  The Square Kilometre Array's Low Frequency instrument (SKA-LOW) will be the
most sensitive aperture array ever used for radio astronomy, and will operate
in the under-sampled regime for most of the frequency band where grating-lobes
pose particular challenges. To achieve the expected level of sensitivity for
SKA-LOW, it is particularly important to understand how interfering sources in
both near and far side-lobes of the station beam affect the imaging
performance. We discuss options for station designs, and adopting a random
element layout, we assess its effectiveness by investigating how sources far
from the main lobe of the station beam degrade images of the target field.
These sources have the effect of introducing a noise-like corruption to images,
which we call the Far Side-lobe Source Noise (FSSN). Using OSKAR, a
GPU-accelerated software simulator, we carried out end-to-end simulations using
an all-sky model and telescope configuration representative of the SKA-LOW
instrument. The FSSN is a function of both the station beam and the
interferometric point spread function, and decreases with increasing
observation time until the coverage of the aperture plane no longer improves.
Using apodisation to reduce the level of near-in side-lobes of the station beam
had a noticeable improvement on the level of FSSN at low frequencies. Our
results indicate that the effects of picking up sources in the side-lobes are
worse at low frequencies, where the array is less sparse.
