Computational complexity of optimal determination of cell sites and base station locations

We consider how to optimally determine the locations for the placement of base stations for a wireless system in an urban setting, and the computational requirements associated with it. We also propose a scheme to determine the optimal cell geometries and the minimum number of cells required to cover a given area of interest. The optimality of the base station locations is with respect to the total coverage area using the minimum number of base stations. Coverage is defined as the percentage of area from where it is possible to establish a communication link with at least one of the base stations. The objective is to provide wireless coverage in a certain area using the minimum number of base stations. We have divided the total area to be covered into grids, and thus the problem translates to providing coverage to all the grid points using the minimum number of base stations. The spacing of the grid can be reduced at the cost of additional computational load. This is basically a resource allocation problem, and we have solved it using concepts from dynamic programming. The computational complexity of the proposed algorithm is analyzed, and an intelligent scheme is suggested to considerably decrease the total computational load. The increase in the computational requirements with the increase in the number of grid points is also studied. The effect of increasing the transmitter power on the computational load is also analyzed. Finally, some simulation results are presented to corroborate the theory