A Useful Form of the Abel Bound and Its Application to Estimator Threshold Prediction

Abstract

International audienceThis correspondence investigates the Abel bound in order to predict the estimators mean square error (mse) threshold effect. A tractable and computationally efficient form of this bound is derived. This form combines the Chapman–Robbins and the Cramér–Rao bounds. This bound is applied to a data-aided carrier frequency estimation problem for which a closed-form expression is provided. An indicator of the signal-to-noise ratio threshold is proposed. A comparison with recent results on the Barankin bound (Chapman–Robbins version) shows the superiority of the Abel-bound version to predict the mse threshold without increasing the computational complexity