  We consider distributed estimation of a Gaussian vector with a linear
observation model in an inhomogeneous wireless sensor network, where a fusion
center (FC) reconstructs the unknown vector, using a linear estimator. Sensors
employ uniform multi-bit quantizers and binary PSK modulation, and communicate
with the FC over orthogonal power- and bandwidth-constrained wireless channels.
We study transmit power and quantization rate (measured in bits per sensor)
allocation schemes that minimize mean-square error (MSE). In particular, we
derive two closed-form upper bounds on the MSE, in terms of the optimization
parameters and propose coupled and decoupled resource allocation schemes that
minimize these bounds. We show that the bounds are good approximations of the
simulated MSE and the performance of the proposed schemes approaches the
clairvoyant centralized estimation when total transmit power or bandwidth is
very large. We study how the power and rate allocation are dependent on sensors
observation qualities and channel gains, as well as total transmit power and
bandwidth constraints. Our simulations corroborate our analytical results and
illustrate the superior performance of the proposed algorithms.
