Error Exponents for Nakagami-m Fading Keyhole MIMO Channels

Along with the channel capacity, the error exponent is one of the most important information theoretic measures of reliability, as it sets ultimate bounds on the performance of communication systems employing codes of finite complexity. In this paper, we derive the closed-form expressions of Gallager's random coding and expurgated error exponents for Nakagami-m fading keyhole multiple-input multiple-output (MIMO) channels under the assumption that there is no channel-state information (CSI) at the transmitter and perfect CSI at the receiver. From the derived analytical expressions, we get insight into an elementary tradeoff between the communication reliability and information rate of the Nakagami-m fading keyhole MIMO channels. Moreover, we can easily compute the necessary codeword length without the extensive Monte-carlo simulation to achieve predefined error probability at a given rate below the channel capacity. In addition, we derive the exact closed-form expressions for the cutoff rate, critical rate and expurgation rate based on easily computable Meijer G-function. Numerical results are presented and verified via Monte Carlo simulation.