We simulate the observations using a formalism mentioned under following points.

We build our foreground sky model keeping closely to the existing observational findings. The sky model includes the main two foreground components -- (i) discrete radio point sources and (ii) diffuse Galactic Synchrotron emissions. The contributions from these two foregrounds dominate in low frequency radio observations and their strength is ~4−5 orders of magnitude larger than the 21-cm signal (Ali, Bharadwaj & Chengalur 2008; Ghosh et al. 2012).

We simulate the point source distribution for sky model using the following differential source counts obtained from the GMRT 150 MHz observation (Ghosh et al. 2012).

The Full Width Half Maxima (hereafter FWHM) of the GMRT primary beam (PB) at 150 MHz is ~3.1°. To understand and quantify how the bright point sources outside the FWHM of the PB affect our results, we have considered a larger region (7°x7°) for point source simulation. We scale the flux of the sources at different frequencies using the following relation

The point sources are allocated a randomly selected spectral index alpha_ps in the of range 0.7 to 0.8. We model the PB of GMRT assuming that the telescope has an uniformly illuminated circular aperture of 45m diameter (D), whereby the primary beam pattern can be written as

Fig. 1 shows one realization of the point source maps at 150 MHz frequency.

Fig. 2 : The simulated intensity map for the diffuse Synchrotron radiation at 150 MHz before (left panel) and after (right panel) multiplying the GMRT primary beam. We construct our sky model of the diffuse Galactic Synchrotron using the measured angular power spectrum (Ghosh et al. 2012).

A_150 = 513 mK^2 and β = 2.34 from Ghosh et al. (2012) and α_syn = 2.8 from Platania et al. (1998). To simulate the diffuse emission, we first created the Fourier components of the temperature fluctuations on a grid using

Omega is the total solid angle of the simulated area, and x(U) and y(U) are independent Gaussian random variables with zero mean and unit variance. Then, we use Fastest Fourier Transform in the West (hereafter FFTW) algorithm (Frigo et al. 2005) to convert ˜ T (U, ν0) to δT (~θ, ν0), the brightness temperature fluctuations or equivalently the intensity fluctuations δI(~θ, ν0) on the grid. The intensity fluctuations δI(~θ, ν) = (2k_B/λ^2) δT (~θ, ν) can be calculated using the Raleigh-Jeans approximation which is valid at the frequency of our interest. Figure 2 shows one realization of the intensity fluctuations δI(~θ, ν_0) map at the central frequency ν_0 = 150 MHz with and without multiplication of the GMRT primary beam.

The simulations were generated keeping realistic GMRT specifications in mind, though these parameters are quite general and similar mock data for any other telescope can be generated easily. The GMRT has 30 antennas. The diameter of each antenna is 45 m. The longest baseline is 26 km. The shortest baseline at the GMRT is 100 m which comes down to around 60 m with projection effects. Fig. 3 shows the full uv coverage for a single channel for the simulated GMRT Observation. Table 1 summarizes the GMRT parameters used in this work.

To calculate the visibilities, we have multiplied the simulated intensity fluctuations δI(~θ, ν) with the GMRT primary beam and we use 2-D FFTW of the product in a grid. For each sampled baseline U<3, 000 (the diffuse syncrotron angular power spectrum drops significantly at the available longest baseline), we interpolate the gridded visibilities to the nearest baseline of the uv track in Figure 3. We notice that the impact of w-term is insignificant in the estimated angular power spectrum of diffuse Synchrotron emission (Choudhuri et al. 2014). But, to make the image properly and also to reduce the point source side-lobes, it is necessary to retain the w-term information. The w-term also improves the dynamic range of the image and enhances the precision of point source subtraction. We use the full baseline range to calculate the contribution from the point sources. The sky model for the point sources is multiplied with the GMRT primary beam A(θ, ν) before calculating the visibilities. The visibilities for point sources at each baseline are computed by summing over all point sources by incorporating the w term.

For a single polarization, the rms. noise in the real or imaginary part of a visibility is predicted to be (Thompson, Moran & Swenson 1986),

All symbols carry usual meaning. For of channel width \delta ν = 125 kHz and integration time t = 16 sec the rms. noise comes out to be σ_n = 1.03 Jy for a single polarization. The GMRT has two polarizations which have identical sky signals but independent noise contribution.

Finally, our simulated visibilities for the GMRT observation are sum of two independent components namely the sky signal and the system noise. The sky signal contains the contribution of the extragalactic point sources and the diffuse Synchrotron emission from our own Galaxy. The visibility data does not contain any calibration errors, ionospheric effects and radio-frequency interference (RFI).