  For MIMO Rayleigh channels, it has been shown that transmitter correlations
always degrade the performance of general space-time codes (STCs) in high SNR
regimes. In this correspondence, however, we show that when MIMO channels
experience single-keyhole conditions, the effect of spatial correlations
between transmission antennas is more sophisticated for general STCs: when
$M>N$ (i.e., the number of transmission antennas is greater than the number of
receiving antennas), depending on how the correlation matrix $\mathbf{P}$
beamforms the code word difference matrix $\mathbf{\Delta}$, the PEP
performance of general STCs can be either degraded or improved in high SNR
regimes. We provide a new measure, which is based on the eigenvalues of
$\mathbf{\Delta}$ and the numbers of transmission and receiving antennas, to
exam if there exists certain correlation matrices that can improve the
performance of general STCs in high SNR regimes. Previous studies on the effect
of spatial correlations over single-keyhole channels only concentrated on
orthogonal STCs, while our study here is for general STCs and can also be used
to explain previous findings for orthogonal STCs.
