Optimal Thresholds for Coverage and Rate in FFR Schemes for Planned Cellular Networks

Fractional frequency reuse (FFR) is an inter-cell interference coordination scheme that is being actively researched for emerging wireless cellular networks. In this work, we consider hexagonal tessellation based planned FFR deployments, and derive expressions for the coverage probability and normalized average rate for the downlink. In particular, given reuse $\frac{1}{3}$ (FR$3$ ) and reuse $1$ (FR$1$) regions, and a Signal-to-Interference-plus-noise-Ratio (SINR) threshold $S_{th}$ which decides the user assignment to either the FR$1$ or FR$3$ regions, we theoretically show that: $(i)$ The optimal choice of $S_{th}$ which maximizes the coverage probability is $S_{th} = T$, where $T$ is the required target SINR (for ensuring coverage), and $(ii)$ The optimal choice of $S_{th}$ which maximizes the normalized average rate is given by the expression $S_{th}=\max(T, T')$, where $T'$ is a function of the path loss exponent and the fade parameters. For the optimal choice of $S_{th}$, we show that FFR gives a higher rate than FR$1$ and a better coverage probability than FR$3$. The impact of frequency correlation over the sub-bands allocated to the FR$1$ and FR$3$ regions is analysed, and it is shown that correlation decreases the average rate of the FFR network. Numerical results are provided, and these match with the analytical results.