Determination of Cramer-Rao Lower Bound (CRLB) and Minimum Variance Unbiased Estimator of a DC Signal in AWGN Using Laplace Transform

Abstract

This paper presents an alternative approach for the determination of Cramer-Rao Lower Bound (CRLB) and Minimum Variance Unbiased Estimator (MVUE) using Laplace transformation. In this work, a DC signal in Additive White Gaussian Noise (AWGN) was considered. During the investigation, a number of experiments were conducted to analyze different possible outputs under different conditions, and then the patterns of the outcomes were studied. Finally closed-form expressions for the CRLB and MVUE were deduced employing the Laplace transformation. The resulting expressions showed that the proposed method has almost the same number of steps as the existing method. However, the latter requires only the knowledge of algebra to arrive at the CRLB expressions contrary to the existing approach where a strong mathematical background is required and hence making it superior over the existing method, in that sense.

Keywords: Additive White Gaussian Noise, Cramer-Rao Lower Bound, DC-Value, Laplace transform, and Minimum Variance Unbiased Estimator (MVUE).