Abstract
To efficiently trade off system sum-rate and link fairness, this paper is dedicated to maximizing the sum of $\alpha$ -fair utility in spectrum-sharing networks, where multiple interfering links share one channel. In the literature, three special cases, including $\alpha=\mbox{0}$ (sum-rate maximization), $\alpha=\mbox{1}$ (proportional fairness), and $\alpha=\infty$ (max-min fairness), have been investigated; the complexity for cases $\mbox{1} and $\mbox{0} is still unknown. In this paper, we prove that the problem is convex when $\mbox{1} and is NP-hard when $\mbox{0} . To deal with the latter case, we transform the objective function and represent it by the difference of two concave functions (D.C.). Then, a power allocation algorithm is proposed with fast convergence to a local optimal point. Simulation results show that the proposed algorithm can obtain global optimality in two-link cases when $\mbox{0} . In addition, we can get a flexible tradeoff between sum-rate and fairness in terms of Jain's index by adjusting $\alpha$ .
Published Version
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