AWGN Channel under Time-Varying Amplitude Constraints with Causal Information at the Transmitter

TL;DR

This paper analyzes the capacity of an AWGN channel with a time-varying amplitude constraint, modeling an energy harvesting transmitter with causal information about energy arrivals, and derives optimal coding strategies.

Contribution

It derives the channel capacity under stochastic amplitude constraints with causal state information and shows that capacity-achieving codes use a finite set of symbols.

Findings

Capacity is characterized for the time-varying amplitude constraint scenario.

Optimal codes are finite-alphabet, similar to Smith's result.

Numerical analysis conducted for binary on-off energy arrivals.

Abstract

We consider the classical AWGN channel where the channel input is constrained to an amplitude constraint that stochastically varies at each channel use, independent of the message. This is an abstraction of an energy harvesting transmitter where the code symbol energy at each channel use is determined by an exogenous energy arrival process and there is no battery for energy storage. At each channel use, an independent realization of the amplitude constraint process is observed by the transmitter causally. This scenario is a state-dependent channel with perfect causal state information at the transmitter. We derive the capacity of this channel using Shannon's coding scheme with causal state information. We prove that the code symbols must be selected from a finite set in the capacity achieving scheme, as in the case of Smith. We numerically study the binary on-off energy arrivals where the amplitude constraint is either zero or a non-zero constant.