  In order to investigate the impact of collective neutrino oscillations (CNO)
on the neutrino signal from a nearby supernova, we perform 3-flavor neutrino
oscillation simulations employing the multiangle effect. The background
hydrodynamic model is based on the neutrino hydrodynamic simulation of a 8.8
\Msun progenitor star. We find that CNO commences after some 100 ms post
bounce. Before this, CNO is suppressed by matter-induced decoherence. In the
inverted mass hierarchy, the spectrum of $\bar{\nu}_e$ becomes softer after the
onset of CNO. To evaluate the detectability of this modification, we define a
hardness ratio between the number of high energy neutrino events and low energy
neutrino events adopting a fixed critical energy. We show that Hyper-Kamiokande
(HK) can distinguish the effect of CNO for supernova distances out to $\sim 10$
kpc. On the other hand, for the normal mass hierarchy, the spectrum of $\nu_e$
becomes softer after the onset of CNO, and we show that DUNE can distinguish
this feature for supernova distances out to $\sim 10$ kpc. More work is
necessary to optimize the best value of critical energy for maximum
sensitivity. We also show that if the spectrum of $\bar{\nu}_e$ in HK becomes
softer due to CNO, the spectrum of $\nu_e$ in DUNE becomes harder, and vice
versa. This synergistic observations in $\bar{\nu}_e$ and $\nu_e$, by HK and
DUNE respectively, will be an intriguing opportunity to test the occurrence of
CNO.
