# MoN15: Fifteenth Mathematics of Networks meeting

## Amy Middleton (Bath) – Comparison of methods for estimating distance of nearest transmitter in a cellular radio network

Ideally in a cellular radio network radio transmitters are placed in locations chosen to optimise network coverage and minimise interference between transmitters. However, with some new technologies it will not be possible to pre-plan or perhaps know the locations of transmitters. We consider a model where the locations of radio transmitters are not pre-planned and instead are chosen independently. In this case the ability of a transmitter to determine the distance to its nearest neighbour is important for choosing an optimal transmit power that maximises coverage and minimises interference. The ability of transmitters to discover the distance to their nearest neighbour and respond appropriately gives the network of transmitters the property of being self-organising.

In our model the locations of the radio transmitters are random and distributed according to a Poisson process. We assume that the signal strength at distance from a transmitter follows a path-loss law where is a fixed variable. It is then possible to estimate the distance to the nearest neighbour based on the total signal received at a given point. Methods for finding this estimation include a simple estimate and two improvements on this method which I will detail. We will compare the accuracy of these methods as well as discuss future planned work.

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Contact:
Keith Briggs
()
or
Richard G. Clegg (richard@richardclegg.org)