On the End-to-End Distortion for a Buffered Transmission over Fading Channel

TL;DR

This paper analyzes the tradeoff between end-to-end distortion and delay for transmitting an analog source over fading channels, showing how buffer delay impacts power efficiency and deriving formulas for different channel configurations.

Contribution

It introduces a closed-form formula for the distortion-delay tradeoff using effective capacity and provides bounds and exponents for SISO and MIMO channels.

Findings

Buffer delay significantly reduces transmission power.

Derived a tight upper bound for distortion-delay in SISO channels.

Computed the distortion SNR exponent for MIMO channels.

Abstract

In this paper, we study the end-to-end distortion/delay tradeoff for a analogue source transmitted over a fading channel. The analogue source is quantized and stored in a buffer until it is transmitted. There are two extreme cases as far as buffer delay is concerned: no delay and infinite delay. We observe that there is a significant power gain by introducing a buffer delay. Our goal is to investigate the situation between these two extremes. Using recently proposed \emph{effective capacity} concept, we derive a closed-form formula for this tradeoff. For SISO case, an asymptotically tight upper bound for our distortion-delay curve is derived, which approaches to the infinite delay lower bound as $\mathcal{D}_\infty \exp(\frac{C}{\tau_n})$, with $\tau_n$ is the normalized delay, $C$ is a constant. For more general MIMO channel, we computed the distortion SNR exponent -- the exponential decay rate of the expected distortion in the high SNR regime. Numerical results demonstrate that introduction of a small amount delay can save significant transmission power.