Asymptotic Optimality of Equal Power Allocation for Linear Estimation of WSS Random Processes

TL;DR

This paper proves that for estimating a wide-sense stationary process with linear methods, equally distributing power across measurements is asymptotically optimal under certain conditions, including Nyquist sampling and noise variance proportional to power.

Contribution

It demonstrates the asymptotic optimality of equal power allocation in linear estimation of WSS processes, a result previously unestablished.

Findings

Equal power allocation is asymptotically optimal for WSS process estimation.

The result holds under Nyquist sampling and noise variance proportional to power.

Provides theoretical foundation for power distribution in signal estimation.

Abstract

This letter establishes the asymptotic optimality of equal power allocation for measurements of a continuous wide-sense stationary (WSS) random process with a square-integrable autocorrelation function when linear estimation is used on equally-spaced measurements with periodicity meeting the Nyquist criterion and with the variance of the noise on any sample inversely proportional to the power expended by the user to obtain that measurement.