Linear Coherent Estimation With Spatial Collaboration

• Published in: IEEE transactions on information theory Vol. 59; no. 6; pp. 3532 - 3553
• Main Authors: Kar, S., Varshney, P. K.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Collaboration; Constrained optimization; Correlation analysis; Data transmission; Detection, estimation, filtering, equalization, prediction; distributed estimation; Estimation; Exact sciences and technology; Graph theory; Information theory; Information, signal and communications theory; linear minimum mean square estimation (LMMSE); Mean square errors; Network topology; Noise measurement; Parameter estimation; Sensors; Services and terminals of telecommunications; Signal and communications theory; Signal to noise ratio; Signal, noise; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Telemetry. Remote supervision. Telewarning. Remote control; Topology; Transmission and modulation (techniques and equipments); wireless sensor networks; Performance evaluation; wireless sensor networks; Wireless telecommunication; Updating; Remote sensing; Mean square error; Distributed processing; Optimal strategy; Linear estimation; Signal detection; Multiple access; distributed estimation; Multisensor; Measurement sensor; Distributed system; Random graph; Constrained optimization; Electrical network; Wireless network; Numerical simulation; Sensor array; linear minimum mean square estimation (LMMSE); Multiple channel; Least mean squares methods; Signal to noise ratio
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2013.2248876

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.