Log-concavity property of the error probability with application to local bounds for wireless communications

TL;DR

This paper proves the log-concavity of error probability in wireless systems with Gaussian noise and fading, enabling the creation of tighter, region-specific bounds for system performance analysis.

Contribution

It introduces a novel analytical framework based on log-concavity to derive local bounds for error probability in wireless communications, improving upon existing bounds.

Findings

Proves log-concavity of error probability for various modulation schemes.

Constructs local bounds that are tighter within specific SNR regions.

Demonstrates the applicability of bounds to system performance assessment.

Abstract

A clear understanding the behavior of the error probability (EP) as a function of signal-to-noise ratio (SNR) and other system parameters is fundamental for assessing the design of digital wireless communication systems.We propose an analytical framework based on the log-concavity property of the EP which we prove for a wide family of multidimensional modulation formats in the presence of Gaussian disturbances and fading. Based on this property, we construct a class of local bounds for the EP that improve known generic bounds in a given region of the SNR and are invertible, as well as easily tractable for further analysis. This concept is motivated by the fact that communication systems often operate with performance in a certain region of interest (ROI) and, thus, it may be advantageous to have tighter bounds within this region instead of generic bounds valid for all SNRs. We present a possible application of these local bounds, but their relevance is beyond the example made in this paper.