We study blind estimation of transmission power of a node based on received power measurements obtained under wireless fading. Specifically, the setup consists of a set of monitors that measure the signal power received from the transmitter, and the goal is to utilize these measurements to estimate the transmission power in the absence of any prior knowledge of the transmitter's location or any statistical distribution of its power. Towards this end, we exploit spatial diversity in received-power measurements and cooperation among the multiple monitoring nodes; based on theoretical analysis we obtain the Maximum Likelihood (ML) estimate, derive fundamental geometrical insights and show that this estimate is asymptotically optimal. Finally, we provide numerical results comparing the performance of the estimators through simulations and on a data-set of field measurements. Categories and Subject Descriptors C.2.1 [Computer-Communication Networks]: Wireless communication--power esti...