On Chernoff Lower-Bound of Outage Threshold for Non-Central $\chi^2$-Distributed MIMO Beamforming Gain

TL;DR

This paper derives a Chernoff-based lower bound for the outage threshold of non-central chi-squared distributions in MIMO beamforming, enabling accurate predictions for ultra-reliable low-latency communication systems.

Contribution

It introduces the Chernoff lower bound as an effective tool for estimating outage thresholds in complex MIMO channels, improving reliability predictions.

Findings

Chernoff lower bound effectively predicts outage thresholds.

Accurate beamforming gain estimation for ultra-reliable communication.

Enhanced reliability and energy efficiency in time-varying channels.

Abstract

The cumulative distribution function (CDF) of a non-central $\chi^2$-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.