  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.
