  In this paper we study the problem of distributed estimation of a Gaussian
vector with linear observation model in a wireless sensor network (WSN)
consisting of K sensors that transmit their modulated quantized observations
over orthogonal erroneous wireless channels (subject to fading and noise) to a
fusion center, which estimates the unknown vector. Due to limited network
transmit power, only a subset of sensors can be active at each task period.
Here, we formulate the problem of sensor selection and transmit power
allocation that maximizes the trace of Bayesian Fisher Information Matrix (FIM)
under network transmit power constraint, and propose three algorithms to solve
it. Simulation results demonstrate the superiority of these algorithms compared
to the algorithm that uniformly allocates power among all sensors.
