Outage Exponent: A Unified Performance Metric for Parallel Fading Channels

TL;DR

This paper introduces the outage exponent, a unified metric based on large deviations theory and Meijer's G-function, to accurately evaluate the performance of parallel fading channels across all SNRs and subchannel counts.

Contribution

It proposes the outage exponent as a comprehensive performance metric that extends beyond asymptotic analysis to finite SNRs and subchannels, enabling precise performance evaluation.

Findings

Accurately estimates outage probability for any number of subchannels and SNRs

Facilitates computation of outage capacity and diversity-multiplexing tradeoff

Provides a fundamental relationship between reliability and efficiency

Abstract

The parallel fading channel, which consists of finite number of subchannels, is very important, because it can be used to formulate many practical communication systems. The outage probability, on the other hand, is widely used to analyze the relationship among the communication efficiency, reliability, SNR, and channel fading. To the best of our knowledge, the previous works only studied the asymptotic outage performance of the parallel fading channel which are only valid for a large number of subchannels or high SNRs. In this paper, a unified performance metric, which we shall refer to as the outage exponent, will be proposed. Our approach is mainly based on the large deviations theory and the Meijer's G-function. It is shown that the proposed outage exponent is not only an accurate estimation of the outage probability for any number of subchannels, any SNR, and any target transmission rate, but also provides an easy way to compute the outage capacity, finite-SNR diversity-multiplexing tradeoff, and SNR gain. The asymptotic performance metrics, such as the delay-limited capacity, ergodic capacity, and diversity-multiplexing tradeoff can be directly obtained by letting the number of subchannels or SNR tends to infinity. Similar to Gallager's error exponent, a reliable function for parallel fading channels, which illustrates a fundamental relationship between the transmission reliability and efficiency, can also be defined from the outage exponent. Therefore, the proposed outage exponent provides a complete and comprehensive performance measure for parallel fading channels.