  The electron cyclotron maser instability (ECMI) of extraordinary mode waves
was investigated with the parameters observed in Saturn's kilometric radiation
(SKR) sources. Previous studies employed simplified dispersion relations, and
did not consider the excitation of the relativistic (R) mode. This mode is
introduced by considering the relativistic effect in plasmas consisting of both
cold and hot electrons. Using particle-in-cell simulations, we investigated the
excitation of R and X modes based on the measured data. Using the reported
value of the density ratio of energetic to total electrons $n_e/n_0=24\%$, the
most unstable mode is the R mode. The escaping X-mode emissions are amplified
only if the energetic electrons are dominant with $n_e/n_0 \ge 90\%$. For these
cases, only the X mode is excited and the R mode disappears due to its strong
coupling. The results are well in line with the linear kinetic theory of ECMI.
The properties of both the R and X modes are consistent with the observed SKR
emissions. This raises questions about the nature of the measured electric
field fluctuations within ``presumed'' SKR sources. The study provides new
insights into the ECMI process relevant to SKR emission mechanisms.
