Theory

To provide some theoretical background for the practical tests, we consider the likely effect on the MOST of continuous narrow-band interference from a terrestrial transmitter. In practice the extent to which astronomical observations are affected will depend on a host of complex factors such as the modulation characteristics of the transmitter and the mode of operation of the MOST.

In-band Interference

If an interfering transmitter produces an irradiance, I, at one section of the MOST, then the interference power, p, in the low noise amplifier (LNA) input is

where g is the sidelobe gain, with respect to an isotropic antenna, in the direction of the transmitter and is the effective collecting area of an isotropic antenna. The noise power, N, also referred to the input of one section of the MOST is

where is the system noise temperature ( 100K) and B is the bandwidth.

The voltages from the east and west arms are combined separately in the multibeaming networks. Power-linear fan beam outputs are then formed by multiplying the signals from the two arms. The ratio, r, of interfering signal to the rms noise fluctuations in a fan beam is

where is the integration time and F is a measure of the extent to which the interference signals from each section add coherently; F is 1 for a random walk addition.

If r is interpreted as the maximum tolerable interference-to-noise ratio, equations 1-3 can be combined to yield an expression for the maximum tolerable interference irradiance:

where

Thus the maximum tolerable interference irradiance is proportional to the input noise power divided by the collecting area of an isotropic antenna.

To proceed we need to assign realistic values to the quantities , r, g and F. The appropriate value for is the time for which the radio telescope integrates signals coherently. For filled aperture instruments this is generally equal to the observing time, which may be many hours. For interferometers the appropriate time is the lobe sweep time, typically measured in seconds (International Telecommunication Union Handbook on Radio Astronomy - subsequently referred to as ITU 1995). During a normal 12 hour MOST synthesis observation celestial signals add coherently, but an interfering signal lasting for much longer than one 24s sampling time would tend to add incoherently into the synthesised image. A suitable value for in equation 3 would appear to be = 24s. In this 24s sample time an ``acceptable'' interference level would be 10% of the rms noise. While this factor is to some extent arbitrary, it conforms with the guidelines specified by the International Telecommunication Union (ITU 1995). Thus in equation 3 we set r = 0.10. The factor g is the sidelobe gain of a section of the MOST far from the main beam. It varies considerably with telescope pointing and the azimuth of the interfering transmitter. Provisionally we adopt the value g = 1, which is equivalent to saying that the gain of one section of the MOST in the direction of the transmitter is equal to that of an isotropic antenna. Interfering transmitters will generally be in the near-field of the MOST (i.e. out of focus) and at a large angular distance from the MOST fan beams. Consequently interfering signals from each section of the MOST will add essentially incoherently and the appropriate value of F in equation 3 is F = 1. The product Fg is the sidelobe gain, relative to isotropic, of the whole telescope. Substituting the above values of , r, g and F into equation 4 yields

This expression for the tolerable interfering irradiance is subject to the uncertainties indicated in the above discussion. In particular we have taken the sidelobe gain of the MOST to be unity. Experimental values of the sidelobe gain based on the current series of tests are presented in Section 5.

Out-of-band Interference

Signals strong enough to overload the MOST receiver system can produce interference by intermodulation. By this mechanism, transmitters well outside the MOST passband can generate interference in the output. The effect is dominated by the third-order term in the receiver response. Intermodulation interference occurs when two sufficiently strong signals have frequencies such that lie within the MOST passband. The magnitude of the interference, expressed as an equivalent in-band power, , at the receiver input is given by

where and are the powers generated in the receiver input and is the third-order input intercept for the receiver. The third-order input intercept is a theoretical point on the RF input versus IF output curve where the desired input signal and third-order products become equal in amplitude as the RF input is raised (Mini-Circuits RF/IF Designer's Handbook 1992). Combinations of signals from three transmitters, or from one transmitter and the input noise can also produce intermodulation interference.

  
Figure 1: Block diagram showing passbands at critical stages in the signal path for one bay of the MOST. Sufficiently strong signals within the passband of the feed can generate interference by intermodulation in the LNAs. Similarly, signals within the narrower band of the interdigital filter can generate interference by the same mechanism in an IF amplifier.

To see how these effects arise in the MOST, consider Figure 1 which shows a simplified block diagram of the receiver system and sketches of the frequency response at each stage. Transmitters with frequencies lying within the passband of the feed system can generate intermodulation interference in the LNAs, for which the measured third-order input intercept is . The MOST is more sensitive to intermodulation interference from transmitters with frequencies lying within the band of the interdigital filter. The non-linearity then occurs in the first stage of the IF amplifier, the third-order input intercept, , having a measured value . The sensitivity of the MOST to (two) out-of-band transmitters can be calculated by using these data and equation 7 in place of equation 1 to express the interference power developed at the input to one section of the telescope.

Overall Sensitivity of the MOST

Figure 2 shows the expected sensitivity of the MOST to interference as a function of frequency. It is based on the preceding discussion and knowledge of the band shapes of the feed system, interdigital filters and IF amplifiers. The sensitivity to intermodulation arising between two transmitters generating equal power in the LNA inputs is typically 80-100 dB below the sensitivity to in-band interference. Two other typical power levels are marked on the graph for reference. These are the level of interference recognised by the ITU (1995) as detrimental to continuum radio astronomy (threshold of -183dBWm interpolated from nearby frequencies), and the MOST rms noise level of 1mJy, seen in a 12 hour synthesis image.

  
Figure 2: Expected sensitivity of the MOST to interference. The solid curve represents the response to in-band interference. Intermodulation caused by two out-of-band interference transmitters is represented by the dotted curves. The equivalent flux density is the irradiance/bandwidth expressed in Janskys.

© Copyright Astronomical Society of Australia 1997