A useful form of the Barankin lower bound and its application to PPM threshold analysis

A form of Barankin's greatest lower bound on estimation error [7] is obtained, which is easy to compute and easy to interpret. This gives a lower bound on estimation error for non-linear modulation systems in an additive Gaussian noise back-ground. Threshold effects are included. This bound is applied to a set of pulse-position modulation waveforms designed to reduce threshold effects. It is shown that these signals do, in fact, offer reduced threshold levels (e.g.,
\approx 3.5
dB) with very small (
\approx \frac{1}{2}
dB) degradation in large signal performance.