Optimal Location of Cellular Base Stations via Convex Optimization: An Analytical Framework and Numerical Algorithms

A novel analytical approach to optimal base station (BS) location problem is proposed. It is based on the widely used system and propagation path models but, unlike known studies, makes use a convex optimization formulation to minimize the total transmit power subject to quality-of-service (QoS, rate) constraints. In contrast to the previously-proposed approaches, the sufficient Karush-Kuhn-Tucker (KKT) conditions are used here to characterize a globally (rather than locally)-optimum point as a convex combination of user locations, where convex weights depend on user parameters, path loss exponent and overall geometry of the problem. Based on this characterization, a number of novel closed-form solutions are obtained. In particular, the optimum BS location is shown to be the average of user locations in the case of unobstructed line-of-sight (LOS) propagation (the path loss exponent equals 2) and identical user parameters but not in general. If the user set is symmetric, the optimal BS location is independent of the pathloss exponent, which is not the case in general. The analytical results show the impact of propagation conditions (e.g. clear/obstructed LOS) as well as system and user parameters (bandwidth, rate demand, etc.) on optimal BS location: the higher the path loss exponent, the heavier the impact of distant users; users with higher rate demands have more impact. The obtained analytical results facilitate insights, which are unavailable from purely numerical studies and which can be used to develop design guidelines. Based on these results, an iterative algorithm is proposed and its convergence is proved. The single BS results are further extended to multi-BS scenarios (e.g. a cell cluster) using the K-means algorithm with proper modifications, so that the total (sum) BS power in a cell cluster is locally minimized, subject to user rate constrains. Numerical experiments validate the analytical solutions and show the effectiveness of the proposed algorithms. Overall, the emphasis is on an analytical framework, solutions and insights rather than on numerical algorithms.