Lower Bounds on Parameter Modulation-Estimation Under Bandwidth Constraints

TL;DR

This paper investigates the fundamental limits of parameter modulation and estimation over bandwidth-constrained AWGN channels, deriving bounds on the exponential decay rate of estimation error moments.

Contribution

It introduces new upper bounds on the MPαE exponent considering bandwidth constraints, extending known bounds for unlimited bandwidth scenarios.

Findings

Derived two upper bounds on the MPαE exponent for bandwidth-limited channels.

Analyzed the asymptotic behavior of bounds at high SNR.

Compared new bounds with existing converse and achievability bounds.

Abstract

We consider the problem of modulating the value of a parameter onto a band-limited signal to be transmitted over a continuous-time, additive white Gaussian noise (AWGN) channel, and estimating this parameter at the receiver. The performance is measured by the mean power-$\alpha$ error (MP$\alpha$E), which is defined as the worst-case $\alpha$-th order moment of the absolute estimation error. The optimal exponential decay rate of the MP$\alpha$E as a function of the transmission time, is investigated. Two upper (converse) bounds on the MP$\alpha$E exponent are derived, on the basis of known bounds for the AWGN channel of inputs with unlimited bandwidth. The bounds are computed for typical values of the error moment and the signal-to-noise ratio (SNR), and the SNR asymptotics of the different bounds are analyzed. The new bounds are compared to known converse and achievability bounds, which were derived from channel coding considerations.