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The use of multiple antenna arrays in transmission and reception has becomean integral part of modern wireless communications. To quantify the performanceof such systems, the evaluation of bounds on the error probability of realisticfinite length codewords is important. In this paper, we analyze the standardGallager error bound for both constraints of maximum average power and maximuminstantaneous power. Applying techniques from random matrix theory, we obtainanalytic expressions of the error exponent when the length of the codewordincreases to infinity at a fixed ratio with the antenna array dimensions.Analyzing its behavior at rates close to the ergodic rate, we find that theGallager error bound becomes asymptotically close to an upper error boundobtained recently by Hoydis et al. 2015. We also obtain an expression for theGallager exponent in the case when the codelength spans several Rayleigh fadingblocks, hence taking into account the situation when the channel varies duringeach transmission.

Gallager Bound for MIMO Channels: Large-N Asymptotics