On the Relationships Between Average Channel Capacity, Average Bit Error
Rate, Outage probability and Outage Capacity over Additive White Gaussian
In wireless communications, average performance measures (APMs) such as
average channel capacity (ACC), average bit error rate (ABER) and outage
probability / capacity (OP / OC) are widely utilized to comprehend the
performance gains/impairments in different environments under various scenarios
and quantify how factors originating from the design / implementation influence
on system performance. To the best of our knowledge, it has not been yet
discovered how these APMs are related to each other. In this article, having
been inspired by the work of Verdu et al. , we propose that one APM can be
calculated using the other APMs without having the SNR characterization.
Particularly, using Lamperti's transformation (LT), we identify the
relationships among APMs; such that these relationships are irrespective of SNR
distribution. Thereby, we propose a tractable approach, which we call LT-based
APM analysis, to establish a relationship between any two given APMs.
Henceforth, we introduce some novel relationships among ACC, ABER and OP / OC
performances for signalling over additive white Gaussian noise channels in
fading environments. We demonstrate how to obtain exact ACC by using ABER
performance, and we discover how OP/OC performances are obtained by using exact
ACC performance. We consider some numerical examples and simulations to
validate our newly derived relationships.