  In this paper, we study the problem of reducing the energy consumption in a
mobile communication network; we select the smallest set of active base
stations that can preserve the quality of service (the minimum data rate)
required by the users. In more detail, we start by posing this problem as an
integer programming problem, the solution of which shows the optimal assignment
(in the sense of minimizing the total energy consumption) between base stations
and users. In particular, this solution shows which base stations can then be
switched off or put in idle mode to save energy. However, solving this problem
optimally is intractable in general, so in this study we develop a suboptimal
approach that builds upon recent techniques that have been successfully applied
to, among other problems, sparse signal reconstruction, portfolio optimization,
statistical estimation, and error correction. More precisely, we relax the
original integer programming problem as a minimization problem where the
objective function is concave and the constraint set is convex. The resulting
relaxed problem is still intractable in general, but we can apply the
majorization-minimization algorithm to find good solutions (i.e., solutions
attaining low objective value) with a low-complexity algorithm. In contrast to
state-of-the-art approaches, the proposed algorithm can take into account
inter-cell interference, is suitable for large-scale problems, and can be
applied to heterogeneous networks (networks where base station consume
different amounts of energy)
