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In this paper, we consider Mobile WiMAX and LTE as the future technologies for primary OFDMA systems and study dynamic spectrum access (DSA) for unlicensed systems coexisting with primary OFDMA systems. We propose an effective DSA scheme that allows an unlicensed system to statistically and opportunistically access the whole spectrum bandwidth during the last consecutive symbols of each primary OFDMA subframe. There is a tradeoff in gaining high normalized throughput by enlarging the access duration in each subframe and keeping low interference caused to the primary system by shorten the access period. Then, we model that tradeoff by deriving the optimization problem that maximizes the normalized throughput of the unlicensed system while guaranteeing the harmful interference constraints set by the primary system. We develop and conduct our simulations in our simulator modified from the powerful WiMAX simulator developed by the WiMAX Forum in Ns-2.