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The performance of the uplink (UL) and downlink (DL) of IEEE 802.16e-2005 or Worldwide Inter-Operability Microwave Access (WiMAX) standard is studied via extensive computer simulations in this paper. The channel estimation is introduced and its impact on the system performance is evaluated under different channel conditions. The main contribution is to address the impact of the hybrid automatic repeat request (HARQ) protocol on the WiMAX system performance. For DL, the schemes include single-input single-output (SISO), Alamouti space-time block coding (STBC), and spatial multiplexing, i.e., vertical coded 2times2 multiple-input multiple-output (MIMO). For UL, the transmission schemes include SISO and 1times2 SIMO. It is observed that the HARQ protocol can improve the system performance dramatically, typically 2 ~ 3.5 dB gain in SNR from the first retransmission. The retransmission gain is also found to be relatively independent of the number of receive antennas.