Asymptotic Capacity Analysis for Adaptive Transmission Schemes under General Fading Distributions

TL;DR

This paper analyzes the asymptotic behavior of ergodic capacity for various adaptive transmission schemes over general fading channels at high and low SNRs, deriving capacity gaps and effects of diversity.

Contribution

It provides closed-form expressions for capacity differences among schemes and shows how diversity enhances capacity at high SNRs.

Findings

Capacity gaps are proportional to SNR loss in dB.

Channel inversion approaches optimal capacity with enough diversity.

Fading improves capacity at low SNR compared to AWGN.

Abstract

Asymptotic comparisons of ergodic channel capacity at high and low signal-to-noise ratios (SNRs) are provided for several adaptive transmission schemes over fading channels with general distributions, including optimal power and rate adaptation, rate adaptation only, channel inversion and its variants. Analysis of the high-SNR pre-log constants of the ergodic capacity reveals the existence of constant capacity difference gaps among the schemes with a pre-log constant of ?1. Closed-form expressions for these high-SNR capacity difference gaps are derived, which are proportional to the SNR loss between these schemes in dB scale. The largest one of these gaps is found to be between the optimal power and rate adaptation scheme and the channel inversion scheme. Based on these expressions it is shown that the presence of space diversity or multi-user diversity makes channel inversion arbitrarily close to achieving optimal capacity at high SNR with sufficiently large number of antennas or users. A low-SNR analysis also reveals that the presence of fading provably always improves capacity at sufficiently low SNR, compared to the additive white Gaussian noise (AWGN) case. Numerical results are shown to corroborate our analytical results.