On Distributed Vector Estimation for Power and Bandwidth Constrained Wireless Sensor Networks

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.