Global Optimization of Long-Term Average Proportional Fair Throughput via Convex Reformulation

Long-term average proportional-fair (LTAPF) throughput optimization through power control is a popular resource allocation problem which is typically approximated by weighted sum-rate (WSR) maximization. WSR optimization is non-convex and strongly NP-hard in general. In this letter, we demonstrate that, in fact, the original sum-log-average-throughput power control problem can be recast as a convex program and thus solved to global optimality efficiently. We also generalize our result to show that the long-term average <inline-formula><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>-fair utility maximization problem can be recast as convex for <inline-formula><tex-math notation="LaTeX">$\alpha \in (1,\infty)$</tex-math></inline-formula>. Numerical results demonstrate a substantial gain in LTAPF throughput compared to state-of-the art algorithms used to solve the max-WSR problem.