Threshold effects in parameter estimation as phase transitions in statistical mechanics

TL;DR

This paper explores how threshold effects in parameter estimation for non-linear waveforms can be understood as phase transitions in statistical mechanics, providing new insights into multi-parameter interactions.

Contribution

It introduces a novel physical perspective by modeling threshold effects as phase transitions, enhancing understanding of parameter interactions in estimation problems.

Findings

Threshold effects resemble phase transitions in disordered systems.

Physical analogy offers new insights into multi-parameter estimation.

Understanding these effects can improve estimation strategies.

Abstract

Threshold effects in the estimation of parameters of non-linearly modulated, continuous-time, wide-band waveforms, are examined from a statistical physics perspective. These threshold effects are shown to be analogous to phase transitions of certain disordered physical systems in thermal equilibrium. The main message, in this work, is in demonstrating that this physical point of view may be insightful for understanding the interactions between two or more parameters to be estimated, from the aspects of the threshold effect.