Gallager´s Exponent Analysis of STBC MIMO Systems over η-μ and κ-μ Fading Channels

In this paper, we analytically investigate Gallager´s exponent for space-time block codes over multiple-input multiple-output block-fading channels with Gaussian input distribution. As a suitable metric of the fundamental tradeoff between communication reliability and information rate, Gallager´s exponent can be used to determine the required codeword length to achieve a prescribed error probability at a given rate below the channel capacity. We assume that the receiver has full channel state information (CSI), while the transmitter has no CSI and performs equal power allocation across all transmit antennas. In the following, novel exact expressions for Gallager´s exponent are derived for two well-known channel fading models, namely η-μ and κ-μ fading models. More importantly, the implications of fading parameters and channel coherence time on Gallager´s exponent are investigated. In addition, we present new expressions for the Shannon capacity, cutoff rate and expurgated exponent for the above mentioned fading models, while in the high signal-to-noise ratio regime, simplified closed-form expressions are also derived. Finally, we highlight the fact that the presented analysis encompasses all previously known results on Nakagami-m, Rician, Rayleigh and Hoyt fading channels, as special cases.