Robust estimation of spatial fields with compressed observations and imperfect phase estimation in M2M capillary networks

In this paper, we 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, we propose a distributed pre-coding scheme based on the Karhunen-Loève (KL) transform. This allows us to obtain an over-the-air compressed representation of such set of observations. In this context, we 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.