  In this paper we consider the problem of transmission power allocation for
remote estimation of a dynamical system in the case where the estimator is able
to simultaneously receive packets from multiple interfering sensors, as it is
possible e.g. with the latest wireless technologies such as 5G and WiFi. To
this end we introduce a general model where packet arrival probabilities are
determined based on the received Signal-to-Interference-and-Noise Ratio and
with two different receivers design schemes, one implementing standard
multi-packet reception technique and one implementing Successive Interference
Cancellation decoding algorithm in addition. Then we cast the power allocation
problem as an optimization task where the mean error covariance at the remote
estimator is minimized, while penalizing the mean transmission power
consumption. For the infinite-horizon problem we show the existence of a
stationary optimal policy, while for the finite-horizon case we derive some
structural properties under the special scenario where the overall system to be
estimated can be seen as a set of independent subsystems. Numerical simulations
illustrate the improvement given by the proposed receivers over orthogonal
schemes that schedules only one sensor transmission at a time in order to avoid
interference.
