In cyclic delay diversity (CDD) based multiple input multiple output (MIMO) orthogonal frequency division multiplexing (OFDM) systems, correlation can evolve among parallel channels due to closeness of antennas or lack of scatterers in the environment. In this work, pseudo random binary phase offsets are induced into the transmitting symbols to mitigate the correlation effect. Average capacity per sub-carrier and pairwise error probability (PEP) are used as metrics to analyze the system performance for an arbitrary number of transmitting and receiving antennas. Our analysis reveals that depending on the channel spatial correlation, some of the sub-carriers have substantially lower average capacity than others and may, therefore, deteriorate the system performance. In such cases, the proposed scheme enables those sub-carriers to recover from correlation effects and reinstates all the sub-carriers with the same upper bound of the average capacity as offered by the uncorrelated channel. Our analysis of PEP demonstrates the effects of spatial correlation on the squared Euclidean distance between any two codewords and shows how the proposed scheme mitigates those effects without knowledge of the channel spatial correlation. We observe in simulation that depending on the channel spatial correlation, our proposed scheme can yield a dramatic performance improvement.