Downlink SINR distribution in a heterogeneous cellular wireless network with max-SINR connectivity

Recent results [1], [2] on the distribution of the downlink SINR in heterogeneous wireless networks assume that the serving base station (BS) for a given user (UE) location is either (a) the BS that is geographically nearest to the UE location [1], or (b) the one that has the highest received power at the UE location [2]. For (a), the distribution of the downlink SINR at an arbitrary UE location can be derived exactly. For (b), the best result for the cumulative distribution function (CDF) of the downlink SINR [2] is exact only for arguments that exceed unity. In this paper, we extend the results in [2] to derive an exact expression for the CDF of the downlink SINR at an arbitrary UE location in a multi-tier heterogeneous network when the serving BS is chosen according to (b). We then explore some interesting implications of the result for coverage probabilities.