7.4.1 Introduction
The fact that we can have detailed information about the radiation pattern of a given (proposed) instrument as well as about the sky brightness distribution implies that we can simulate the power received by an antenna with that given radiation pattern, located at a known position on the Earth.
If we do this for one complete (sidereal) day, we end up with a theoretical quiet-day curve (QDC, see chapter 3). This curve will, of course, not contain any absorption effects, since it is based on a static map of the sky brightness distribution and does not take the ionosphere into account at all.
perfectly quiet day, due to inaccuracies of the sky map in use and the inherent inaccuracies in any theoretically derived radiation pattern. For example, most sky maps do not cover the entire celestial sphere, so some areas consist of interpolated data. Some sky maps where originally recorded at different frequencies, and all sky maps will contain to some extent sidelobe effects from the original instrument that was used to record the map. Refer to section 6.4 for a list of the sky maps that are currently integrated into RIOSIM.
Note that due to the object-oriented structure of RIOSIM, new sky maps can be added as they become available, and they will seamlessly integrate with all the existing functions. Of course, we can also use several sky maps simultaneously. This enables us to compare results obtained from different sky maps to indirectly compare the suitability of the various sky maps for the task at hand.
7.4.2 Mathematical Background
To generate a quiet-day curve, one simply loops through the time span in question. For each moment in time, the convolution of antenna radiation pattern and radio background noise gives the (simulated) received power. Plotting the resulting power values over time gives the QDC for the period of time in question.
The exact formula that needs to be evaluated is given in, for example, [Tao04] as
Pr=k·TA·∆f (7.1)
wherePris the received power, k is Boltzmann’s constant and ∆f is the bandwidth of the
receiver.
TAis the antenna temperature in Kelvin, calculated as
TA=
R
TB(θ,φ)·G(θ,φ)·sinθdθdφ
R
G(θ,φ)·sinθdθdφ (7.2) whereTB(θ,φ)is the sky background temperature in Kelvin at the given direction as returned
byCSkyMap::getSkyTemp()andG(θ,φ)is the antenna gain in the given direction as returned byRRadPat::getGain().
To evaluate 7.2 numerically, the integral needs to be evaluated as a sum. Care must be taken when evaluating this sum. For infinitely small steps∆θ,∆φ→0, the discrete sum and the
CHAPTER 7. APPLICATIONS OF THE RIOSIM TOOLKIT 128
integral become the same. However, as the resolution within the simulation is not quite infinite — in fact, only around 200 elevation angles are normally used for the sake of processing speed — care must be taken to match the internally used resolution to the requirements of the radiation pattern under investigation. The default resolution of the desiredRRadPatobject is usually a good starting point.
7.4.3 RIOSIM Implementation: maketheoreticalqdc()
Several versions of quiet-day curve generators have been implemented since the inception of the RIOSIM toolkit. The latest version,maketheoreticalqdc(), is the most versatile one, and interfaces well with S. Marple’s MIA toolkit [Marc] in that it directly outputsmia_qdcobjects. Previous development versions were optimised for certain processing patterns, for example by relying on an externally-instantiated sky map when deriving multiple QDCs. While this ap- proach did show advantages in terms of the processing time required for certain simulations,
maketheoreticalqdc()sacrifices speed for versatility, enabling the user to create QDCs for ar- bitrary radiation patterns and using arbitrary sky maps without having to know anything about the internal workings of the quiet-day curve generator.
maketheoreticalqdc()can take the following parameters, but will use reasonable default values for most parameters if omitted:
res_az, res_el Resolution for internal grid used during the discrete summation (equation 7.2).
instrument Instrument ID for which to calculate the QDC, this gets passed on to the radiation pattern beam factory (see section 6.6.3) to create the actual radiation pattern objects for the requested beams.
This can also be a MIA instrument object, in which case aRMIAPatadaptor (see sec- tion 6.3.11) is used to utilise MIA’s directivity information instead of a native RIOSIM radiation pattern for the QDC reception process.
beams The beam numbers for which to generate QDCs.
skymap TheCSkyMapobject to be used for simulating the reception process.
time Date around which the QDC will be calculated. The QDC will be generated for one sidereal day, starting with sidereal midnight closest to the specified date. This parameter is only of very limited use, as theoretical QDCs will be identical for all sidereal days. Real
MIA QDC object knows about date and time.
resolution Time resolution for the QDC. The lower the time resolution (higher time span val- ues), the quicker the simulation.
location Instrument location. (Take care when specifying existing MIA instruments with the instrument parameter, in which case the location parameter will overwrite the instrument’s inherent location.)
bandwidth Instrument bandwidth (overwrites default bandwidth) .
showtimebar Show a graphical progress bar using Chad English’stimebar()function [Eng02] (turn off for non-interactive use) .
offset Arbitrary offset for post-calibration in dBm, used to shift the generated QDC up or down. QDCs are returned in a way consistent with the existing MIA toolkit [Marc], namelyrio_qdc
objects. Therefore, theoretical QDCs can be substituted in all the places where real QDCs would otherwise be used.
Figure 7.4 shows a set of theoretical QDCs (red) for each IRIS beam, plotted using the standard MIA toolkit functions. Underlayed are real QDCs as measured by IRIS (blue). An offset has been introduced to match the absolute power of theoretical and measured QDCs.
The QDCs in figure 7.4 were generated using aCTaohSkyMapobject and a RPharrPat
radiation pattern object, consisting of CXDipNielsenPat element patterns (the RRadPat ob- ject returned by the riometer beam pattern factory for the ‘kil’ instrument). As can be seen, the theoretical QDCs fit the real measurements very well. The somewhat flattened peaks in the theoretically derived QDCs as compared to real data stem from the fact that the used sky map contains only the continuous background noise, not the bright radio stars (see chapter 3 section 3.6).
7.4.4 Predicted ARIES QDCs for the 2002 Experiment
Armed with the quiet-day curve generator from the previous section, it is now possible to derive simulated quiet-day curves for the beams of the (at the time non-existent) ARIES riometer. At the time, no real data was available for comparison purposes, as ARIES pencil beams were of
CHAPTER 7. APPLICATIONS OF THE RIOSIM TOOLKIT 130
Figure 7.4: Theoretical QDCs for IRIS (red) compared to real QDCs (blue). An offset has been introduced to align the curves vertically.
what sort of fluctuations to expect from the new instrument.
Quiet-day curves were derived for all the central pencil beams, as well as for all the special beams as described byspecialbeams.txt(see the description of the riometer beam radiation pattern factory in section 6.6.3).
These curves were used for validating the received signal from the actual array during the 2002 experiment, and we will present a number of comparisons and results in chapter 9.
At this stage, we will simply present an overview plot of all QDCs for all central ARIES pencil beams, see figure 7.5. This figure provides an insight into how much signal variation to expect in any given beam. We can clearly see the relatively low variation in beams that point near the celestial pole (around beams 304 and 305). Also, large variations due to beams passing through the bright galactic plane and radio stars can be seen very clearly.
This is a good starting point for trying to identify a ‘worst-case’ beam for real-life investiga- tion during initial experiment setups. We will expand on this topic in the next section.