Simulated Predictions for HI at $z = 3.35$ with the Ooty Wide Field Array (OWFA) -- II: Foreground Avoidance

Considering the upcoming OWFA, we use simulations of the foregrounds and the $z = 3.35$ HI 21-cm intensity mapping signal to identify the $(k_{\perp},k_{\parallel})$ modes where the expected 21-cm power spectrum $P(k_{\perp},k_{\parallel})$ is substantially larger than the predicted foreground contribution. Only these uncontaminated $k$-modes are used for measuring $P(k_{\perp},k_{\parallel})$ in the "Foreground Avoidance" technique. Though the foregrounds are largely localised within a wedge. we find that the small leakage beyond the wedge surpasses the 21-cm signal across a significant part of the $(k_{\perp},k_{\parallel})$ plane. The extent of foreground leakage is extremely sensitive to the frequency window function used to estimate $P(k_{\perp},k_{\parallel})$. It is possible to reduce the leakage by making the window function narrower, however this comes at the expense of losing a larger fraction of the 21-cm signal. It is necessary to balance these competing effects to identify an optimal window function. Considering a broad class of cosine window functions, we identify a six term window function as optimal for 21-cm power spectrum estimation with OWFA. Considering only the $k$-modes where the expected 21-cm power spectrum exceeds the predicted foregrounds by a factor of $100$ or larger, a $5\,\sigma$ detection of the binned power spectrum is possible in the $k$ ranges $0.18 \leq k \leq 0.3 \, {\rm Mpc}^{-1}$ and $0.18 \le k \le 0.8 \, {\rm Mpc}^{-1}$ with $1,000-2,000$ hours and $10^4$ hours of observation respectively.