| Summary: | Abstract The cell range expansion (CRE) is encouraged to be applied in the heterogeneous cellular networks (HCNs), to enhance the capacity by offloading macro users to small cells. However, the enhanced inter-cell interference coordination (eICIC) techniques are supposed to be used for mitigating the strong cross-tier interference suffered by the offloaded users and small cell edge users. To address this, a novel soft frequency reuse (SFR) scheme is adopted in this paper. We analyze multichannel downlink scenarios for the SFR scheme using the tools of stochastic geometry. In consideration of the random resource allocation and practical cell load model, the analytical results of coverage probability and average user rate are derived and validated through Monte Carlo methods. Furthermore, our results can reduce to simple closed-form under reasonable special case for modern urban cellular networks. The main evaluation of the performance in terms of average user rate is presented, and the optimal combination of association bias and parameters of the SFR scheme is also investigated. Numerical results show that the SFR scheme outperforms the frequency resource partitioning (FRP) scheme in any load condition. Moreover, the CRE with SFR scheme can improve the average user rate significantly.
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