  In a densely deployed heterogeneous network (HetNet), the number of
pico/micro base stations (BS) can be comparable with the number of the users.
To reduce the operational overhead of the HetNet, proper identification of the
set of serving BSs becomes an important design issue. In this work, we show
that by jointly optimizing the transceivers and determining the active set of
BSs, high system resource utilization can be achieved with only a small number
of BSs. In particular, we provide formulations and efficient algorithms for
such joint optimization problem, under the following two common design
criteria: i) minimization of the total power consumption at the BSs, and ii)
maximization of the system spectrum efficiency. In both cases, we introduce a
nonsmooth regularizer to facilitate the activation of the most appropriate BSs.
We illustrate the efficiency and the efficacy of the proposed algorithms via
extensive numerical simulations.
