Abstract
A wireless sensor network (WSN) is an energy-scarce network in which the energy is primarily dissipated by the nodes during data transmission to the base station (BS). The location of the BS dramatically affects the energy dissipation, the throughput, and the lifetime. While in certain studies the optimal positioning of a BS is considered, the system parameters are optimized when the BS location is known in advance in many others. Herein, we provide a general-purpose mathematical framework to find the expected distance value between every point within any n-sided simple polygon shaped sensing field and an arbitrarily located BS. Knowing this value is imperative particularly in random deployment as it is used for energy-efficient clustering. Although similar derivations appear in the related literature, to the best of our knowledge, this study departs from them, since our derivations do not depend on the shape of the field and the orientation of BS relative to it.
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