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In this paper, the authors focus on the use capillary M2M (Machine-To-Machine) networks for the estimation of spatial random fields. The observations (samples) collected by the sensors are spatially correlated and, for this reason, they propose a distributed pre-coding scheme based on the Karhunen-Loeve (KL) transform. This allows the user to obtain an over-the-air compressed representation of such set of observations. In this paper, they derive a closed-form expression of the optimal power allocation strategy which is robust to residual phase synchronization errors and minimizes the estimation error for a given power constraint.
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