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.