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.

I. Introduction

It has been shown, both theoretically [1], [2] and experimentally [3], that wireless multiple-input multiple-output (MIMO) communication systems can experience non-fully correlated but rank-deficient fading. This phenomenon occurs when there is rich scattering around the transmitter and the receiver, respectively, but a barrier with a hole (e.g. a tunnel) between the transmitter and the receiver leads to a reduction of the rank of the channel matrix [3]. This effect, which is known as keyhole or pinhole effect, may have a negative impact on the achievable performance of MIMO systems and therefore needs to be well understood by system designers. This is particularly true for systems employing space-time codes (STCs) in the hope of increasing the diversity gain of the system.