A 21-cm power spectrum at 48 MHz, using the Owens Valley Long Wavelength Array

The Large-aperture Experiment to detect the Dark Age (LEDA) was designed to measure the 21-cm signal from neutral hydrogen at Cosmic Dawn, $z \approx$15-30. Using observations made with the $\approx$ 200 m diameter core of the Owens Valley Long Wavelength Array (OVRO-LWA), we present a 2-D cylindrical spatial power spectrum for data at 43.1-53.5 MHz ($z_{\rm median}\approx 28$) incoherently integrated for 4 hours, and an analysis of the array sensitivity. Power from foregrounds is localized to a "wedge" within $k_\perp, k_\parallel$ space. After calibration of visibilities using 5 bright compact sources including VirA, we measure $\Delta^2(k) \approx 2 \times 10^{12}\ \mathrm{mK}^2$ outside the foreground wedge, where an uncontaminated cosmological signal would lie, in principle. The measured $\Delta^2(k)$ is an upper limit that reflects a combination of thermal instrumental and sky noise, and unmodelled systematics that scatter power from the wedge, as will be discussed. By differencing calibrated visibilities for close pairs of frequency channels, we suppress foreground sky structure and systematics, extract thermal noise, and use a mix of coherent and incoherent integration to simulate a noise-dominated power spectrum for a 3000 h observation and $z =$16-37. For suitable calibration quality, the resulting noise level, $\Delta^2(k) \approx 100$ mK$^2$ (k = 0.3 Mpc$^{-1}$), would be sufficient to detect peaks in the 21-cm spatial power spectrum due to early Ly-$\alpha$ and X-ray sources, as predicted for a range of theoretical model parameters.