Error exponents for multi-keyhole MIMO channels

Along with the channel capacity, the error exponent is one of the most important information-theoretic measures of reliability, because it sets ultimate bounds on the performance of communication systems employing codes of finite complexity. In this paper, we derive closed-form expressions for the Gallager random coding and expurgated error exponents for multi-keyhole multiple-input multiple-output (MIMO) channels, which provide insights into a fundamental tradeoff between the communication reliability and information rate. We investigate the effect of keyholes on the error exponents and cutoff rate. Moreover, without an extensive Monte-Carlo simulation we can easily compute the codeword length necessary to achieve a predefined error probability at a given rate, which quantifies the effects of the number of antennas, channel coherence time, and the number of keyholes. In addition, we derive exact closed-form expressions for the ergodic capacity and cutoff rate based on the easily computable Meijer $G$-function. Finally, we extend our study to Rayleigh-product MIMO channels and keyhole MIMO channels.