Load balancing by proactively offloading users onto small and otherwise lightly-loaded cells is critical for tapping the potential of dense heterogeneous cellular networks (HCNs). Offloading has mostly been studied for the downlink, where it is gener
ally assumed that a user offloaded to a small cell will communicate with it on the uplink as well. The impact of coupled downlink-uplink offloading is not well understood. Uplink power control and spatial interference correlation further complicate the mathematical analysis as compared to the downlink. We propose an accurate and tractable model to characterize the uplink SINR and rate distribution in a multi-tier HCN as a function of the association rules and power control parameters. Joint uplink-downlink rate coverage is also characterized. Using the developed analysis, it is shown that the optimal degree of channel inversion (for uplink power control) increases with load imbalance in the network. In sharp contrast to the downlink, minimum path loss association is shown to be optimal for uplink rate. Moreover, with minimum path loss association and full channel inversion, uplink SIR is shown to be invariant of infrastructure density. It is further shown that a decoupled association---employing differing association strategies for uplink and downlink---leads to significant improvement in joint uplink-downlink rate coverage over the standard coupled association in HCNs.
