SKA Simulation research

The initial simulation project is concentrating on the technical and engineering side of the SKA with the aim of making comparisons of the various SKA designs.

We are simulating various aspects of the array at a base-level. Working on the individual telescope elements and the data stream that each one provides, together with a correlator.

Software correlator

The software correlator produced it's first multi-processor fringes on 12 Aug 2003.

Interferometer data generation and simulation

The correlator requires data to work! These data could come from either a weal world situation from real telescopes, or generated and simulated in whatever form is required.

In a process similar to the Single telescope case (below), a source in the sky is created. Data are then retarded according to a delay model, and telescope-dependent noise is added. This process is done at each telescope and the data are then ready for processing in the correlator.

Single telescope / RFI

A single telescope in a station can be simulated with a variety of parameters. Pure Gaussian noise data streams are simulated, one including noise from an astronomical source, and one only including system noise.

To simulate a continuum source, two random Gaussian noise streams with a mean of zero are created. The spread in the Gaussian distribution is related to the amount of radio power received in the telescope, so one stream represents just the receiver noise, and the second stream represents the receiver noise + astronomical source. This gives an on and off-source observation.

Data are sampled at the Nyquist frequency to give two data points per spectral channel. For example, for a bandwidth of 1 GHz, data must be sampled at the Nyquist rate of 1 / 2 * 1 GHz = 0.5 ns. If we are simulating 2000 spectral channels, then 4000 data points must be created. This gives a time sample of 4000 * 0.5 ns = 2 micro-seconds of data. (repeated for both the on and off source data streams).

Once we have a stream of data, an auto-correlation is performed to produce spectral lags. This produces two lags for each spectral channel, for both the on and off source data stream.

This step of creating lag spectra for both on and off-source observations is repeated over a specified integration time (typically 0.1 or 1 second), and lag spectra are incrementally summed to form a sum on-source, and a sum off-source. This means that large numbers of iterations are required for even a second of data. With a 2 ms data stream, 500,000 iterations are required for a second of data. Therefore, for a 1 GHz bandwidth over 2000 spectral channels, with both on and off-source streams, a total of 4 billion data points are required. This takes around 2 hours to simulate on a single machine.

The lag spectrum can be Fourier transformed to produce the baseband spectrum for the source or background. Once this is done, a simple calibration to subtract the background is performed, and the calibrated continuum spectrum is formed.

This method of simulation agrees very well with real telescopes, as shown in the following table. The difference in the noise levels can be equated to our simulated data having (effective) infinite bit sampled, and the Parkes data being 2 or 4-bit sampled, which introduces noise.

Simple RFI can be injected into the baseband in both the on and off-source data. Simple RFI is simulated as a sine-wave in the raw data stream, which then gets converted to a Gaussian spike in the baseband. Click on an image for a larger view

More complicated spectral line simulations can also be created. The programme can take a file of Gaussian components with varying widths, mimicking a maser source. The sum of all Gaussian components are then broken down into discrete delta functions of varying heights, each of which are assigned a sine-wave in the raw data stream. When noise is added, and auto-correlated, this simulates complex maser sources to a high degree.

Noise in these simulations agrees very well with expected noise from real telescopes. This figure shows the continuum average over the baseband for a 5-Jy source observed with a telescope with Parkes parameters. The standard deviation and signal to noise ratio is also shown.

Data sets: Processing and storage considerations