On the impact of duty cycle on the estimation of spatial fields 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 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. We assume that sensors operate with (independent) duty-cycles and we derive a closed-form expression of the optimal power allocation strategy which minimizes the estimation error for a given power constraint. For benchmarking purposes, we also assess the performance of another scheme based on a particularization of the partial KL transform.