On the Relationships Between Average Channel Capacity, Average Bit Error Rate, Outage probability and Outage Capacity over Additive White Gaussian Noise Channels
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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. [1], 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.
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