Threshold effects in parameter estimation as phase transitions in statistical physics

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. Our main message is in demonstrating that this physical point of view is insightful for understanding the interactions between two or more parameters to be estimated, from the aspects of the threshold effect.