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

Abstract

We consider the distributed estimation of a Gaussian vector with a linear observation model in an inhomogeneous wireless sensor network, in which a fusion center (FC) reconstructs the unknown vector using a linear estimator. Sensors employ uniform multi-bit quantizers and binary PSK modulation, and they 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 the 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 that the performance of the proposed schemes approaches the clairvoyant centralized estimation when the total transmit power or bandwidth is very large. We investigate how the power and rate allocations are dependent on the sensors' observation qualities and channel gains and on the total transmit power and bandwidth constraints. Our simulations corroborate our analytical results and demonstrate the superior performance of the proposed algorithms. Index TermsDistributed estimation, Gaussian vector, upper bounds on MSE, power and rate allocation, ellipsoid method, quantization, linear estimator, linear observation model.

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