A Modified Union Bound on Symbol Error Probability for Fading Channels

TL;DR

This paper introduces a new, tighter upper bound on symbol error probability for fading channels, improving accuracy over traditional bounds by considering deep fading events and optimizing the channel gain threshold.

Contribution

It proposes a novel upper bound on error probability that is tighter than the union bound, using a threshold-based approach and optimization techniques.

Findings

The new bound is significantly tighter than the traditional union bound.

The bound is applicable to correlated Rayleigh fading channels.

Analytical and numerical examples demonstrate the bound's effectiveness.

Abstract

In this paper, we propose a new upper bound on the error probability performance of maximum-likelihood (ML) detection. The proposed approach provides a much tighter upper bound when compared to the traditionally used union bound, especially when the number of pairwise error probabilities (PEPs) is large. In fact, the proposed approach tightens the union bound by first assuming that a detection error always occurs in a deep fading event where the channel gain is lower than a certain threshold. A minimisation is then taken with respect to the gain threshold in order to make the upper bound as tight as possible. We also prove that the objective function has a single minimiser under several general assumptions so that the minimiser can be easily found using optimisation algorithms. The expression of the new upper bound under correlated Rayleigh fading channels is derived and several analytical and numerical examples are provided to show the performance of the proposed bound.