  Cosmic dawn represents critical juncture in cosmic history when the first
population of stars emerged. The astrophysical processes that govern this
transformation need to be better understood. The detection of redshifted 21-cm
radiation emitted from neutral hydrogen during this era offers a direct window
into the thermal and ionization state of the universe. This emission manifests
as differential brightness between spin temperature and the cosmic microwave
background (CMB). SARAS experiment aims to detect the sky-averaged signal in
the frequency range 40-200 MHz. SARAS's unique design and operation strategy to
float the antenna over a water body minimizes spectral features that may arise
due to stratified ground beneath the antenna. However, the antenna environment
can be prone to configuration changes due to variations in critical design
parameters such as conductivity and antenna tilts. In this paper, we connect
the variations in antenna properties to signal detection prospects. By using
realistic simulations of a direction and frequency-dependent radiation pattern
of the SARAS antenna and its transfer function, we establish critical
parameters and estimate bias in the detectability of different models of the
global 21-cm signal. We find a correlation between the nature of chromaticity
in antenna properties and the bias in the recovered spectral profiles of 21-cm
signals. We also find stringent requirements for transfer function corrections,
which can otherwise make detection prospects prohibitive. We finally explore a
range of critical parameters that allow robust signal detection.
