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. Thus, 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). This work provides pairwise error probabilities for general space-time codes in keyhole condition. We present design criteria in high SNR, providing guidelines for codes that are robust to keyhole conditions. Also included is the proof of the intuitive result that the diversity under keyhole condition is min(M, N), where M and N are the number of transmit and receive antennas, with a slightly unexpected twist in the case of M = N.