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In most existing works, perfect knowledge of channel state information at the transmitter (CSIT) is assumed to realize the potential benefit of cross-layer scheduling and spatial multiplexing gains of MIMO/OFDMA systems. However, perfect knowledge of CSIT is not easy to achieve in practice due to estimation noise or delay in feedback. In this paper, we shall focus on the cross-layer design of downlink multi-antenna OFDMA systems with imperfect CSIT for slow fading channels. We shall show that our proposed cross-layer scheduler can exploit the multiuser diversity and spatial multiplexing gain even in the presence of moderate CSIT error.