# On the Relationships Between Average Channel Capacity, Average Bit Error Rate, Outage probability and Outage Capacity over Additive White Gaussian Noise Channels

## TL;DR

This paper introduces a novel Lamperti's transformation-based method to relate and compute key average performance measures in wireless channels without relying on SNR distribution, simplifying analysis of system performance.

## Contribution

It proposes a new LT-based approach to derive relationships among average channel capacity, bit error rate, and outage metrics, enabling empirical evaluation without SNR distribution.

## Key findings

- Derived relationships among ACC, ABER, and outage metrics.
- Validated the approach with numerical examples and simulations.
- Enabled empirical calculation of ACC without SNR distribution.

## Abstract

In the theory of wireless communications, average performance measures (APMs) are widely utilized to quantify the performance gains/impairments in various fading environments under various scenarios, and to comprehend how the factors arising from design/implementation affect system performance. To the best of our knowledge, it has not been yet discovered in the literature how these APMs relate to each other. In this article, having been inspired by the work of Verdu et al. [1], we propose that one APM can be calculated using the other APMs instead of using the end-to-end SNR distribution. Particularly, using the Lamperti's transformation (LT), we propose a tractable approach, which we call LT-based APM analysis, to identify a relationship between any two given APMs such that it is irrespective of SNR distribution. Thereby, we introduce some novel relationships among average channel capacity (ACC), average bit error rate (ABER) and outage probability/capacity (OP/OC) performances, and accordingly present how to obtain ACC from ABER performance and how to obtain OP/OC from ACC performance in fading environments. We demonstrate that the ACC of any communications system can be evaluated empirically without using end-to-end SNR distribution. We consider some numerical examples and simulations to validate our newly derived relationships.