  In this paper, we consider the problems of minimizing sum power and
maximizing sum rate for multi-cell networks with load coupling, where coupling
relation occurs among cells due to inter-cell interference. This coupling
relation is characterized by the signal-to-interference-and-noise-ratio (SINR)
coupling model with cell load vector and cell power vector as the variables.
Due to the nonlinear SINR coupling model, the optimization problems for
multi-cell networks with load coupling is nonconvex. To solve these nonconvex
problems, we first consider the optimization problems for single-cell networks.
Through variable transformations, the optimization problems can be equivalently
transformed into convex problems. By solving the Karush-Kuhn-Tucker (KKT), the
optimal solutions to power minimization and rate maximization problems can be
obtained in closed form. Based on the theoretical findings of optimization
problems for single-cell networks, we develop a distributed time allocation and
power control algorithm with low complexity for sum power minimization in
multi-cell networks. This algorithm is proved to be convergent and globally
optimal by using the properties of standard interference function. For sum rate
optimization in multi-cell networks, we also provide a distributed algorithm
which yields suboptimal solution. Besides, the convergence for this distributed
algorithm is proved. Numerical results illustrate the theoretical findings,
showing the superiority of our solutions compared to the conventional solution
of allocating uniform power for users in the same cell.
