Coding and diversity gain tradeoff in space-time codes for correlated MIMO channels

Most space-time codes are designed for multiantenna systems assuming the ideal i.i.d. channel model, but their performance degrades over correlated channels. This paper investigates space-time code design for correlated channels using the pair-wise error probability (PEP) criterion. It is shown that, unlike i.i.d channels, performance depends not just on the code error covariance matrix but also its interaction with the channel covariance matrix. Using the example of orthogonal space-time block codes, it is shown that linear precoding can facilitate this interaction to improve performance over correlated channels. Depending on the channel covariance matrix, it may be optimal to trade diversity for higher coding gain even at high signal-to-noise ratios (SNR), i.e better performance is obtained by lower diversity codes by pumping more power along the dominant transmit signal space dimensions to improve coding gain. This results in reduced dimensional codes which have improved performance than codes without precoding.