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In this paper, we propose two novel methods for downlink preamble detection and initial coarse time synchronization for mobile WiMAX systems and other OFDM Systems that adopt similar preamble structures. The two methods are based on frequency domain processing. The two methods are compared to the conventional time domain method for frame detection in WiMAX and to another frequency domain algorithm in the literature. The proposed methods are less complex while providing similar or superior performance in the SNR range of interest. The performance measures are the detection and false alarm probabilities, in addition to the Mean Acquisition Time which is evaluated for all the considered methods. Since in the initial state the mobile station is in the state of searching for the downlink preamble, we take into account the interfering effect from other nearby Mobile Stations transmission in the uplink subframe with power larger than the received power from the Base Station in the downlink subframe. Simulation results show the robustness of the new proposed methods in different channel conditions and interference environments.