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Opportunistic resource allocation in orthogonal frequency division multiple access (OFDMA) with limited feedback improves the performance of wireless networks and it has been considered in several studies. However, the performances of reduced feedback schemes have not been characterized analytically. In this paper, the analysis of the resource allocation in downlink OFDMA with limited feedback is presented. OFDMA system with a practical resource fair round robin allocation and erroneous feedback channel is considered. The performances of the resource allocation based on three feedback methods are analyzed and compared. A resource-wise signal-to-noise ratio (SNR) quantization based feedback method is considered and two feedback strategies are based on the best-M method, where the M best resource blocks are informed to the transmitter. Analytical bit error probability (BEP) expressions are derived for binary phase-shift keying (BPSK) modulation for each feedback strategy. Furthermore, an asymptotic BEP performance for large SNR values is derived for the best-M feedback schemes. The outage capacity results are derived for the considered feedback schemes to illustrate performance with slow link adaptation. Numerical results based on the analysis are compared to those obtained by computer simulations to validate the correctness of the proposed analysis.