CRLB via the characteristic function with application to the K-distribution

The Cramer-Rao lower bound (CRLB) is widely used in statistical signal processing as a benchmark to evaluate unbiased estimators. However, for some random variables, the probability density function (pdf) has no closed analytical form. Therefore, it is very hard or impossible to evaluate the CRLB directly. In these cases the characteristic function may still have a closed and even simple form. In this paper, we propose a method to evaluate the CRLB via the characteristic function. As an example, the CRLB of the scale parameter and the shape parameter of the K-distribution is accurately evaluated with the proposed method. Also, it is shown that for pdfs with a scale parameter, the CRLB for the remaining parameters do not depend on the scale parameter. This allows for easier evaluation of the bound.