Load balancing through proactive offloading users onto small cells is critical for tapping the potential of dense heterogeneous cellular networks (HCNs). However, the impact of such offloading on the uplink performance is not well understood, primarily due to the lack of tractable models. Uplink power control and spatial interference correlation further complicate the mathematical analysis as compared to the downlink. In this paper, we propose a tractable and general model to characterize the uplink SIR and rate distribution in a K-tier HCN as a function of the association and power control parameters. 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. Minimum path loss association is shown to maximize uplink rate coverage. Moreover, with minimum path loss association and full channel inversion, uplink coverage is shown to be invariant of infrastructure density.
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