TY - JOUR

T1 - How much information can one get from a wireless ad hoc sensor network over a correlated random field?

AU - Sung, Youngchul

AU - Poor, H. Vincent

AU - Yu, Heejung

N1 - Funding Information:
Manuscript received April 22, 2008; revised February 17, 2009. Current version published May 20, 2009. The work of Y. Sung was supported by the IT R&D program of MKE/IITA [2008-F-004-01 “5G mobile communication systems based on beam-division multiple access and relays with group cooperation”.] The work of H. V. Poor was supported in part by the U. S. National Science Foundation under Grants ANI-03-38807 and CNS-06-25637.

PY - 2009

Y1 - 2009

N2 - New large-deviations results that characterize the asymptotic information rates for general d-dimensional (d-D) stationary Gaussian fields are obtained. By applying the general results to sensor nodes on a two-dimensional (2-D) lattice, the asymptotic behavior of ad hoc sensor networks deployed over correlated random fields for statistical inference is investigated. Under a 2-D hidden Gauss-Markov random field model with symmetric first-order conditional autoregression and the assumption of no in-network data fusion, the behavior of the total obtainable information [nats] and energy efficiency [nats/J] defined as the ratio of total gathered information to the required energy is obtained as the coverage area, node density, and energy vary. When the sensor node density is fixed, the energy efficiency decreases to zero with rate Θ (area1/2) and the per-node information under fixed per-node energy also diminishes to zero with rate O(Nt-1/3 as the number Nt of network nodes increases by increasing the coverage area. As the sensor spacing dt increases, the per-node information converges to its limit D with rate D - √̄ dne-αdn for a given diffusion rate α. When the coverage area is fixed and the node density increases, the per-node information is inversely proportional to the node density. As the total energy Et consumed in the network increases, the total information obtainable from the network is given by O (log Et) for the fixed node density and fixed coverage case and by Θ(Et2/) for the fixed per-node sensing energy and fixed density and increasing coverage case.

AB - New large-deviations results that characterize the asymptotic information rates for general d-dimensional (d-D) stationary Gaussian fields are obtained. By applying the general results to sensor nodes on a two-dimensional (2-D) lattice, the asymptotic behavior of ad hoc sensor networks deployed over correlated random fields for statistical inference is investigated. Under a 2-D hidden Gauss-Markov random field model with symmetric first-order conditional autoregression and the assumption of no in-network data fusion, the behavior of the total obtainable information [nats] and energy efficiency [nats/J] defined as the ratio of total gathered information to the required energy is obtained as the coverage area, node density, and energy vary. When the sensor node density is fixed, the energy efficiency decreases to zero with rate Θ (area1/2) and the per-node information under fixed per-node energy also diminishes to zero with rate O(Nt-1/3 as the number Nt of network nodes increases by increasing the coverage area. As the sensor spacing dt increases, the per-node information converges to its limit D with rate D - √̄ dne-αdn for a given diffusion rate α. When the coverage area is fixed and the node density increases, the per-node information is inversely proportional to the node density. As the total energy Et consumed in the network increases, the total information obtainable from the network is given by O (log Et) for the fixed node density and fixed coverage case and by Θ(Et2/) for the fixed per-node sensing energy and fixed density and increasing coverage case.

KW - Ad hoc sensor networks

KW - Asymptotic Kullback-Leibler information rate

KW - Asymptotic mutual information rate

KW - Conditional autoregressive model

KW - Gauss-Markov random fields

KW - Large deviations principle

KW - Stationary Gaussian fields

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U2 - 10.1109/TIT.2009.2018333

DO - 10.1109/TIT.2009.2018333

M3 - Article

AN - SCOPUS:66949160796

SN - 0018-9448

VL - 55

SP - 2827

EP - 2847

JO - IRE Professional Group on Information Theory

JF - IRE Professional Group on Information Theory

IS - 6

ER -