Conservative Cell Load Approximation for Radio Networks with Shannon Channels and its Application to LTE Network Planning

The aim of this work is wireless network design and optimization. The well-known Shannon-Hartley formula describes the achievable bitrate of a noisy transmit channel. The downlink air-interface of UTRAN Long Term Evolution (LTE) seems to closely follow such a law, when it is modified with appropriate bandwidth and signal to noise ratio (SNR) efficiency factors. Motivated by this observation, we address the problem to characterize the cell loads in large radio networks when the achieved downlink air interface bitrates follow modified Shannon-Hartley laws. We take advantage of the concavity of an appropriate transform of these laws in order to establish a system of conservative cell load and call acceptance probability equations. This approximation achieves a dimension reduction from the number of mobiles to the number of cells. We suggest to solve the obtained fixed-point equations through a direct iteration and to deduce the network capacity from the solution. This procedure yields network capacity evaluations which are fast enough to support network planning processes. For this purpose we sketch a simple local search algorithm for the selection of base station locations and optimization of cell parameters. In an example we show that the proposed cell load calculation and network capacity optimization is fast enough to support this site selection and cell configuration planning method for LTE networks.