On the scaling laws of dense wireless sensor networks: the data gathering channel

• Published in: IEEE transactions on information theory Vol. 51; no. 3; pp. 1229 - 1234
• Main Author: El Gamal, H.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Ad hoc networks; Applied sciences; Capacitive sensors; Channels; Coding; Communication channels; Data collection; Distributed source-channel coding; Exact sciences and technology; H infinity control; Information theory; Network topology; Networks; Peer to peer computing; Random sequences; relay channel; Remote sensors; sensor networks; Sensor phenomena and characterization; Sensors; Systems, networks and services of telecommunications; Telecommunication traffic; Telecommunications; Telecommunications and information theory; the many-to-one channel; the separation principle; Traffic control; Transmission and modulation (techniques and equipments); Transport; Wireless networks; Wireless sensor networks; Wireless LAN; Channel capacity; Joint source-channel coding; Transmission channel; Distributed source-channel coding; sensor networks; Separation principle; the many-to-one channel; Random field; Scaling law; Random sequence; relay channel; the separation principle; Coding; Sensor array
• DOI: 10.1109/TIT.2004.842563
• ISSN: 0018-9448

We consider dense wireless sensor networks deployed to observe arbitrary random fields. The requirement is to reconstruct an estimate of the random field at a certain collector node. This creates a many-to-one data gathering wireless channel. In this note, we first characterize the transport capacity of many-to-one dense wireless networks subject to a constraint on the total average power. In particular, we show that the transport capacity scales as Theta(log(N)) when the number of sensors N grows to infinity and the total average power remains fixed. We then use this result along with some information-theoretic tools to derive sufficient and necessary conditions that characterize the set of observable random fields by dense sensor networks. In particular, for random fields that can be modeled as discrete random sequences, we derive a certain form of source/channel coding separation theorem. We further show that one can achieve any desired nonzero mean-square estimation error for continuous, Gaussian, and spatially bandlimited fields through a scheme composed of single-dimensional quantization, distributed Slepian-Wolf source coding, and the proposed antenna sharing strategy. Based on our results, we revisit earlier conclusions about the feasibility of data gathering applications using dense sensor networks.