Asymptotic Analysis of Space-Time Codes in Generalized Keyhole Fading Channels

The keyhole phenomenon, i.e., non-fully correlated but rank-deficient fading, can lead to significant performance degradations in multiple-input multiple-output (MIMO) systems and has to be carefully taken into account for system design. In this paper, we consider generalized keyhole fading including Rayleigh, Ricean, Nakagami-q, Nakagami-m, and Weibull fading. We derive simple and elegant closed-form expressions for the asymptotic pairwise error probability (PEP) of both single-antenna transmission and space-time coded transmission with two transmit antennas. The obtained PEP expressions provide significant insight into the impact of various system and channel parameters such as the types of fading at the transmitter and receiver side, the numbers of transmit and receive antennas, and the space-time code design on performance. This insight can be exploited for system design and to explain the differences in the performance of space-time codes in non-keyhole and keyhole fading channels. Furthermore, the presented asymptotic PEP expressions can be utilized to obtain tight asymptotic approximations for the bit, symbol, and frame error probabilities of arbitrary, not necessarily orthogonal, space-time codes. Simulation results confirm the accuracy and usefulness of the derived results.