Neighborhood Relations between Fields with Applications to Cellular Networks

In some spatial applications the objects of interest are fields, caused by spatially distributed sources, and one of the central questions is to find neighborhood relations between these fields. The motivating example for this paper is a cellular network: base transceiver stations transmit signals with continuous distribution, the signal strength, in an urban environment. In order to avoid interference, neighbored transceivers must not use the same frequency, so that neighborhood knowledge is one key to frequency planning. In this paper we define a concept of neighborhood for fields, and we propose a vector-based model to determine neighborhoods between given fields. In contrast to this vector-based model, the commonly used raster-based models suffer in urban areas from their resolution as well as from the prediction of signal propagation.