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In OFDMA, the subcarrier allocation process amongst the users has a significant role in governing the performance of the system. In this paper, we study the application of interleaver based subcarrier allocation schemes for ensuring uniform BER across all the active users. We show that for a slowly changing multipath channel, individual user's BER performance can vary from each other to a great extent, which implies that the propagation channel effect is unfairly distributed on the users. Applying different types of frequency interleaving mechanisms, we show that the choice of interleaving can ensure better BER fairness on an individual user basis. In particular, by introducing the application of cyclically shifted random interleaver, we demonstrate its effectiveness in achieving BER fairness (dispersion in individual users BER reduced by 94% compared to no interleaving at 20dB SNR) with reduced system complexity and manageable PAPR.