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The capacity of multiple input multiple output (MIMO) systems increases linearly with the number of transmit and receive antennas. The asymptotic growth rate of capacity with the number of transmit and receive antennas has been derived for the flat fading channel (see Chuah, C. et al., IEEE Trans. Inform. Theory, vol.48, p.637-50, 2002). We show that for OFDM based spatial multiplexing systems over the frequency selective fading channel, the capacity growth is also linear in the number of transmit and receive antennas. We consider both the independent and correlated fading cases. We adopt the MIMO correlated fading model of H. Bolcskei et al. (see IEEE Trans. Commun., vol.50, p.225-34, 2002). We investigate the influence of the physical parameters (such as antenna spacing, cluster angle spread, and total angle spread) on the capacity scaling of the MIMO OFDM systems.