CRLB for the localization error in the presence of fading

Localization accuracy is crucial in sensor networks. A wireless sensor network (WSN) with M anchors and one node is considered in this paper. The estimation is based on time of arrival (TOA) in the presence of fading channels. The Cramer-Rao lower bound (CRLB) for localization error in the presence of fading is derived under different scenarios. Firstly, fading coefficients are considered as unknown random parameters with a prior distribution. The ML estimator for this case is also derived. If the distribution of fading is unknown to the estimator then the modified CRLB (MCRLB) is applied and shown to be equal to the CRLB in the absence of fading. This is used to conclude that fading always deteriorates the CRLB in localization. It is shown that there is a loss of about 5dB in CRLB due to Rayleigh fading.