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Theoretical outage capacity analysis for resource allocation in a downlink orthogonal frequency division multiple access (OFDMA) with limited feedback is presented. OFDMA system with practical resource fair round robin scheduler and erroneous feedback channel is considered. Two feedback methods are analyzed and compared. In the set best-M feedback method, the feedback word indicates the group of the M best resource units. The other feedback method is based on the resource-wise signal-to-noise ratio (SNR) quantization. Results indicate that the set best-M feedback scheme is attractive due to the low feedback overhead and significant allocation gain when few resource units are used and M les 3. The allocation based on the resource-wise one bit feedback outperforms the set best-M schemes especially with erroneous feedback at the cost of the larger feedback overhead.