  We devise novel techniques to obtain the downlink power inducing a given load
in long-term evolution (LTE) systems, where we define load as the fraction of
resource blocks in the time-frequency grid being requested by users from a
given base station. These techniques are particularly important because
previous studies have proved that the data rate requirement of users can be
satisfied with lower transmit energy if we allow the load to increase. Those
studies have also shown that obtaining the power assignment from a desired load
profile can be posed as a fixed point problem involving standard interference
mappings, but so far the mappings have not been obtained explicitly. One of our
main contributions in this study is to close this gap. We derive an
interference mapping having as its fixed point the power assignment inducing a
desired load, assuming that such an assignment exists. Having this mapping in
closed form, we simplify the proof of the aforementioned known results, and we
also devise novel iterative algorithms for power computation that have many
numerical advantages over previous methods.
