ALGOSENSORS 2015: Algorithms for Sensor Systems pp 13-26

# Connectivity of a Dense Mesh of Randomly Oriented Directional Antennas Under a Realistic Fading Model

• Amitabha Bagchi
• Francesco Betti Sorbelli
• Cristina Maria Pinotti
• Vinay Ribeiro
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9536)

## Abstract

We study mesh networks formed by nodes equipped with directional antennas in a high node-density setting. To do so we create a random geometric graph with n nodes placed uniformly at random. The antenna at each node chooses a direction of orientation at random and edges are placed between pairs of nodes based on their distance from each other and their directions of orientation according to the gain function of the antennas. To model the directionality of the antennas we consider a realistic gain function where the signal fades away from the direction of orientation. We also consider an idealised function that concentrates the gain uniformly in a sector of angle $$2\theta$$ centred around the direction of orientation. In this setting we show theoretically that with probability tending to 1 the optimal power required for achieving connectivity is significantly lower than that needed for connectivity in an omnidirectional setting. We capture mathematically the relationship between this optimal power level and the maximum gain of the antenna, showing that as the directionality of the antenna increases the power needed for connectivity decreases. However this optimal power level is also inversely proportional to the probability of connectivity of two randomly placed nodes, which decreases as directionality increases. We validate these results through simulation.

## Keywords

Random Graph Mesh Network Directional Antenna Fading Model Gain Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer International Publishing Switzerland 2015

## Authors and Affiliations

• Amitabha Bagchi
• 1
• Francesco Betti Sorbelli
• 2
• Cristina Maria Pinotti
• 2
• Vinay Ribeiro
• 1
1. 1.Computer Science and Engineering DepartmentIITDelhiIndia
2. 2.Department of Computer Science and MathematicsUniversity of PerugiaPerugiaItaly