  In this work, we analytically study the impact of spectrum allocation scheme
in picocells on the coverage probability (CP) of the Pico User (PU), when the
macro base stations (MBSs) employ either fractional frequency reuse (FFR) or
soft frequency reuse (SFR). Assuming a fixed size for the picocell, the CP
expression is derived for a PU present in either a FFR or SFR based deployment,
and when the PU uses either the centre or the edge frequency resources. Based
on these expressions, we propose two possible frequency allocation schemes for
the picocell when FFR is employed by the macrocell. The CP and the average rate
expressions for both these schemes are derived, and it is shown that these
schemes outperform the conventional scheme where no inter-cell interference
coordination (ICIC) is assumed. The impact of both schemes on the macro-user
performance is also analysed. When SFR is used by the MBS, it is shown that the
CP is maximized when the PU uses the same frequency resources as used by the
centre region.
