Coherent MU-MIMO in Block Fading Channels: A Finite Blocklength Analysis

This paper investigates the maximum coding rate of the multiple-user multiple-input-multiple-output (MU-MIMO) uplink in coherent block-fading channels and with finite blocklength. The backoff of the maximum coding rate from the capacity caused by finite blocklength is precisely characterized by a parameter, called the channel dispersion. In particular, we derive exact analytical and approximation results for a large number of the base station (BS) antennas. By analyzing these results, we observe that even when considering the channel dispersion, the maximum coding rate still increases with respect to the number of BS antennas, whilst the SNR for each user can also improve the performance to a ceiling limited by the inter-user interference. Fast channel dynamics (shorter coherence time) and high diversity gain (large number of blocks) are beneficial for the maximum coding rate under finite blocklength and coherent setting. Moreover, to obtain a certain fraction of the capacity with fixed error probability, the minimum required blocklength (delay) can be reduced by increasing the number of BS antennas. We also show that the channel dispersion will converge to a constant while the minimum required blocklength can approach to zero with massive number of the BS antennas. Hence, from a theoretical viewpoint, deploying a large number of the BS antennas is beneficial for low latency communications.