$\alpha$-Fair Power Allocation in Spectrum-Sharing Networks

To efficiently trade off system sum-rate and link fairness, this paper is dedicated to maximizing the sum of α-fair utility in spectrum-sharing networks, where multiple interfering links share one channel. In the literature, three special cases, including α = 0 (sum-rate maximization), α = 1 (proportional fairness), and α = ∞ (max-min fairness), have been investigated; the complexity for cases 1 <; α <; ∞ and 0 <; α <; 1 is still unknown. In this paper, we prove that the problem is convex when 1 <; α <; ∞ and is NP-hard when 0 <; α <; 1. 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 0 <; α <; 1. In addition, we can get a flexible tradeoff between sum-rate and fairness in terms of Jain's index by adjusting α.