Asymptotically Efficient Moment-Based Estimator of the $\kappa $ Parameter for the $\kappa -\mu $ Distribution

The κ- μ distribution is a general fading model applied to predict multipath faded envelope in wireless channels, under a line-of-sight propagation condition. However, its algebraic moment-based estimator of the parameter κ available in the literature depends on higher-order statistical moments, which impose a high penalty over the estimator efficiency. In this letter, we have proposed a new moment-based estimator of the parameter κ, which depends on a simple average of the normalized envelope and takes advantage of lower estimation errors. We have proved that the proposed estimator is asymptotically efficient, from a practical point of view, since its normalized asymptotic variance closely attained the Cramer-Rao lower bound for the useful range of κ. In addition, big sample size Monte Carlo simulations have revealed that the algebraic estimator is positively biased with a highly broad sample confidence region, in contrast to the almost unbiased proposed estimator with a much narrower sample confidence region. Furthermore, the proposed estimator yielded a much lower sample variance for the wide range of sample number when compared to the algebraic one.