  We test the bandpass smoothness performance of two prototype Square Kilometre
Array (SKA) SKA1-Low log-periodic dipole antennas, the SKALA2 and SKALA3 (`SKA
Log-periodic Antenna'), and the current dipole from the Murchison Widefield
Array (MWA) precursor telescope. Throughout this paper, we refer to the output
complex-valued voltage response of an antenna when connected to a low noise
amplifier (LNA), as the dipole bandpass. In Paper I (de Lera Acedo et al.
2017), the bandpass spectral response of the log-periodic antenna being
developed for the SKA1-Low was estimated using numerical electromagnetic
simulations and analyzed using low-order polynomial fittings and it was
compared with the HERA antenna against the delay spectrum metric. In this work,
realistic simulations of the SKA1-Low instrument, including frequency-dependent
primary beams and array configuration, are used with a weighted least-squares
polynomial estimator to assess the ability of prototype antennas to perform the
SKA Epoch of Reionisation (EoR) statistical experiments. This work complements
the ideal estimator tolerances computed for the proposed EoR science
experiments in Trott & Wayth (2016), with the realised performance of an
optimal and standard estimation (calibration) procedure. With a sufficient sky
calibration model at higher frequencies, all antennas have bandpasses that are
sufficiently smooth to meet the tolerances described in Trott & Wayth (2016) to
perform the EoR statistical experiments, and these are primarily limited by an
adequate sky calibration model, and the thermal noise level in the calibration
data. At frequencies of the Cosmic Dawn (CD), which is of principal interest to
SKA as one of the first next-generation telescopes capable of accessing higher
redshifts, the MWA dipole and SKALA3 antenna have adequate performance, while
the SKALA2 design will impede the ability to explore this era.
