  We consider the problem of minimization of sum transmission energy in
cellular networks where coupling occurs between cells due to mutual
interference. The coupling relation is characterized by the
signal-to-interference-and-noise-ratio (SINR) coupling model. Both cell load
and transmission power, where cell load measures the average level of resource
usage in the cell, interact via the coupling model. The coupling is implicitly
characterized with load and power as the variables of interest using two
equivalent equations, namely, non-linear load coupling equation (NLCE) and
non-linear power coupling equation (NPCE), respectively. By analyzing the NLCE
and NPCE, we prove that operating at full load is optimal in minimizing sum
energy, and provide an iterative power adjustment algorithm to obtain the
corresponding optimal power solution with guaranteed convergence, where in each
iteration a standard bisection search is employed. To obtain the algorithmic
result, we use the properties of the so-called standard interference function;
the proof is non-standard because the NPCE cannot even be expressed as a
closed-form expression with power as the implicit variable of interest. We
present numerical results illustrating the theoretical findings for a real-life
and large-scale cellular network, showing the advantage of our solution
compared to the conventional solution of deploying uniform power for base
stations.
