Abstract
The cumulative distribution function (CDF) of a non-central χ2-distributed random variable (RV) is often used when measuring the outage probability of communication systems. For adaptive transmitters, it is important but mathematically challenging to determine the outage threshold for an extreme target outage probability (e.g., 10 −5 or less). This motivates us to investigate lower bounds of the outage threshold, and it is found that the one derived from the Chernoff inequality (named Cher-LB) is the most effective lower bound. The Cher-LB is then employed to predict the multi-antenna transmitter beamforming-gain in ultra-reliable and low-latency communication, concerning the first-order Markov time-varying channel. It is exhibited that, with the proposed Cher-LB, pessimistic prediction of the beamforming gain is made sufficiently accurate for guaranteed reliability as well as the transmit-energy efficiency. Index Terms—Chernoff bound, beamforming gain, non-central χ2-distribution, reliability, multi-input multi-output (MIMO).