Weighted sum of per cell min-rate maximization for multi-cell downlink OFDMA with opportunistic DF relaying

This paper considers a multi-cell relay-aided orthogonal frequency division multiple access (OFDMA) downlink system, in which all stations are coordinated by a central controller for resource allocation (RA). The decode-and-forward (DF) protocol with opportunistic relaying (OR) and high spectrum efficiency (HSE) is applied. The problem of maximizing the weighted sum of per cell min-rate (WSMR) with per-cell total power constraints is formulated, and its per-cell maximum fairness property is proven. An iterative RA algorithm is proposed to optimize mode selection (decision whether the relay should help or not), subcarrier assignment (MSSA) and power allocation (PA) alternatively. Each iteration is composed of the MSSA stage and the PA stage. During the MSSA stage, the original problem is decoupled into mixed integer linear programs (MILPs) with the tentative PA results, which can be solved by typical MILP solvers. To solve the MILPs more efficiently in polynomial time, a randomized rounding-based MSSA (RR-MSSA) algorithm and a direct rounding-based MSSA (DR-MSSA) algorithm are further proposed. During the PA stage, an algorithm based on single condensation and geometric programming (SCGP) PA is designed to optimize PA with the tentative MSSA results. The convergence and the per-cell user fairness of the proposed RA algorithm are proven. Finally, the performance of the RA algorithm and the benefits of using OR and the HSE protocol are illustrated through numerical experiments.