  We study a contactless target probing based on stimulation by a radio
frequency (RF) signal. The transmit signal is dispatched from a transmitter
equipped with a two-dimensional antenna array. Then, the reflected signal from
the targets are received at multiple distributed sensors. The observation at
the sensors are amplified and forwarded to the fusion center. Afterwards, the
fusion center performs space-time post processing to extract the maximum common
information between the received signal and the targets impulse responses.
Optimal power allocation at the transmitter and amplification at the sensors is
investigated. The sum-power minimization problem turns out to be a non-convex
problem. We propose an efficient algorithm to solve this problem iteratively.
By exploiting maximum-ratio transmission (MRT), maximum-ratio combining (MRC)
of space-time received signal vector is the optimal receiver at sufficiently
low signal-to-interference-plus-noise-ratio (SINR). However, zero-forcing (ZF)
at the fusion center outperforms MRC at higher SINR demands.
