# Analytical Approach for Channel Assignments in Cellular Networks

## Abstract

In the present paper channel assignments in cellular architectures are considered. This is quite important in cell and channel planning since reusing channels in cells allows to manage resources and to serve users effectively in the system. The optimal solution is offered here for the case of co-channel interference. Previous solutions on co-channel interference are based on regular hexagonal models for service areas. A novel technique is employed in this work that does not depend upon any geometric form of cells. It is obtained that the optimal number of channels equals the density of a special graph. Earlier analytical results on span minimization show lower bounds meanwhile we provide the upper bound in this paper.

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