Abstract
We address a fundamental problem in wireless sensor networks, how many hops does it take a packet to be relayed for a given distance? For a deterministic topology, this hop-distance estimation reduces to a simple geometry problem. However, a statistical study is needed for randomly deployed WSNs. We propose a maximum-likelihood decision based on the conditional pdf of . Due to the computational complexity of , we also propose an attenuated Gaussian approximation for the conditional pdf. We show that the approximation visibly simplifies the decision process and the error analysis. The latency and energy consumption estimation are also included as application examples. Simulations show that our approximation model can predict the latency and energy consumption with less than half RMSE, compared to the linear models.
Highlights
The recent advances in MEMS, embedded systems, and wireless communications enable the realization and deployment of wireless sensor networks (WSN), which consist of a large number of densely deployed and self-organized sensor nodes [1]
We proposed a Bayesian decision based on the conditional pdf of f (r | Hi)
Since f (r | Hi) is computationally complex, we proposed an attenuated Gaussian approximation for the conditional pdf, which visibly simplifies the decision process and the error analysis
Summary
The recent advances in MEMS, embedded systems, and wireless communications enable the realization and deployment of wireless sensor networks (WSN), which consist of a large number of densely deployed and self-organized sensor nodes [1]. The constant value γ is a good lower bound, but might not be enough to describe the nonlinear relation between Euclidean distance and network distance Their relation is often treated as linear for convenience, for example, [r/R] + 1 is widely used to estimate the needed number of hops to reach distance r given transmission range R. Against this simple intuition, the relation between Euclidean distance and network distance is far more complex. Vural and Ekici reexamined the study under the sensor networks circumstances in [12], and gave the mean and variance of multihop distance for 1D Poisson point distribution They proposed to approximate the multihop distance using Gaussian distribution.
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