  Deployment of small cell base stations (SBSs) overlaying the coverage area of
a macrocell BS (MBS) results in a two-tier hierarchical small cell network.
Cross-tier and inter-tier interference not only jeopardize primary macrocell
communication but also limit the spectral efficiency of small cell
communication. This paper focuses on distributed interference management for
downlink small cell networks. We address the optimization of transmit
strategies from both the game theoretical and the network utility maximization
(NUM) perspectives and show that they can be unified in a generalized Nash
equilibrium problem (GNEP) framework. Specifically, the small cell network
design is first formulated as a GNEP, where the SBSs and MBS compete for the
spectral resources by maximizing their own rates while satisfying global
quality of service (QoS) constraints. We analyze the GNEP via variational
inequality theory and propose distributed algorithms, which only require the
broadcasting of some pricing information, to achieve a generalized Nash
equilibrium (GNE). Then, we also consider a nonconvex NUM problem that aims to
maximize the sum rate of all BSs subject to global QoS constraints. We
establish the connection between the NUM problem and a penalized GNEP and show
that its stationary solution can be obtained via a fixed point iteration of the
GNE. We propose GNEP-based distributed algorithms that achieve a stationary
solution of the NUM problem at the expense of additional signaling overhead and
complexity. The convergence of the proposed algorithms is proved and guaranteed
for properly chosen algorithm parameters. The proposed GNEP framework can scale
from a QoS constrained game to a NUM design for small cell networks by trading
off signaling overhead and complexity.
