So far I have ignored the problem of calculating the *amplitude* of the reflection based on the computed scattering cross-section, mostly because after a couple of trial calculations, it feels like what I am seeing from the beacons is more like a specular reflection, perhaps 10-20dB more signal than simple forward scattering would suggest. On 23cm, the amplitude variations seem to be either very slow or very fast, so either they are of a similar period to the reflection duration, or the averaging of the waterfall is probably smearing them out. They are certainly not as apparent as they are on A/S on 2m. I’ll have to try it with GB3DUN, where the reflections are a decent strength.
I guess the three-dimensional picture will be something like the fringing patterns discussed by DJ5HG for MS reflections, but from a point source.
I certainly see the beating effect of interference between the tropo and A/S path from the beacons I can hear directly, and that does look like the Lille transmitter tests in the G3BGL 1966 RSGB Bulletin article.
There are some Czech research papers about using passive bistatic and multistatic radar, but it looks like the majority of this work is probably classified.
The tests I have done with off-axis aircraft scatter using QRO with G4BAO and others have signal levels about the same as those of the direct-path reflections from the beacons. As the stations are using beams and QRO, I reckon the off-axis path loss must be 30dB or so higher than the direct forward reflections from the beacons.
Once I’ve got the analytical equation for the doppler sorted, I’ll try plugging in the actual signal levels to the bistatic radar scattering equation for a typical plane cross-section and see what it suggests the signal levels should be for the JO02 path to here via a scattering point near Newbury (about 60 degrees off-axis for JO02 station and 40 degrees for me) versus direct. I can see there is a problem of variation of the effective cross-section of a plane depending on its orientation and whether it is off-axis or directly in line or beyond the beacon – I seem to get a fair number of reflections when there are no planes shown between me and the beacon, they can’t all be military flights. However I haven’t been able to identify a specific case where the reflection came from a plane beyond MHZ or DUN, so at the moment that is still just surmise.
One thing I have found is that the angle to the plane from here is very important, same as for EME without elevation, owing to the deep nulls between the lobes of my yagi on 23cm. Some large planes close to me at an elevation of 2 degrees show no reflections at all, whereas a much lower or higher plane at the same range produces a very good reflection. Guess I need to map the vertical lobes against an EME signal, as I have done on my 2m antenna with KB8RQ’s mammoth signal as the moon sets from 20 degrees downwards. The same probably applies to the vertical pattern of the beacon, but I’ve not been able to verify that. I can certainly see the curved doppler trace of planes approaching Doncaster airport as they decelerate in their final apprach and map that against the actual airspeed from the ADS-B feeds.
I’ll re-read the VK7MO paper and see if I can lift some of the DJ5HG Matlab code to use in simulations based on those scattering cross-sections. However, first job is to get the new 6m/4m PA built, then the synth LO for the 9cm gear. Oh, and the mounting brackets and airline for the second SCAM12 pump-up. So many projects, so little time….