Power allocation schemes for spatial field estimation with compressed observations 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 to use 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 closed-form expression of the optimal power allocation strategies for two problems of interest: the minimization of the estimation error (distortion) for a given power constraint, and the minimization of the transmit power for a given distortion target. We assess the performance of the proposed pre-coding scheme by means of computer simulations. Other uncompressed transmission schemes are used as benchmark.