Error Exponent for Nakagami-m Fading Massive MIMO Channels

In this paper, we analytically investigate the closed form of error exponent expression for Orthogonal Space-Time Block Coded (OSTBC) Nakagami-m fading massive multiple input multiple output (MIMO) channels with Gaussian input. We assume that the transmitter has no channel state information (CSI) and full CSI at the receiver. We study an elementary tradeoff between the communication reliability and information rate of the OSTBC Nakagami-m fading massive MIMO channels by the derived expression which is approached by the Hankel determinant in terms of Painlevé differential equations. It can be used to find the necessary codeword length to achieve a prescribe error probability at a given rate below the channel capacity. Moreover, we derive the approximation expressions for the Gallager's random coding error exponent, expurgated error exponent and cutoff rate based on Coulomb fluid linear statistics methods. Numerical approximation results are presented and verified via the exact analytical results.