  The utilization of RF signals to probe material properties of objects is of
huge interest both in academia as well as industry. To this end, a setup is
investigated, in which a transmitter equipped with a two-dimensional
multi-antenna array dispatches a signal, which hits objects in the environment
and the reflections from the objects are captured by distributed sensors. The
received signal at those sensors are then amplified and forwarded to a multiple
antenna fusion center, which performs space-time post-processing in order to
optimize the information extraction. In this process, optimal design of power
allocation per object alongside sensors amplifications is of crucial
importance. Here, the power allocation and sensors amplifications is jointly
optimized, given maximum-ratio combining (MRC) at the fusion center. We
formulate this challenge as a sum-power minimization under per-object SINR
constraints, a sum-power constraint at the transmitter and individual power
constraints at the sensors. Moreover, the advantage of deploying zero-forcing
(ZF) and minimum mean-squared error (MMSE) at the fusion center is discussed.
Asymptotic analysis is also provided for the case that large number of sensors
are deployed in the sensing environment.
