The effect of baseline layouts on the EoR foreground wedge: a semi-analytical approach

The 2D power spectrum is a cornerstone of the modern toolkit for analysis of the low-frequency radio interferometric observations of the 21 cm signal arising from the early Universe. Its familiar form disentangles a great deal of systematic information concerning both the sky and telescope, and displays as a foreground-dominated brick' and wedge’ on large line-of-sight scales, and a complementary `window’ on smaller scales. This paper builds on many previous works in the literature which seek to elucidate the varied instrumental and foreground factors which contribute to these familiar structures in the 2D power spectrum. In particular, we consider the effects of $uv$-sampling on the emergence of the wedge. Our results verify the expectation that arbitrarily dense instrument layouts in principal restore the missing information that leads to mode-mixing, and can therefore mitigate the wedge feature. We derive rule-of-thumb estimates for the required baseline density for complete wedge mitigation, showing that these will be unachievable in practice. We also discuss the optimal shape of the layout, showing that logarithmic regularity in the radial separation of baselines is favourable. While complete suppression of foreground leakage into the wedge is practically unachievable, we find that designing layouts which promote radial density and regularity is able to reduce the amplitude of foreground power by 1-3 orders of magnitude.