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

Abstract

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., <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\approx 3.5</tex> dB) with very small ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\approx \frac{1}{2}</tex> dB) degradation in large signal performance.