In closed-loop methods for obtaining exact channel state information at the transmitter (CSI-Tx), the overhead associated with the feedback can be excessive for fast mobiles. Channel statistics-based CSI-Tx requires a much smaller overhead and is, therefore, attractive for use with fast mobiles. We study ways to exploit correlation-based CSI-Tx in a multiple-input multiple-output (MIMO)-orthogonal frequency-division multiplexing (OFDM) system. We focus on a channel environment in which spatial and tap correlations are present. We propose a channel model for the case that spatial and tap correlations can be separated and show that in this case channel correlation decreases the ergodic capacity of an MIMO-OFDM system when no CSI-Tx is available. However, this decrease can be mitigated when correlation-based CSI-Tx is exploited. We introduce an optimal precoding approach to maximize capacity with spatial and tap correlation-based CSI-Tx. We also propose a statistical waterfilling scheme, which leads to almost optimal capacity performance without requiring computationally intensive numerical optimization. Based on these approaches, the impact of spatial and tap correlations is investigated.