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An upper bound on the estimation error in the threshold region

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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.

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Information Theory, IEEE Transactions on  (Volume:16 ,  Issue: 6 )