Estimation of Ricean and Nakagami distribution parameters using noisy samples

The problem of estimating the Ricean and Nakagami-m distribution parameters in noisy slowly fading channels is studied. Previous published works have mainly examined estimation based on a noiseless sample model. The predicted performances of these estimators can only be achieved by having knowledge of the values of the individual noise samples and subtracting them from the noisy signals, an impractical case. In this paper, a system model which uses samples corrupted by noise is examined. The probability density functions of noisy channel samples are derived. Novel maximum likelihood estimators as well as moment-based estimators for operation in noisy environments are developed based on these density functions. The sample means and sample root mean square errors of the estimators are determined. Numerical results show the new estimators have superior performances over estimators designed for noiseless samples in applications where noise is present.