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We study the impact of physical layer (PHY) transmit rate control on energy efficient estimation in wireless sensor networks. A sensor network collects measurements and transmits them to a Fusion Center (FC) with controllable PHY transmission rates. The FC performs estimation of an unknown parameter process based on sensor measurements, and it needs to adhere to an estimation error constraint. The objective is to maximize network lifetime. High transmission rates consume more energy per transmitted bit, however they convey larger amount of data per unit time and thus can aid in satisfying the estimation error constraint. We identify basic structural properties of the optimal solution, and we propose an iterative algorithm for reaching a solution based on light-weight feedback from the FC.