0701196v3 - arXiv:cs/0701196v3 [cs.IT] 26 Jul 2007 Onebit...

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Unformatted text preview: arXiv:cs/0701196v3 [cs.IT] 26 Jul 2007 Onebit Distributed Sensing and Coding for Field Estimation in Sensor Networks Ye Wang, Prakash Ishwar, and Venkatesh Saligrama Abstract This paper formulates and studies a general distributed field reconstruction problem using a dense network of noisy onebit randomized scalar quantizers in the presence of additive observation noise of unknown distribution. A constructive quantization, coding, and field reconstruction scheme is developed and an upperbound to the associated mean squared error (MSE) at any point and any snapshot is derived in terms of the local spatiotemporal smoothness properties of the underlying field. It is shown that when the noise, sensor placement pattern, and the sensor schedule satisfy certain weak technical requirements, it is possible to drive the MSE to zero with increasing sensor density at points of field continuity while ensuring that the persensor bitrate and sensingrelated network overhead rate simultaneously go to zero. The proposed scheme achieves the orderoptimal MSE versus sensor density scaling behavior for the class of spatially constant spatiotemporal fields. I. INTRODUCTION AND OVERVIEW We study the problem of reconstructing, at a data fusion center, a temporal sequence of spatial data fields, in a bounded geographical region of interest, from finite bitrate messages generated by a dense noncooperative network of sensors. The datagathering sensor network is made up of noisy lowresolution sensors at known locations that are statistically identical (exchangeable) with respect to the sensing operation. The exchangeability assumption reflects the property of an unsorted collection of inexpensive massproduced sensors that behave in a statistically identical fashion. We view each data field as an unknown deterministic function over the geographical space of interest and make only the weak assumption that they have a known bounded maximum dynamic range. The sensor observations are corrupted by bounded, zeromean, additive noise which is independent across sensors with arbitrary Y. Wang, P. Ishwar, and V. Saligrama are with the Department of Electrical and Computer Engineering, Boston University, Boston, MA 02215. Email: { yw,pi,srv } @bu.edu . 1 dependencies across field snapshots. This noise has an arbitrary, unknown distribution but a known maximum dynamic range. The sensors are equipped with binary analogtodigital converters (ADCs) in the form of comparators with random thresholds which are uniformly distributed over the (known) sensor dynamic range. These thresholds are assumed to be independent across sensors with arbitrary dependencies across snapshots. These modeling assumptions partially account for certain realworld scenarios that include (i) the unavailability of good initial statistical models for data fields in yet to be well studied natural phenomena, (ii) unknown additive sensing/observation noise sources, (iii) additive...
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This note was uploaded on 11/03/2009 for the course COMPUTERS CS537 taught by Professor Salman during the Spring '09 term at Texas A&M University–Commerce.

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0701196v3 - arXiv:cs/0701196v3 [cs.IT] 26 Jul 2007 Onebit...

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