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In this paper, the estimation of a scalar field over a bidimensional scenario (e.g., the atmospheric pressure in a wide area) through a self-organizing wireless sensor network (WSN) with energy constraints is investigated. The sensor devices (denoted as nodes) are randomly distributed; they transmit samples to a supervisor by using a clustered network. This paper provides a mathematical framework to analyze the interdependent aspects of WSN communication protocol and signal processing design. Channel modelling and connectivity issues, multiple access control and routing, and the role of distributed digital signal processing (DDSP) techniques are accounted for. The possibility that nodes perform DDSP is studied through a distributed compression technique based on signal resampling. The DDSP impact on network energy efficiency is compared through a novel mathematical approach to the case where the processing is performed entirely by the supervisor. The trade-off between energy conservation (i.e., network lifetime) and estimation error is discussed and a design criterion is proposed as well. Comparison to simulation outcomes validates the model. As an example result, the required node density is found as a trade-off between estimation quality and network lifetime for different system parameters and scalar field characteristics. It is shown that both the DDSP technique and the MAC protocol choice have a relevant impact on the performance of a WSN.
Wireless sensor networks, modeling techniques, algorithm/protocol design and analysis, environmental monitoring, energy efficiency.

D. Dardari, R. Verdone, C. Buratti and A. Conti, "Mathematical Evaluation of Environmental Monitoring Estimation Error through Energy-Efficient Wireless Sensor Networks," in IEEE Transactions on Mobile Computing, vol. 6, no. , pp. 790-802, 2007.
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