The Distribution of Link Distances in Distributed Multiple-Input Multiple-Output Cellular Systems

The probability density function (pdf) of the distance between randomly located user equipment (UE) and its nth closest base station (BS) is studied in this paper. The knowledge of these pdfs is essential in the analysis of cellular distributed multiple-input multiple-output (MIMO) systems where N BSs cooperate in transmission or reception. We show that earlier results on ordered distance distributions in regular point patterns can be applied to the analysis of distributed MIMO systems when the UE distribution is uniform and the BS locations form a regular lattice. We present previously unpublished pdfs of the distance between a cell edge UE, whose distance to the closest BS is at least r, and four closest BSs in the hexagonal cell topology. The pdfs are verified by simulated histograms. As an example on the application of the results, we show how the signal-to-noise ratio (SNR) gain from uplink cooperative reception increases as the transmitting UE moves further from the cell center. The results from this paper can be applied to the analysis of received and transmitted (in case of power adaptive transmission) power in distributed MIMO systems.