High SNR linear estimation of vector sources

In this letter, we extend our prior work and consider decentralized estimation of unknown random vectors under high observation signal-to-noise ratio (SNR). A linear model is considered for decentralized estimation of vector sources. Observation models and sensor operations are both linear. Furthermore, the channel between the wireless sensors and fusion center (FC) is a coherent multiple access channel (MAC). Each sensor observes a different vector source. Sensors are designed to minimize the total mean square error (MSE) at the FC subject to the individual transmit power constraints at the sensors. We first provide the solution for scalar sources under high observation SNR regime. Then, we use the provided solution for scalar sources and extend it to the case of vector sources.