Space-time codes in keyhole channels: analysis and design

The keyhole condition, where the MIMO channel has only one degree of freedom, impairs the performance of MIMO systems. In cases that this condition is likely, one may wish to design codes that are robust to this condition. So far, a general analysis of space-time codes in keyhole conditions has not been available (except in the special case of orthogonal space-time block codes). In this work, we provide pairwise error probabilities for general space-time codes in the keyhole condition. We present design criteria in high SNR, providing guidelines for codes that are robust to keyhole conditions. We also prove the intuitive result that the diversity under the keyhole condition is min(M,N), with a slightly unexpected twist in the case of M=N.