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.

翻译：利用RF信号探测物体物质特性对学术界和工业界都非常感兴趣。为此,对一个装置进行了调查,在这种装置中,配备了二维多防天线阵列的发射机发出信号,射中环境中的物体和物体的反射由分布式传感器捕捉。这些传感器接收的信号随后被放大并传送到一个多天线聚变中心,该中心进行时空后处理,以优化信息提取。在这一过程中,与传感器扩增一样,每个物体的动力分配的最佳设计至关重要。这里,电力分配和传感器扩增是联合优化的,条件是在聚变中心进行最大比例的组合(MRC),我们在每个物体的SINR限制、发射机的总能量限制和传感器的个别能量限制下,将这一挑战作为一种总能量最小化。此外,在聚变中心部署零力(ZF)和最小平均误差(MMSE)的好处也得到了讨论。在聚变电中心部署大量传感器的情况下,还进行了感应变分析。