A power-constrained sensor network that consists of multiple sensor nodes and a fusion center (FC) is considered, where the goal is to estimate a random parameter of interest. In contrast to the distributed framework, the sensor nodes may be partially connected, where individual nodes can update their observations by (linearly) combining observations from other adjacent nodes. The updated observations are communicated to the FC by transmitting through a coherent multiple access channel. The optimal collaborative strategy is obtained by minimizing the expected mean-square error subject to power constraints at the sensor nodes. Each sensor can utilize its available power for both collaboration with other nodes and transmission to the FC. Two kinds of constraints, namely the cumulative and individual power constraints, are considered. The effects due to imperfect information about observation and channel gains are also investigated. The resulting performance improvement is illustrated analytically through the example of a homogeneous network with equicorrelated parameters. Assuming random geometric graph topology for collaboration, numerical results demonstrate a significant reduction in distortion even for a moderately connected network, particularly in the low local signal-to-noise ratio regime.Index Terms-Constrained optimization, distributed estimation, linear minimum mean square estimation (LMMSE), wireless sensor networks.

In the context of distributed estimation, we consider the problem of sensor collaboration, which refers to the act of sharing measurements with neighboring sensors prior to transmission to a fusion center. While incorporating the cost of sensor collaboration, we aim to find optimal sparse collaboration schemes subject to a certain information or energy constraint. Two types of sensor collaboration problems are studied: minimum energy with an information constraint; and maximum information with an energy constraint. To solve the resulting sensor collaboration problems, we present tractable optimization formulations and propose efficient methods which render near-optimal solutions in numerical experiments. We also explore the situation in which there is a cost associated with the involvement of each sensor in the estimation scheme. In such situations, the participating sensors must be chosen judiciously. We introduce a unified framework to jointly design the optimal sensor selection and collaboration schemes. For a given estimation performance, we show empirically that there exists a trade-off between sensor selection and sensor collaboration.Comment: IEEE Transactions on Signal Processin

Abstract-In this paper, we aim to design the optimal sensor collaboration strategy for the estimation of time-varying parameters, where collaboration refers to the act of sharing measurements with neighboring sensors prior to transmission to a fusion center. We begin by addressing the sensor collaboration problem for the estimation of uncorrelated parameters. We show that the resulting collaboration problem can be transformed into a special nonconvex optimization problem, where a difference of convex functions carries all the nonconvexity. This specific problem structure enables the use of a convexconcave procedure to obtain a near-optimal solution. When the parameters of interest are temporally correlated, a penalized version of the convex-concave procedure becomes well suited for designing the optimal collaboration scheme. In order to improve computational efficiency, we further propose a fast algorithm that scales gracefully with problem size via the alternating direction method of multipliers. Numerical results are provided to demonstrate the effectiveness of our approach and the impact of parameter correlation and temporal dynamics of sensor networks on estimation performance.

We consider the design of identical one-bit probabilistic quantizers for distributed estimation in sensor networks. We assume the parameter-range to be finite and known and use the maximum Crameŕ–Rao lower bound (CRB) over the parameter-range as our performance metric. We restrict our theoretical analysis to the class of antisymmetric quantizers and determine a set of conditions for which the probabilistic quantizer function is greatly simplified. We identify a broad class of noise distributions, which includes Gaussian noise in the low-SNR regime, for which the often used threshold-quantizer is found to be minimax-optimal. Aided with theoretical results, we formulate an optimization problem to obtain the optimum minimax-CRB quantizer. For a wide range of noise distributions, we demonstrate the superior performance of the new quantizer—particularly in the moderate to high-SNR regime

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