A low-complexity optimization scheme is proposed to balance the tradeoff between system capacity and proportional fairness in orthogonal frequency division multiple access(OFDMA) based multicast systems. The major challenge is to solve the non-convexity optimization problem with strict proportional fairness. Constrained team progress algorithm(CTPA) solves this non-convexity problem by allocating sub-channels to each group based on sub-channel gains and proportional fairness constraint. Mapping power algorithm(MPA) guarantees strict proportional fairness with efficient power allocation which utilizes the mapping relation between power and throughput. CTPA-MPA is analyzed in three aspects: complexity, fairness and efficiency. We numerically show that when the system capacity is slightly increased in lower power region compared with several previous approaches, CTPA-MPA improves the proportional fairness in a typical scenario with 4 groups over 16 sub-channels, while reducing the complexity from exponential to linear in the number of sub-channels. It is also proved available in a more complicated system.
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