Asymptotic Behavior of Error Exponents in the Wideband Regime

TL;DR

This paper analyzes the fundamental tradeoff between rate and bandwidth under error exponent constraints in wideband channels, showing QPSK's near-optimality for AWGN and fading channels with full CSI.

Contribution

It extends Verdú's spectral efficiency work by characterizing optimal rate-bandwidth tradeoffs with error exponent constraints and demonstrating QPSK's near-optimality.

Findings

Calculated optimal $R_z(0)$ and $ ext{dot} R_z(0)$ for AWGN channels.

QPSK is near-optimal among a large class of input distributions.

Results also apply to fading channels with full CSI at the receiver.

Abstract

In this paper, we complement Verd\'{u}'s work on spectral efficiency in the wideband regime by investigating the fundamental tradeoff between rate and bandwidth when a constraint is imposed on the error exponent. Specifically, we consider both AWGN and Rayleigh-fading channels. For the AWGN channel model, the optimal values of $R_z(0)$ and $\dot{R_z}(0)$ are calculated, where $R_z(1/B)$ is the maximum rate at which information can be transmitted over a channel with bandwidth $B/2$ when the error-exponent is constrained to be greater than or equal to $z.$ Based on this calculation, we say that a sequence of input distributions is near optimal if both $R_z(0)$ and $\dot{R_z}(0)$ are achieved. We show that QPSK, a widely-used signaling scheme, is near-optimal within a large class of input distributions for the AWGN channel. Similar results are also established for a fading channel where full CSI is available at the receiver.