cell massive MIMO
system. The proposed precoding design jointly considers the issues of power
control, interference management, antenna switching and user throughput in a
cluster of base stations (BS). We demonstrate that the precoding design can be
formulated into a general sparsity-inducing non-convex problem, which is
NP-hard. We thus apply a smooth approximation of zero-norm in the antenna power
management to enable the application of the gradient-based algorithms. The
non-convexity of the problem may also cause slow convergence or even divergence
if some classical gradient algorithms are directly applied. We thus develop an
efficient alternative algorithm combining features from augmented multiplier
(AM) and quadratic programming (QP) to guarantee the convergence. We
theoretically prove the convergence conditions for our algorithm both locally
and globally under realistic assumptions. Our proposed algorithms further
facilitate a distributed implementation that reduces backhaul overhead by
offloading data-intensive steps to local computation at each BS. Numerical
results confirm that our methods indeed achieve higher energy efficiency with
superior convergence rate, compared to some well-known existing methods.
