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Using the channel state information (CSI) at transmitter can enhance the performance of the system. From practical point of view, those algorithms that require a limited feedback, from receiver to transmitter, are very attractive. In spatially correlated channels, one method of using such a limited feedback is statistical eigen-beamforming (EBF). In this paper, assuming a limited CSI feedback, we derive an exact formula for the ergodic capacity of a MIMO-OFDM system with statistical EBF. Then, we propose a combination of power allocation and statistical EBF in such a system. The results have been verified by simulation. Our simulation shows that the proposed power allocation scheme significantly improves the ergodic capacity of the system, at the expense of only few more bits of feedback.