  In this paper, we calculate the frequencies of geodesic orbits in self-dual
spacetime on the equatorial plane and obtain the leading-order effects of loop
quantum parameters $P$ on the energy flux and angular momentum flux in
eccentric extreme mass ratio inspirals. The gravitational waveform under
different eccentricity is carried out by improved "analytic-kludge" method.
Through the calculation of waveform mismatches for the LISA detector, the
constraints on loop quantum parameters will be improved by 1 to 2 orders of
magnitude, compared to the weak field experiments in the solar system, and can
reach the level of $10^{-8}$.
