An upper bound on the estimation error in the threshold region

An upper bound on the estimation error in the threshold region (probability of threshold effect and mean-square error) is obtained for nonlinear pulse modulation systems. The problem is viewed in an
N
-dimensional Euclidean space. The space of all received signals is divided into two regions, corresponding to the two types of error: weak-noise approximation and threshold effect. The threshold region is geometrically upper bounded by a larger region, and the estimation error is obtained as a sum of incomplete
\Gamma
functions. The resulting bound on the mean-square error was found to be quite close for the cases calculated. An extension of the method to PPM system is also presented.