In this paper, the problem of multi-user sub-carrier allocation by metric of channel gain in an OFDMA system is formulated as an assignment problem in order to investigate an optimal solution. An optimal channel sub-carrier allocation (OCSA) strategy (extension of Hungarian Method [1]) is proposed for fair bandwidth allocation and highest total perceived channel gain. Additionally, two sub-optimal algorithms are considered: One is an extension of the DSA algorithm in [2], the other is maximum gain sort-swap (MGSS) which is an extension of the algorithm in [3]. The DSA algorithm is of particular interest since it has been shown in [5] to combine well with MIMO. The algorithms can outperform OFDMA with pseudo-random sub-carrier allocation by up to 6dB. Simulation results show that the DSA algorithm achieves perceived channel gains within a fraction of a dB of the optimal solution.