A low-complexity optimization scheme is proposed to balance the tradeoff be-tween system capacity and proportional fair-ness in orthogonal frequency division multiple access (OFDMA) based multicast systems. The major challenge is to solve the non-con-vexity optimization problem with strict pro-portional fairness. Constrained team progress algorithm (CTPA) solves this non-convexity problem by allocating sub-channels to each group based on sub-channel gains and propor-tional fairness constraint. Mapping power al-gorithm (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 effi-ciency. We numerically show that when the system capacity is slightly increased in lower power region compared with several previous approaches, CTPA-MPA improves the pro-portional 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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